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Analytical Chemistry Basics This index provides an introduction to some of the fundamental concepts and methods of analytical chemistry. The topics are arranged in the order in which they are commonly presented in an undergraduate analytical chemistry course. Many of the documents listed here contain links to introductory material and related topics. General steps in a chemical analysis An introduction to the processes and protocols of analytical chemistry Chemical equilibrium Review of chemical equilibrium and equilibrium constants. Gravimetric analysis Introduction to gravimetric analysis and solubility products with links to precipitation reactions. Titration Introduction to titrations with links to acid-base chemistry. Electrochemistry Introduction to electrochemistry with links to oxidation-reduction reactions. Spectroscopy Introduction to spectroscopy with descriptions of absorption, emission, scattering, and links to the Beer-Lambert Law and advanced examples. Separations Introduction to separation science with basic descriptions of partitioning, extractions, chromatography, and electrophoresis. Appendix: Data Analysis Definitions of accuracy and precision, and basic rules for significant figures and errors. Introduction to treatment of experimental data and graphs and graphical methods. Links to statistical methods pages. Appendix: Analytical Standards Definitions of primary and secondary standards, and working curves.
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General Steps in a Chemical Analysis
Introduction The analytical process often begins with a question that is not phrased in terms of a chemical analysis. The question could be "Does lead in petrol enter our food supply?" or "Is this water safe to drink?" or "Does emission testing of automobiles reduce air pollution?" A scientist translates such questions into the need for particular measurements. An analytical chemist then must choose or invent a procedure to carry out those measurements, When the analysis is complete, the analyst must translate the results into terms that can be understood by others preferably by the general public. A most important feature of any results is its limitations. What is the statistical uncertainty in reported results? If you took samples in a different manner, would you obtain the same results? Is a tiny amount (a trace) of analyte found in a sample really there or is it contamination? Once all interested parties understand the results and their limitations, then they can draw conclusions and reach decisions.
The Process Formulating the question Selecting analytical procedures Sampling Sample preparation
Analysis
1. 2.
3. 4. 5.
6. 7.
Reporting and interpretation
8.
Drawing conclusions
9.
Translate general questions into specific questions amenable to being answered through chemical measurements. Search the chemical literature to find appropriate procedures or, if necessary, develop original procedures to make the required measurements. Obtain a representative bulk sample from the lot. Extract from the bulk sample a homogeneous laboratory sample. Convert the laboratory sample into a form suitable for analysis, which usually means dissolving the sample. Samples with a low concentration of analyte may need to be concentrated prior to analysis. Remove or mask species that interfere with the chemical analysis. Measure the concentration of analyte in several aliquots. The purpose of replicate measurements (repeated measurements) is to assess the variability (uncertainty) in the analysis and to guard against a gross error in the analysis of a single aliquot. The uncertainty of a measurement is as important as the measurement itself, because it tells us how reliable a measurement is. If necessary, use different analytical methods on similar samples to make sure that each method gives the same result and that the choice of analytical method is not biasing the result. You may also wish to construct and analyse several different bulk samples to see what variations arise from your sampling procedure. Deliver a clearly written, complete report of your results, highlighting any special limitations that you attach to them. Your report might be written to be read only by a specialist (such as your instructor), or it might be written for a general audience (such as your mother). Be sure the report is appropriate for its intended audience. Once a report is written, the analyst might or might not be further involved in what is done with the information, such as modifying the raw material supply for a factory or creating new laws to regulate food additives. The more clearly a report is written, the less likely it is to be misinterpreted by those who use it. The analyst should at least have the responsibility to ensure that conclusions drawn from his or her data are consistent with the data.
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Introduction to Chemical Equilibrium Introduction A chemical specie will always exist in equilibrium with other forms of itself. The other forms may exist in undetectable amounts but they are always present. These other forms arise due to the natural disorder of nature that we call entropy (it's impossible to be perfect). As an example, pure water consists of the molecular compound and dissociated ions that exist together in equilibrium: H2O(l) H+(aq) + OH-(aq) The (l) subscript refers to the liquid state, and the (aq) subscript refers to ions in aqueous solution.
