[bratoljub_h._milosavljevic]_lab_packet_for_chem_4(z-lib.org).pdf

Lab Packet FOR

CHEM 457 Experimental Physical Chemistry Spring, 2017 Instructor : Dr. Bratoljub H. Milosavljevic Revised: January, 2017

Foreword

Experimental Physical Chemistry, CHEM 457 course is designed to reinforce the theoretical Physical Chemistry courses with the introduction of physical chemistry applications in a laboratory environment. Placing abstract concepts in an experimental framework, physical chemistry may become more self-explanatory and more enjoyable. This laboratory course mainly utilizes fast kinetics, thermodynamics, electrochemistry, surface chemistry, and spectroscopy experiments. The topics for this course are chosen to improve the science and engineering students theoretical and experimental physical chemistry backgrounds and skills.

In addition, each student will work on a special

project to demonstrate her/his independent ability in performing literature searches, planning and designing the experiment, interpreting the data, communicating in written scientific language, by writing a paper in the format of a Physical Chemistry Journal, and in verbal scientific language, by presenting a poster.

The synopsis of the eleven

experiments performed in this course is given below.

1) Dissociation of a Propionic Acid Vapor

The equilibrium constant for the dissociation of propionic acid dimer in the vapor phase will be determined as a function of temperature. From this data, thermodynamic

constants and enthalpy and entropy changes will be calculated. The change in enthalpy is a measure of the strength of the hydrogen bonds in the dimer.

2) Adsorption from Solution An adsorption isotherm will be constructed for the adsorption of acetic acid onto

charcoal. Using this isotherm, the surface area of the charcoal will be determined. The relation between adsorption and surface chemistry will be introduced.

11

3) The determination of thermodynamic functions of the reactions in commercial alkaline-manganese dioxide galvanic cell (Duracell®) Temperature resolved measurement of the electromotive force of AA Duracell® galvanic cell will be performed in order to determine the thermodynamic parameters such as ~rG

0

, ~rS

0

and ~rH

0

•

4) Real Gas Behavior: Determination of the Second Virial Coefficient of C02 The pressure vs. amount of COi relation under isochoric condition will be studied in order to determine departure from ideal behavior in the pressure range 0 to 10 bar. The data obtained will also be used to determine the second virial coefficient of C02.

5) Nanosecond Laser Photolysis Study of Pyrene Fluorescence Quenching by

r

Anion Pyrene in its singlet excited state oxidizes iodide anion. The pyrene fluorescence decays in the presence of various iodide concentrations will be measured using pulse laser photolysis technique in order to determine the second order reaction constant.

6) Modeling Stretching Modes of Common Organic Molecules with the Quantum Mechanical Harmonic Oscillator The use of the harmonic oscillator model to interpret a vibrational spectroscopy will be introduced. Using a refined value for the effective single-bond force constant,

stretching mode frequencies will be estimated to within about ±10% with a simple calculation.

7) Resonance Energy of Naphthalene by Oxygen Bomb Calorimetry The resonance energy of naphthalene will be determined by calculating its standard enthalpy of combustion both experimentally using bomb calorimeter and by using bond energies.

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8) Pyrene Excimer Formation Kinetics

Combined steady state fluorimetry and time resolved laser photolysis measurements will be performed in order to explore a complex kinetic system comprising two parallel and two consecutive reactions, that is, to determine the kinetic rate constants associated with pyrene excimer formation and decay using laser photolysis.

9) Polypropylene Phase Transitions Studied by Differential Scanning Calorimetry

The enthalpy of melting and Tg of two different polypropylene samples will be measured using a first class research grade instrument as an illustration of a typical industrial problem solved in material chemistry labs. 10) Fluorometric Determination of the Rate Constant and Reaction Mechanism for Ru(bpy)32+ Phosphorescence Quenching by 02 A Stem-Volmer plot will be constructed to find an experimental kq for the

quenching of Ru(bpy)32+ by oxygen The fundamental principles of fluorescence measurements as well as quenching mechanisms will be covered.

11) Determining the Spin-Lattice Relaxation (Tt) of 1-Hexanol using 13C-NMR

The spin-lattice times (T1) of each C atom of n-hexanol will be determined by using NMR spectroscopy. The inversion recovery method will be utilized to obtain T1 times of C atoms of n-hexanol.

The observed times will be related to atomic motion of C

J

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Table of Contents I. Preliminaries

1. Forward ... ..... ................ ............. ........... ....... ..... ............... ..... .

2. Table of Contents............................ .. ....... ..... ............. ... ...... .. ...

1v

3. General Information.. .... .. ....... ............. .... .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

v111

II. The Experiments

1. Dissociation of a Propionic Acid Vapor

Objectives................ ..................... ... .... ....... .. ......................... 1-1 Introduction.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1-1

Laboratory Procedure.. ... .. ............... ..........................................

1-5

In Lab Questions.. .. ............. ...... ... ... .... .. .... ... ..... ...... .... .. ..........

1- 12

Data Analysis.......... ..... .... ........ ..... .. .. .. .. ..... .. ......... .... ... ..........

1-13

Report Questions............. .. ..... ................. ... .... .... .... ... ..... ...... ...

1-15

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-15

2. Adsorption from Solution Objectives... ..................... ... .. .. .... ........ .. ........ ...... . ........ ..... .....

2-1

Introduction..... .. ................... .. ..... ... ............ ......... ...... ... .... ... ...

2-1

Laboratory Procedure... ......... .......... .... ... .... .................. .............. 2-4 In Lab Questions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-6 Data Analysis........ .. .... ............ ............ ..... ... ... ............. .... .. ...... 2-6 Report Questions............................. ................ ....... ...... .. ....... ... 2-9 References.. ........... ..... ......... ..... ........ .... ... ... .. .. ..... .. .. ....... ........

2-9

v 3. The determination of thermodynamic functions of the reactions in commercial alkaline-manganese dioxide galvanic cell (Duracell®)

Objectives........................ ......... ............ ................... . .. ........... 3-1 Introduction.... .............. .. ..... .... .................. ... ....... .... .... . .... .. ....

3-1

Laboratory Procedure.. ........ .. ... .............. ... ................ .... ... .. ........ 3-2 Data Analysis..... . .............. . ........ ....... .....................................

3-4

References.. .... ................... ... .................................................

3-5

4. Real Gas Behavior: Determination of the Second Virial Coefficient of

C02

Objectives..... ... ...... ................. ..... ........ .. .. ... ..... .. ..... ............... 4-1 Introduction .... ................................. .. .. ...... :.................... ........ 4-1 Laboratory Procedure........................ .............. . .. .... ... .... . ............ 4-4 Data Analysis........ .. .. ..................... .......... . .............. .... .. . ......... 4-6 Report Questions................... .. ... .. ................................. . .......... 4-7 References........... . .............. ... ...................................... . ..........

4-7

5. Nanosecond Laser Photolysis Study of Pyrene Fluorescence Quenching by 1- Anion Objectives....... .......... ... ....................... .. ........ ... ......... ............ . 5-1

Introduction.... .... .. .. ............... ..... . ....... ...... .......... ...... ........ ......

5-1

Laboratory Procedure.... . ................... ............. ... ... .. ... .. ..... .... ...... 5-5 Data Analysis... ............. .. ......................................... .. .......... ...

5-7

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6. Modeling Stretching Modes of Common Organic Molecules with the Quantum Mechanical Harmonic Oscillator (QMHO)

Objectives..... ........... ..... ... ........ ....... ... .. ............. ... ....... ..... .. .

6-1

Introduction................ ............. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ...

6-1

Laboratory Procedure.. ........ ... .. .... ..... .... .... .. ... ............. ...... .. .....

6-10

In Lab Questions... ... .... .... ......... ............ ..................... ........ .. ..

6-13

Data Analysis.................. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ...

6-14

Report Questions.............. .. ...................... ........ ................. .....

6-15

References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

6-16

7. Resonance Energy of Naphthalene by Bomb Calorimetry

Objectives...... ... ...................... .... ................................... ... ..... 7-1 Introduction...... .... .. ..... ............ .. .... ............. ... ................ ..... ...

7-1

Laboratory Procedure......... .. ...... ........ ...... ... ... ..... .... ........ .... ... ... 7-11 In Lab Questions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

7-1 7

Data Analysis......... ................ ...... .. .... ... .. ... .... .... ....................

7-18

Report Questions......................... ...... .. .......... ... ...... .. ..... ..........

7-22

References ..... ................... ... ... ........ ... .. .. ........ ... ......... ....... .. .. 7-22

8. Pyrene Excimer Formation Kinetics

Objectives. .... ........ ...... .... ... ..... ....... .. ...... ... ....... .... ................ .. 8-1 Introduction............. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-1 Laboratory Procedure............. ................ ......... ........................... 8-3 Data Analysis........ .......... ........................... ........... ..... ... .... ... ... 8-5 References.............................. ...... .... ... ........ ... .... .. ..... .............

8-8

vu 9. Polypropylene Phase Transitions Studied by Differential Scanning Calorimetry

Objectives..... ..... .. ...... ...... ... ...... .. ...... .. .. .... ... .......... .. .............. 9-1 Introduction........... .. ...... ........... .... .... . .......... ... ... ....................

9-2

Laboratory Procedure....... .... .... ... . ... ... . ........................... ... ..... ... 9-3 Data Analysis... . ........ ......................... .. ... ... ............. .. ..... ...... ..

9-5

References.............................. .... ..... ........................ .. ........ . ...

9-5

10. Fluorimetric Determination of the Rate Constant and Reaction Mechanism for Ru(bpy)32+ Phosphorescence Quenching by 02

Objectives........... . .... ... ..... . .. ... .......... .. .... ................... . .... .. ......

10-1

Introduction........ .. .... . .................... . ....................... .......... ... .. ..

10-1

Laboratory Procedure. .. .... .............. .. . .. ............ . ............. .. ...........

10-8

In Lab Questions... ... .. . ... ............. .. .... ...... ...... ...... ..... .. ... .... .. .. ...

10-9

Data Analysis............... .. ... ......... ... ............. .. .. .............. .... .......

10-10

Report Questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

10-1 0

References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ...

10-10

11. Determining the Spin-Lattice Relaxation (Ti) of 1-Hexanol using 13

C-NMR

Objectives.. ........ . ... .... ... ... ... . .... ..... ... .. .... ..... .. .... .. .. ... ...... ........

11-1

Introduction................... .......... ..... ............ .... .... . ..... ....... . . ... ....

11-1

Laboratory Procedure.......... ... . . .. .... .. ................. .................. ....... 11-8 In Lab Questions... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

11-18

Data Analysis. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..

11-1 9

Report Questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

11-19

References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ... 9-19

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3. General Information Instructor:

Dr. Bratoljub H. Milosavljevic 331C Whitmore, 865-7481, bhml [email protected]

Office Hours:

As announced in class and by appointment

Prerequisite:

CHEM450

Materials Needed 1) CHEM 457 Lab Packet. 2) Lab notebook with alternate tear-out carbonless copy pages. 3) A flash drive. 4) Approved safety gogg]es.

Eye Protection There are three types of eye protection acceptable for use in the Penn State Undergraduate Chemistry Labs. You MUST wear one of these models in the laboratory AT ALL TIMES!

1) Safety Glasses: Comfortable and offer better peripheral vision compared to gogg]es. However, they offer less protection than goggles. The bookstore has Panaspec Plus (Bouton). 2) Visor goggles: Reasonably comfortable, good splash protection, better peripheral vision than goggles. The Penn State Bookstore carries, Visorgogs (Jones and Company). 3) Goggles: The highest level of splash protection. However, fog may build up and limit peripheral vision. There are four different kinds of goggles available at the Penn State Bookstore.

Course Requirements You need to complete eight experiments, and a special project to fulfill the requirements of this laboratory course. A student should submit the following for each

lX

experiment: a pre-lab quiz (before the start of the lab), and in lab questions (when applicable) and the data collected (after the completion of the lab). Eight experiments are required to be written in full lab report format (in the format of a Journal of Physical Chemistry paper). Special projects are to be reported by a full lab report, a PowerPoint presentation, and a poster presentation.

Only the special project report, PowerPoint

presentation, and poster presentation will be submitted per group and all the remaining will be submitted individually. During the experiments students will be working collaboratively in the groups of 2 or 4. In the data analysis and lab report preparation, students may study with their group members; however, when submitting the lab reports and uncertainty assignments, each student must present his/her own original individual work.

What is Needed for Each Experiment?

Pre-Lab Quiz (10 points): Each Pre-Lab Quiz will be posted on the ANGEL Course Management system and must be completed and turned in before the start of the lab session.

In-Lab and Report Questions (when applicable): Number the answers including subdivision that may exist. If the question has parts (a) and (b), the answers should not be together but labeled and answered separately. In lab questions must be handed to your TA or the instructor at the end of the experiment,

before leaving the lab, otherwise they will not be accepted.

Data Collected: Hand in a copy of the primary data collected during the experiment to the TA BEFORE leaving the lab on the day the experiment is performed. These data will consist of entries you made in your lab notebook and any printouts of data you have.

Data Analysis: Special instructions of the data analysis should be followed as given in the manual.

x Full or Short Lab Reports:

Full formal laboratory reports will be submitted to your TA or instructor the week following the completion of the laboratory experiment. Your lab report will be in the format of a journal paper. Although students work in groups, in this laboratory work, the reports must be prepared individually.

Reports must demonstrate your own

understanding of the scientific work. You may not paraphrase or use other students' reports in the preparation of your own reports. Otherwise actions will be taken due to academic dishonesty. Furthermore, data analysis will be used in the preparation of the lab report.

An electronic copy of each laboratory report will be submitted in the

appropriate drop-box on the ANGEL Course Management system to check reports for possible plagiarism.

Supplementary Information to Lab Reports:

Lab reports must be accompanied by the supplementary documents of the related experiment: sample calculations and uncertainty analysis.

1-1

Dissociation of a Propionic Acid Vapor Objectives

•

To determine the equilibrium constant for the dissociation of propionic acid dimer as a f'Unction of temperature.

•

To calculate the enthalpy of dissociation by collecting pressure - temperature data.

•

To calculate the entropy and the free energy changes for the dissociation process. •

To relate the experimental enthalpy of dissociation to the strength of hydrogen bonds.

1. Introduction

When low molecular weight carboxylic acids vaporize, they go into the gas phase as a mixture of dimers and monomers. The dimers form as a consequence of hydrogen bonding and have a structure roughly similar to that shown in Figure 1.

H H

I

I

o----H-o

I

I

"o-H----cf

H-c-c-c~ H H

H H

I

I

I

I

H H

I

I

I

I

"\.c-c -c-H -----2 x H-c-c- c /

H H

H H

o--

H

~

Figure 1. The dissociation of dimers of propionic acid vapor

In this experiment the gas pressure of a fixed amount of vaporized_propionic acid is measured as its temperature is raised. From these data, the equilibrium constant for the dissociation of acid vapor dimers into monomers is calculated. The enthalpy change (Aff0 ) fo r the dissociation process is determined from the slope of the best-fit line in a plot of the natural log of the equilibrium constant against the reciprocal temperature. The magnitude of Aff0 can be considered a measure of the strength of the hydrogen bonds in

1-2

the dimer since hydrogen bonds hold the acid vapor monomers in the dimer form, as suggested in Figure 1. The entropy (~S 0) and free energy (~G 0) of the acid dissociation can be calculated from the calculated Aff0 .

Theoretical Background By measuring the total pressure (at a known temperature and volume) of a known mass of a volatile carboxylic acid, the equilibrium constant for the gas phase dissociation of the acid dimers into monomers can be obtained.

If the entire vapor were in its

monomer form, the total pressure would be rnice of what it would be if the entire vapor were in its dimer form. If some of the vapor were monomer, and some dimer, the total pressure would be somewhere in between.

A measurement of the pressure can be

converted to relative amounts of dimer and monomer. From this the equilibrium constant can be determined. Any homogeneous gas phase dissociation equilibrium can be written as in Eq. (1).

D !+ 2M

(1)

Under low pressure conditions where all species behave ideally, the equilibrium constant,

Kp, can be expressed in terms of pressures by:

(~)'

(

~

K,

(2)

(; )

where PM and Pn are the partial pressures of the monomer and dimer and P0 is the pressure of the standard state. P0

1.0 atm (see physical chemistry textbook for a

=

discussion of the choice of units and standard states). Allowing a (a number between 0 and 1) to represent the degree of dissociation of the dimer, PM can be expressed as:

p =(~)p M

I+a

(3)

1-3

where

(~) represents the mole fraction of monomers, since two monomers (2a.) are l+a

produced from each dimer dissociation. As each dimer dissociates, there is a net increase of one particle which results in the total number of particles present in the system being (1 +a). Pis the total pressure of the gas mixture. Similarly, Po can be expressed as: p D

where,

(1-a) --

l +a

= (~)p l+ a

(4)

represents the mole fraction of dimers, since (1-a.) indicates that one

dimer is lost for each dissociation and there is a net increase of one particle (1 +a.) for the total number of particles in the system, as each dissociation occurs. By substituting Eqs. (3) and (4) into Eq. (2) the following for Kp expression is obtained:

KP

= (~JP l-a 2

f5)

At equilibrium, because number of moles of dimer (no}, bulb volume (V), temperature (T), and pressure (P) are known, the total number of moles of gas molecules, no(l +a.) is given by PV

n0 (l+a)= -

RT

{6)

Stated in slightly different terms, this relationship is: p

l+a = -

(7)

Pi

where, ,Pi is the pressure that would be observed if there were no dissociation.• Pi can be calculated using the following equation: P I

=n vRT =( (A1W)V gR J r ) 0

(8)

where, g is the mass of the carboxylic acid vaporized and MW is the molecular mass of the carboxylic acid dimer. By substituting Eq. (7) into Eq. (5) and Eq. (9), Kp for the dissociation of carboxylic acid dimers is obtained from the experimental pressures at the measured temperatures, volume and mass of vapor.

1-4

(9)

K = 4(P-P;'j 2P-P

P

I

All quantities on the right-hand side of the equation are determined from the experimental data. The value of Kp depends on the pressure units. (Express the pressure units in atm.) Based on Kp and its temperature dependence, standard thermodynamic quantities can be readily obtained using the following thermodynamic relationships.

(10)

Mi°

-d(lnKP)

R

d(I I T)

--=

(11)

(12)

thl o = '3H o -11G o) T

where, .AG0 , .AH0 and .AS0 are the standard free energy, enthalpy and entropy for the dissociation of the carboxylic acid dimers. Temperature (K) corresponds to Kp. Note that the right-hand side of Eq. (11) is the negative slope of a plot ofln Kp versus lff. The experimental value of entropy, L).S 0 , can be compared with the theoretical

prediction using Sackur-Tetrode equation for entropy. In this approach only translational part of entropy is calculated.

!hl 0 sackur- Tetrode = 2S,w - SD !13) where, Srvds the entropy of the monomer and SD is the entropy of the dimer.

S = 2.303{- log P + ~log T + ~ log(M)-0.5053} R 2 2

(14)

In Eq. (14), Pis in atm, Tis in K, and Mis the molecular mass of the species (monomer

-

or dimer) in g mo1-1• When calculating S0 , pressure is in 1 atm and temperature is 25.0°C

'

1-5

(see your physical chemistry textbook for a discussion of the Sackur-Tetrode equation and for further explanation of its derivation and usage).

2. Laboratory Procedure

In this experiment, a known amount of propionic acid will be expanded into a known volume of an evacuated glass bulb.

The bulb is attached to a capacitance

manometer and enclosed in an oven to measure the pressure change while raising the temperature in. increments of 3-5°C from approximately 20°C to 70°C. rThe temperature will be measured using a thermocouple in conjunction with a digital multimeter. Capacitance manometer, measures the pressure, has a transducer and a digital readout

outside the ovefil Figures 2 and 3 show the experimental setup. Before filling the bulb with the propionic acid vapor, all the gaseous molecules ,-

from the system must be removed under vacuum. Figure 2 shows a series of valves and glass lines that are used to carry out the evacuation of the system and for theiintro-~uction of the acid vapor into the bulb.

To the oven -7

~To

vacuum

Figure 2. Vacuum line of the acid dissociation apparatus.

le

1-6

CAUTION:

The vacuum system is made of glass and is fragile.

If not properly

handled, it could implode or explode and send glass flying throughout the laboratory.

GOGGLES MUST BE WORN AT ALL TIMES DURING THE EXPERIMENT!! Please become familiar with the valves and the fragile components of the vacuum line in order to work efficiently and safely. When turning valves and stopcocks, use two bands

to avoid applying torsion on the glass tubing. Do not overly tighten the stopcocks that are hard to close or unscrew them very far to open. Ask a TA or instructor to show you how the o-ring seals operate. The o-rings have to be replaced quite often due to the corrosive nature of the acid vapor in the system.

Gas line

Gross adjust oven temperature knob

Fine adjust oven temperature knob

Figure 3. Oven part of the acid dissociation apparatus.

1.

Fill large Dewar flask with liquid nitrogen. This flask will be fit around the vacuum trap at step #7.

CAUTION: Do NOT put your hands into the liquid nitrogen. Liquid nitrogen boils at 77K; and can freeze tissue quickly and painfully. Ask for help from your TA or instructor to get this for you.

1-7

2.

Check the acid sample container; it should be at least half full and all o-rings should be in good condition. Have a TA or instructor demonstrate the proper method for the turning off the valves.

3.

Close valve A that vents to the room. If valve A is left open for approximately 20 minutes after liquid nitrogen is placed around the trap, air will begin to liquefy in the trap which could lead to a potentially dangerous situation when the vacuum pump is turned on and the liquefied air is vaporized. Another reason for having valve A closed is to prevent sample distribution into the air in the room. Also close valve D.

4.

Carefully place the large Dewar of liquid nitrogen around the vacuum trap and firmly clamp the Dewar into position. Wear the blue cryo gloves when doing this or have the TA do it for you.

5.

Start the vacuum pump by pushing on the toggle switch on the cord.

6.

Open valves B, C, and E, if they are not already open. Notice an almost immediate drop of pressure. If there is no sudden drop in the pressure, check if valve A is completely closed. Allow the system to fully evacuate for 5-10 min. While waiting for the full evacuation move to step #10. Later on, this step will be called the residual pressure step and the pressure value will be recorded.

7.

WhHe waiting for the evacuation to take place, cool the sample by carefully placing the small Dewar containing the ice-water bath prepared in step #4 around the sample container. Clamp the Dewar securely into place. This step is to cool down the sample to avoid pumping away too much vapor during outgassing.

8.

When the pressure reading is between 0.60 and 0.40 torr, close valve E (***do not over tighten metal valve E doing so will damage the valve and cause a leak in the vacuum system). This pressure reading will be recorded and called the initial residual pressure.

1-8 9.

When the sample is cold, open valve D and pump on the sample for approximately 1 to 1.5 min to completely outgas the sample. Outgassing purifies the sample from any air dissolved in the acid or in the sample container environment.

10. Close valve D and remove the ice-water bath. Place the ice water Dewar on the lab bench and place the thermocouple reference wire into it, as you will soon be recording temperatures. 11. Close valve C and with a kimwipe, remove the acid container from the vacuum line. Kimwipes prevent fingerprints on the sample container, as fingerprints will affect the mass. Set the container on the lab bench in a manner so that the acid inside does not touch the valve. Refer to Figure 4 and let sample container warm to room temperature. Once room temperature is reached, place a small square piece of plywood on the balance and weigh it, then place the acid container on the plywood and record the weight. Since accurate mass determinations are crucial to the success of this experiment, be consistent in weighing measurements.

Figure 4. Proper placement of an acid container on a plastic weight tray as it warms up to room temperature to be weighed.

15. The thermocouple reference wires are already in the small Dewar containing icewater mixture and connected the leads to the voltmeter. Compare the reading on the voltmeter and the thermometer, which is on the top of the oven. Voltmeter and thermometer readings should be in close agreement, if not seek the assistance of a TA or the instructor.

1-9 16. Reattach the sample container to the vacuum line. The volume between valves C and D must be evacuated before the sample can be admitted into the system.

Therefore, open valve C and pump for 1-2 min. Do not open valve D at this time.

17. Check the pressure reading, it may have slightly increased. Record this pressure as the current residual pressure. If the pressure is above 0.40 torr, open valve E and allow the bulb to pump down to a pressure between 0.40 and 0.20 torr. Record this as the final residual pressure.

18. Open valve E (if it hasn't been opened in step # 17). 19. You are now ready to expand the sample into the bulb in the oven (volume of the bulb is 3.4 L

± 0.1

L). Close valve B and open valve D and allow the pressure to

reach 2.85 to 3.35 torr, such that the subtraction of the residual pressure gives a net pressure of at least 2.25 to 2.75 torr. Do not fill the bulb to greater than 3.35 torr.