Equilibrium Constant The equilibrium between reactants and products is described by an equilibrium constant. For the balanced reaction: aA + bB cC + dD The equilibrium constant, Keq is defined as: Keq
[C]c [D]d = --------[A]a [B]b
where the [] brackets indicate the concentration of the chemical species. For the example of water, H2O
H+ + OH-, the equilibrium constant is:
[H+] [OH-] Keq = ---------[H2O]
The concentration of water in a water solution is constant and this expression simplifies to: Kw = (55.56 M)*Keq = [H+] [OH-] where Kw is called the dissociation constant of water and equals 1.00x10-14 at room temperature. The concentrations of [H+] and [OH-] therefore equal 1.00x10-7 M.
Rules for Writing K Expressions
1. Products are always in the numerator. 2. Reactants are always in the denominator. 3. Express gas concentrations as partial pressure, P, and dissolved species in molar concentration, [].
4. The partial pressures or concentrations are raised to the power of the stoichiometric coefficient for the balanced reaction. 5. Leave out pure solids or liquids and any solvent. Example: Zn (s) + 2 H+(aq)
Zn2+(aq) + H2 (g)
PH2 [Zn2+] K = ----------[H+]2
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Gravimetry Introduction Gravimetry is the quantitative measurement of an analyte by weighing a pure, solid form of the analyte. Since gravimetric analysis is an absolute measurement, it is the principal method for analyzing and preparing primary standards. A typical experimental procedure to determine an unknown concentration of an analyte in solution is as follows: • • • • •
quantitatively precipitate the analyte from solution collect the precipitate by filtering and wash it to remove impurities dry the solid in an oven to remove solvent weigh the solid on an analytical balance calculate the analyte concentration in the original solution based on the weight of the precipitate
Examples of Gravimetric Lab Procedures
Gravimetric Determination of Iron 1. Determine constant weight of the crucibles 2. Oxidation of iron sample 3. Precipitation of iron hydroxide 4. Ignition of iron hydroxide to iron oxide 5. Determine constant weight of the crucibles plus iron oxide 6. Calculation of iron in the sample
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Titration Introduction Titration is the quantitative measurement of an analyte in solution by completely reacting it with a reagent. The point at which all of the analyte is consumed is called the endpoint and is determined by some type of indicator that is also present in the solution. For acid-base titrations, indicators are available that change color when the pH changes. When all of the analyte is neutralized, further addition of the titrant causes the pH of the solution to change causing the color of the indicator to change. The analyte concentration is calculated from the reaction stoichiometry and the amount of reagent that was required to react with all of the analyte.
Instrumentation Manual titration is done with a burette, which is a long graduated tube to hold the titrant. The amount of titrant used in the titration is found by reading the volume of titrant in the burette before beginning the titration and when the endpoint is reached, and taking the difference. The most important factor for making accurate titrations is to read the burette volumes reproducibly. The figure shows how to do so by using the bottom of the meniscus to read the reagent volume in the burette. For repetitive titrations, autotitrators with microprocessors are available that deliver the titrant, stop at the endpoint, and calculate the concentration of the analyte. The endpoint is usually
detected by some type of electrochemical measurement. Some examples of titrations for which autotitrators are available include: • • •
Acid or base determination by pH measurement with potentiometric detection. Determination of water by Karl Fischer reagent (I2 and SO2 in methyl alcohol and pyridine) with coulometric detection. Determination of Cl in aqueous solution with phenylarsene oxide using amperometric detection.
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Electrochemistry Introduction Electrochemistry can be broadly defined as the study of charge-transfer phenomena. As such, the field of electrochemistry includes a wide range of different chemical and physical phenomena. These areas include (but are not limited to): battery chemistry, photosynthesis, ion-selective electrodes, coulometry, and many biochemical processes. Although wide ranging, electrochemistry has found many practical applications in analytical measurements.
Electroanalytical chemistry A good working definition of the field of electroanalytical chemistry would be that it is the field of electrochemistry that utilizes the relationship between chemical phenomena which involve charge transfer (e.g. redox reactions, ion separation, etc.) and the electrical properties that accompany these phenomena for some analytical determination. This relationship is further broken down into fields based on the type of measurement that is made. Potentiometry involves the measurement of potential for quantitative analysis, and electrolytic electrochemical phenomena involve the application of a potential or current to drive a chemical phenomenon, resulting in some measurable signal which may be used in an analytical determination.
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Potentiometry Introduction Potentiometry is the field of electroanalytical chemistry in which potential is measured under the conditions of no current flow. The measured potential may then be used to determine the analytical quantity of interest, generally the concentration of some component of the analyte solution. The potential that develops in the electrochemical cell is the result of the free energy change that would occur if the chemical phenomena were to proceed until the equilibrium condition has been satisfied.