Pressure change should start almost immediately.

If not inform a TA.

It will take

approximately 10 minutes to fill the bulb to the prescribed pressure. Do not fill the bulb for any longer than 15-20 min even if you have not reached a net pressure of2.25 torr. If time needed to reach pressure is too short inform TA, you may have leak in the system. 20. Once the desired pressure is achieved, isolate the sample (which is propionic acid vapor) in the bulb by closing valve E. 21.

Since only the mass of the gas in the sample bulb is of interest, the remaining vapor must be condensed back into the sample container. Therefore, place a

small Dewar containing liquid nitrogen (filled by the TA) around the acid sample container and allow the vapor in the line to condense back into the sample container for 2 to Smin. 22. Close valves C and D. Remove the liquid nitrogen, and allow the acid container to return to room temperature (since this procedure takes several minutes, continue onto the next step and come back to this step when room temperature is reached).

Once room temperature is attained, re-weigh the sample container and record the weight. The difference between this and the initial weight gives the mass of the propionic acid in the sample bulb.

1-10

NOTE: An accurate measurement of the weight difference is crucial to the success of this experiment. A weight difference in the range of 0.070 - 0.091 g must be otherwise consult with your TA BEFORE continuing.

23. Begin taking readings while waiting for the acid sample to warm up. Record the temperature and corresponding pressure readings at this time. This will be the initial set of data points.

24. Now, close the oven door. Set the left-hand dial (gross adjust oven temperature knob) to low by turning it counter-clockwise. This will turn on a red light. Tum the

right-hand dial (fine adjust oven temperature knob) clockwise, until the lower orange light just comes on. This should cause the temperature to rise at a slow enough rate that accurate readings can be taken. When the orange lights goes off, the right-hand dial should be turned just far enough to bring the orange light back on again. Using this method of heating, temperature readings should be taken at

approximately every 3°C with the corresponding pressure readings. It is suggested that one person read the pressure and temperature readings while the other records them. In this way, the most accurate data sets will be obtained.

The uncertainty of the pressure reading is AP = ±o.20%. A sample data/results table may look like this:

T, 'C

I

P, mm Hg

I

P, atm

I

P;, atm

I

Determine 1) Pin atm., 2) Pi, and 3) Kp to answer one of the in-lab questions.

BEFORE leaving lab: The conversion between the P in mm Hg or torr to P in atm. is: P(atm) =

p mmHg

760

{15)

1-11

Refer to the introduction to obtain the equations needed to calculate Pi and Kp. Use an Excel spreadsheet to do these calculations; though you should do one set by hand so that you are sure you have the formulas put into the spreadsheet correctly.

25. Continue taking readings at 3°C increments up to approximately 70°C. This process will take approximately one hour. 26. Whlle waiting for the temperature to change during the experiment, calculate the Kp values for the previous set of readings. (You may do this on a spare computer using an Excel spreadsheet.) The Kp values should be 0 ~ Kp ~ 1 and should increase or decrease in a regular pattern. NOTE: Have the second mass of your sample before calculating Kp.

You may find that some values ofKp are negative (due to the denominator in Eq. (9) being negative). If this happens with only one or two of the high temperature points and the others seem reasonable you may ignore this. If it happens with any of your first few points, stop and get help.

27. Once you have collected 7-10 good data points (the more, the better), shut off the . oven at the dials and open the oven door. In order to get a good idea of the quality of the data points, plot a graph of In Kp versus lff, K- 1. Generally the slope of the best-fit line should be - 7000 to - 15000 with a fairly high R 2 value. 28. Pump the propionic acid from the bulb by opening valves B and E. (Be careful! Valve E may be HOT! ) 29. Leave the liquid nitrogen in the Dewars for the next lab group, unless you are the last lab group for the day. Pour the ice water down the drain and dry out this Dewar for the next lab group that will use it. 30. Tum in your in lab questions BEFORE leaving the lab. Also be sure your lab area is neat and clean before leaving the lab.

1-12 3. In Lab Questions

1. Explain why the total pressure of a given sample of propionic acid completely in its dimer form would be half the total pressure if the same sample were completely in its monomer form. 2.

Explain why it is important to let the propionic acid sample warm up to room temperature before weighing it. You should be as thorough as possible in answering this question.

3. Think about what is going on at the molecular level as the prop ionic acid dimers dissociate. What sign do you expect LiH0 to have? Do you expect the magnitude of ll.H0 to be relatively large or small compared to ll.H0 for the combustion of propionic acid? What sign do you expect ll.S 0 to have? Give reasons for all your answers. 4. Prepare a table for collecting the data and tabulating your results similar to that shown in Step 24 of the procedure. Be prepared to hand in a table of your calculated values of Kp BEFORE leaving the lab.

4. Data Analysis

1. Carry out the calculations needed to complete the table shown in Step 24 of the

procedure. Calculate the corresponding uncertainties for each result as you proceed through the calculations and report these uncertainties along with the tabulated calculated results.

It is best to put the uncertainties in their own columns in a

spreadsheet for ease of calculations. You may find it easiest to break down the error propagation of Kp into parts and put these intermediate values and their uncertainties into their own columns on the Excel spreadsheet. 2. Plot ln Kp versus lff, where the temperature is in reciprocal of Kelvin. 3. Determine the best-fit line for this data and display the equation of the line and its R 2 value on the graph.

Also carry out the least squares fit for this line using the

regression analysis program on Excel used for your error analysis problem set.

1-13 Determine the standard error of the slope, Sm, and the standard error of the yintercept, Sb, from the regression analysis printout. Report the uncertainty in the slope as the Sm value and the uncertainty in they-intercept as the Sb value.

4. Calculate the Kp and its uncertainty at 25.0°C. In the uncertainty calculation, use the Sm and Sb values, respectively, from the linear regression analysis. Simplification

rules #1 and #4 given in this manual can be found helpful in the uncertainty analysis. 5. Calculate the value of Af1° using the slope (-£\H0 /R) of lnK.p vs 1/T graph. Use the uncertainty in the slope to determine the uncertainty in Af1°.

6. Calculate AG0 • (Keep in mind that 0 means at 298. 15 Kand l atm.) Then calculate AS0 from the calculated value of £\G0 and the value of Af1° determined in step #5.

Once again remember to calculate the corresponding uncertainties in each. 7. Use Reference 2 to find the literature values for £\H0 , £\G0 and £\S 0 at the conditions closest to your experimental conditions (MacDougall's values) in Table 1 and Table 2 (a copy of this reference exists in the lab on the bulletin board and also in the Chem 457 binder on reserve). Find the literature values for only £\H0 and £\S0 . From these values, calculate 6G0 and use its value as the literature value for 6G0 • 8. Calculate the AS0 sackur-Tetrode value corresponding to the changes in translational entropy as the dimers are dissociated into their monomer form.

Use standard

thermodynamic values for the temperature (298.15 K) and pressure (1 atm) in the Sackur-Tetrode equation. 9.

Compare the values of the experimental 6S0 and the 6S0 saclrur-Tetrode. Calculate the difference for these two values and comment on their differences. This means you

should suggest possible reasons for these differences. The comments should appear m your summary. 10.

Finally compare the value of the experimental MI0 to the MI0 of a hydrogen bond3 . Discuss this comparison in the report questions.

Reminders:

Carry out the error analysis on each of the values calculated and report them as the calculated value± propagated error reported to a value between 3 and 30, such as 25.02

1-14

± 0.30 g, but not 25.02 ± 0.50 g. The latter should be reported as 25.0 ± 0.5 g. Present your data in a table. Show detailed sample calculations for each different kind of calculation and a detailed error analysis for each sample calculation shown. If unsure of what is expected here, refer to your introductory course material or ask one of the TAs or the instructor.

5. Report Questions 1.

B~ed

on your results, what happens to the dimer-monomer equilibrium as the

temperature increases? Does the reaction shift to more dimer or more monomer at higher temperatures? Does this agree with what you would predict from Le Chatelier's principle? Give reasons for each of your answers to the above questions. 2. Do both .6.H0 and .6.S 0 contribute to .6.G0 in the same way? Explain. 3. Discuss how the experimental .6.H0 compares with typical hydrogen bond energies.

References: 1. Barton, D.; Ralph, R.; Kane, K. J Chem. Educ. 1968, 45, 440. 2. Allen, G.~ Caldin, E. F. Quarterly Reviews 1953, 7, 255. 3. Pauling, L. The Chemical Bond; Cornell University Press, 221 (1967). Additional references used but not cited in the experiment: Clagnue, A. D. H.; Bernstein, H.J. Spectrochimica Acta 1969, 25A, 593. Joesten, M. D.; Schaad, L. J. Hydrogen Bonding, 2 (1974).

2-1

Adsorption from Solution

Objectives

•

To understand and apply the general adsorption phenomenon and its kinetics in surface chemistry.

•

To utilize the Langmuir model isotherm for determining the surface area of charcoal.

1. Introduction

Adsorption plays a major role in industries, from petrochemical to food processing, due to its involvement in chemical, biochemical reactions, and purification, filtration processes, and catalysis. In general, adsorption describes the greater concentration of adsorbed molecules at the surface of the solid than in the gas phase or in the bulk solution. Solid adsorbents consisting of small particle sizes having surface defects such as cracks and holes increase the surface area per unit mass over the apparent geometrical area. These adsorbent particles may have specific surface areas from 10 to 2000 m 2g· 1• Some common adsorbents are charcoal, silica gel (Si02), alumina (Ah03), zeolites, and molecular sieves. In this experiment the adsorption of acetic acid on an activated charcoal surface is investigated.

Adsorption

Adsorption onto a surface (for example charcoal) is a separation process in which certain components (adsorbates) of gaseous or liquid phase are selectively transferred to the surface of a solid adsorbent. 1 In general, there are two adsorption mechanisms: chemisorption and physisorption. In both mechanisms, the adsorbate becomes attached to the surface of the solid as a result of the attractive forces at the solid surface (adsorbent). The main differences between chemisorption and physisorption are

2

:

2-2 1) Physisorption occurs when the adsorbate becomes physically fastened to the adsorbent by electrical attractive forces (weak van der Waals forces). Chemisorption involves the formation of chemical bonds between adsorbate and adsorbent. 2) In physisorption, depending on the strength of the attractive forces, desorption can easily be accomplished by reducing the pressure or increasing the temperature (low energies on the order of 40 kJ mol- 1). reversible.

Therefore, the process is fully

In chemisorption, higher temperatures are required to break the

chemical bonds (requires high heats of adsorption: 40 to 400 kJ mol- 1) . 3) Physisorption layers can be many molecules thick depending on adsorption conditions and adsorbate concentrations.

In chemisorption, only monolayer

adsorption occurs . .

Isotherms An adsorption isotherm describes the equilibrium adsorption of a material at constant temperature. The amount adsorbed per gram of solid is related to the specific area of the solid, the equilibrium solute concentration in solution, temperature, and the specific molecules involved. By analyzing isotherms the relations between the amount adsorbed, the nature of the molecules, and even the surface area can be determined at a specific temperature.

"

.

:o

Figure 1. Freundlich isotherm

Figure 2. Langmuir isotherm

2-3 An adsorption isotherm can be plotted by drawing N, the number of moles adsorbed per gram of solid vs c, the equilibrium solute concentration at constant temperature. One of the first efforts involves the Freundlich isotherm utilizing Eq. (1): 3

(1)

N=K·ca where Kand a are constants that can be obtained from a plot of log N vs log c. The

Freundlich isotherm fails to predict the behavior at low and high concentrations (at low concentrations, N is often directly proportional to c; at high concentrations N usually approaches a constant limiting value, which is independent of c).

Another isotherm theory suggested by Langmuir can be applied to simple systems. Here simple systems refer to cases where only one layer of molecules can be adsorbed at the surface. One layer of molecule adsorption, namely "mono layer adsorption" describes the complete coverage of the surface of the adsorbent by a layer of one molecule thickness.

In monolayer adsorption the amount adsorbed reaches a maximum value at moderate concentrations and remains constant with increase in concentration thereafter. The Langmuir isotherm can be derived from kinetic or equilibrium arguments.3.4 Eq. (2) shows the surface coverage fraction based on the Langmuir theory for adsorption from solution:

B =--5_ l+kc

C2)

where eis the fraction of the solid surface covered by adsorbed molecules and k is a constant at constant temperature. B can be replaced by N!Nm, where N is the number of moles adsorbed per gram of solid at equilibrium solute concentration c, and Nm is the number of moles per gram required to form a monolayefJand Eq. (3) can be obtained as follows:

c

c

1

- = -+ -N Nm kNm

(3)

Based on the assumption of the Langmuir isotherm as the adequate description of the adsorption process, a plot of c/N versus c yields to a straight line with slope I/Nm. Once

2-4 the slope is found from this graph with the knowledge of, a , area occupied by an adsorbed molecule on the surface, the specific area, A (in square meters per gram), can be calculated:

A = N m · N 0 ·a .10-20

(4)

where No is Avogadro's number and a is area in square angstroms. Plotting the adsorption isotherms at several temperatures, the slopes of the c/N vs c graphs can be predicted to be the same if the number of adsorption sites, Nm, is independent of temperature. Although slopes are expected to be the same with changing temperature, the intercepts are expected to be different, due to the fact that k ~s a function of temperature. Eqs. (5) and (6) can be used to relate the thermodynamic theory of adsorption from solution with Nm, solution ·concentration, and the k values.

(8arlnc)

= RT

p, 8

(5)

2

where, D. His a differential heat for adsorption at constant pressure p and coverage e. The interpretation of D.H is complicated, since adsorption process involves the adsorption of solute and the displacement of solvent molecules. Eq. (5) can be rearranged, since l lkNm is equal to co.s!Nm (from Eq. (3)), and co.sis the equilibrium concentration at 8 = 0.5 (where N

= Y:z Nm).

dln(l / kNm) = dT •

The W

At 1 atm:

(8lnc) 8T

8 = 05

D.H RT 2

(6)

in Eq. (6) is usually found to be positive, indicating greater extent of

adsorption at lower temperatures.

Materials 7 x 250 ml Erlenmeyer flasks, their glass-stoppers or rubber stoppers; 3 x funnels; funnel holders (or three rings, with clamps and stands); 3 x 250 ml beakers; stirring rod; one 10 and one 50 ml burette; burette stand and holder; several 100 ml titration flasks; a 5, 10, 25, 50, and 100 ml pipette; spatula. Activated charcoal (acid-free, 10 g); fine porosity filter paper;

2-5 Various molarity acetic acid solutions; 0.1 M sodium hydroxide (150 ml); and phenolphthalein indicator.

2. Laboratory Procedure

1. Organize and label clean and dry seven 250 ml Erlenmeyer flasks and their stoppers.

2. Weigh approximately 1 g of activated charcoal accurately to the nearest milligram. Record the weight (and the corresponding label number) and place the charcoal into the flask. Repeat this procedure for six flasks.

3. Using a 100 ml volumetric flask accurately measure 100 ml of acetic acid solution and add this to each flask. Use the previously prepared acetic acid solutions with concentrations of 0.15, 0.12, 0.09, 0.06, 0.03, and 0.015 M (check with your instructor or TA proper handling of the pipettes).

4. One of the flasks will contain no charcoal. Add 100 ml of 0.03 M acid to this flask; and use this solution as a control solution.

5. Once charcoal is placed and all seven flasks with the solutions are prepared have them tightly stoppered, and allow them to stand in the drawer to equilibriate until next week.

6. The following week, sample solution will be filtered through a filter paper. Discard the first 10 ml of the filtrate to prevent adsorption of the acid by the filter paper. Ask your TA to show you how to fold the filter paper.

2-6 7. Titrate two 25 ml aliquots with 0.1 N standardized sodium hydroxide solution using phenolphthalein as an indicator. To titrate 0.03 and 0.015 M solutions, use a 10 ml burette. Ask your TA to demonstrate a titration.

Cleaning and Order

l. Wash the flasks and the burettes with soap solution and rinse multiple of times with distilled water and let them dry on the rack. 2. Wash the funnels and let them dry on a paper towel. 3. Make sure the balances are left clean. 4. Put the used filter papers into trash bin. 5. Get approval of your TA that everything is nicely ordered and cleaned to not to get any deductions from your lab grade.

3. In lab Questions

1. Describe physisorption and chemisorption. Based on this description; a. Compare their relative heats of adsorption. b. Explain why the heat of adsorption of the physisorption and chemisorption are so different.

2. What is a Langmuir isotherm? How is it derived? Describe how surface area of a solid can be calculated employing the Langmuir isotherm.

3. Calculate the final concentration of acetic acid for each sample. The value for the control solution should agree with its initial value.

2-7

4. Data Analysis

1. Using the initial and final concentrations of acetic acid in 100 ml of solution calculate the number of moles present before and after adsorption and obtain the number of moles adsorbed by difference. Prepare a table as shown in Table 1 which can be filled as you continue on working out the data and complete the units.

'

2-8

Table I. Initial acetic acid concentrations ([HAc];), charcoal mass (fficharcoaJ), titration data (VNaOH.; and VNaOH. r) and their uncertainties (D.).

Flask

Run

1

1

[HAc];

[HAc]r

fficharcoal

tilllcharcoal

VNaOH,i

aVNaOH. i

VNaOH. f

/':i.VNaOH, f

2

2

1 2

3

1 2

4

1

2 5

1

2 1

6

2

2. a) Calculate N, the number of moles of acid adsorbed per gram of charcoal. Prepare a table as sho\Vn in Table 2 which can be filled as you continue on working out the data. b) Plot an isotherm of N versus the equilibrium (final) concentration c in moles per liter.

1

2-9

Table 2. Summary of all ca lculated values and their uncertainties. The amount of NaOH used in each titration is VNaOH.

Flask

Run

V NaOH

D. VNaOH

c

(ml)

(±ml)

(M)

tic

N

(±M)

(mol/g)

(±

1

cfN

D.N

~olJ

D.c!N

(~) (±~)

1 2

2

1 2

3

1 2

4

1 2

5

l 2

6

1 2

3. a) Plot c/N vs c, using Eq. (3). b) Calculate Nm from the slope of this plot. c) Assume that the adsorption area of acetic acid is 21A 2, and calculate the area per gram of charcoal using Eq. (4).

4. Compare the surface area obtained from this experiment to its literature value5 ( 400 m2/g).

5. By linear regression analysis, calculate the uncertainties in the intercept and the slope.

- - -- - -- - - - - - -

-

-

--

2-10 6. Calculate the uncertainty in final acetic acid molarity.

7. Calculate the uncertainty of the surface area.

5. Report Questions

1. What are the three asswnptions the Langmuir isotherm based on?

2. Check whether the adsorption in your experiment exceeded mono layer coverage. 3. How does room temperature and pressure can change the result of this experiment?

References 1. Stenzel, M. H.; Chem. Engr. Prog. 1993, 89, 36. 2. Byrne, J. F.; Marsh, H. Porosity in Carbons, Halsted Press: New York, 1995.

3. Moore, W. J. Physical Chemistry; 4th Ed.; Prentice-Hall: Englewood Cliffs 1972, pp. 484-487. 4.

Rushbrooke, G. S. Introduction to Statistical lvfechanics; Oxford Univ. Press: New York, 1949, pp. 211 -214; Hill, T. L. Introduction to Stalistical Thermodynamics; Addison-Wesley, Reading: Massachusetts, 1960, pp. 124.

5. Sigma-Aldrich Catalog, 2004.

3-1

The determination of thermodynamic functions of the reactions in commercial alkaline-manganese dioxide galvanic cell (Duracell®)

Objectives

• • •

To determine the thermodynamic parameters for reactions in a commercial alkalinemanganese dioxide galvanic cell including .6.rG, .6.rS and .6.rH To compare .6.rH to the calculated enthalpy of formation (.6.rH0 ) of ZnO and Mni03. To determine the equilibrium constant (K) for the reaction in a commercial alkalinemanganese dioxide galvanic cell

Introduction

Galvanic cells, devices in which the transfer of electrons occurs through an external pathway rather than directly between reactants, are useful portable electronic power sources. Alkaline cells are the most common (Duracell® is an example) and are commercially important (this is a billion dollar industry, with 10 10 alkaline batteries produced annually). In the 1960s and 1970s, the alkaline cell gained popularity because of the vvidening field of consumer electronics.

Make-up and Chemistry In the alkaline battery (Figure 1), the anode (negative terminal) is composed of zinc powder (Zn) (which allows more surface area for increased rate of reaction, and therefore increased electron flow) and the cathode (positive terminal) is composed of manganese dioxide (Mn02). (/\Ikaline batteries use potassium hydroxide (KOH) as an electrolyte. The concentrated KOH solution provides high ionic mobility with a low freezing point.'

Zn(s)

As the alkaline-manganese dioxide cell discharges, oxygen-rich manganese dioxide is Figure 1. DURACELL® cylindrical alkaline cen.131 reduced and the zinc becomes oxidized, while ions are transported through the conductive alkaline electrolyte. The half-reactions are: Cathode: Anode: Overall:

2 Mn02 (s) + H20 (l) + 2e- -tMil203 (s) + 2 OH- (aq) Zn Cs)+ 20H- (aq) -t ZnO Cs) + H20 CD + 2eZn (s) + 2 Mn02 (s) -t ZnO (s) + Mn203 (s)

+ 0.80 v

- 0.76 v +1.56 v

3-2 The anode and cathode are separated by a porous, highly absorbent and ion-permeable fabric. The porous nature of the anode, cathode, and separator materials allows them to be thoroughly saturated with the alkaline electrolyte solution. The high conductivity of the electrolyte enables the cell to perform well at high discharge rates and continuous service. It is also responsible for the low internal resistance and good low temperature performance.

Electrochemistry and Thermodynamics Spontaneous chemical reactions inside the galvanic cell result in current. The relationship between the reaction Gibbs energy (LirG) and the electromotive force (emf), E, of the cell is given by (1)

Where Fis the Faraday constant (9.6 x 104 C mot 1) and Eis the voltage. In the experiment, v = 2 because this reaction involves two electrons for the zinc to be oxidized and Mn02 to be reduced. · The maximum amount of electric energy that can be obtained from a commercial galvanic cell is equal:

(2) where mis the mass of reactants in the battery, MMzn is the molar mass of Zn, MMMn02 is the molar mass of Mn02, and LirG is the reaction Gibbs energy. If the reaction has reached equilibrium, the equilibrium constant K can be calculated from the Nernst equation. lnK= vFEo

RT

(3)

Although in this experiment you are not measuring the standard electromotive force, the equilibrium constant can be estimated from the battery potential. The temperature coefficient of the standard cell emf dE0 /dT, gives the standard entropy of the cell reaction. In this experiment, you will determine the entropy of the electrochemical reaction in the Duracell battery. From the thermodynamic relationship (8G/8T)p = -S and equation 1:

dE dT

LirS vF

-=--

(4)

From the results of equations 1 and 3, the reaction enthalpy corresponding to the Duracell battery can be calculated

(5)

Equation 4 provides a noncalometric method for determining the LirH.

3-3 Laboratory Procedure

In this experiment, the voltage of a commercial alkaline-manganese dioxide galvanic cell, namely an AA Duracell® battery, will be recorded at various temperatures in the range of - 25 °C to +40°C. The galvanic cell will be placed into a dewar filled with ethanol. The temperatures will be measured using digital thermometers. The voltage will be measured with a digital multimeter. In order to increase the precision of the voltage versus temperature measurements, a circuit consisting of the measured and the reference battery will be assembled. The complete experimental setup is shown in Figure 3. The galvanic cell holder has wires soldered to both the negative (black) and positive (red) poles; the same colors are used for corresponding voltmeter leads (Figure 3). Assemble Single Battery Circuit

1. Connect the positive lead from the voltmeter to the positive end of the battery holder (red to red). 2. Connect the negative lead from the voltmeter to the negative end of the battery holder (black to black). 3. Record the temperature and voltage. This information is the voltage (not the voltage difference) and will be used in Equation 1 to calculate l:irG. Important notes: Do not allow the leads of the cell to make contact, even for a fraction of second. This action will short the battery, and cause the system to disequilibriate, resulting in a battery that can't be used for this lab anymore (keep in mind you are working with 1 µV precision).

Important: These leads must not contact each other.

Thermocouple head should touc.~~pattery. Figure 2. Battery Holder Assembling Measured and Reference Cell Circuit:

1. Assemble the circuit according to the figures below. Simplified diagrams and a photograph of the experimental setup are shoVvn.

3-4

Dewar

Dewar

Stir plate Figure 3. (Left) Circuit diagram of experiment. (Right) Simplified diagram of experimental setup. Dewars are insulating storage vessels typically used for handling liquids at temperatures other than ambient room temperature. Double-walled vacuum-sealed construction minimizes heat transfer through the vessel wall. For this reason, it is not possible to heat liquids in a dewar using a hot plate. An internal heat source, such as a heating coil, must be used instead.

Figure 4. Photo of experimental setup.

2. Place the battery into the battery holder. Use a rubber band to secure the head of the thermocouple to the body of the battery (Figure 2). Red is positive, and black is negative for our battery holder. Ensure that the alligator clips remain clamped on their wire insulation sleeves to prevent shorting the circuit. Pay attention throughout the experiment to avoid shorting and have a lab member help you during assembly. 3. Starting at the voltmeter:

3-5 Connect the positive end from the voltmeter (red, top connection) the positive end of the measured cell (Figure 3). The measured battery is the one you intend to vary the temperature for, so place it into the dewar resting on the stir plate. Find a wire with red insulation that has alligator clips at both ends. Use this to connect the negative leads of the measured and reference cells (Figure 3). Place the reference cell into the reference dewar (kept at 0 °c using ice+ water). Now connect the positive end of the reference battery to the negative end of the voltmeter (black). Add the ice bath to the reference dewar. Your circuit is now complete. Taking Voltage Measurements:

Note: All temperature variation is performed on the measured battery only. The reference battery should be maintained at 0 °C throughout the experiment. 1. Begin the experiment by measuring the circuit voltage at room temperature. Record both the temperature and voltage.

T {°C)

AE (µV)

-9- --~-

- 5 -1 -(-3)

2. Heating instructions: Place the heating coil inside the measuring dewar with ethanol, and set the Varistat to 10 if you need to heat the battery and stir using a stir bar. Allow the galvanic cell to equilibrate for 10 minutes. To maintain temperatures, add small pieces of dry ice once the desired temperature is reached. Once thermally equilibriated, record both the temperature and voltage. NOTE: DO NOT TURN THE HEAT ON THE HEATING PLATE (the left knob)! For stirring purposes, make sure to use the right knob ONLY.

3. Cooling instructions: Begin adding dry ice to the ethanol while stirring. Allow battery to thermally equilibriate at each of your cooling data points (25°C, 21°C, l 7°C, l 3°C, 9°C, 5°C, 1°C, -3°C) for 10 minutes before you record both the temperature and voltage for those points. Also, wear protective cryogenic gloves (blue) when handling dry ice. SEVERE frostbite can result in a very short period of time.

3-6 4. Clean-up. Be sure to turn the power off for stir plates and the digital thermometers. Leave the voltmeter powered on. Dr. M will do the rest. Data Analysis

1. Tabulate your temperature and voltage data. A sample data/results table might look like this: T (°C)

AE (µV)

25 21 2. Calculate the llrG from equation 1. 3. Calculate the equilibrium constant, K, from equation 3. 4. Plot E versus T. Determine the best-fit line for this data and display the equation of the line and its R 2 value on the graph. A lso carry out the least squares fit for this line using the regression analysis program on Excel (or whichever analysis program used).

5. From the slope, determine the llrS for the galvanic cell. Use the uncertainty in the slope to determine the uncertainty in llrS. 6. From the llrS, determine the llrH. Once again, remember to calculate the corresponding uncertainty. 7. Use the enthalpies of formation, llrH0 , to calculate llrH and compare to the value determined in step 6. Explain the difference. 8. Calculate the maximum amount of electric energy that can be obtained from the battery used in this experiment.

References

(1) Brown, T.L., LeMay, H.E. , Bursten, B.E. and Murphy, C.J., Chemistry: The Central Science, Eleventh Edition. (2009) Pearson-Prentice Hall: Upper Saddle River, New Jersey. (2) Atkins, P. and de Paula, J., Physical Chemistry, Seventh Edition. (2002) W.H Freeman and Company: New York City, New York. (3) Duracell® Alkaline Manganese Technical Bulletin (2005)

4-1

Real Gas Behavior: Gravimetric Determination of the Second Virial Coefficient of C02 Objectives •

To observe deviations from ideal gas behavior in the pressure range up to 10 bar

•

To understand the reasons for a gas to behave in a non-ideal manner

•

To determine the second virial coefficient for C02 using the relationship between compressibility and the inverse of V m

Introduction An equation of state is a mathematical operation that links the state properties of gas. The ideal gas equation stems from three individual gas laws: Boyle' s law, Charles' law, and Avogadro's principle and is shown in Eq. (1). 1 PV_=_nRT

r i >

.

(I)

A gas which abides by Eq. 1 under all conditions is defined as

t5 E

8

ideal.

I arc:

1

A real gas closely resembles an ideal gas if it is monatomic, at low

pressures, high temperatures, or large molar volumes. 1 The compression

CD

:§

E

~

factor, Z, is used to assess deviations from gas ideality. 1 This can be done

J

l r - -- ----:::=-

through Eq. (2), where the actual molar volume, V m, is measured in

§

relation to the ideal molar volume, V m0 . 1

·;;;

~

dominant

Z= Vm/ Vm0

.!!

Figure I. Potential energy of intermolecular interactions. 1

(2)

When V mis less than V m0 , the gas is moderately compressed, and attractive forces dominate (Z
1

On the other hand, under very high

pressure conditions, Vm is greater than Vm0 because repulsive forces are dominant, causing the gas to expand beyond its ideal volume (Z> 1). 1 Figure 1 is a potential energy curve that illustrates how the attracting and repulsive forces that affect Z depend on intermolecular distance.

4-2

Since the V m0 of an ideal gas is equal to RTIP, an equivalent expression for the compression factor can be derived as Eq. (3). 1

(3)

PVm=RTZ

A variety of expressions have been adapted to account for deviations from ideality. One of these is the viral equation of state as shown in Eq. (4), where the first term illustrates the ideal gas law. 1 This equation of state can be derived from statistical mechanics and is used to explain thermodynamic quantities and their departure from ideality.2 PVm=RT[l +(BNm)+(CN2m)+ ... ]

(4)

The series in brackets is analogous to the compression factor Z (refer to Eq. (3)). 1 The constant Bis the second virial coefficient and correlates to interaction between two molecules (C is consistent with three, etc.). Bis a function of temperature and is large and negative at low temperatures and small and positive at high temperatures. 2 The purpose of this lab is to derive the value for the second virial coefficient of carbon dioxide. The first virial coefficient is equal to l and B/ V m >> CNm2, with respect to molar volumes, making B most significant in deviations from ideality. 1 The Boyle temperature, Ta, corresponds to the temperature at which the second virial coefficient is zero, allowing real gases to sustain quasi ideal behavior over a larger range of pressures.

1

Here Z approaches 1 with slope equal to

zero, Eq. (5). 1 Under ideal gas conditions, the slope for Z is always zero.

dZ/d(l/ Vm) -7 Bas Vm-7 oo and p -7 0

(5)

Figure 2 shows the relationship between the Boyle temperature and an ideal gas. The Boyle temperature can be derived if B is set equal to a portion of the Van der Waals equation, Eq. (6), where a depends on attractive Figure 2. Compression Factor, Z, versus Pressure for three different temperatures in relation to an ideal gas.'

forces and b defines repulsive interactions.

2

4-3

B= b - (a/RT)

(6)

Table 1 lists second virial coefficient values of four different gases with their corresponding Boyle temperatures.

Table 1. Second Virial Coefficients, ( cm3/mol) for four gases and Boyle temper atures. 1 Virial Coefficient, B at 273K

at 600K

Ts(K)

Ar

-21.7

11.9

411.5

C02

-149.7

-12.4

714.8

N1

-10.5

21.7

327.2

Xe

-153.7

-19.6

768.0

Other equations which aim to estimate deviations from ideal gas behavior are the van der Waals, Berthelot, and Dieterici equations (refer to Atkins page 19 for more detail). Modern day methods for predicting the second virial coefficient include those used by Iglasias-Silva and coworkers. 3 The third virial coefficient for carbon dioxide has also been predicted at high temperatures. 4 Modern research involves determining third and fourth virial coefficients for hard prolate spherocylinders. 5

Experimental Procedure Part 1: Balance Calibration 1. Tare the balance. While wearing the provided gloves, place the vessel on the balance and

record its mass. 2. Using tweezers, add a one gram weight standard to the balance, and record the

combined mass of the weight and vessel. 3. Repeat step 2, each time adding the next combination of weights (two grams, three grams, four grams, etc.) and recording the new mass, until you reach 10 grams. 4. Repeat steps 2 and 3 three times to ensure good statistics. 5. Be sure to record the predicted masses of the weights. You will need these for your calculations.

3

4-4

Part 2: Evacuation of Vessel 6. Using the provided gloves, attach the vessel to vacuum line C. Clamp it so it does not fall. 7. Fill a large dewar with liquid nitrogen, and place it around the vacuum trap. Make sure the vacuum pump is turned on. 8. Open valve C (while the vessel is still screwed shut) in order to evacuate the vacuum line. Continue to evacuate until the pressure is 0.02 Torr (verify with manometer). This .should take approximately 10 minutes. 9. While the line is being evacuated, measure atmospheric pressure using the Ashcroft pressure gauge. 10. Once the line is evacuated, open the valve on the vessel. Evacuate the vessel to a pressure of 0.02 Torr for approximately 10 minutes. 11 . Close the valve on the vessel, close valve C, and detach the vessel from the line. 12. Record the mass of the evacuated vessel

Part 3: Data Collection Therrn-ocoupJe.

Pressure

Stainless Steel Sleeve

.Adj ustment

Ultra Pure

Carbon Oicxid.e Constant Temperature

Water Bath

Figure 3. Experimental apparatus schematic.

4

4-5

13. Study figure 3 and identify the corresponding parts in the lab setup. Identify the gas regulator (annotated by the arrow), which will be used to control C02 loading into in the vessel. The inlet gauge (right) shows tank pressure; the outlet gauge (left) shows the pressure at which the regulator will cease delivering gas from the tank. 14. Ensure the small round black valve (labeled C) is shut for this step: Open the tank valve (D), and set the regulator to load the correct pressure for C02 by turning the regulator knob. Verify that the loading pressure has been set to 9 bar by reading the outlet gauge on the.pressure regulator. 15. Attach the vessel to the yellow C02 line, and place it in the stainless steel sleeve. Do not allow the vessel to touch water! 16. While the vessel is still closed, fill the line with C02 until it reaches approximately 9 bar (valves C and D). Next, purge the line until the pressure is just above 0 bar (valve B). Do not purge the line completely or air will enter the line. Repeat.

I 7. Open valve A on the vessel 18. Allow the pressure to equilibrate for 5 minutes. 19. Next, record the pressure and the thermocouple temperature.

*

All pressure readings are NIST calibrated within 0.05%. Thermocouple temperature readings have uncertainties of ± 0.1 °C.

20. Close valve A on the vessel. 21. Open valve B below the pressure gauge to release remaining C02 from the line. 22. Unhook the tank from the C02 line, and record the mass of the vessel.

23. Readjust the regulator valve for the next data point by turning the knob counterclockwise. (Note that a positive pressure must be maintained within the regulator for the outlet gauge to correctly display the pressure at which it is set to stop delivering gas.)

24. Reattach the vessel to the C02 line and place it in the stainless steel sleeve. 25. Open valve A on the vessel. The pressure should drop to approximately 8 bar (i'.lP =I bar). If i'.lP < l bar, open valve B below the pressure gauge to release extra C02 from the line until the desired pressure is reached.

5

4-6

26. Using the same procedure, obtain temperature and mass readings for six additional C02 pressures (7, 6, 5, 4 and 3). Remember, these are only approximate pressure values and they indicate gauge pressures. 27. Remember to obtain the atmospheric pressure. (Go to the organic labs on the second floor of Whitmore.)

4. Data Analysis 1. To assure balance accuracy with the added mass of the vessel, plot predicted mass values against obtained mass values (from Part 1). An R 2 value close to one indicates acceptable measurements were obtained. Include this plot, regression line, and R 2 value in your report.

2. Convert the pressure data obtained in lab (Part 3) to absolute pressure in units of Torr. Keep in mind that gauge pressures were recorded (in bar). 3. Determine the amount of carbon dioxide in the vessel in each trial by subtracting the evacuated cylinder's mass from the trial' s mass (cylinder plus gas) and converting to moles. 4. Calculate the molar volume of each trial. (Vessel Volume = 0.5612 L) V m = V vesse1/moles of C02 5. Create a table including pressure (in Torr) (step 1), temperature (in K), moles of C02 (step 2) and molar volume (step 3). 6. Make a plot of Pressure versus moles. Indicate a line which represents ideal behavior. Include this graph in your report. 7. Calculate the compression factor Z for each trial. Z = PV.'11 KT

8. Plot Z - 1 versus lNm. Find the linear relationship ben.veen points of this data. Include the R 2 value in your report. 9. Report the experimental second virial coefficient of carbon dioxide, B. Calculate the error associated with this measurement using linear regression output data. I 0. Report the uncertainty associated with the calculation of Z.

6

4-7

11. Report they-intercept calculated in step 6 and its associated uncertainty. Indicate its ideal value. Explain any deviation from this ideal value.

Report Questions

1. Why is it important to account for the atmospheric pressure when completing your data analysis? 2. Compare your value for the second virial coefficient to the literature value. Don't forget

to take temperature dependence into account. Consider possible sources of error for this experiment and the influence they could have on your results. 3. What is happening at the molecular level that is causing the C02 to deviate from ideal behavior?

References

1. Atkins, P.; De Paula, J. Atkins' Physical Chemistry 8'11 ed. W.H. Freeman and Company: New York. 2006, 14-16, 19. 2. Diamond, J.H.; Smith E.B. The Virial Coefficients ofGases: A Critical Compilation

Oxford University Press. 1969. vii-xii. 3. Iglesias-Si lva, G.A.; Hall, K. R. Ing. Eng. Chem. Res. 2001, 40 (8), 1968.

4. Colina, C.M.; Olivera-Fuentes, C. Ind. Eng. Chem. Res. 2002, 41(5), 1064. 5. Boublik, T. J Phys. Chem. B. 2004, 108 (22), 7424.

7

5-1

Time Resolved Pulsed Laser Photolysis Study

of Pyrene Fluorescence Quenching by r Anion

Objectives

• • •

Understand how fluorescence decay can be used to measure rate constants of photochemical reactions utilizing a nanosecond laser photolysis technique. Measure the rate constant for the inherent unimolecular decay of the pyrene first singlet state (spontaneous fluorescence decay) Measure quenching rate constant for the reaction of r with excited pyrene

Introduction

Fluorescence spectroscopy is a powerful tool used tor gain information regarding the electronically excited states of various molecule.s. Molecules in an excited. state can have very different physical and chemical properties from those in the ground state. For example, the reduction potential of pyrene (Py) in the ground state differs from that of the excited state. Excited pyrene will undergo redox chemistry in the presence of another chemical species with a sufficiently low (or high) reduction potential. Such an excited-state reduction reaction will be measured in this experiment. This lab will explore the lifetime of the excited state of the pyrene (*Py) to determine its relaxation rate through various modes focusing primarily on fluorescence. This lab will also determine how r- quenches the fluorescence of pyrene and calculate the quenching rate constant through lifetime kinetics.

5-2

Photophysics A photon of sufficient energy, in this case 337. l nm, is absorbed by pyrene to yield an excited state pyrene molecule (*Py). An electron is promoted from the ground state energy level into an excited state. This excited state can then relax back to the ground state either by fluorescence of a photon or by radiationless decay as the molecule loses energy in the form of heat. The ratio of fluorescing molecules to total excited molecules is a value known as the quantum yield. During the lifetime of the excited state, there are some small vibrations which occur that lowers the energy of the fluorescent photon. This difference between the energies of the excitation and emission photons is called the Stokes shift.

Py+ hv1 - *Py *Py - Py+hv2 *Py - Py + heat *Py

*Py

Py

Py

Figure 1

The time delay mentioned above between the excitation pulse and photon emission lasts on the order of hundreds of nanoseconds. This excited state lifetime as well as the decay rate will be measured in this experiment and will be discussed further in the kinetics section.

Photochemistry Excited state pyrene, as has been mentioned, is a good electron acceptor. In the presence of r excited pyrene undergoes a reductive transition back to a lower energy state through the formation of the Py- anion and the

r- radical.

5-3

*Py+ r·

B

3L bPy-+ 1· Py ~

I"

Figure 2

Transition A in figure 2 is not energetically favorable, and pyrene in the presence of 1- is quite stable and will undergo no reaction. However, if transition B is induced by excitation from a photon source, *Py will readily accept an electron from

r

through process C to form Py- and I.

This process is referred to as a photo-induced electron transfer reaction. Kinetics The lifetime of the excited state can be treated in the same manner as one would treat

reactants in basic reaction kinetics. The number of molecules relaxing from the excited state to the ground state is proportional to the number of molecules currently in the excited state multiplied by some constant ko (equation 1). Solving the simple differential equation and treating intensity I as being proportional to excited pyrene concentration yields equation 2. -d[*Py]/dt = ko[*Py]

( 1)

(2)

Plotting the natural logarithm of intensity versus time yields a plot in which the slope of the line is equal to -ko. An example of such a plot is shown in figure 3. This plot is for a simple, one component system as discussed in the photophysics section.

5-4

-2.5

-3.0

>-

1-

-3 .5

Cf)

z

w

Linear Regres sio n: Y = A + B • X

-4.0

1-

z z .....!

Value

Parameter

Error

-4 . 5 A B

- 2.4381 - 0.00335

R

SD

0.00297 S.668SE-6

-5 .0 N

p

0.0681

2212

-5 .5 - 0.99686

0

200

400

T I M E

<0 .00 01

600

1000

800

(n s )

Figure 3

To determine the quenching rate constant, kq, of the reaction of *Py with iodide anion, the equation used to determine the rate must include the concentrations of both parts of the system. The general equation for this reaction is given as equation 3. However, in special cases when one concentration (A) is much larger than the other (B), the reaction can be treated as a pseudo-first order reaction only dependent upon the concentration of the lower concentration component (B). For this approximation, formation of product molecules does not significantly change the concentration of larger component as shown in eqliation 4. In this experiment, the concentration of 1- is much greater than the concentration of excited pyrene formed. -d(B)/dt = k[A][B]

(3)

-d(B]/dt = k'[B]

(4)

k'

=

k[A]

(5)

When determining the rate constant for the decay of the excited state in the presence of

r-,

the rate constant is comprised of two primary means of relaxation, fluorescence and

5-5

quenching. The fluorescence rate constant is already known from working with the single component system, but the quenching rate constant still has yet to be determined. If the rate constant for pyrene in the presence of r is measured, then the observed rate constant, kobs, is equal to ko plus the constant of the 1- quenching k'. The rate constant for the r quenching can be determined using equation 4 . From the pseudo first order reaction approximation, the quenching rate is proportional to the

r

r

concentration (equation 5). Making this substitution

yields an equation for the rate in terms of both the fluorescence and quenching decay pathways (equation 6) where k' is kq [r]. -d[*Py]/dt = (ko + kq [r]) [*Py] In I = ln Io - (ko + kq [r])t

(6) (7)

Solving the differential equation for 6 and treating [*Py] as being proportional to the fluorescent intensity, the relationship between the observed relaxation rate kobs, the fluorescence rate ko and the quenching rate kq becomes evident. Once kobs is determined for each r concentration, a plot of kobs versus concentration [r] will yield a line with a slope of kq and with a y-intercept of ko.

Experimental Procedure This experiment is done using a laser photolysis setup. A diagram of the setup is given in figure 4. The excitation source is a pulsed nitrogen laser emitting a lN light the wavelength of which is 337.1 nm. The optical filter absorbs light below 350 nm; any scattered laser light will not reach the photodiode, whereas emitted light (370 nm < A < 480 nm) is unaffected. Emitted photons are collected using a photodiode. Photodiodes use semiconductors (photovoltaic) that, when impacted by a photon, produce a charge/potential difference. The current of charge is then converted into the signal on the oscilloscope, hence, the charge read on the oscilloscope is proportional to the number of photons fluoresced and allows for a photon count to be obtained.

5-6

laser oscilloscope

optical filter

sample cell

1---~

I-

photo diode

Figure 4

Sample Preparation

Samples for analysis should be prepared in l 0 mL volumetric flasks having 10 µM pyrene concentrations and KI concentrations of 0, 10, 20, 30 and 40 mM. KI solutions will be prepared by serial dilution. Calculate the amount of KI needed to prepare 10 mL of a 0.1 M solution and weigh the corresponding amount on a balance. Carefully transfer the solid into the volumetric flask labeled "40 mM". Next, transfer approximately 50 mL of the provided 50% ethanol-water solution from the

volumetric flask to a graduated cylinder. Using a Pasteur pipet, fill the " 40 mM" flask approximately halfuray -with the 50% ethanol-water solution in the graduated cylinder and mix until all of the KI is dissolved. Fill to the line with 50% ethanol-water solution and mix again. From this solution,

CAREFULLYpipet 1.00 mL into the flask labeled "10 m1v1". Then pipet 2.00 mL from the "40 mM" flask into the flask labeled "20 mM". Finally, pipet 3.00 mL from the "40 mM'' flask into the flask labeled "30 mM" . If any of the pipet transfers are done incorrectly, the serial dilution must be completely repeated. There will be a 100 µM pyrene in ethanol solution provided. From this solution, pipet 1 mL in each flask (including the "O mM" flask). This will produce the required 10 µM pyrene solution. Carefully mix each solution. Finally, fill each volumetric flask up to the line with the provided 50% water-ethanol solution and mix. Oxygen must be purged from the cell because it quenches pyrene fluorescence. To do this, place the desired sample in the cell and put the long needle to the bottom of the cell to make sure all of

5-7

the oxygen is purged from the sample. Cap the cell with the needle in it. After the needle and cap are in place, connect the purge needle to a nitrogen line with a slow flow and purge for 5 minutes. After 5 minutes, while keeping the cap in place, increase the nitrogen flow (be very careful not to increase the flow too much while the needle is still under the solvent level) and slowly remove the needle. Make sure to keep the cap on and minimize any exposure to ambient oxygen. Data Collection

Before operating the photolysis apparatus, make sure that everyone in the vicinity (including others working nearby) is wearing eye protection that blocks 337 nm light. UV light can cause damage to the eye; plastic and amorphous glass will not transmit UV light at 337.1 nm. Normal lab goggles will sufficiently protect your eyes for this experiment. To operate the photolysis apparatus, turn the key to turn on the laser. The small black knob on the laser controls the laser pulse rate. Turn on the oscilloscope, press ACQUIRE then SAMPLE then RUN. At this point you may want to adjust the pulse rate. Then press STOP. The signal on the oscilloscope is the fluorescent lifetime of the pyrene sample. Press SAVE/RECALL then SAVE TO FILE. This will save the file to a USB drive located on the front of the oscilloscope. Note the file name given on the oscilloscope screen. Data analysis

1. Plot the fluorescence intensity vs. time data from the .CSV file (originally saved from the oscilloscope) in an appropriate software program (i.e., Excel, Origin, Mathematic, etc.). 2. Fit the plot with an exponential trend line and determine the best-fit equation and R2 value. Note: An exponential fit will require that you delete the raw data associated with the initial baseline and increase in your fluorescence lifetime curve. 3. Determine the

k obs

for each [i-] from the best-fit equation (y = ae·"').

4. Determine the k9 by plotting kobs vs. [I-] and find the best-fit equation and R2 • (Note: What is the value ofko and what does the value mean?) 5. Estimate uncertainty of kq from linear regression analysis. Report in appropriate format the quenching rate constant with uncertainty. ·6. Determine and report the uncertainty for [KI] for each serial dilution.

6-1

Modeling Stretching Modes of Common Organic Molecules with the Quantum Mechanical Harmonic Oscillator (QMHO)

Objectives

•

To understand the influence of reduced mass and bond order on the observed wavenumber for various bond stretching modes.

•

To develop a simple model to predict the frequencies of the infrared absorptions associated with the vibrational stretching modes of single, double, and triple bonds in covalently bound (CHON) molecules.

•

To calculate the force constant predicted by the model.

•

To visualize the vibrations of atoms in a molecule using its optimized geometry by the Gaussian 09 software and to understand the limitations of modeling.