This concept is typically introduced in quantitative analysis courses in relation to electrochemical cells that contain an anode and a cathode. For these electrochemical cells, the potential difference between the cathode electrode potential and the anode electrode potential is the potential of the electrochemical cell.
If the reaction is conducted under standard state conditions, this equation allows the calculation of the standard cell potential. When the reaction conditions are not standard state, however, one must utilize the Nernst equation to determine the cell potential.
Physical phenomena which do not involve explicit redox reactions, but whose initial conditions have a non-zero free energy, also will generate a potential. An example of this would be ion concentration gradients across a semi-permeable membrane. This can also be a potentiometric phenomena, and is the basis of measurements that use ion-selective electrodes.
Instrumentation See the documents on ion-selective electrodes and pH meters.
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Coulometry Introduction Coulometry is an analytical method for measuring an unknown concentration of an analyte in solution by completely converting the analyte from one oxidation state to another. Coulometry is an absolute measurement similar to gravimetry or titration and requires no chemical standards or calibration. It is therefore valuable for making absolute concentration determinations of standards. Coumetry uses a constant current source to deliver a measured amount of charge. One mole of electrons is equal to 96,485 coulombs of charge, and is called a faraday. Schematic of a coulometric cell
Coulometric Titration Due to concentration polarization it is very difficult to completely oxidize or reduce a chemical species at an electrode. Coulometry is therefore usually done with an intermediate reagent that quantitatively reacts with the analyte. The intermediate reagent is electrochemically generated from an excess of a precursor so that concentration polarization does not occur. An example is
the electrochemical oxidation of I- (the precursor) to I2 (the intermediate reagent). I2 can then be used to chemically oxidize organic species such as ascorbic acid. The point at which all of the analyte has been converted to the new oxidation state is called the endpoint and is determined by some type of indicator that is also present in the solution. For the coulometric titration of ascorbic acid, starch is used as the indicator. At the endpoint, I2 remains in solution and binds with the starch to form a dark purple complex. The analyte concentration is calculated from the reaction stoichiometry and the amount of charge that was required to produce enough reagent to react with all of the analyte.
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Spectroscopy Absorption | Emission | Scattering
Introduction Spectroscopy is the use of the absorption, emission, or scattering of electromagnetic radiation by atoms or molecules (or atomic or molecular ions) to qualitatively or quantitatively study the atoms or molecules, or to study physical processes. The interaction of radiation with matter can cause redirection of the radiation and/or transitions between the energy levels of the atoms or molecules. A transition from a lower level to a higher level with transfer of energy from the radiation field to the atom or molecule is called absorption. A transition from a higher level to a lower level is called emission if energy is transfered to the radiation field, or nonradiative decay if no radiation is emitted. Redirection of light due to its interaction with matter is called scattering, and may or may not occur with transfer of energy, i.e., the scattered radiation has a slightly different or the same wavelength.
Absorption When atoms or molecules absorb light, the incoming energy excites a quantized structure to a higher energy level. The type of excitation depends on the wavelength of the light. Electrons are promoted to higher orbitals by ultraviolet or visible light, vibrations are excited by infrared light, and rotations are excited by microwaves. An absorption spectrum is the absorption of light as a function of wavelength. The spectrum of an atom or molecule depends on its energy level structure, and absorption spectra are useful for identifying of compounds. Measuring the concentration of an absorbing species in a sample is accomplished by applying the Beer-Lambert Law.
Emission Atoms or molecules that are excited to high energy levels can decay to lower levels by emitting radiation (emission or luminescence). For atoms excited by a high-temperature energy source this light emission is commonly called atomic or optical emission (see atomic-emission spectroscopy), and for atoms excited with light it is called atomic fluorescence (see atomicfluorescence spectroscopy) or molecular fluorescence (see molecular fluorescence spectroscopy). For molecules it is called fluorescence if the transition is between states of the same spin and phosphorescence if the transition occurs between states of different spin. The emission intensity of an emitting substance is linearly proportional to analyte concentration at low concentrations, and is useful for quantitating emitting species.