1. Introduction

Infrared Absorption and Vibrational Motion

A molecule absorbs infrared radiation by undergoing a net change in its dipole moment as a result of its vibrational motion. Consequently stretching and bending may be observed as the two major classes of the vibrational motions. Stretching vibrational motion appears as a change in the interatomic distance between two bonded atoms. A bending vibration is characterized by a change in the angle between two bonds. There are four types of bending vibration, which are scissoring, rocking, wagging, and twisting. These vibrational motions are shown in Figure 1. Absorption bands in the 4000 to 1450 cm· 1 infrared region are usually due to stretching vibrations of diatomic units. In stretching bands, the functional groups are found in a higher frequency region than the corresponding bending frequencies. More energy is required to stretch (or compress) a bond, than to bend it. The region below 1500 cm· 1 is often referred as the fingerprint region which may be quite complex but is a unique pattern for the molecule. 1

6-2

a) Stretching vibrations: symmetric and asymmetric (from left to right).

b) Bending vibrations: In-plane rocking, in-plane scissoring, out of plane wagging, out-ofplane twisting (from left to right). Figure 1. Molecular vibration types: (+)refers to motion from page towards the reader · and(-) motion away the reader. 1

To calculate the total number of possible vibrations in a polyatomic molecule, the molecular degrees of freedom must to be found. A molecule's degrees of freedom refer to the minimum set of coordinates that completely describe its mechanical motion. This system is based on the number of atoms in the molecule (N) to be fixed in space and the total number of molecular motions resulting in 3N degrees of freedom. Considering that a molecule has three different motions; translational, rotational, and vibrational, by subtracting the sum of the translational and the rotational motions from the total number of degrees of freedom, the degrees of vibrational freedom are found. A linear polyatomic molecule containing N atoms has 3N-5 and a nonlinear molecule has 3N-6 normal modes of vibration (fundamental vibrations). Normal mode is an independent, synchronous motion of atoms or groups of atoms that may be excited without leading to the excitation of any other normal mode and without involving translation or rotation of the molecule as whole. 5 Not all normal modes might be seen in IR spectrum. The selection rule for normal mode active in infrared is that the motion corresponding to a normal mode should be accompanied by a change of dipole moment. 5

Simple Harmonic Motion and Quantum Harmonic Motion The stretching vibration can be analyzed using a simple harmonic motion and Hooke' s Law. 1' 2 In simple systems, atoms are considered to be point masses and linked to a spring with a force constant of k. The spring is assumed to be hanging from a fixed location, such as a wall. Figure 2 and Eq. (1) illustrates Hooke's law.

6-3

mass

- -[:~

-: quilibrium

--- +x

Figure 2. Vibration of a mass on a spring

(1)

F=-k·x

where, F is the restoring force, k is the force constant, and x is the displacement from the equilibrium point due the force applied along the spring axis. Once the mass is moved from the equilibrium point, the force along the axis becomes negative and acts as a restoring force. The force is proportional to the displacement with proportionality being the force constant, which reflects the rigidity of spring. When the mass reaches the equilibrium point, the force is equal to zero, but the velocity is not zero and the mass will continue to move. Displacement of the mass results in a simple harmonic motion. The amplitude of vibration depends on the initial position and the initial velocity of the mass. In classical mechanics any value of the total energy (sum of the potential and kinetic energies) of the oscillator is possible. When the same potential energy function (force is the first derivative of potential energy) is used in quantum mechanics the total energy of the oscillator can only be equal to specific values, see Figure 3. The energy levels of a quantum mechanical harmonic oscillator (QMHO) are given by: (2)

where, n is the quantum number of the energy level,

n=}!__, and 2n

m is angular frequency,

The state of minimum energy of a quantum mechanical harmonic oscillator is named the ground vibrational state. It occurs when n=Oand its energy is not zero but rather E0

-

nm . 2

6-4 This energy is termed the zero-point energy of the oscillator. In the case of a diatomic molecule the same equation for frequency can be used by replacing mass by the effective or reduced mass: µ

=

mm 1 2

,

where m1 and m2 are the masses of the two atoms.

mi +m2

> ~ --- - + - - - - - - -Jj .... Qi

---! v = 6

v=5 v

(ij ......

"E

2 ······ ·

=4

v=3

g_

fi w

v =O

0

Displacement, x

Figure 3. Potential energy diagram of quantum mechanical harmonic motion.

Infrared spectroscopy commonly utilizes wavenumber, v (cm- 1), the reciprocal of wavelength to determine the frequency or the energy, since, vis directly proportional to the energy (E

=hvc).

Modeling In this experiment, the vibrational frequencies ( v cm-1) for the stretching modes of various covalent bonds will be predicted using the QMHO model. 3 The development of this model is based on two major assumptions: In the first assumption, a stretching mode of vibration effectively involves two atoms. Although this assumption is not completely accurate, for example, C-H stretching motions of a methyl group, involves more than two nuclei in the vibrational motion, it is safe to assume that atoms further away from the bond being considered do not contribute significantly to the vibration. In the second assumption, the force constant for a given bond is directly proportional to the bond order.

In this study a common organic "CHON" family \.\ill be used, which consists of covalently bonded molecules containing only C, H, 0, and N elements.

The reason for

choosing C, H, 0, and N elements in the construction of the CHON family is due to the

6-5 similar magnitude diatomic bond strengths.

Typical covalent bonds in common organic

molecules, have bond dissociation energies in the range of 300-400 kl/mole and the effective force constants are found to be in between 500-700 Nm- 1• The following steps will be followed in the modeling of stretching modes of common organic molecules.3

A. Force constant determination: Specific bonds will be modeled as pseudo diatomic molecules.

Using the assumption mentioned above, the wavenumber of the stretching

vibrational mode of the pseudo-molecule can be defined as a function of the reduced mass and the force constant of the bond (3)

[k

-

1 v = 2;rrc 1{;;

where, c is the speed of the light (in cm·s- 1) , k is the force constant of the bond in question (in N·m- 1), and µis the reduced mass of the system (in kg). Using Eqs. (1) and (2) and the observed wavenumbers, V:,bs

, force constants for each of the bond types studied can be

calculated.

B. Effective force constant determination: In the development of the model it is assumed that the force constant for a given bond is directly proportional to the bond order. See Table 1 for illustration. Based on this assumption each force constant is divided by the number of bonds and effective single-bond force constants,

=

k eff

k eff ,

are calculated. (4)

k

bond order

Averaging the k.ff values of all the bond types studied, an effective averaged force constant, k:J/ , is approximated. 34 T able 1: Bond 0 rders an dF req uenc1es o fC arbon an dN'1tro2en Md 0 es ·

Mode C-N C=N C=N

Bond Order

Frequency ( cm-1)

1 2 3

1180-1360 ~1660

2100-2260

6-6

C. Predicting wavenumbers: Employing

k:;/

along with the bond order, wavenumbers of

stretching modes of the CHON family can be predicted.

I =--

vpre

(5)

k:; · bond order µ

2nc

D. Evaluating the performance of the model: By plotting

v bs 0

vs.

vpre

and fitting a straight

line (passing through the origin), the performance of the model is evaluated. If the model predicts perfectly, the slope of the line should be 1. The first approximation to

k':;/

may result

in significant error in the prediction of vpre . Therefore, optimization of k:J/ should take place in the next stage of this study.

E. Optimization of the model: The model can be optimized in a number of ways and trial and error is one of the approaches. obtained and plotted against

vobs

By systematically varying

k':J/

a new set of

vpre

is

until a fit with a slope of 1 is obtained. (6)

v pre = m . v obs where m is the slope.

If the predicted wavenumber is not equal to observed wavenumber (slope is not equal to 1), using the slope of the fitted line a correction factor, effective force constant,

k:J' .

f3, can be calculated to optimize the

The relations of k'J' and

f3, and f3 and m are shown in Eqs.

(7), (8), and Eqs. (9), (10), respectively. Multiplying the unrefined wavenumbers by

fji , a

set of refined wavenumbers is obtained and optimization is continued till a slope of 1.00 ± 0.0 1 is achieved. k opt eff

= j3. k eff ave

(7)

- opt V pre

=

1-

(8)

V pre

m' V ohs =---

- opt V pre

and using Eqs. 5 and 7,

·Vobs

1-

·Vobs

(9)

6-7

kave eff

R

JJ

k ave

=m

l

and f3

=-m 2

elf

(10)

Table 2. shows the group frequencies for organic compounds. Note: This study is modeled for only stretching motion of two atoms and it -vv'ill not work for

bending and other complicated motions of vibrations.

6-8

Tabel 2. Group frequencies for organic compounds.4 Frequency Ranae, cm-1 2850-2970

Intensity

1340-1470

Strong

3010-3095

Medium

675-995

Strong

3300

Strong

30 I 0-3100

Medium

690-900

Strong

Monomeric alcohols, phenols

3590-3650

Variable

Hydrogen-bonded alcohols, phenols

3200-3600

Variable, sometimes broad

Monomeric carboxylic acids

3500-3650

Medium

Hydrogen-bonded carboxylic acids

2500-2700

Broad

N-H

Amines, amides

3300-3500

Medium

C=C

Alkenes

1610-1680

Variable

C=C

Aromatic rings

1500-1600

Variable

C=C

Alkynes

2 100-2260

Variable

C-N

Amines, amides

1180-1 360

Strong

C=N

Nitrites

2210-2280

Strong

C-0

Alcohols,ethers, carboxylic acids, esters

1050-1300

Strong

C=O

Aldehydes, ketones, carboxylic acids, esters

1690-1760

Strong

Bond C-H

C-H

Type of Compound Alkanes

Alkenes

C-H

A lkynes

C-H

Aromatic rings

0 -H

()c=c(H) (-C=C - H)

Strong

6-9

The Fourier Transform Infrared Spectroscopy The Fourier Transform (FT) is a mathematical process converting intensity and time information to intensity and frequency.

FTIR conveniently records the same spectrum a

number of times, since recording a spectrum is on the order of a second, and displays an averaged spectrum.

Using averaged spectrum a reasonable signal to noise ratio can be

obtained even with a little amount of sample. There are two methods used to resolve an IR spectrum in modern IR instruments. The first method (dispersion) consists of a monochromator with a diffraction grating blazed for the IR region. The second method, FT-IR, uses the Fourier Transform on the interferogram produced by different IR wavelengths that constructively /destructively interfere causing a signal at the detector. The Michelson interferometer, a device which is used to split electromagnetic radiation and recombine it to cause an interference pattern, is employed to create the interferogram which is recorded as signal pattern as a function of time. This interference pattern undergoes a Fourier Transformation from the time to the frequency domain and the frequency spectrum, this is the final product. FT-IR (instrument is shown in Fig. 4) has several advantages over the classical dispersion methods: 1) Scan times are much shorter since all frequencies are monitored at once. 2) Since more scans can be performed in a shorter amount of time, the signal to noise ratio can be increased as the ratio increases proportionally to the square root of the number of scans performed. The intensities of each scans can be added together digitally. 3) The resolution of a properly tuned FT-IR instrument can be as accurate as 0.125 cm·1 •1

6-10

HeNe Shield

rR

detector \

detector Interferometer flat mirror

windows

Sample a rea

Purge cover

Adjustable toroidal window

Figure 4: A single beam FTIR spectrometer. 1

2. Laboratory Procedure

The following organic liquids will be analyzed using FTIR spectrometer and their

spectra will be recorded: Acetone, methanol, acetonitrile, cyclohexene, 1-butanamine (nbutylamine). Use the K.Br (NaCl) plates provided. Note: Do not use water in these cells since they are made out of salt. Part 1. Experimental determination of stretching modes.

1. Clean the two KBr salt plates by placing a couple drops of acetone on both sides of the plates and wipe them out by kimwipes. It is important to properly clean the salt plates before each run, and to wear gloves when handling the plates. 2. Place the two clean and dry plates in front of the light beam (make a sandwich) and take their background spectrum.

Once the background spectrum is taken, FTIR spectrometer

6-11

corrects the real sample spectrum for the background absorption before recording sample spectrum. 3. Prepare the sample. Place several drops of solvent on the K.Br salt plate that you have just taken the background spectrum. Then place the second plate on top of the first plate to evenly distribute the liquid as a thin layer between the plates.

4. Take the FTIR spectrum of the sample. On a typical spectrum you should average at least four spectra. Be sure you average a similar number of background spectra.

5. Record the spectra.

6. Find frequency of stretching modes by using software. Use Table 2 as reference. Record frequency.

Part 2. Visualization of stretching modes. 7. To calculated and visualize modes of the molecules studied using Gaussian, go to the

Chemistry Department computer laboratory in 207 Whitmore. 8. Log onto the computer. 9. To access Gaussian, you must log onto the high performance computer Hammer by running X term Software. To run this program from the Windows Start Menu select: I All Programs/Internet Applications/Communications/Cygwin/Cygwin Bash Shell This command will open a new terminal window. Once the prompt appears, type the command: Xwin -multiwindow Then run the program "Secure Shell Clinet" from the Windows Start Menu: I All Programs/Internet Applications/Communications/SSH Secure Shell/Secure Shell Client The first time you run this program you will need to check/change settings under: /Edit/Settings/Tunneling Make sure that "Tunnel XI 1 Connections" (Profile Settings/Tunneling) and "Enable SSH2 Connections" (Profile Settings/Authentication) are both checked.

6-12 From the SSH Secure Shell window, choose /File/Connect and enter the host computer you wish to connect to: hammer.aset.psu.edu and your user name (the same name and password as your PSU Access account). To access Gaussian, on the SSH Secure Shell window, type the follO\\-ing [yourPSUaccessID@ritchie

~]

$ module load gaussian

[yourPSUaccessID@ritchie

~]

$ module load gview

[yourPSUaccessID@ritchie

~]

$ gview

10. Two new windows should appear on the screen entitled "GaussView 4.1.2" and "Gl:Ml:Vl -New".

11. Start drawing a molecule of interest. You should be able to learn how to build molecules using the Help menu, especially by stepping through some of tutorials available.

12. Once the molecule is constructed adjust the geometry of the molecule based on defined set of rules by using menu EDIT->CLEAN. This adjustment is only first rough approximation.

13. Now you are ready to perform a calculation. Your goal is to obtain IR frequencies. However, the first step in the calculation is to optimize the geometry of the molecule. To enter the parameters of the calculation go to the menu CALCULATE->GAUSSIAN.

14. A new window, "Gaussian Calculation Setup", will pop up. Choose the Job Type tab and OPT+FREQ as job type. Go to Method tab and change basis set to 6-31 G++.

15. Go to the Title tab and type the molecule name and description of job you are running.

16. Go to the NBO tab and choose CHECKPOINT SAVE: DON'T SAVE.

17.Go to SOLVATION tab and ensure that MODEL is set to NONE. Now you are ready to run calculation!

6-13 18. Press the SUBMIT button. The program will ask you to save the input file. Click the SAVE button. Type an appropriate file name using extension ".com". Check the box WRITE CARTESIAN and then click SAVE button.

19. Click OK to submit file to Gaussian.

20. Wait until program reports that your job has completed. (depends on molecule size it may take 5 to 15 minutes) Click YES to open the result file. Choose FILE TYPE as Gaussian Output Files and than choose your file (the output file has the same name as the input file but with the extension changed to ".log").

21. Go to menu RESULTS-> VIBRATIONS, which bring up a table with calculated IR frequencies. Choose a frequency you want to visualize. Check box Show Displacement Vector. Click the Start button. You can see the vibrational motion that corresponds to the IR frequency selected. Find stretching modes. You need a total of two nice images of normal modes for the report to illustrate the assumptions of the proposed model. You may save more than 2 images. Before saving an image click Stop button. To save an image go to the menu FILE->SAVE IMAGE. Type a filename, choose File Types as JPEG Files, choose Save As as JPEG FILE. You have to check box WHITE BACKGROUND. Click the SAVE button.

22. Go back to the frequency table and choose the next IR frequency of interest, visualize it and save the image if you need.

23. Calculated IR frequencies should be scaled to match experimental frequencies. The scale factor is 0.897 (J Phys. Chem., 100, 16502 (1996))

24. To transfer JPEG files to the local computer use program ~'SSH Secure File Transfer". Click "Quick Connection" and type hammer.aset.psu.edu as "Host Name'', your PSU ID as "Name", click the CONNECT button. Move files to Desktop for example and ensure that they are good.

25. To close Xwin software type "exit".

6-14

3. In Lab Questions

I. What is the usual IR region used in the infrared spectroscopy? (Hint: The IR region includes not only stretching modes).

2. Describe the type of vibration motions.

3. What is the importance of fingerprint region?

4. What is a normal mode?

5. Visualize the vibrational modes of acetone in Gaussian. Identify each stretching mode. Determine the symmetry and IR activity of each of these modes.

4. Data Analysis

I. Draw each molecule to be analyzed and find their individual stretching modes.

Using

infrared interpretation tables determine their stretching frequencies. Make a table or fill the data table below to list the stretching modes of each compound analyzed.

6-15

Table l. Calculation of Effective Force Constants Mode

Bond Order

Mass l

Mass2

Reduced Mass (kg)

Observed frequency (cm·1)

Calculated frequency (cm· 1)

k (Nm-')

ke1T (Nm-1)

C=O C-H (spJ)

C-N N-H

C=C C-H (spl)

C-0

O=N 0-1-1

k eff a""=

2. Write down the experimentally observed frequencies into the data table. You may average the C-H stretching modes involving sp3 carbon and the ones involving sp2 carbon. Record the stretching mode and the corresponding ·stretching frequency on the spectrum. Do not try to analyze the C-C bond stretching modes, since they are not identifiable in infrared spectra due to their weak intensity.

3. Using Eq. (3) and the assumption that "vibration is associated with a molecule of two atoms'', calculate the force constant for each stretching mode~

4. Using the assumption "the force constant for a given bond is directly proportional to the bond order", divide the calculated force constants by the bond order to find the effective single-bond force constants, keff . Averaging keff values obtain k:;e for modeling which should be in the order of 102 N m· 1.

6- 16

5. Plotting

v

0

bs

vs

vpre, obtain a best-fitted line which passes through the origin.

If the slope

of this best fitted line is 1.00, there is a good match between the observed and the predicted frequencies, which means that model is working perfectly. If the slope is different than 1.00, the slope needs to be optimized until the slope of the linear regression line is equal to 1.00 ± 0.01.

6. For optimization please follow section Modeling part E.

7. Discuss in your report the influence of model assumptions on prediction of stretching frequency.

8. Estimate the uncertainty of effective force constant from linear regression analysis.

5. Report Questions

1. What is the selection rule for normal mode to be infrared active?

2. What is the method that Gaussian 09 software is using to calculate infrared frequency?

3. If you were to use

k:;/

and compute the frequency of C-H stretching modes using the

model, they would show a single peak. As you saw in acetone, this is not the case. Explain.

4.

Overlay the experimental spectrum of acetone with the calculated IR active modes.

(identified during the In-Lab questions) Discuss the differences between calculated and experimental results.

References:

6-17 1. Skoog, D. A.; Holler F. J.; Nieman, T. A., Principles of Instrumental Analysis, 5th Ed.; Brooks: Cole, 1998. 2. Pavia, D. L.; Lampman, G. M.; Kriz, Jr., G. S. Introduction to Spectroscopy: A Guide for

Students ofOrganic Chemistry, W. B. Saunders Co.: Philedelphia, 1979, p. 21. 3. Pamis, J.M.; Thompson, M. G. K. ; J Chem. Educ. 2004, 81, 1196.

4. Silverstein, R. M.; Bassler, G. C.; Morrill, T. C. Spectroscopic Identification of Organic

Compounds; 5th Ed.; Wiley: New York, 1991. 5. Atkins, P.; de Paula, J. Physical Chemistry;

gth

Ed.; W. H. Freeman and Company: New

York, 2006, p.461.

General Reading: McQuarrie, D. M . Quantum Chemistry; University Science Books: Mill Valley, CA, 1983, Chapter 5.

7-1

Resonance Energy of Naphthalene by Bomb Calorimetry Objectives

•

To determine the heat of combustion of naphthalene and compare it to the literature value

•

To calculate the theoretical heat of combustion of solid naphthalene using bond energies, the heat of sublimation of naphthalene and the heat of vaporization of water

•

To relate the heat of combustion of naphthalene determined from bond energies to the literature value and discuss the reason for the differences as well as the what this difference tells us about the resonance energy in naphthalene

1. Introduction The purpose of this experiment is to measure the standard enthalpy of combustion of naphthalene, t"lH0comb using a Parr oxygen bomb calorimeter. The enthalpy of combustion is useful for calculating other thermochemical information of such as heats of formation, bond energies and resonance stabilization energies for aromatic molecules. Naphthalene (C10Hs) is one such aromatic compound and its resonance energy will be determined indirectly in this experiment. The structure of naphthalene is shown below.

Figure 1: Structural Formula for Naphthalene

Theoretical Background The study of the heat produced or required by chemical reactions is called thermochemistry. 6 It involves the measurement of temperature changes that result from the evolution of heat during the course of the reaction. The changes in internal energy (AU) or in

7-2 enthalpy (Ml) for chemical reactions can be determined from such measured temperature changes. These values can then be used to gain insight into the nature of the chemical bonding in the compounds involved in the reaction. Complete combustion of hydrocarbons in the presence of excess oxygen generally produces only two products, C02 and H20. Combustion reactions are conventionally written for the combustion of one mole of material. Therefore, for benzene:

C6H6(l) + 7 Yz 02(g) 7 6 C02(g) + 3 H20(l) AH°comb

(1)

= - 3268 kJ /mol

The conditions of phase must be specified. This is particularly important for compounds such as water which can exist in more than one phase under common conditions. Experimental heats of combustion are usually determined in a bomb calorimeter. In the Parr bomb calorimeter, a sample is burned completely in excess 02 gas at a relatively high pressure (25-30 atm). The bomb is flushed with oxygen prior to firing to displace any nitrogen present and to eliminate the formation of nitric acid that forms at high temperatures in the presence of nitrogen, oxygen and water. The heat produced upon combustion is transferred to the water in which the bomb is immersed, as well as to the other parts of the calorimeter, though the water is the greatest heat sink. The _heat capacity of water (Cw) is. taken as 4.1798 Jg- 1K· 1 in the temperature range of interest. The heat capacity of the entire calorimeter

(Ccalorimeter),

including the water, will be determined in this experiment, usirig a standard sample with a known enthalpy of combustion. According to the First Law of Thermodynamics:

13.U = Q+W

(2)

where the heat, Q, is negative if it is lost by the system and the work, W, is negative if it is done by the system. Since the combustion in the bomb is carried out at constant

f

volume, the p-V work, defined as - pdV is zero. Assuming no other type of work (such as electrical work) is done, then W

= 0 and equation (2) becomes: 13.Uv = Qv

(3)

Thus, the heat (Qv) released during combustion is equal to the change irI the internal energy for the reaction. The direct experimental measurement yields the value of '3.Ubomb, the heat of reaction as carried out in the bomb at constant volume and elevated pressure.

7-3 The enthalpy change for the process is related to the observed internal energy change,

~U,

by:

M! = ~u + ~(pv) where

~{p V) =(p V)products -

the term

~(p JI)

(4)

(p V)reactants • For reactions involving only solids or liquids,

is negligible. However, if gases are involved in the reaction, the term can

be significant, leading to an ideal gas behavior:

As a result, ~(pV)= ~n(g)RT , where W(g) is equivalent to moles of gaseous products minus the moles of gaseous reactants. This

~n(g)

is used in Eq. (6).

Mf = ~u +~n(g)RT

(6)

where T is the temperature, T60%, as defined in Figure 2. This equation will be used

when carrying out the calculations for this experiment. It should be noted that the Mf is at constant volume, Mfv, in Eqs. (4) and (6).

Another factor to consider is the pressure of 25-30 atm inside the bomb, which is far from the standard pressure of one atmosphere. The enthalp)'. of a gas varies with its pressure as shown below. 1

(8HJ =V-T(oV) 8T P

(7)

op r

Using ideal gas equation p V = nRT, and one mole equation (7) becomes:

(8)

= V-T( R J=V-V= 0 (oHJ op p T

Thus for a process where gases are assumed to act ideally, the Mf of the .reaction is not dependent on the magnitude of the pressure. Though oxygen and carbon dioxide do not behave ideally at 25-30 atm, the difference between Affv and be neglected in this experiment.

~Hp

is very small, and can

7-4 Ignition of the sample in the bomb causes combustion, and heat is released. This energy is transferred from the system (the reactants) to its surroundings (the calorimeter with all its parts, including the water) as described by Eq. (9). Q reaction

(9)

= -Qcalorimeter

The reaction temperature is over 2000°C, the calorimeter is at room temperature and will absorb a specific amount of heat per unit mass for every 1°C change in its temperature. This specific quantity is known as the heat capacity of the calorimeter

(CcaJorimeter),

and

includes the constant volume of water surrounding the bomb. fthe calorimeter heat capacity must be determined experimentally by combusting a massed sample with a known enthalpy of reaction in the calorimeter, and measuring the resulting change in temperature (AT) of the water in the calorimeter. Thermal equilibrium between the bomb and the water is assumed so that t:.T is considered to be the same for both. Using the definition of heat capacity at constant volume: (10)

Cv = (-)( dUtherma/) dT v

Assume

Cv

to be independent of T over the small temperature range being used, and

integrated Eq. (10) to give: !::.U = -Cv!::.T = - Cv(Tjinal -T,nilial)

where

Cv is

equal to

Ccalorimeter·

(11)

This value is specific for the calorimeter used.