Scattering When electromagnetic radiation passes through matter, most of the radiation continues in its original direction but a small fraction is scattered in other directions. Light that is scattered at the same wavelength as the incoming light is called Rayleigh scattering. Light that is scattered in transparent solids due to vibrations (phonons) is called Brillouin scattering. Brillouin scattering is typically shifted by 0.1 to 1 cm-1 from the incident light. Light that is scattered due to vibrations in molecules or optical phonons in solids is called Raman scattering. Raman scattered light is shifted by as much as 4000 cm-1 from the incident light.
Related topics Optics Descriptions of the optical components in spectroscopic instrumentation. Interaction of light with matter A qualitative quantum mechanical description. Spectroscopic techniques The spectroscopy section of the Contents.
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Electromagnetic Radiation Introduction Electromagnetic radiation is a transverse energy wave that is composed of an oscillating electric field component, E, and an oscillating magnetic field component, M. The electric and magnetic fields are orthogonal to each other, and they are orthogonal to the direction of propogation of the wave. A wave is described by the wavelength, , which is the physical length of one complete oscillation, and the frequency, , which is the number of oscillations per second. The figure shows one wavelength of a wave of light. The names we give electromagnetic radiation for different wavelength and frequency ranges are listed in the electromagnetic spectrum document.
Schematic of an electromagnetic wave
Velocity of light Electromagnetic waves travel through a vacuum at a constant velocity of 2.99792x108 m/s, which is known as the speed of light, c. The relationship between the speed of light, wavelength, and frequency is: c= When light passes through other media, the velocity of light decreases. For a given frequency of light, the wavelength also must decrease. This decrease in velocity is quantitated by the refractive index, n, which is the ratio of c to the velocity of light in another medium, v: n=c/v
Since the velocity of light is lower in other media than in a vacuum, n is always a number greater than one. The table lists the refractive index of several examples. Refractive index is an intrinsic physical property of a substance, and can be used to monitor purity or the concentration of a solute in a solution. The refractive index of a material is measured with a refractometer, and is usually made versus air. If the precision warrants, the measurements can be corrected for vacuum. Note that the difference between nair and nvacuum is only significant in the fourth decimal place. For anisotropic materials, such as quartz crystals, light of different polarizations (see below) will experience different refractive indices. These indices are called the ordinary refractive index, no, and the extraordinary refractive index, ne.
medium
n*
air
1.0003
water
1.333
50% sucrose 1.420 in water carbon disulfide
1.628
crystalline quartz
1.544 (no) 1.553 (ne)
diamond
2.417
*measured with 589.3 nm light
Polarization An incoherent light source, such as the hot filament of a light bulb, consists of multiple, randomly oriented light emitters, which produce electromagnetic waves with their electric-field vector oriented in all directions. The resulting light emission is called unpolarized light. Linearly (or plane) polarized light is light in which the electric-field vector is oscillating in only one direction. Linearly polarized light is produced by isolating one orientation of the electric field with a polarizer, or from lasers that contain polarized optical components. Circularly polarized light is light in which the electric field vector is rotating around the axis of light propogation. The electric field vector can rotate in either the right or left direction (as viewed in the direction of light propogation), and the light is called right circularly polarized or left circularly polarized, respectively.
Wave-particle duality Electromagnetic radiation shows both wave and particle characteristics depending on how the radiation is observed. Einstein first postulated that the energy of radiation is quantized and that radiation is composed of energy packets that were later named photons. The energy, E, of one photon depends on its frequency (or wavelength): E=h
= hc /
where h is Planck's constant (6.62618x10-34 Js), of light, and is wavelength.
is the frequency of the radiation, c is the speed
de Broglie equation Moving particles; such as electrons, protons, and neutrons; have wave properties as described by the de Broglie equation: =h/p
where is wavelength, h is Planck's constant, and p is the momentum of the particle. Beams of particles can therefore show wave effects such as interference.