The amount of heat generated from the complete combustion of the standard sample (benzoic acid) and the partial burning of the nickel alloy fuse wire is calculated from their known heats of combustion (found on their containers).

The total heat

generated by the sample and the fuse is equivalent to t:.U in Eq. (1 1). Knowing this, Cca1orimeter for

a given calorimeter can be calculated from the following equation. Cca1orime1er

= (-)

[ (t:. Vwmple msample ) + (t:. !:lT

ufuse t:.mfu.~e )J

(12)

where t:.U is heat of combustion of the sample or fuse, in Ji g, m is mass of the sample combusted, D.m is difference between the initial mass of fuse and final mass of fuse after

7-5 combustion, and tiT is difference between final and initial temperatures of water. NOTE that

these are negative values, since combustion is an exothermic process In considering t!.T, assume that the bomb calorimeter being used is only

approximately adiabatic.

The calorimeter is normally assembled with the water

temperature being slightly below room temperature; therefore, heat leaks to the calorimeter from the surroundings and there is a slight rate of increase in temperature over time. When the sample is ignited the temperature inside the bomb increases. As the heat from the bomb is transferred to the water and the calorimeter bucket, their temperature rises until they are all at thermal equilibrium, i.e. the same temperature. The temperature usually goes through a maximum, and then a slightly negative slope is observed in the temperature vs. time graph due to heat leaking from the calorimeter to the surroundings. One other factor to conside:r: is that there is usually a stirrer present to hasten thermal equilibration. The mechanical work done on the system by the stirrer results in the continuous addition of energy to the system at a small, approximately constant rate. Absorption of heat by or loss of heat from the calorimeter is minimized by having the water temperature in the calorimeter close to the surrounding room

temperature. As observed in Figure 6, the temperature variation as a function of time (dT/dt, drift rate) is approximately linear. Therefore, in our system we can reasonably assume that the rate of gain or loss of energy by the system resulting from the stirrer work and the heat leakage is reasonably constant with time at any given temperature. In the same figure, it can also be observed from the sl-opes of the pre-ignition (dT/dt)i and post-ignition (dT/dt)r lines that the drift rate is quite small. The vertical line, t60%, is placed at the time when the temperature has reached 60% of the maximum value for the reaction. This somewhat arbitrary choice is made to account for the heat produced by the stirrer and the loss from heat transfer. The value of 160% (6.5 min.) is then used in each of the best-fit line equations to determine Ti and Tr and !!.T. The point of intersection of t6o% and the ignition curve provides the temperature,

T6o%, for Eq. (6). When collecting data for this experiment, one should follow the temperature variation before and after the reaction for a period long enough to allow a good

7-6 evaluation of (dT/dt)r and (dT/dt)r. This is usually between 5 and 10 minutes. A plot, like shown in Figure 6, must be constructed. The best value for t6o% should then be determined and used to calculate the values of Tf and Ti from the equations of the preand post-ignition lines.

f).T

can then be calculated from Tr - Ti. It should be noted that

the slope of each the pre- and post-ignition lines provide the uncertainty for the value of the calculated temperatures.

Of course the tolerance level of the temperature-

measuring device must also be taken into account and whichever yields the greater uncertainty should be the uncertainty used in determinations of propagated uncertainties or error.

27.0 y_

=-0.0019x + 26.586 l

26.5

l ---- pre-ignition line

0

26.0

i :J ...cu

II

Tso% 25.5

II __...,_post-ignition line

()

~

-+-Ignition of BA

Cl)

a. E Cl) 25.0

-

t24.5 - - - - - y = 0.0004x + 24.197 24.0 0.00

5.00

10.00

15.00

-

Linear (postignition line)

- - - - Linear (pre-ignition line)

20.00

time, min.

Figure 2. Temperature-time plot for the combustion ofbenzoic acid standard.

1

Though the majority of the discussion thus far has pertained to the acquisition of thermochemical data directly from experimental work in the lab, there are some reactions that are not suited for direct calorimetric measurement. The thermochemical information for such reactions can be determined indirectly using Hess's law of

J

7-7

constant enthalpy summation or estimated from the manipulation of bond energies if the structural formulas for all species involved in the reaction are known.

If the structure of the molecules involved in a chemical reaction are known, it is possible to express the enthalpy for that reaction as an additive property of the bond energies of the bonds being broken (positive bond energies) and being formed (negative bond energies) in the course of the reaction. Bond energy is defined as the amount of energy needed to break one mole of a particular bond in a gaseous molecule to give electrically neutral fragments. Bond energies are specified in two ways. The average bond energy is the average molar enthalpy change when all similar bonds in a gaseous molecule are cleaved under standard thermodynamic conditions. The true bond dissociation energy is the L\H0 needed to break one mole of a specific chemical bond. Consider the difference in these energies for the C-H bonds in methane.

In gaseous methane (CR4) the breaking of all four C-H bonds to form gaseous carbon and hydrogen atoms requires a total of 1661 kJ mo1· 1 of CH4, giving an average bond energy of 415 kJ mo1· 1 for the C-H bond in methane.

CH4cg> ~ CH3(g) + Hcg> CHJ(g)

~

CH2cg) + H(g}

CH2cg) ~ CHcg> + Hcg)

L\H0 = 427 kJ moi- 1 L\H0

=

460 kJ mol

L\H0 = 435 kJ mo1- 1

L\H0

=

339 kJ mo1- 1

1661 kJ mo1· 1 Average bond energies are usually tabulated from experiments involving many hydrocarbons and can be used in determining estimates for enthalpies of reactions. Some common average bond energies are shown in Table l . These energies are not taking into account the molecular environment of the bond in most cases. The one exception is the C=O values given.

It is possible to estimate the stabilization or resonance energy of aromatic compounds using bond energies. For example, in benzene (with 6 C-H bonds, 3 C-C bonds and 3 C=C bonds) the conjugated carbon-carbon bonds are thermodynamically more stable than three isolated C=C and three isolated C-C bonds in a cyclic system. This increased stability of benzene is called the "resonance energy" and is associated with the delocalization of the six n-electrons occupying the six carbon 2pz atomic orbitals.

7-8 This resonance stabilization energy can be estimated by comparing the experimental heat of combustion (which takes into account the molecular environment of the chemical species in the reaction) to the theoretical heat of combustion (determined from the relevant bond energies and does not take the molecular environment of the bonds into account).

Table 1. Average Bond Energies, LlH0 , at 25°C (in gaseous state) 4 Diatomic Molecules (kJ mol-1)

8

Polyatomic Molecules (kJ mol- 1)

H-H

436

C- H

414

C- F

485

F-F

157

C- C

347

C-Cl

339

Cl-Cl

243

C=C

610

C-Br

284

Br-Br

194

C=C

836

C- 1

213

I-I

153

C- 0

359

0 - H

464

H-F

568

C= oa

803

0-0

146

H - Cl

431

C= Ob

694

0 - Cl

217

H - Br

365

C= oc

736

0 - Br

201

H-I

299

C= Od

748

N-H

389

O=O

498

C-N

305

N- N

163

N=N

945

C =N

615

N-0

221

C=N

890

N=N

418

S- H

339

N=O

606

S- S

229

carbon dioxide; bformaldehyde; caldehydes; dketones.

Experimental (The Parr Calorimeter) Oxygen bomb calorimetry involves the burning of a known amount of a substance in an excess of oxygen in a rigid (constant volume) vessel. The heat of combustion is determined from the change irI the temperature of the cooling water in the calorimeter bucket before and after combustion. The Parr 1341 Oxygen Bomb Calorimeter is shown below in Figure 3 and 4.

7-9

IJ.4t Cak:orimfJlttt with lgniOO:ri Urtit

Figure 3. 1341 Parr Calorimeter with Ignition Unit. 2

To become familiar with the parts of the calorimeter, look at the following cross-section diagram of the calorimeter and locate the following parts: l. Oxygen combustion bomb, where the sample will be placed and filled with oxygen, 2. oval bucket, which will hold the water, and the bomb, thermometer, thermistor, and stirrer will be immersed, 3. stirrer and its pulley,

4. ignition wires, and, 5. calorimeter jacket and cover.

As seen in Figure 4, the oxygen combustion bomb (or "bomb") sits in a oval calorimeter bucket which will hold 2 L of water when the sample in the bomb is ignited. It is the temperature of this water that is monitored to measure the flow of heat from the combustion occurring inside the bomb. 2 •3 In the set-up that you will be using there is a thermistor attached to the thermometer and a multimeter. The multimeter transfers voltage data corresponding to the temperature of the water in the calorimeter to the bomb calorimeter software in the

7-10

PARTS FOR THE 1341 CALORIMETER

l<ey No. Part No. Description 1603 Tbennometer, 19-35° C. •2 A39C Thermometer bracket 3 52C Th.u mometer support waah.er 4 3003 Thermometer reading lens 5 SC Thermollltlter support rod 6 A30M3 Mowr a.oeembly with pulley 7 36M4 Motor pulley 8 37M2 Stirrer drive ~I• 9 37C2 Stirrer pulley 10 AZTA Stirrer bearing assembly 11 A468E Ignition wire 12 A30A2 Stiner shaft with propeller 13 A391DD Oval bucket 14 A461E Calorimeter jacket with cover -15 1108 Oxygen combustion bomb

6

12----Y-1~

13-----fll--14 --~

15----1~-1.1--11----+--1

Figure 4. Cross-section of the Parr 1341 Calorimeter. 2

computer. This software in turn converts the voltages to temperatures in degrees Celsius and collects the data electronically in the computer. The bomb consists of a high-pressure cell made up of a cylindrical body and a head piece, which are held together by a large threaded cap. A check valve for filling the bomb with oxygen and a needle valve for venting the bomb are found on the top of the head piece (see Figure 5). The head piece also contains a pair of electrical terminals. A

7-11

short length of fuse wire that is in contact with the sample is connected to these terminals. Electrical ignition of this wire serves as a means of initiating the combustion of the sample, which is placed in the small metal pan (the combustion pan) (see Figure 6). Electrical terminals

-~-_.....

Fuse wire

1108 Oxygen Bomb

Figure 5. Parr oxygen bomb. 2

Figure 6. Cross-section of Parr

oxygen bomb.2

The bomb is expensive

(~$3500)

and must be handled carefully. In particular,

care must be taken not to dent, scratch or strip the threads on the screw cap. When the bomb is unloaded after a run, the head piece should be placed on its support stand and the screw cap should be placed on a clean, folded paper towel and wiped clean.

2. Laboratory Procedure

1.

Check if your bomb is clean and dry otherwise rinse with acetone. There should be no leftover fuse wire on the terminals of the bomb head piece.

Inside of the

calorimeter pail should also be dry. 2.

Weigh a preformed benzoic acid pellet (for standardizing the calorimeter, Parr cat. No. 3413). Its mass should not be greater than 1.2 grams. If it is, the tablet should be shaved to reduce its mass to 1.2 grams.

7-12

3.

Make note of the heat of combustion for the benzoic acid standard that is given on the pellet container. This should be in units of MJ/kg. This will be needed for later calculations.

4.

Using tweezers, place the pellet into the combustion pan, close to its center.

5.

Cut 10 cm of the nickel alloy fuse \Vire (Parr 45C10), wire should have no kinks or sharp bends in it. Weigh it accurately. Record the wire's heat of combustion.

6.

Set the bomb head on its support stand, if it not already there. Insert one end of the wire into the eyelet at the end of the stem of the electrode and wrap the fuse wire around the stem of the electrode several times to ensure good electrical contact. Then push the cap downward to pinch the wire into place. Repeat with the other end of the wire and the other electrode stem.

7.

Be sure that the combustion pan is sitting snugly in its holder and that it is level. Then bend the fuse wire so that the loop bears down firmly against the top of the pelleted sample so that it will not slide against the side of the combustion pan. Be sure that the fuse wire does NOT touch the metal pan at any point or it will short out before causing the sample to combust. Figure 7 illustrates how this is to be done.

. ,-J Figure 7: Attaching the fuse3 .

8.

Using a pipette and 10 mL graduated cylinder, carefully place 1.0 mL of distilled water in the bottom of the bomb, below the combustion pan (not in the

combustion pan!!!). This is to saturate the atmosphere in the bomb with water vapor, so that the water produced by the combustion will all be in the liquid state.

7-13 9.

Closing the bomb. Care must be taken not to disturb the sample when moving the bomb head from the support stand to the bomb cylinder. Gently set the head into the cylinder and push it down as far as it will go. Make sure it is level.

10. Set the screw cap on the cylinder and turn it down firmly by hand. Do not use a wrench. Hand tightening should be sufficient to secure a tight seal. 11. Charging the bomb with oxygen. Carefully carry your closed bomb to the lab bench to the left of the entrance to the calorimetry room. Have a TA fill the bomb \.Vith oxygen for you. They will filJ it to 15 atm. twice and vent it and then will finally fill it to 30 atm. and it will be ready to use. Why must the bomb be flushed

with oxygen before filling it? 12. Assembly of the calorimeter. Be sure that the bucket in the calorimeter is sitting so that the raised points correspond to the plastic knobs under the bucket. If they don't, turn the bucket around. If there are problems or questions about this, see a TA. 13. Set the bomb in the bucket in the calorimeter, making sure it is centered on the raised circle in the bucket. The bomb should not touch the walls of the bucket. 14. Insert the electrical connections into the electrode terminals at the top of the bomb and make sure they are tight. 15. Fill a 2.0 L volumetric flask with deionized water to its marked level at room temperature. Use the water from the carboys in the calorimetry room to fill the bucket. Carefully pour the water into the bucket and over the bomb, so none of the water splashes out. The water should completely cover the bomb when it is all poured into the bucket. Use the same amount of water every time the calorimeter is used and not to lose any in the transfer. Why? Important NOTE: If you see bubbles continually rising from the bomb at this time, seek a TA. DO NOT continue, until a TA has looked at the bomb. 16. Refill the 2.0 L volumetric flask to the mark for the next run. 17. Put the calorimeter lid fmnly in place with the stirrer m the back and the thermometer in the front. Check to be sure that the thermometer/thermistor are in

7-14

the bulk of the water. NOTE: Be sure to pick up the paper on the ledge above the sink about the thermistor and its tolerance levels. 18. Turn the stirrer by hand to check it runs freely; then slip the drive belt onto the pulleys and start the motor. Collection of Data via the Computer and the Multimeter

19. Open the bomb calorimetry program using one of the following: a) double-click the bomb calorimetry icon on the PC desktop (upper left) OR

b) the program may already be running 20. When ready to initiate the run, click on the START button on the bottom of the computer screen. 21. A Dialog Box will appear and ask you to choose a File Name where your data will be saved at regular time intervals during the run. Choose to save your file in the appropriate folder for your section on the desktop. Choose a File Name such that you can identify it as yours AND you will know what sample is being combusted, for example, BA for benzoic acid and naph for naphthalene. Once you have saved the file name, the digital read-out on the multimeter should convert to degree Celsius readings. 22. Do not perform any other tasks on the computer while your data is being collected otherwise you might lose data. 23. At this point, the run will

be~

started. It will take about five seconds to show

readings on the screen. Then it will take readings every five seconds until you stop the run. 24. Take readings for five minutes or until you have a temperature change at a very slow linear rate (on the order of 0.00l°C per minute) for at least 5 minutes. This will give you the pre-ignition line for later calculations, see Figure 2. 25. When you are ready to ignite the sample, make note of which calorimeter you are using, have everyone leave the room, shut the door, and press the ignition button

/

7-15 for the calorimeter you want to ignite for about 5 seconds. You should see a brief flash of light at the ignition box, indicating the passage of current for the instant required to bum through the fuse wire. In nearly all cases the burning wire will ignite the pellet, and after a period of about 20 s the measured water temperature will begin to rise. Wait outside the room for 30 seconds before reentering.

26. The rise in temperature "'ill be very rapid for the first few minutes; then it will become slower as the temperature approaches a stable ma."Ximum. The total increase in temperature will be 1. 5 - 3 degrees C over a period of 5-10 minutes. 27. After the temperature reaches a maximum, continue to take readings for at least five more minutes, so that you have a very slow linear rate of temperature change for your post-ignition line in Figure 2. 28. Click on the STOP button at the bottom of the computer screen ONCE when you are finished with the run. The programs will run for several seconds longer, then stop and save your last few data points. The data is saved continually during the run, so if some problem occurs you will have your data saved up to that point. 29. Transfer your data from the PC to a flash drive. The data can be open in Microsoft Excel. 30. Go back to the bomb calorimetry program so that the other lab group can carry out a run, while you prepare your apparatus for the naphthalene run. Disassembling the Calorimeter 31. Tum off the stirrer motor, remove the belt and lift the cover from the calorimeter. Set it on its support stand. 32. Gently dry off the thermometer, thermistor and stirrer with a paper towel. 33. Lift the bomb out of the bucket, remove the ignition leads and wipe them, dry the bomb with a paper towel. 34. Set the dried bomb on the lab bench and open the needle valve on the bomb head slowly to release the gas pressure BEFORE attempting to remove the cap. This release should proceed slowly over a period of at least one minute.

7-16

35. After all the pressure has been released, unscrew the cap; lift the head out of the cylinder and place it on its support stand. You may have to wiggle the head back and forth slightly to loosen it enough to pull it out of the cylinder. Examine the interior of the bomb for soot or other evidence of incomplete combustion. Make note of what you see.

If it is apparent that combustion was grossly incomplete, discard this run and do another with the same substance.

36. Wipe to dry all bomb parts. Wipe clean inside of the bomb and the combustion pan using acetone in the fume hood. 37. Remove and weigh any unburned fuse wire; ignore globules unless attempts to crush them reveal that they are fused metal rather than oxide. Subtract the mass of the unburned fuse wire from the initial fuse wire mass to obtain the net mass of the fuse

wire combusted. After weighing, discard the unburned wire to garbage. 38. Dump the water out of the calorimeter bucket and dry it thoroughly. Dry the inside of the calorimeter jacket before placing the bucket back in. Remember to line up the bumps in the bucket with the knobs in the calorimeter.

Naphthalene Combustion 3 9. Repeat step # I. In step #2, weigh 0.6 grams of naphthalene crystals on a tarred piece

of weighing paper. (Do NOT obtain more than 0.7 grams.) Transfer the naphthalene to a mortar and pestle and grind to a fine powder. The mortar and pestle is either in the

fume hood or on the lab bench near the bulletin board in the main lab room next to the pellet press. 40. Refer to the paper next to the pellet press showing how to make a pellet with the

pellet press. Transfer the naphthalene powder to the die and form a firmly pressed pellet. Once you have removed the pellet from the die, use forceps to pick up the tablet and weigh it on a tarred weighing paper. Record this mass.

Rinse all equipment and glassware that has contacted the naphthalene with acetone over a funnel inserted into the acetone-naphthalene waste bottle in the fume hood. Return cleaned equipment to its proper location for someone else to use. 41 . Continue on with steps #4 through #42

7-17 CLEANING AND ORDER:

1. Calorimeter is dismantled and its parts are cleaned and dried. 2. All extraneous paper and unburned fuse wire is.in the garbage. 3. Volumetric flask is filled to the 2.000 L mark with room temperature distilled water. 4. Get approval of your TA that everything is m an order to not to get any deductions from your lab grade.

3. In Lab Questions

1. Why is it important to keep from interchanging parts between the two calorimeters available to use during the experiment? Would the same concern arise from using different amounts of water in the calorimeter bucket for each run? 2. Why must the bomb be flushed with oxygen gas before it is finally filled for the combustion? If it is not flushed with oxygen, do you think it would affect the quality of your results? 3. In a bomb calorimetry experiment where a bomb was immersed in water at 25°C, the following data were obtained: on calibration by combustion of 0.771g of benzoic acid (C6HsCOOH, the temperature of the water rose by l.97°C; and on combustion of

1.214 g of solid naphthalene (C10Hs) the temperature of the water rose by 4.78°C. Calculate the standard heat of combustion for naphthalene in MJ mo1· 1. For benzoic acid, ~H 0combustion

=

-26 430 Jg· 1 at 25°C (combustion to liquid water). NOTE: You

can assume ~H = ~U in this problem under stated conditions. 4. If benzene is made up of 6 C-H bonds, 3 C-C bonds and 3 C=C bonds, estimate the resonance stabilization energy for benzene vapor in kJ mo1· 1. Use the average bond energies from Table 1 for the different chemical bonds in benzene and its combustion reactants and products to estimate benzene's enthalpy of combustion. The

7-18

experimentally measured enthalpy of combustion of liquid benzene at 25°C to give carbon dioxide gas and water vapor is -3135.6 kJ mo1· 1• The standard enthalpy of vaporization of benzene at 25°C is 33.62 kJ mo1·1• Comment on the difference between the measured and estimated (theoretical) enthalpy of benzene combustion. 4. Data Analysis

1. Construct a graph in Excel like is shown in Figure 6, using your data for each run. This is accomplished on Excel by the following:

a) Highlight all data, click on chart wizard and choose the x-y scatter with the smooth lines connecting the points. b) At step 2 - Chart Source Data choose series c) Then click on add. Use name

=

pre-ignition line; choose x-values by

highlighting time values up to the ignition time (where the temp. begins to rise more rapidly); choose the corresponding y-values by highlighting them. d) Then add series three using name

=

post-ignition line; choose the x-

values for the time when the temperature begins to level off and choose

the corresponding y-values. e) Go back to series 1 in the left menu and highlight it. Give it the name = ignition line, then choose the x-values by highlighting the last time value for the pre-ignition line to the first value of the post-ignition line. Choose the corresponding y-values. f) Click on next and continue by adding the title and axes labels.

g) Double-click on any point on the graph to change its color; shape or series line color as well as ordering the series list. It is best to have the series listed in the same order that they appear on the graph.

7-19 h) Lastly, to do the linear regression on the pre- and post-ignition lines, which will be needed for determining Ti and Tr, go to the menu at the top of the screen. Under chart choose add trendline, choose the linear for either the pre- or post-ignition line. Go to the options tab and check

display equation on chart. Do this for both the pre- and post-ignition lines i)

ti

= 160%

shown in Figure 2. In placing this vertical line on your graph,

you have several options for choosing the estimated Ti and Tr. You may use the last point of the pre-ignition line as the estimated Ti and the first point of your post-ignition line as the estimated T f OR you can use the yintercept of the pre- and post-ignition lines as the estimated Ti and Tr values. Find the difference of these values (Ti and Tr) and then take 60% of this difference and add it to the estimated Ti to determine T 60%

= Td.

The value of t6o% is best determined using your Excel spreadsheet of the numerical data and finding the time that corresponds to your T60% value. To add the t6o% line to your graph, go to the Autoshapes or drawing

feature of Excel and place the vertical line so that it intersects at 60% of the rise. j) Make any other adjustments you wish to make your graph easier to interpret. 2. Calculate the instantaneous values of Ti and T f at the time of ignition, by using the 160%

value in the equations of the best-fit pre- and post-ignition lines. Report the

value of Ti, Tf and

160%

and explain how each was determined in the results

section of your report. NOTE: The slope of the best-fit line is an indication of the heat lost from the calorimeter

and the heat gained by the calorimeter from sources other than the combustion of the sample in the bomb. These slopes should be quite small and are generally smaller than the tolerance limit of the thermistor used to measure the temperatures. IF you had to carry out uncertainty analysis on this experiment, you would have to use the larger of the

7-20 two values (slope of the best-fit line and the thermistor tolerance limit) as the uncertainty in Ti and Tf that would be propagated. 3. Calculate the heat capacity of the calorimeter.

4. Calculate the heat of combustion of naphthalene, AU in kJ g- 1• 5. Calculate the molar heat of combustion of naphthalene, AUmo1arin kJ mo1-1• 6. Using the molar heat of combustion of naphthalene, calculate the experimental enthalpy of combustion of naphthalene,

AHcombustion naph(s)

in kJ moJ- 1 usmg

equation 6. Reference to the caption of Figure 6 may be helpful here. 7. Find the value for the enthalpy of sublimation of naphthalene as well as the

enthalpy of combustion, &II°, by referring to: http://webbook.nist.gov click on: NIST chemistry webbook then click on: search options then click on: name put in naphthalene and check phase change and condensed phase boxes Use the average

.Mlsub

for naphthalene that you come to at the bottom of the

first table. Use the average .Mlc0 for naphthalene. This will be considered the literature

value for AH0 combustion, naph(S). 8. Determine the theoretical AHcombustion.naph(g) from the bond energies given in Table 1. Keep in mind these values are for gaseous molecules only. Write the result as a thermochemical equation.

9. Using Hess's law with the

LlRsub, naph

found on the NIST website, the heat of

vaporization of water as 40.67 kJ/mol and the thermochemical equation determined in data analysis #8, calculate the theoretical

AHcombustion,naph(S)

starting with solid

naphthalene reacting with gaseous oxygen and producing gaseous carbon dioxide and

7-21

liquid water. Show the summation of thermochemical equations and the net

thermochemical equation for this determination. 10. Compare the experimentally determined Affcombustion, naph(s) to the literature value for ~Hcombustion,naph(s)

found on the NIST website.

11. Calculate the absolute value of the difference between the theoretical ~Hcombustion,naph(s)

calculated in data analysis #9 and the literature value for

Affcombustion,naph(s) found on the NIST website. 12. Be sure that you have shown detailed sample calculations for each different kind of

calculation. If unsure of what is expected here, refer to your introductory material for the course or ask one of the T As or the instructor.

13. Calculate uncertainty of all experimental values you reported. 5. Report Questions

1. Convince that the uncertainty in

result.

~T

is the single major source of error in the final

A concrete example such as, showing how much the experimental

Aff 0 combustion,naph(s) changes if you change ~T by 0 .1 K is expected.

2. a) Comment on the meaning of the difference between the theoretically determined ~Hcombustion,

naph(S) and the literature value for Affcombustion,naph(S) found on the

NIST website. b) Look up the resonance energy of benzene in reference 5 and see how it compares

to the resonance energy of naphthalene. Is this what you expected? Explain.

7-22

References: 1. Shoemaker, D. P.; Garland, C. W.; Nibler, J. W. Experiments in Physical

Chemistry, 6th ed., McGraw-Hill Co., Inc., 1996, p. 145-158. 2. Instructions for the 1341 Plain Jacket Oxygen Bomb Calorimeter, Manual No.

147, Parr Instrument Co., Moline, Ill. 3. Operating Instructions for the 1108 Oxygen Combustion Bomb, Sheet No. 205M, Parr Instmment Co., Moline, Ill. 4. Pine, S. H. Organic Chemistry, 5th Ed., McGraw-Hill: New York, 1987. 5. McMurray, J. Organic Chemistry, 5th ed, Brooks/Cole Publishing Co.: CA, 2000,

p. 564-566 6. Atkins, P.; de Paula, J. Physical Chemistry, 7th Ed. , W. H. Freeman and Company: New York, 2002, p.55.

8-1

Pyrene Excimer Formation Kinetics Objectives

•

To study the complex photophysics (luminescent properties) of pyrene using fluorimetry.

•

To explore a complex kinetic system comprising two parallel and two consecutive reactions, that is, to determine the kinetic rate constants associated with pyrene excimer formation and decay using time-resolved laser photolysis.

Introduction

Polycyclic aromatic molecules, such as pyrene (Py), in the singlet excited state can react with a ground state molecule of the same type forming an excited state dimer called an

excimer[ll. This laboratory exercise will explore the excited state of pyrene (*Py) and its excimer (*Ex) to determine the rate constants associated with the various steps in this complex kinetic system.

Pyrene excimer formation Pyrene is a planar, polycyclic aromatic hydrocarbon (Figure 1). Pyrene and its derivatives are used commerciall]'.'. to

Figure 1. Structure ofpyrene.

produce dyes and as molecular probes in fluorescence spectroscopy due to its high quantum yield and long lifetime.

The emission spectrum of pyrene is sensitive to solvent polarity; therefore,

pyrene has been used as a probe to assess solvent microenvironments. The pyrene absorption spectrum lies in the UV region of electromagnetic radiation; therefore, UV light will excite pyrene (Py) from its ground state to a singlet excited state (*Py). The quantum yield for pyrene fluorescence is relatively high, so the resulting emission is intense, and due to the relatively long lifetime it is easy to detect. The emission spectrum sho\.\n in figure 4 varies depending upon the concentration of pyrene, suggesting multiple luminescent species, which makes the emission decay rate wavelength-dependent. We will use interference filters to observe each of the species (*Py and *Ex) separately during laser photolysis as their emission is well resolved. The pyrene monomer has structured emission at a shorter wavelength than the broad structureless emission of the excimer. The absorption spectrum of highly concentrated pyrene solutions is a near mirror image of the pyrene emission. This emission and

8-2 absportion corresponds to the 1Lb (Platt notation, see ref 2) excited state of pyrene, which is the lowest energy excited state. This is not seen for the ~ 10 µM solution because it is weak due to symmetry. The absorption seen for that low concentration solution corresponds to the transition from the 1A ground state to the 1La excited state. U) :t= c

1.2

w

1.0

()

z

0.8

-2.285mM -1.725 mM 0.973mM - 0.506mM 0.0098mM

Cl'.'.:

.....

~

e

·u; c

(!) ....,,

0.6

c 0

' ii)

Ill

E

w 0.0 310

2

fl)

<{ 02

320

330

340

350

360

WA V E L E N GT

370

380

390

t

il

I!

2rnM l.5mM

-

t rnM

-

0.5m11

- 0 . 0 l mM

I\

4

c

0.4

-

~

~

0 (/)

tLb

.0

4'. Ill

*Ex

8

::J

i)

,l

0

3!;'.)

H (nm)

400

4~0

500

55C

WAVELENGTH

eoo

C.fil

1~-0

(nm}

Figure 4. Left: Absorption spectra (left) of pyrene in decane with wavelength resolved pulse profiles of our dye (366 nm) and nitrogen (337 nm) lasers. Right: Emission spectra ofpyrene in decane

As mentioned previously, excited pyrene (*Py) can react with ground state pyrene (Py) to form an excited state dimer (*Ex), referred to as the pyrene excimer. The reaction mechanism is described by the following reactions: Py + hv - - . *Py

(excitation)

(1)

•Py--. ko Py+ hVM

(singlet pyrene decay accompanied with fluorescence)

(2)

rfn addition to processes l and 2, at high pyrene concentration the following reactions occur: ..

Py+ Py

k1

k1 * Oil

k-~ Ex (excimer formation)

*Ex ~2Py + hvE (excimer decay accompanied with fluorescence)

(3) (4)

The rate constants~ and kz also include nonradiative decay mechanisms (not show in scheme). Photo-induced chemical reactions differ from thermally-induced ones. In the case of photochemical reactions, the reaction will not occur if the reactants do not encounter each other within the lifetime of the excited state. This is why Py and *Py do not react in dilute solutions. In sufficiently concentrated solutions (where the collision frequency is high enough), *Ex formation competes with *Py luminescence decay. For these concentrated solutions, the absorbance at 337 nm is so high (Figure 4) that laser excitation creates a concentration gradient

8-3 of *Py within the cell. The absorption spectrum of the concentrated pyrene solution can be used to identify a different wavelength for which the absorbance is in the right range (0.2
Rate constants describing the pyrene photophysics and photochemistry The complex kinetics of the pyrene system involves a number of rate constants (Figure 2). The first order decay of *Py fluorescence to the ground state is described by ko. The secondorder rate constant for the formation of *Ex is k1 and the first-order rate constant for the dissociation of *Ex to Py and *Py is k- 1. The fluorescence decay rate constant of *Ex is k1. Py + *Py *Ex

hvl

hvo

absorption 1 fluorescence ko

Distance

Figure 2. Jablonski diagram for pyrene photochemistry.

Using Figure 2 and using that k1 is negligibler3•4J, the rate equations that describe the time-dependent concentrations of *Py and *Ex can be written: (5)

d[*Py]=-(k +k[Py]\f*Py]

dt

d[* Ex]

dt

0

l

JI.

=-(k2 ~* Ex]+k1 [Py]

(6)

(*Py]

By assuming pseudo-first order kinetics, the system can be solved analytically by first solving equation 5 and substituting into equation 6. Applying the conditions that the initial concentrations of *Py and *Ex are [*Py]o and zero, respectively, gives:

[*Py]= [*PyJoe -x' [*Ex]=

(7)

(k1 [Py][*PyL )(e-x' _

e -k1

k2 - X

1)

(S)

8-4 WhereX= ko+ k1[Py]. Photodiode

Laboratory Procedure sample Holder

The instructor or the teaching assistant will provide detailed directions for the use of the Horiba Scientific Fluorolog FL-3 spectrofluorimeter, the Cary 4000 Varian UV-VIS spectrophotometer, and the laser photolysis apparatuses with lasers from SRS (model NL-100, A.em= 337.1 nm, pulse width= 3.5 ns)

• I I

Optical filter

D

Nitrogen Laser

Oscilliscope (50-0terminator)

and OBB (model, ~m = 366 nm, pulse width = 0.8 ns half width),

a photodiode from

Electro-Optics

Figure 3. Laser photolysis setup.

Technology, Inc (model 23-2618A, rise time= 0.5 ns), (400 ± 5) nm optical interference filter, 500 nm band-pass optical filter, and a Tektronix 200 MHz and 500 MHz storage oscilloscope (model TDS 2022B and TDS 3022B). To obtain sufficient data to determine the reaction rate constants for pyrene excimer formation, measure the luminescence decays of nitrogen-purged 10 µM , 0.5 mM, 1.0 mM, 1.5 mM, and 2 mM pyrene in decane solutions.

The samples are

nitrogen-purged to prevent quenching by oxygen. In addition, absorption and emission spectra of the pyrene solutions are needed. A 2.0 rnM solution of pyrene in decane will be provided. Important: In order to finish this lab in the allotted time, your group will need to be organized

and split up to complete several

e~eriments

at a time. The steps do not need to be done in order.

The absorption spectra can be{aicen before purging with nitrogen, but the laser photolysis and fluorimetry must be done after purging with nitrogen. 1.

Dilute the 2 rnM pyrene in decane solution provided to create 10 µM, 0.5 rnM, 1.0 mM, and 1.5 mM solutions. Use the density of decane (0.73 g/rnl) to determine the appropriate masses of decane to add.

2.

Take an absorption spectrum of each of the pyrene solutions between the wavelengths 300 and 400 nm. The literature extinction coefficient for pyrene is

8335

= 5.40 x 104

M· 1cm· 1 (1). Determine and record the optical density (O.D.) at 337. l and 366 nm from the absorption spectrum. 3.

Deoxygenating the pyrene solutions. The samples will be purged and sealed in advance.

8-5

4. Take an emission spectrum of each pyrene solution. The TA will have the instrument and lamp on and ready to run samples. Please do nor touch any switches or shutters on the instrument. The measurement will be that of an emission scan with A.excitation= 337.1

nm for the 10 µM solution and 366 nm with the others. The emission scan range will be from 350 to 500 nm for the 10 µM sample and 375 to 700 nm for the other samples. 5.

A laser pulse profile is required as a test of the detection system to ensure that results of luminescence decays for samples are not artifacts from continuous excitation within the laser pulse. This is especially true at short time scales. To take a laser pulse profile, remove the filters from in front of the photodiode. Use the 5 ns/division time scale. NOTE: When using the laser photolysis apparatus, EVERYONE near the setup MUST be

wearing eye protection (protection goggles for 366 nm can be found in the laser dark room)! UV light can cause irreversible damage to the eye, plastic and amorphous glass will not transmit UV light at 337.1 nm. Place a piece of aluminum foil in front of the laser (at a 45 degree angle with respect to the photodiode). The instructor or TA will start the laser. The small black knob on the laser controls the laser pulse rate. Turn on the oscilloscope, press ACQUIRE then SAMPLE then RUN. At this point you may want to adjust the pulse rate. The signal on the oscilloscope is the laser pulse profile. Press SAVE/RECALL and save as a .CSV file to a USB flash drive located on the front of the oscilloscope. Note the file name given on the oscilloscope screen. 6.

Remove the aluminum foil and carefully tape a 400 nm filter to the front of the photodiode.

Take a luminescence decay of each pyrene solution with this filter by

placing the cuvette in front of the laser pulse and photodiode with for the 10 µM solution and 7.

A.excitation=

A.excitation

= 337.1 run

366 nm for all others.

For all of the solutions other than the 10 µM , take a luminescence trace using the 500 nm filter. Use an excitation wavelength of 366 nm.

Data Analysis

1.

Plot the absorption spectra and identify the 337 nm and 366 nm excitation wavelengths on the graph. The comparison indicates the need to use different excitation wavelengths.

8-6 2.

Normalize the emission spectra with respect to the third vibrational peak in the monomer spectrum. The increase in the intensity of excimer fluorescence on increasing the pyrene concentration indicates that the pyrene ground state is involved in excimer formation.

3.

Determining ko. Plot the luminescence decays (Figure 5) for all pyrene solutions on the same graph (obtained with a 400 nm filter), normalize them, and fit them with single exponential decays.

From the fit of the luminescence decay for the 10 µM pyrene

solution, determine kobs,o (this is ko) and from the fits of the other luminescence decays, determine kobs values for each concentration of pyrene. o,ot ..........

en

±!

c

ocs

-

0,01mlil

-

0.51111! ~ 1mM

.

_o

ro

00!

z. ·w c

oo:;

_Q

s"'

"'"-'

-:i. :" 0"1.!

-.:...:!~;!.

..."'

::i '-

-

-4

-·e~

., ~

Q)

.......

c

o~A

-~

c 0

·w (/)

0 ·J' ~

1~

w

0 00 0

1O\l

200

3Xl

T I M E Figure S.

Fluores~ence

!OQ

soc

600

;-oo

(ns}

decays of the pyrene monomer with single exponential fits over a range of concentrations. The natural logs are plotted in the inset.

4. Determining kJ. Plot the values of kobs versus pyrene concentration. Apply a linear fit to these data to show that pseudo-first order kinetics is obeyed and detennine the value of k1 from the slope.

5.

Determining k-1. Explain why the value of k-1 is negligible in comparison to the other rate constants at room temperature using the emission spectrum of concentrated pyrene (Hint: Look at the Jablonski diagram and try to approximate the binding energy of the excimer). Also, plot the natural log of the luminescence decays of the pyrene solutions with the 400 nm filter and explain how these results also suggest k-1 is negligible.

6.

Plot the laser pulse profile and luminescence build up (5 ns/division) of concentrated pyrene obtained with the 500 nm filters on the same graph (Figure 6). This will show that the laser is fast enough to monitor excimer formation.

8-7 ,,........ rn ±::

0,;)~

/

c

::J

-

.__

() ,;) 4

~

0!.)3

..Q

ro

/'

(/)

c

Q}

.......

c

0 .02

- - pulse profile - - 1 mM , i_..... =

c 0

(/)

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nm

·) !) 1

(/)

"E~

w

0 .') •)

-
1J

tO

20

30

T I M E

40

5·)

60

(ns)

Figure 6. Luminescence decay taken with 500 nm filter and laser pulse.

7.

Determining ki. Use a mathematical fitting program such as MATLAB and Equation 8

to fit the excimer fluorescence traces using the rate constants already determined in steps 3 and 4. A MATLAB script will be provided by your TA. If necessary for a good fit, ko

and ki may be adjusted within experimental error. Average the values obtained and use their range as an approximate experimental error in the rate constant.

Report Question: Why is it important to have an approximately homogeneous distribution of

excited state pyrene molecules when performing laser photolysis to study the kinetics of the system?

References

1. Birks, J.B. Photophysics ofAromatic Molecules; Wiley-Interscience: London, 1970.

2. Platt, J. R. J Chem. Phys. 1949, 17, 484-495. 3. Hanlon A .D. and Milosavljevic B.H., Photochem. Photobiol. Sci. , 12 (5), 787-797 (2013) 4. Hanlon A.D. and Milosavljevic B. H., J Lumin., 157, 16-20 (201 5)

9-1

Polypropylene Phase Transitions Studied by Differential Scanning Calorimetry (DSC) Objectives •

To determine and compare the phase transitions of amorphous and isotactic polypropylene.

•

To determine the enthalpy of crystallization of isotactic polypropylene.

•

To calculate the degree of crystallinity of the "supposed" amorphous and isotactic polypropylene samples.

•

To determine the glass transition temperatures (Tg) of amorphous PP and prove that there is no glass transition in isotactic polypropylene.

•

To calculate the entropy of crystallization of the isotactic polypropylene.

•

To calculate the entropy change associated with the glass transition.

Hazards The differential scanning calorimeter used in this experiment is extremely sensitive, can be damaged easily and repair costs are exorbitant; therefore, extreme care must be used when operating the instrument. The following concerns are of special importance: • The cell (sample compartment) lid is automated and must not be opened manually or severe damage will be done to the instrument. • The nitrogen gas must be maintained at a pressure of no higher than 20 psi, or again, severe damage can be done to the instrument. • The cell and its components get very hot and the thermocouples inside are very fragile therefore only use tweezers to load sample pans. • If you are unsure of a procedure or want to attempt a new procedure on the DSC, you must consult Dr. Milosavljevic or a T.A.

•Turning on and shutting off of the DSC, along with any maintenance will be performed by Dr. Milosavljevic or a T.A.

Isotactic PP

Atactic PP

1

9-2

Materials and Instrumentation • TA Instrument DSC Q200 differential scanning calorimeter • Emachines T3300 desktop pc •Software: TA Instrument's Explorer and TA Universal Analysis 2000 • 3 Hermetic Tzero aluminum sample pans and a set of tweezers • Amorphous polypropylene, Aldrich (CAS 9003-07-0) • lsotactic polypropylene, Aldrich (CAS 25085-53-4) •Ultra-high purity nitrogen cylinder (CAS 7727-37-9)

Introduction Differential scanning calorimeters are a widely used therm6analytical instruments due to their. ease of use, relatively fast data collection times and the ability to use small sample sizes. 1 DSC has been applied to many fields such as the characterization of materials (especially polymers), quality control such as purity determination, biochemical research into the stability of proteins, nucleic acids and membranes, kinetic investigations, the evaluation of phase diagrams and other areas as well. A DSC measures the energy as heat flow to or from a sample at constant pressure during a chemical or physical change in the sample.2 The measurement is made by linearly heating the sample and a reference at the same rate; to maintain the sample and reference at the same temperature when the sample is undergoing a physical or chemical change, more or less energy must be supplied to the sample compared to the reference depending on whether sample is undergoing an endothermic or exothermic process. This difference in energy being supplied to the sample relative to the reference is the measured heat flow. The heat transferred to a sample when there is no chemical or physical change is q = p

C LJT, where LJT =T - T and the heat capacity C is assumed to be independent of temperature. p

0

p

During a chemical or physical process there is excess heat transferred q

p.ex

2

to the sample

2

9-3

compared to the reference, and the total heat transferred is therefore q + q p

2

p,ex

. The excess heat

can be viewed as a change in the heat capacity, and the resulting heat capacity is C + C P

p,ex

which

gives 2

qp + qp,ex = (Cp + Cp,e) L1T C

p,ex

thus

= q.p,ex I t1T

The DSC data in a thermogram is therefore a plot of C

p,ex

against T. A physical or chemical

change represented by a peak in a thermogram can be used to find the corresponding enthalpy of the transition from

2

where T and T are the beginning and ending temperatures of the transition. I

2

In this lab, two types of the polymer polypropylene which have different tacticities will be studied by DSC. Tacticity indicates the local stereochemistry of the pendent groups (H, CH3) in polymers.

3

Polypropylene is a Jong carbon chain in which each backbone carbon atoms has one H and CH3 group. In isotactic polypropylene all of the methyl groups ire in the same position at each stereocenter in the carbon backbone. Amorphous or atactic polypropylene has a random distribution of methyl groups. Isotactic polypropylene is able to form a crystalline structure which is geometrically ordered in the appropriate temperature range. Due to the random arrangement of the methyl groups in atactic polypropylene, it is not able to crystallize and can only form an amorphous solid. The degree of crystallinity of a sample of isotactic polypropylene can be found by divi<;ling the enthalpy of fusion of the crystalline melting peak by the enthalpy of fusion of a pure sample of isotactic polypropylene.

3

9-4 Experimental Procedure

1. To the right of the desk.top PC, in the top drawer, you will find three bottles labeled PPA, PPC and R. These bottles contain your polypropylene samples and reference (PPA = amorphous, PPC = isotactic and R =reference). Also, in one of the black TA boxes in the same drawer is the tweezers you will use to load the cell. 2. Check that the pressure gauge on the nitrogen tank reads 20 psi, if it does not, ask a TA to adjust the pressure. Exceeding 20 psi can damage the instrument. 3. On the desk.top pc, open the TA Instrument Explorer program by clicking on its desk.top icon. 4. Next, double click on Q200-1 724 at the left side of the window. 5. Check that the cell is at room termperature and that the sample purge flow is 50 mL/min by looking in the signal pane in the upper right hand side of the window (see figure below). 6. If the cell is not at room temperature, go to control (top left side of window) and in the pull down menu click on Go to Standby Temp and check that the temperature adjusts accordingly. If the sample purge flow rate is not 50 mL/min, click on the Notes tab at the top of the middle pane. Then type 50 in the box labeled Flow Rate and click apply at the bottom of the middle pane. 7. Next you will load the cell with one of the polypropylene samples and the reference. First, go to control and in the pull down menu click on lid and then open. (If the cell does not open, notify a TA) 8. Use the tweezers to remove the reference from the R bottle (bottom of pan is not crimped) and gently place pan on the top of left rear cylindrical thermocouple. (Caution: the thermocouples can be easily damaged) 9. Place a sample pan (PPA or PPC) on the right.front thermocouple with the tweezers. 10. Then click on control and in the pull down menu click on lid and then close. 11. Next, at the top of the middle pane click on summary and check that the mode is standard, the test is custom and that the sample size is either 9.3 mg/or PPA or 9.5 mg for PPC. Also, take not of the number at the end of the datafile name. Your file will be listed as the next higher number. 12. Click on the procedure tab at the top of the middle pane. Check that the test is custom and that the method name is PPA-1 . You should take note of the temperature program in the segment description either in the middle procedure pane or in right middle pane labeled Running Segment Description. · 13. After you have checked all your experimental parameters, you can start the experiment by clicking on the green circle with the black triangle at the top left of the window. The

4

9:.5 red circle with the black square, to the right, is if you need to stop the experiment otherwise the experiment will stop on its own after completing the temperature program.

14. The status bar at the bottom of the window will indicate when the run is complete. The data will be automatically stored. You can then run your remaining sample by following the same procedure. /

Data Analysis.

I. Minimize the Explorer window and open the TA Universal Analysis program by clicking on its desktop icon. 2. To open your data file follow the path: File--+ Open - DSC - CHEM457--+ "your file". 3. A check parameters window will appear, click OK, then your DSC thermogram will be displayed. 4. To zoom in on a feature, left click near the feature and drag a box around. Then left click in the box. 5. To find the glass transition temperature, click on the Tg icon or you can find it in the analyze pull down menu at the top of the screen. A red crosshairs should appear, if it does not, left click on the thermogram. To move the crosshairs, left click on it and drag. To set a marker, double left click on the marker. When you have set the first marker to one side of the glass transition, set a marker on the other side by left clicking on the thermogram. Then right click to accept limits and temperatures will appear next to the glass transition. By convention the inflection point is taken as Tg. 6 . To integrate a peak, go to analyze and in the pull down menu click on integrate and then linear; or you can click on the linear integration icon on the toolbar. Left click on the . thermogram next to the peak you want to integrate and then left click on the thermogram on the opposite side of your peak. Right click to accept limits. The enthalpy of the transition should appear along with the peak temperature. 7. Create a plot showing the change of entropy versus temperature for amorphous polypropylene in the temperature range (Tg- 20 °c, Tg + 20 °c). Follow the instructions below: Open your data in Excel, where you will see four columns. The second column contains temperature data. The third column contains heat flow data. Start by preparing two new columns containing 1) Cp and 2) C/f'. (Hint: Divide heat flow column by the heating rate to get Cp. Divide Cp column by temperature column to get CplT.)

5

9-6

Plot this column against temperature to get ~ vs T. You are now ready to integrate the T

areas under this curve to obtain .'.18 values at different temperatures.

J;dr T:z

LlS=

T.

Tg+20 I

Tg-17

T~~-;1 -- Tg-20\ ,, ,, \ ~~ L -1rt Poll'll Int Patig1 3..t '"

MC

~a

«lt11 pomt

v

I I

J I

J )

.....

.... ,_,_ ~ ~

To obtain a column for L1S values at different temperatures, you will perform 40 separate integral calculations for the temperature range (Tg - 20 °c, Tg + 20 °C).

...

TEMPERATURE

The lower boundary condition (Tg- 20 °C) will be the same for every integration. The upper boundary condition varies for each data point: The first data point will range from T g- 20 °c to Tg - 19 °c; the second data point will range from Tg - 20 °c to Tg - 18 °c, etc. You are increasing the range by I degree Celsius each time.

When you're finished you should have a column for .'.18 at every temperature from (Tg - 20 °c, Tg + 20 °c). Plot this column as a function of temperature. 8. Refer to the Atkins handout on ANGEL and compare your plot with the one shown in the handout. Comment on the differences in the observed slopes between the two splots and explain them using what you know about heat capacity.

References 1. Hahne, G.; Hemminger, W.; Flarnmersheim, H.J. Differential Scanning Calorimetry; Springer: New York, 1995, p. 3. 2. Atkins, P.; de Paula, J.; Physical Chemistry, Vol. 1, Oxford University Press: Great Britain, 2006, pp. 46, 47. 3. Anslyn, E. V.; Dougherty, D. A. ; Modern Physical Organic Chemistry, University Science Books: U.S.A., 2006, p . 331.

6

10-1

Fluorom·etric Measurement of the Rate Constant and Reaction Mechanism for Ru(bpy)32 + Phosphorescence Quenching by 02

Objectives •

To understand the_basic principles of luminescence spectroscopy.'

•

To construct the Stem-Volmer plot m order to detennine the rate constant for luminescence quenching.

•

To determine the quenching mechanism

In trod uctio.n Luminescence spectroscopy has been a remarkable tool in the last two decades, mostly due to light induced chemical changes observed in many photochemical reactions including biological processes. 1•2•3 These chemical changes occur as a result of the promotion of molecules from ground-to excited energy levels. While the applicable areas for use and the instrumentation of luminescence spectroscopy are getting broader, it would be an asset to understand the basic principles of luminescence.

Molecular Photophysics

In the ground energy state molecules exists in their lowest energy state, where all the electrons are in their most stable orbitals. Upon absorption of light, an electron gets promoted from an orbital that is filled in the ground state to a vacant orbital of higher energy. The excited molecules prefer to return back to their ground energy states and the energy of the excited state may dissipate in a number of ways. processes are given in Figure 1.2

Structure of Ru(bpy)3 2+

.1

An outline of these

10-2

Absorption of light

Electronic excitation

Dissipation mechanisms Radiationless

Radiative

1) Fluorescence 2) Phosphorescence

Light 7 Light hv 7 hv'

Chemical 1) Singlet 2) Triplet

Physical 1) Internal conversion 2) Intersystem crossing

Light 7 Chemistry hv7~G

Light 7 Heat hv7Q

Figure 1. Overview of molecular photophysics and photochemistry.2

In the next sections, radiative and radiationless (non-radiative) energy dissipation

processes are briefly outlined.

Radiative Mechanism In the radiative mechanism, a molecule loses its energy as a photon and goes from a higher energy state to a lower state. The type of the radiative process is determined by the multiplicity of the states between which transitions are taking place. In the excited state, two unpaired electrons in different orbitals can exist with opposed spin or with parallel spin orientation. Different spin orientation results in a singlet, and parallel spin orientation results in a triplet state multiplicity. Based on the multiplicity of the states, there are two major radiative processes: fluorescence and phosphorescence.

In

fluorescence, which is a spin-allowed process, transition takes place between the states of the same multiplicity, S1 7 So. In phosphorescence, which is a spin forbidden process, transition takes place between the states of different multiplicity T 17So. Figure 2 shows the processes which may take place during absorption and radiative energy dissipation processes along with the orientation of the electron spin.

2

10-3

hv

+

~

t electron jump

Singlet (spins paired)

hv

+

~

Singlet (spins paired)

f

(Spin allowed absorption)

Excited singlet

(spins paired)

t electron jump and spin flip

t

(Spin forbidden absorption)

Triplets (spins parallel)

electron jump

electron jump

+ hv (fluorescence)

+ ltv •Ph?Sphoresa:nce)

and spin ftip

Figure 2. Absorption and radiative energy dissipation processes along with the orientation of the electron spin.2

Radiationless Mechanism In radiationless or non-radiative mechanisms, a molecule loses its energy without any photon emission. The radiationless mechanism can involve both photophysical and photochemical processes.

Photophysical processes can be categorized as internal

conversion (transitions between states of the same multiplicity, such as from S2 to S1 or from T1 to T1), and intersystem crossing (transitions between states of different multiplicity, such as from S1 to T1). In photochemical processes the excited state of one molecule and a state (usually the ground state) of another molecule participate into radiationless transitions. The Jablonski diagram presents the processes that occur between the absorption and emission of the light as shown in Figure 3 .1 Radiative and radiationless mechanisms are shown by solid and dashed arrows, respectively. In this diagram So represents the ground, and S1 and S2 represent the electronic excited energy states. Each one of the electronic states has a number of vibrational energy levels shown by 0, 1, and 2. This figure shows that upon absorption, molecules get excited to higher vibrational energy level of either S1 or S2. Molecules at the upper vibrational energy levels relax back to the 3

10-4

lowest vibrational energy level of S 1 through internal conversion in 10-12 s- 1 or less. This relaxation is generally followed by the fluorescence emission which takes around 1o-8 s- 1•

: Internal 1

Conversion

I

\I

--- - - - -Intersystem - -'rossing

v

--~

Absorption Fluorescence .::f

50

hv,.""

I" rel="nofollow"> hVF ~

2 l

hVp«'

Phosphorescence,. ,•

0

Figure 3. Jablonski Diagram. 1

Quantum Yield These radiative and non-radiative mechanisms are all governed by individual rate constants. These rate constants can all be related to each other by a rate constant ratio, ¢, which is called quantum yield.

¢ = rate of formation of product sum of all rates

Quenching Quenching represents the decrease in the fluorescence intensity. Collisional quenching, which is one of the quenching mechanisms, occurs due to deactivation of the excited-state molecule upon collision with a quencher (another molecule) in solution. As a result of the quenching a decrease in the fluorescence intensity is observed and can be quantified using the Stern - Volmer equation (as given in Eq. 10). 1•4•5

Ru(bpy)l+ Luminescence and Quenching In this experiment, you will be studying the luminescent properties of the transition metal complex ruthenium (II) tris-bipyridine, Ru(bpy)3 2+.

Irradiation of

Ru(bpy)32+ with UV light causes the molecule to absorb energy and get promoted to one of its excited singlet states (*Ru(bpy)/+), where Ia shows the absorption rate.

4

10-5 la

Ru(bpy)~+ + hv-0-* Ru(bpy)~+ d[*Ru(bpy)j+] dt

(1)

=I a

At this stage *Ru(bpy)32+ can do a number of things: 1. *Ru(bpy)32+ can undergo rapid (- 10- 12

10- 13 s) relaxation to its lowest excited

-

energy state and then fall back to its ground state by emitting a photon (fluorescence). This is a first-order fluorescence decay process where the fluorescence rate constant is denoted kt-.

k;

*Ru(bpy)~+ -0-Ru(bpy)j+ +hvf d[*Ru(bpy)j+] dt

= -k

[*Ru(bpy)2+]

I

(2)

3

2. * Ru(bpy)5+ can lose its energy in a nonradiative fashion through heat transfer to the solvent and return to its ground state. These non-radiative transitions of* Ru(bpy)j+ in its excited state can be described in a first-order rate process with a rate constant of

knr· knr

* Ru(bpy)5+ -0- Ru(bpy)5+ +heat

d[*Ru~py)j+] = -knr [*Ru(bpy)J+ ]

(3)

3. * Ru(bpy)j+ can undergo an intersystem crossing to a triplet state and then relax back into its ground state through phosphorescence. k1sc

* Ru(bpy)j+ -0- T Ru(bpy)j+ kph

T Ru(bpy)5+ -0- Ru(bpy)j+

+ hup

5

10-6

d[*Ru(bpy)~+] =-k dt

(*Ru(bpy)2+] 3

!SC

d[T Ru~py)5+]

(4)

= k1sc[*Ru(bpy)5+]- kph[T Ru(bpy)j+]

Phosphorescence in solution is very uncommon, but in the case of Ru(bpy)32+, does indeed occur.

This luminescence activity can be quenched by molecular oxygen

according to two proposed schemes: kq

TRu(bpy)5+ ~Ru(bpy)5+ +8 02

Scheme A

Scheme B

For Scheme A, the relaxation of singlet oxygen to the ground state triplet form releases a photon of 1400 run. This provides a way to test the proposed mechanism using a stateof-the-art IR detector.

The situation described above can be simplified to the following scheme for the purposes of this lab. Ia

Ru(bpy)5+ + hq ~ * Ru(bpy)5+

Excitation

Luminescence knr

* Ru(bpy)~+ ~ Ru(bpy)5+ +heat kq

*Ru(bpy)5+ + 02 ~

Quenching Products

Nonradiative Relaxation Quenching

(5)

These reactions come to a steady state if the exciting light intensity is constant and no irreversible photochemical reactions exist.

6

10-7

The quantum yield, ¢> 0 , is equal to the radiative luminescence decay rate divided by the sum of the radiative and nomadiative decay rates.

kf [ * Ru(bpy)J2+ ]

0

=



*

2+

*

(6) 2+

k j[ Ru(bpy)J ] + knr[ Ru(b!JY)3 ] (7)

In the presence of quencher, the quantum yield expression becomes

The relation of kq with other rate constants and the relative quantum yield are determined from Stem-Volmer equation in Eq. (10). (10) Replacing the relative quantum yield by the relative areas measured from fluorescence spectroscopy, (area) 0 /(area) vs [02] is plotted. The slope of this plot gives the relation between the rate constants of radiative and nonradiative radiations. In the absence of a quencher, the rate of disappearance of excited Ru(bpy)3 2+ can be obtained from Eq. (12).

d[

*

2+

Ru~py) 3

]

= -ki(Ru(bpy)~+]-knr(Ru(bpy)j+]

= - (kf + knr)[ *Ru(bpy)J2 + ] *

and

d~

2+

Ru(bpy;3 ] [ Ru(bpy)J +]

(11)

= -(kf + knr) dt, giving the following equation when

integrated: (12)

7

10-8 The slope of the plot of time vs natural logarithm of Ru(bpy)32+ fluorescence intensity, provides kr + knr. Once k1 + knr is known, the quenching rate constant can be found from the slope of the Stem-Volmer plot. 5

Experimental Procedure

The instructor or the TA will give detailed directions for the use of the FluroLog luminescence spectrometer, the Varian UV-VIS spectrometer, and the laser photolysis apparatus. To obtain sufficient data for a Stem-Volmer plot, you will need to measure the luminescence of three samples of Ru(bpy)32+: an air-saturated sample, a nitrogensaturated sample, and an oxygen-saturated sample. In addition, you will also need to take the absorption spectrum of the complex. The TA ""ill provide the Ru(bpy)32+ sample for you and will give you the laser photolysis data.

Absorbance: 1) The TA will demonstrate how to use the instrument. You will first need to take a blank with pure water before you take your spectrum. You will be using a specially modified cuvette that allows for attachment of a rubber septum. You should scan between 250 and 650 nm. the complex is

E4s1 =

The literature extinction coefficient for

1.41 x 104 M· 1cm· 1•

Luminescence: 2) The TA will have the instrument turned on and ready to run the samples. Please

do not touch any switches or shutters on the instrument. The measurement will be that of an emission scan with

A.excitation =

450 nm and the emission scan range

from 500 to 700 nm. 3) The first sample will be the air-equilibrated sample. Use the same cuvette used in the absorbance measurement. Run the scan and save your file to the appropriate folder. You will want the Sl data set (You can also include S l/Rl).

Once

complete, go to Analysis, and then Calculus, and choose Integrate. Record the Area and the

Amax.

You will calculate the oxygen concentration under prevailing

8

10-9 atmospheric conditions (make a note of the current barometric pressure and temperature). 4) The next measurement will be on an oxygen free sample. Take the cuvette to the laser photolysis lab table and purge with nitrogen using the set-up there. First place the vent needle into the septum and then insert the nitrogen needle all the way to the bottom of the cuvette. Let nitrogen bubble through the solution for 5 minutes and then remove both the nitrogen needle and the vent needle at once. Take an emission scan and analyze using the procedure in step 3. 5) The final measurement will be on an oxygen saturated sample.

Place a new

septum onto the cuvette and bubble pure 0 2 through the solution for 5 min using the same procedure as in step 4. Take an emission scan and analyze as you did before. You will calculate the (02] for the saturated sample. 6) On the same sample, you will need to take an IR emission spectrum to test the viability of quenching scheme A. The instructor or TA will demonstrate this for you.

Laser Photolysis: 7) You will obtain laser photolysis data on the Ru(bpy)3 2+ sample. Please refer to pages 11-1 in the lab packet for the theory and data analysis procedure.

In-Lab Questions

1. Explain the terms ground and excited states, radiative and nonradiative decays, and quantum yield. Give examples of radiative and nonradiative decays. 2. How does Stem-Volmer plot enable one to determine the rate constant for fluorescence quenching? 3. Why are you using area under the fluorescence spectrum in this calculation?

9

10-10

Data Analysis

1. Make a table to list the sample number, corresponding concentration of 02 in M and corresponding (area) 0 /(area) ratio.

2. Plot (area) 0 /(area) (y-axis) vs concentration of 02 and obtain kq/ (kr + knr) from the slope of the Stem-Volmer plot.

3. Using the data provided in the laser photolysis experiment, plot natural log of fluorescence intep.sity vs time and obtain the slope (kr+ knr).

4. Calculate the quenching rate constant, kq using the results of step 2 and 3. 5. Estimate uncertainty of quenching rate constant from linear regression analysis. Report in appropriate format the quenching rate constant with uncertainty.

6. The collision rate of A and B reactants in solution can be calculated using Eq. (13)

kd

_ 8RT -

(13)

317

where, kct is the collision rate constant in L·mol· 1sec· 1, R is the gas constant in 8.314 J K· 1 mo1· 1, T is the temperature in K, and T/ is solvent viscosity ( ry = 1.0020 cP for water at 20°C). Calculate the value of kd for water at 20°C.

Report Questions 1. What is the importance of kd (the collision rate constant)? (Hint: The reciprocal of kq can be considered as the average time it takes for a given excited Ru(bpy)i+ molecule to become quenched by 02 at a concentration of 1.0 M 02). 2 . What is major source of error in calculation of quenching rate constant? 3. What are three common mechanisms for bimolecular quenching of an excited state?

10

10-11

Reference

1. Lakowicz, J. R. Principles ofFluorescence Spectroscopy;

2nd

Ed.; Kluwer

Academic/ Plenum: New York, 1999, pp. 1-12., and pp. 237-259. 2. Turro, N. Modern Molecular Photochemistry; University Science Books: Sausalito, 1991, pp. 1-15. 3. Barltrop, J.; Coyle J. D. Principles of Photochemistry; Wiley & Sons, Inc.: New York, 1978, pp. 1-100. 4. Lagenza, M. W.; Morzzacco, C. J.; J Chem. Educ. 1977, 54, 183. 5. Stern, O.; Volmer, M.; Physik, Z. 1919, 20, 183.

11

11-1

Determining the Spin-lattice Relaxation (T1) of 1-Hexanol using 13C-NMR

Objectives

• To determine the spin-lattice relaxation times (T1) of each C atom of n-hexanol • To relate -re values to the atomic motion of each C atom on n-hexanol

1. Introduction

Nuclear magnetic resonance (NMR) has become one of the primary tools in organic and biochemistry for structure elucidation, primarily through routine experiments detecting 1H,

13

C, or 15N. However, NMR has the capability to far exceed the basics;

almost e·very nuclei in the periodic table has at least one NMR active nuclei, and many possess spin 1/2, making them as straightforward to detect as 13C (figure 1).

K

Ca

Rb

Sr

Cs

Ba

•

Spin 1/2

D

Spin>l /2

Figure 1. Nuclear magnetic resonance periodic table. Black squares contain atoms that have at least 1 NMR active isotope having spin 1/2, while white boxes contain atoms that have at least 1 NMR active nuclei having spin greater than 1/2 (quadrupolar nuclei).

11-2 Experiments to determine inter-nuclear distance, through space coupling, coordination number and octahedral distortion are available through the use of NMR. This laboratory will focus on spin relaxation of a simple organic solvent measured through NMR. The data generated from this T l experiment will be fit to a relaxation equation using Mathematica.

Theoretical Background Nuclear magnetic resonance (NMR) spectroscopy exploits small energy differences in nuclear spin levels when spins are subjected to an external magnetic field (figure 2). This energy difference is described by the Boltzmann distribution, Ni,upper

= e(-r;IJli! kT)

(1)

N i.lower

where N represents the spin population of nuclei i in either the upper or lower energy states, y; is the gyromagnetic ratio of nuclei i, B is the external magnetic field in units of Tesla (T), h is planck' s constant, k is the Boltzmann constant and Tis the temperature. The population difference in a sample of H20 in an external magnetic field of9.4 Tesla

is:

N H ,upper

=e

2.675 l9x l08 s- 1-r- 1·9.4T·l.05457 x!0-34 J·s 23

1

1.38065xW- JX- ·293K

=

0.999934

N H,lower

Since the signal intensity of all spectroscopic techniques relies on population differences this extremely small population difference has important consequences for NMR: the amount of sample required for NMR experiments is large, thereby increasing the absolute number of spins and increasing the absolute population difference. The presence of an external magnetic field causes the nuclear spins to align themselves with or against the applied magnetic field, dependant upon the initial energy state of the spin (figure 3) with the energy difference between the two spin states given by M = rB/z.

11-3

Energy levels for spin 1/2 (ex: 1 H, 13()

00 00 m =-1/2

......

·.....

'•

"~ '

... •··•·.•.

No Field

·-.. initial populations determined .../ by the Boltzmann distribution

j:.•. •······

"-... 00000 E

..

m

=112

Applied Magnetic Field (B0 )

Figure 2. Energy level diagram for a spin system.

The magnetization vector along the z-axis is given by the vector addition of magnetization of them = 112 and them = - 112 (figure 3).

z

z m = 1/2

----- -- -

l:m;

'

--'

,

y

,

x

--- m = -1/2

y

~

~

x

Figure 3. Magnetization vectors along +z and -z axis representing the two population states, followed by the resultant magnetization vector along the +z axis generated by vector addition. However, in order to measure the difference and generate a spectrum the spin system is perturbed from equilibrium (magnetization along the z-axis) by application of an RF pulse (figure 4). The applied pulse has a tip-angle 8, which is determined by the time length of the applied field is turned on (pulse length).

11-4

z

z 0 90 '

'

y

y

; ;

x

x

Figure 4. Application of a 90° pulse along the y-axis moves the magnetization vector from the z-axis to the x-axis. The tip angle is given by 8 0 0 the angle between the initial magnetization vector (Iz) along the z-axis and the magnetization vector after the applied pulse (Ix)Once the applied field is removed the magnetization vector relaxes back to equilibrium along the z-axis. This relaxation effect is termed spin-lattice relaxation, or Ti relaxation (Figure 5).

z

z 'tl

---

y x

x

z I

't2 ''

y

y x

Figure 5. Spin-lattice relaxation (Tl relaxation). Left: initial magnetization vector after a 90° pulse along y-axis; after a time period -r1 the magnetization vector along x has diminished and the magnetization along z is growing in. Right: equilibrium magnetization after time period -r2. Spin-lattice relaxation occurs due to field fluctuations at the nucleus, and may be caused by • • • • •

Magnetic dipole-dipole interactions Electric quadrupole interaction Spin-rotation interaction Scalar-coupling interaction Chemical shift anisotropy

11-5

Mathematically, T 1 relaxation is described by the Bloch equation, eq. 2, aM . OJ t) + M YB cos( OJ t ) - • = - y(M xB1 sm( 1

&

(M

z - lvf 0 ~

J

(2)

The T l decay may be modeled quantitatively by setting Mx =My= 0 in eq. 2,

d~, = {

M, ;, M,

J

(3)

Integration of eq 3 yields, -I

(4)

which will be used to model the Ti relaxation data.

Procedure/Data Analysis

Two pulse sequences may be used to acquire Ti relaxation data: the inversion recovery method, tlir, or the T1 saturation recovery, tlsat (figure 6). Note the two methods differ in their mathematical fitting equations, we will use the T 1 inversion recovery method (Figure 6).

(180)

( 90)

1-t

~1

aCXl

M(t)=M0 (1-2e -tfT1 )

-Mo .....____ _ _ __ t

Figure 6. Pulse sequence and fitting equation for Tl inversion recovery experiment.

11-6 How does T1 relate to Atomic Motion?

The Tl tells us the spin-lattice relaxation of a nuclei, in this case, different carbon-13 atoms, but it can be extended to give us useful information about th~ molecule. NMR active nuclei interact in many ways, but for this experiment it is the dipole-dipole coupling which is the most important interaction. This depends on the orientation and the distance between the two spins. (In this case, both 13C and 1H are NMR active and so they interact). The dipolar interaction (d) is described by 2

d = µ o n r1Y2 47r r 3

(5)

where y1 & y2 =gyromagnetic ratio of the nuclei and r is the distance between atoms. The Ti relaxation is proportional to

d2!h2. As the carbon containing group (CH2 or CH3)

moves around, these distances between atoms (nearby 1H's change), and these changes are transmitted to the carbon through coupling interactions. Thus it has been shown that T1 relates to motion of each group in the alkyl chain through a variable -re, the effective correlation time for rotational reorientation, through the following equation.

J_ -_

Ti

N'( µ o ) 47r

re=6.72881x107 s-1 T 1 ; where

re &

2

n r~r~ re

2

T~H

(6)

m=2.67519 x 108 s-1 T 1

YH are the gyromagnetic ratio of 13 C and 1H respectively, Jk = permeability in

a vacuum, N is number of directly bonded H atoms (to the C of interest), and r cH is the CH distance. 1

The Experiment

For this experiment, you will be determining the T 1 relaxation of all six carbons of 1-hexanol. A degassed sample of 1-hexanol (70% in CDCb, sealed under vacuum) was placed in the spectrometer. This sample was tuned, meaning the NMR' s two

11 -7

channels were tuned to the exact frequency of 13C and 1H respectively. The sample was locked to the frequency of the deuterated solvent (CDCb). NMR spectrometers are tuned to the frequency of the nuclei they study, in this case 13C (the frequency is approximately 100 MHz on this spectrometer). In order to stay correctly calibrated, we relate this frequency to another value. Deuterium becomes this standard. Deuterium is NMR-active, and so can be used as a comparison. This is what 'Lock' does, and why it must be done for every experiment. Without lock, your spectra wilJ come out unreadable. Next the exact 90-times for this sample had to be determined for both 13C and 1H. This is the length of time that the spectrometer must pulse to rotate the magnetization vector 90 degrees. Hydrogen must be considered because the spectrum will be decoupled, and if the exact 90 time is not used for the 1H-channel, you could see splitting (coupling) of your 13C signal. You will be given these values in the procedure. You will set-up and run the inversion-recovery experiment yourself on the 400

MHz Bruker spectrometer. The actual run time is approximately 35 mins. After this, you will process and analyze your data. Both running and processing your experiment will utilize XWIN NMR 3.1 software. A T1 experiment is a pseudo-2D experiment, and it will give a 2D spectrum. In one direction (x-axis) you will be taking frequency information, this is the 13C-NMR spectrum for your sample. You must vary the delay time, 't, this will become the y-axis of a 2D spectrum. (see below) I

I

I

I

I

I

I

I

I

i

't ,

I

secs

I I Shift, ppm

Figure 7. Pseudo-2D spectrum you will get from this experiment.

Fitting the plot of integral vs. twill give you a plot similar to that shown in Figure 6. This is an exponential function. You will be asked to CHOOSE your values to place in

11 -8 a vdlist. What is the best way to sample an exponential function? Where do you want to take the most points on the curve (Figure 6)? Think about this as you choose your values. The better your picks for the vdlist, the better your Tl fit to the data will be!

2. Laboratory Procedure

Experimental Set-up

1. Welcome to XWIN, a software program designed to run Bruker NMR spectrometers. The program should be open. This is the program you will be using both to run and to process your NMR T 1 experiment.

2. First you will want to familiarize yourself with the layout ofXWIN. Notice menus are at the top. In this procedure, Menus> "Will be written with arrows for the initial menu and the pull-down choices. (e.g File>Search). All the buttons you need later on to process will be on the left side. In these instructions, buttons will be underlined. Also, at the bottom of the window is a line where you will type commands. In these instructions, "commands" will have quotes. Always hit enter after typing a command!

3.

"re filename" The filename depends on your section and group, and should be in the form chem457_s#_g% where# = your section number and% = your group number (Don't forget underscores!) For example, if you are in section 2, group 1 the filename would be: chem457_s2_gl , and you would type "re chem457_s2_gl"

4. Choose the type of experiment you wish to run. For this experiment, you are running an inversion-recovery experiment. This has a pulse sequence of 180-'t-

90.

11-9 "rpar" Choose: c13_ Chem457_hex (include underscore). This file contains parameters you need to run the experiment.

5. Enter the 90-time for

13

C by typing "pl". Then enter the value 7.25. (This is 7.25

µsec)

6. You must also enter the 90-time for 1H since this experiment uses the proton channel for decoupling. Because it is the pulse length for decoupling, you must type "pcpd2", then enter the value 109. (This is 109 µsec)

7. Between each pulse on the carbon channel, you must allow time for the spins to relax to zero (equilibrium). The common protocol is to wait AT LEAST 5 times the longest Tl in the sample. For hexanol, a delay of 30 secs is sufficient. Type "dl" then enter the value 30.

8. "edlist" Choose: vd on the pop-up menu. At the bottom of the pop-up window type your filename (see step 3).

9. This will open a notepad window. In this type 10 values. This is your vdlist (see intro), and it will contain your

't

values. You will want to make sure you include

more points at the curve of the function (Figure 6). To do this, values should be closer together then spread out as they increase. Values of the vdlist must be typed in a certain format. Type one number per line. Do NOT include units - the program will assume the values are in SECONDS! Values less than 1 must have a zero in front of the decimal. See example below for format, but DO NOT use these values, you MUST CHOOSE YOUR OWN using the instructions below!

11 -10

f'

kchex922 - Notepad

t;]LQJ~

Fde Edit Format View Help

50 30 25 20 15 10 8 6 4. 5 3 2. 5 2 1

o. 5

Start with 10., hit enter, continue in the same manner with the next 8 time delays (your choice). This list is the vdlist explained in the introduction (p. 6-7). Type time delays in decreasing order. For the final (1 oth) point type 0.2.

You must write down YOUR values in order (with the units).

10. Choose File>Save, then close the window (or File>exit).

11 . type "vdlisf' choose the name of the vd list you made in steps 8-10.

12. "eda" In the open window, type "sol" in the bar at the bottom of the window. Look for PROSOL and make sure the value directly below it says TRUE. If not, click it once, and it should change.

13. "ii" This double-checks your parameters for format errors. Wait until is says ' ii finished'.

14. "rga" wait until is says ' rga: finished' at the bottom of the window.

11-11

15. "expt" This will tell you the length of your experiment. Make sure it is not too long!! It should be approximately 35 minutes. lfit is much longer, see a TA for help.

16. "zg" You experiment is now running. You can use this time to work on questions for the lab.

Processing Tl Experiment

1. Once your experiment is finished, you can begin processing. This experiment should be processed in the computer lab in Whitmore (rm 207). {Data transfers from the NMR computer to the lab computers every 15 minutes.}

2. Log-on to one of the NMR processing computers (computer lab, left side. There are 3 of them.) If they are all full, but you see that someone is doing NON-NMR work on one, you may kick them off! Sign-on, then find the X-WIN NMR 3.1 icon and double-click to open the program.

3. On the top, far left of the screen is the File> menu. Click this, then Search.

4. For this experiment, choose the following: Directory = d:/data

user= chem 457

*name= your filename

*this list is in alphabetical order, search here for your sample name Double click the filename, and then click filmly. Now click close

5. Look underneath the top menu and you should see your filename in the top left of the screen. The middle of the screen will be blank except for a message ' type xfb to process' Do NOT do this. Type "xt2"

6. "edtl" Change FCTTYPE to invrec, this tells the program what functions to use to calculate the Tl values.

11-12

Phasing key Should show full rainbow, reds and purples Figure 8: The pseudo-2D spectrum. Note the full phasing key is shown.

7. Click the +/- button 2 times, to give the full rainbow of colors on the phasing key(see Figure 8). This should show both the positive and negatively phased peaks. If you cannot see any negative peaks, try clicking *2 to enlarge the spectrum on the top left several times (more peaks will appear). Similarly, /2 decreases the spectrum.

8. Click phase. The screen will become a split-screen. The top left window is your full 2D spectrum. All the buttons at the top left relate to this window. The 3 window on the right are for taking pieces of the spectrum. Buttons at the bottom left relate to these. (Figure 9).

11-13 Click in the full 2D window, now click the+/- button 2 times. You can also enlarge the spectrum similar to step 6.

9. Look at the peaks on the right side of the full spectrum (these are lower shifts, ppm). Click row, then middle-click on the lowest one (on the y-axis).

10.

Move to position 1, by finding mov on the left side of the window, and clicking the 1 button. You should see a spectrum appear in box 1, the screen should look like Figure 9.

CD

C/J

-g(')

r+

c ::+ 0

:::J (/)

2 O' 3 -, 2'

Figure 9: Moving rows, in order to phase.

11. Now on the original 2D spectrum, find the highest (on the y-axis) peak in the same column as you chose before. Click row, then middle-click the highest peak.

12. Move to position 2, by finding mov on the left side and clicking the 2 button.

11 -14 13. Find Qig on the left. Click the 2. button next to it. (Figure 10)

14. Click the phO and HOLD it. While holding move the mouse up and down until your spectra looks phased (see Figure 11). All peaks should be above the baseline. Also, look at the left and right side of each peak, both should look the same (symmetrical). However, if you have more than one peak overlapping, these may be unsymmetrical and that is normal. 15. Use Ph.l (the same way as phO) to make sure all peaks in each spectrum are phased.

Figure 10: Phasing your spectra

11-15

Spectrum After Phasing

Spectrum Before Phasing

\

'

-~+)~~~ ~\ ~~-~JJ1~ ~~ \

r - -r---r---

6.4

l

6.2

6.0

5.8

5.6

5.4

5.2

5.0

1

H Frequency (referenced from TMS)

6.4

6.2

6.0

5.8

5.6

5.4

52

5.0

1

H Frequency (referenced from TMS)

Figure 11. On the left is a portion of a spectrum before phasing (unphased). To the right is that SAME spectrum after phasing. ·

16. Click return, then save & return

17. Type "rspc". This will give you a ID spectrum of the first 't value from your vdlist. By integrating or picking peaks peaks in this window, the software "'' ill automatically transfer this information to integrate or pick the same peaks for all 10 't values from the vdlist!

18. Click integrate to enter a new window. Integrating will tell you the area under each peak. As i; decreases, this will decrease down to null, then become more negative. Thus we can use the changing integral values to monitor the change in magnetization as a function of the delay time.

19. Spread out the spectrum so that you can see the peaks well. (See Moving Around section below for buttons.) Also you may need to increase the peak size. Make sure you can tell where one peak ends and another begins.

11-16

Moving Around in XWIN

For many tasks, you will need to change the view of the spectrwn. Gettug a close-up view, spreading peaks apart, increasing or decreasing the size of the peaks, etc. To move around in your spectrum, use the following:

· 11<11>1 1 Expand to show full spectrum

Move to left

Expand incrementally

INCREASE size of spect , X2

DEGRE.A.

~:

size of spE. Jra X2

Move to rig ht

Condense incrementally

INCREASE size of spectra XS

DECREASE size of spectra X8

20. Cli\, 1< t:1e le;, mouse button once. A white arrow should appear where the pointer is: th. is called select mode. Middle click to the left side of (where it is still flat), then (where it becomes flat again) on the right side of a peak. Usually a number (the integral) will appear on the bottom.

21. Repeat step 19 for all 6 peaks (NOT the solvent peak, at 77.0 ppm), moving around the spectrum as described above.

22. When you are done integrating, click return button (bottom left). Now click Save as ' intmg' and return on the pop-up menu. This will return you to regular mode.

11 -17 23. For the next step you will need to see all the peaks. First spread out the spectrum, so that you can clearly see the tip of each peak, by first clicldng the expand button. Left clicking in the spectral window will put you in select mode. Now, middle-click to the left of your highest ppm peak in the sample, then middle-click to the right of your lowest ppm peak in the sample. This will change your viewing window.

24. Type "basl" to enter a new window. This is where you will tell the program which peaks it should find Tl values for.

25. Click def:·pts on the left side of the screen (towards the top).

26. On the spectrum, left click once to enter select

mode. For each of the 6 peaks (NOT the solvent peak!), middle click at the very tip of the peak. A small green arrow will appear to indicate a selected peaks. (see Figure 12).

27. When you have selected all 6 peaks, click return, and then save & return.

28. Click 20 in the bottom Left comer.

29. "pd"

Figure 12. basl Screen. Note the small arrow above a selected peak. 30. Analysis> relaxation (tl/t2). This will show the data for the first peak (highest shift, ppm).

11-18 31. ''ctl" to calculate the Tl value. It will show you the T 1 curve for this peak. If you want, you can continue to view each curve by typing "nxtp" and repeating the "ct l " command.

32. You can get a printout of all the ·calculated Tl values, as well as the integrals for each value from your vdlist, by typing "datl", and click 'Print' . Turn in this

printout with your final report.

3. In Lab Question

1. The following is a plot of one doublet changing as a function of pulse length (pl). Explain what is happening overall and at each point A, B and C. (All peaks ARE phased correctly.)

A

..

•• , ""'

B

..... r. r ....,,

.

JJ-

.

c Pulse length (pl , in seconds) 2. You enter two important parameters for experiment, p 1 and d 1. Explain why they are important and what is the meaning of these two parameters? 3. Write the equation you used to determine Ti times.

11-19

4. Data Analysis

1. At the end of this report, a plot of the final

13

C-NMR is given for 1-hexanol. Label

each peak with the corresponding carbon (letters A-F). Ignore the solvent peak (a triplet at 77.0 ppm). Note: the shift of Cc< shift of Co, which is NOT what you would expect (this is a special exception for this gamma atom).

2. Using the data in your printouts, make a plot of "t versus intensity using a program other than XWIN. Apply a non-linear fit to these plots. Calculate the error.

3. Using the Tl data from XWIN, calculate the -re values for each peak. Make a chart with this information. Peak Letter

shift (ppm)

T l (s) -re (ps)

5. Report Questions

1. Compare the Tl data obtained XWIN to that of another program (data compiled in Data Analysis #2). What are the differences? What would account for these differences? Which do you think is more accurate and why?

2. Using the spectra and table made in data analysis (#1 & #3), explain the trend of 'tC

values along the backbone of the 1-hexanol molecule. The molecule has been

modeled and there are movies available in 207 Whitmore (see Dr. Arzhantsev for details). What do these tell you about the -re values?

3. What is hydrogen bonding? How important is hydrogen bonding in this experiment?

References: 1. Gasyna, Z.; Jurkiewi cz, A. J Chem. Ed 2004, 1038.

A-1

Treatment of Experimental Data In Chem 457 the following terminology is very important m the evaluation of the experimental data.

Precision: a measure of reproducibility of a set of results from replicate runs.

The closeness of agreement between independent test results obtained by applying the experimental procedure under stipulated conditions. The smaller the random part of the experimental errors which affect the results, the more precise the procedure. A measure of precision (or imprecision) is the standard deviation.

Accuracy: a measure of the closeness of an experimental value to the true value or

accepted value; correctness. The agreement between the values can be determined by absolute error or percent error. If an error occurs consistently, it affects the accuracy and classified as a systematic error.

To avoid a consistent error, a standard should be run or a correction factor needs to be applied during the experimentation or data analysis.

If an error occurs inconsistently, it affects the precision and classified as a random error.

To avoid an inconsistent error, measurements should be taken number of times and averaged.

Uncertainty: Parameter, associated with the result of a measurement, that characterizes

the dispersion of the values that could reasonably be attributed to the measurand (particular quantity subject to measurement).

Error: anything qualitative or quantitative causing a measurement to differ from the true

or accepted value. Error of measurement: Result of a measurement minus the true value of the measurand.

Since a true value cannot be determined, in practice the conventional true value is used.

A-2

Common Statistical Calculations: 1) Mean: To select a typical data value or to obtain an average value, all data values are added up and divided by the number of data items. 1

N

N

i=I

x=-Ix;

2) Estimated Standard Deviation:

The most common way to describe the range of

variation in the collected data.

S=

I(x;- x)2 (N -1)

3) Estimated Standard Deviation of the Mean: Answers the following question: How much variation is there in the estimated standard deviation?

Example Problem: Calculate the a) mean, b) estimated standard deviation, and c) estimated standard deviation of the mean for the following sample data. Sample Data (Length, cm) 2.5 ± 0.5 3.2 ± 0.5 2 .7 ±0.5

x = 2.5 + 3.2 + 2.7 + 2.4 + 2.2 = .!]_ = 2.6 5 /')' ( Y . -

X)2

5 Jn n 1 ..L n ~h. ..L n n 1 ..L n nLI. ..L n

1 h.

A-3 2.4 ± 0.5 2.2 ± 0.5

A-4

How to Collect and Analyze the Data? 1. Record measurements properly: a) to the correct number of decimal places b) with units and c) with indication of the uncertainty associated with the measurement (±)

The uncertainties or the tolerance levels of the common glassware used m the laboratories are as given in Table 1.

Table 1. Glassware Tolerances- for class B glassware (class A glassware tolerances are

Yz those of class B) Transfer Pipettes Size, mL

Tolerance(±)

Volumetric Flasks Size, mL Tolerance (±)

1&2 5 10 25 50

0.012 0.02 0.04 0.06 0.10

50 100 250 100 2000

0.1 0 0.1 6 0.24 0.60 LOO

If tolerance levels are not available, use the rules of thumb to determine the uncertainties. Table 2. Estimating the tolerance levels, where they are not available. Instruments Linear scales Digital readout Mettler balances Vernier scales

Tolerance(±) 0.5 1 - 5 0.4mg 0.1

of the smallest division in the last digit = ± 0.0004 g of the smallest division on the non-Vernier scale

In addition, the tolerance level information can be found for most of the instruments from their instrument instruction manuals if needed. In case of an assumption on the tolerance level estimation, clearly state the conditions under which the measurements were taken and clearly explain it in your report.

A-5

2. Rejection of Apparently Inconsistent Replicated Data: Before replicated data or replicated results can be rejected, a statistical Q test needs to be performed to decide whether the points have to be rejected. If the calculated value of Q is LARGER than the tabulated value, the data point can be rejected. This test is valid for small samples (3-10 data points).

Q = Difference between the point in question and the next nearest data point Range of data points

Table 3. Critical Q values for rejection of discordant values at 90 percent confidence level. 1

N

3

4

5

6

7

8

9

IO

Qc.

0.94

0.76

0.64

0.56

0.51

0.47

0.44

0.41

3. Determine Deviations for Each Replicate Measurement A) For 20 or more number of data points: Random error needs to be statis6cally treated to prevent imprecision. Normal error probability function is expressed in the following Gaussian curves as shown in Figure 1. 1 If large number of data points are available (at least 20 and more) these curves

provide satisfactory precision. Pu -µ)

PU'-µ)

I

.r - µ -.

(a l

- 1.96a

0

1.96<1

!bl

Figure 1. Integrated probability P for normal error distribution. 1 a) Standard deviation error limits, ± u b) 95% confidence limits, ±l.96u

.r - µ -+

A-6

Table 4 shows the uncertainty values and their corresponding level of confidence. 1 Table 4. Correspondence between uncertainty value and level of confidence. 1 Uncertainty

±cr

± 1.64 (j

±1.96 (J

±2.58 (J

±3.29 (j

Confidence level

68.26

90

95

99

99.9

B) For less than 20 number of data points:

For experiments with number of data points between 1< N < 20, the student t distribution curve should be used. 1

P (t )lk_.,,

- 3

- 2

- 1

0

2

3

Figure 2. Student t distribution function curve ( v : number of degrees of freedom, P(r): student distribution function). 1 ~ 0 .95

represents 95% confidence limit in the mean.

(s

t -- 0.95 .,[ii

J

To determine the t, critical value, a brief table, Table 5 needs to be used, where P is the probability of the mean and v is the degrees of freedom that can be calculated by subtracting the number of variables from the number of data points as follows:

A-7

v = N - l when using a series of replicated measurements, one variable exists. v

= N -2 Owhen using

a series of replicated measurements two variable exists.

For more complete t tables check the elementary statistics books.2

. . I va ues t o be used when c alcuIf a mg uncert"f Ta ble 5. t cnt1ca am ies. p 0.90 0.95 v 0.50 0.80 0.98 1

1.00

6.31

3.08

12.7

31.8

0.99

0.999

63.7

637.0

II

I I

2

0.816

I .89

2.92

4.30

6.96

9.92

31.6

3

0.765

1.64

2.35

3.18

4.54

5.84

12.9

4

0.741

1.53

2.13

2.78

3.75

4.60

8.61

5

0.727

1.48

2.02

2.57

3.36

4.03

6.87

6

0.718

1.44

1.94

2.45

3.14

3.7 1

5.96

7

0.711

1.41

1.89

2.36

3.00

3.50

5.41

8

0.706

1.40

1.86

2.31

2.90

3.36

5.04

9

0.703

1.38

1.83

2.26

2.82

3.25

4.78

10

0.700

1.37

1.81

2.23

2.76

3.17

4.59

15

0.691

1.34

1.75

2.13

2.60

2.95

4.07

20

0.687

1.33

1.72

2.09

2.53

2.85

3.85

30

0.683

1.31

1.70

2.04

2.46

2.75

3.65

00

0.674

1.28

l.64

1.96

2.33

2.58

3.29

J

I !

I

P is the probability that the mean µ of the population does not differ from the sample mean x by a factor of more than t, the critical value corresponding to degrees of freedom.

4. Reporting Results of Calculations: a)

"The final result of a calculation should be reported with the estimated uncertainty and the proper units". The uncertainty may be a limit of error (confidence limits), standard error, or probable error; it is important to indicate which, to avoid possible confusion. A "±" sign without further explanation is generally understood to indicate a limit of error.

b) Reported values and uncertainties are to be expressed in the same notation (either both scientific or both in normal notation.

A-8

c) If a result will be used in the later calculations, that result should not be rounded until the final answer that is to be reported.

5. Calculate the composite error: Composite error (propagation of uncertainties or propagation of error) quantifies the precision of the results, identifies the principle error source, and suggests improvement. Once the uncertainties of each individual measurement are made, their combined effect on the quantity of interest needs to be found.

Knowing the uncertainty in x, Ax, the

uncertainty in some function, F(x), can be estimated as shown below:

Li(F) = l :ILix Example:

Li(lnx) =ld:xlLix=

~&

If function depends on several variables, F = F (x, y, z,... ) a partial derivative method can be applied to find the uncertainty of the function as shown.

=(8F) ax

2

Li(F)2

Li(x) 2

+ (8FJ 8y

Helpful Simplifications: 1 1. For F = ax ± by ± cz,

2. For F = axyz (or axy/ z or ax/yz or a/xyz) 2

Li (F)

2

Li (x)

2

Li (y)

2

Li (z)

- p- + y2 - - + -2 2 =x2 2 3. For F =ax", Li2 (F) ,t:.,.2 (x) Li(F) Li(x) - - = n 2 --~--=n-2 F2 x F x

2

(ap) oz 2

Li(y) 2 +

Li(z)2 + ...

A-9

4. For F = aeX,

5. For F =a ln x, 6 2 (F) =a: A2 (x)-> A(F) =a L\(x)

x

x

6. Determining Uncertainty for Values Obtained from Graphical Data:

In most of the cases, result of an experiment depends on the slope of a straight line in the

graph. A straight line may be represented by the following equation: y

= mx+b

where, m is the slope, and b is the intercept. The best straight line equation can be obtained by drawing the best straight line in the graph using Excel or Mathematica (or any other mathematics software). In the uncertainty and the graphical analyses for the lab reports, linear regression analysis is required. For that reason, it is recommended to learn how to do the linear regression analysis using the data analysis tool pack of Excel or using Mathematica.

Linear Regression Using Excel

Please follow the instructions, to do linear regression analysis on excel using a MAC or a PC. 1. Enter the data into a spreadsheet. For a straight line you may enter the x values

into column A and the corresponding y values into column B. Place the units in the column heading for each set of values and NOT in the individual cells with

the numerical values. You may use the following example in practicing linear regression analysis.

A-10

A (x-values)

B (y-values)

1.0

2.1

2.0

3.9

3.0

5.8

4.0

8.3

5.0

10.3

6.0

11.9

2. Go to the Tools menu and select Data Analysis. (If the Data Analysis is NOT in the Tools menu, go to Add-ins in the Tools menu and select analysis tools pack. Then restart your computer. If it is not on the add-ins menu, it may not have been installed. 3. From the Data Analysis list, scroll down to Regression and select it. 4. Jn the Regression window, enter the range of the x data (Al:A6 in our example) and of they data (Bl:B6). Check the line fit plots box. 5. Check the confidence level box and set it at 95%. If you are using Excel 98 for Macintosh or Excel 97 for Windows, you \Vill need to check the new workbook box, due to minor revisions in these versions of Excel. 6. When you have completed the regression \\
A-11

Table 6. Linear regression analysis output (obtained by excel) SUMMARY OUTPUT

Regression Statistics Multiple R 0.998407331 RSquare 0.996817198

Equation of the line Adjusted R Square Standard Error Observations

0.996021498 0.238746728 6

y

= 2.02 x

-0.02

ANOVA

SS

d[ l 4

Regression Residual Total

71.407 0.228 71.635

5

MS 71.407 0.057

F 1252.754

Coefficients Standard Errort Stat P-value Intercept Kl.22226 1108 Y-interc_'Tfb 0.08998 0.932625 Sb 2 D.057071384 X Variable 1 Slope 2 02 Sm 35.394273.8E-06

Observation

4

5 6

~2ofidim~1:

Lower 95%

limit

Uooer 95%

I

I

-0.637097043 0.597097

I

I

1.86 1544 107 2.178456

RESIDUAL OUTPUT

1 2 3

Siwzif!.cance F 3.80287E-06

Predicted Y Residuals 2 0. 1 4.02 6.04 8.06 10.08 12.l

-0.12 -0.24 0.24 0.22 -0.2

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References: 1. Shoemaker, D.P., Garland, C.W., and Nibler, J.W. , in Experiments in Physical Chemistry, 7th Ed., McGraw-Hill Co., 2003. 2. Downie, N. M. and Starry, A. R. in Descriptive and Inferential Statistics, Harper and Row, New York, 1977.

General Reading: Bevington, P. R. and Robinson, D. K. in Data Reduction and Error Analysis for the Physical Sciences, 2nd Ed, McGraw-Hill, New York, 1991. Mortimer, R. G. in Mathematics for Physical Chemistry, Macmillan, New York, 1981.

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Chem 457 Error Analysis Problem Set

Instructions: Write down the initial values with uncertainties and units Write down what you are determining Write down the equation you will be using Substitute the values into the equation, including units Circle your final answer, which is expressed in correct number of digits with uncertainties, and units. Problems: 1. Repeated measurements of the mass of a pellet of benzoic acid on a Mettler balance

with a tolerance limit of ± 0.0004g gave the following results: 1.0109, 1.0145, 1.0097, 1.0101, and 1.0115 g. a) b) c) d)

What is the mean for this data set? What is the estimated standard deviation, S, of this data set? What is the estimated standard deviation of the mean value, Sm? How would you report the mass of the sample using the 95% confidence limit?

2. In order to calibrate the volume of a large bulb it is filled with argon and the temperature, pressure, and mass are measured several times producing the following results: Temperature (K) = 304.7 ± 0.5 Pressure (mm Hg)= 742.5 ± 1.3 Mass (grams) = 9.3182 ± 0.0001 Note: These uncertainties are given in the 95% confidence limit. Assuming that argon behaves like an ideal gas with molecular mass of 3 9. 948 g mo1- 1, what is the best estimate for the volume of the bulb (in L) and the uncertainty in the estimate? (The gas constant, R = 0.0820579 L atm K 1moi- 1, can be assumed to be known exactly, as can the molecular mass.) 3. Suppose one wants to apply the van der Waals equation of state,

P=

RT (Vm -b)

a V~

to predict the pressure of a non-ideal gas. Assuming that the constants, R = 0.0820579 L atm K- 1 mo1- 1, a= 1.345 atm L 2 mo1-2, and b = 0.0322 L mo1- 1 are known exactly, what is the uncertainty in the predicted pressure P due to the uncertainties in the measured molar

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volume, V m = 54.21 ± 0.11 L mo1- 1, and temperature, T = 342. 7 ± 0.3 K? Report your answer as the calculated P ±AP. 4. An experiment is performed to determine the force constant k of a spring by measuring its length as a function of the applied load. The following data are obtained:

Mass fa) 10.0 20.0 30.0 40.0 50.0

Length (cm) 5.1 8.8 10.9 14.3 18.0

Generate a graph along with its best fit Jine using Excel or a similar program. Display the equation of the best fit line and its R2 value on the graph. Remember to title the graph and label the axes with quantity and unit. The line plotted has the general equation of: Length= Lo+ k(mass) Use the regression program under the data analysis menu in Excel to carry out the regression analysis on your set of graphed data. Use the resulting print-out to determine the uncertainties of Lo and k as discussed in the error analysis lecture. Show clearly how you used the information on the printout to determine these uncertainties. Include the regression printout with your work to be graded.

Report the values of Lo and k and their associated uncertainties with 95% confidence limit.

CHEM 457

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