Related topics • •
Electromagnetic Spectrum Introduction to Spectroscopy
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Electromagnetic Spectrum
Visible Spectrum
Electromagnetic Spectrum Type of Radiation gamma-rays x-rays ultraviolet visible near-infrared infrared
Frequency Range (Hz) 20 24 10 -10 1017-1020 1015-1017 4-7.5x1014 1x1014-4x1014 1013-1014
Wavelength Range -12 <10 m 1 nm-1 pm 400 nm-1 nm 750 nm-400 nm 2.5 um-750 nm 25 um-2.5 um
microwaves
3x1011-1013
1 mm-25 um
radio waves
<3x1011
>1 mm
Type of Transition nuclear inner electron outer electron outer electron outer electron molecular vibrations molecular vibrations molecular rotations, electron spin flips* nuclear spin flips*
*energy levels split by a magnetic field
Related topics • •
Electromagnetic radiation Introduction to spectroscopy
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Separations
Introduction A sample that requires analysis is often a mixture of many components in a complex matrix. For samples containing unknown compounds, the components must be separated from each other so that each individual component can be identified by other analytical methods. The separation properties of the components in a mixture are constant under constant conditions, and therefore once determined they can be used to identify and quantify each of the components. Such procedures are typical in chromatographic and electrophoretic analytical separations. A mixture can be separated using the the differences in physical or chemical properties of the individual components. As an example, dumping spaghetti and water in a colander separates the two components because the liquid water can run through the colander but the solid spaghetti cannot (assuming that it is not grossly overcooked as prepared in some university dining halls). Some water will stick to the spaghetti and some spaghetti may go down the drain because the colander is not 100% efficient. An analagous example is the filtering of a solid precipitate to separate it from a solution. These separations are based on the states of matter of the two components, other physical properties that are useful for separations are density and size. Some useful chemical properties by which compounds can be separated are solubility, boiling point, and vapor pressure.
Simple separation procedures • • • • •
Centrifugation Crystallization Distillation Extraction Filtering
Instrumental separation procedures • •
Chromatography Electrophoresis
<
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Extraction Introduction Extractions use two immiscible phases to separate a solute from one phase into the other. The distribution of a solute between two phases is an equilibrium condition described by partition theory. Boiling tea leaves in water extracts the tannins, theobromine, and caffeine (the good
stuff) out of the leaves and into the water. More typical lab extractions are of organic compounds out of an aqueous phase and into an organic phase. Illustration of an extraction in a separatory funnel
Analytical Extractions Elemental analysis generally requires fairly simple (not necessarily easy) sample preparation. Solids are usually dissolved or digested in caustic solution and liquids are sometimes extracted to separate the analyte from interferences. Organic analysis is often much more complicated. Real-world samples can be very complicated matrices that require careful extraction procedures to obtain the analyte(s) in a form that can be analyzed.
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Data Analysis Introduction Since analytical chemistry is the science of making quantitative measurements, understanding the difference between accuracy and precision is vital. Also, it is important that raw data is manipulated and reported correctly to give a realistic estimate of the uncertainty in a result. Presentation of data in the form of graphs is extremely useful. Simple data manipulations may only require keeping track of significant figures. More complicated calculations require propagation-of-error methods. The uncertainity in a result can be categorized into random error and systematic error. See the statistical formula document for more quantitative descriptions of describing and testing data sets.
See the statistics of sampling document for information about uncertainty involved in sampling.
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General Steps in a Chemical Analysis
Introduction The analytical process often begins with a question that is not phrased in terms of a chemical analysis. The question could be "Does lead in petrol enter our food supply?" or "Is this water safe to drink?" or "Does emission testing of automobiles reduce air pollution?" A scientist translates such questions into the need for particular measurements. An analytical chemist then must choose or invent a procedure to carry out those measurements, When the analysis is complete, the analyst must translate the results into terms that can be understood by others preferably by the general public. A most important feature of any results is its limitations. What is the statistical uncertainty in reported results? If you took samples in a different manner, would you obtain the same results? Is a tiny amount (a trace) of analyte found in a sample really there or is it contamination? Once all interested parties understand the results and their limitations, then they can draw conclusions and reach decisions.
The Process Formulating the question Selecting analytical procedures Sampling Sample preparation
Analysis
1. 2.
3. 4. 5.
6. 7.
Reporting and interpretation
8.
Drawing conclusions
9.
Translate general questions into specific questions amenable to being answered through chemical measurements. Search the chemical literature to find appropriate procedures or, if necessary, develop original procedures to make the required measurements. Obtain a representative bulk sample from the lot. Extract from the bulk sample a homogeneous laboratory sample. Convert the laboratory sample into a form suitable for analysis, which usually means dissolving the sample. Samples with a low concentration of analyte may need to be concentrated prior to analysis. Remove or mask species that interfere with the chemical analysis. Measure the concentration of analyte in several aliquots. The purpose of replicate measurements (repeated measurements) is to assess the variability (uncertainty) in the analysis and to guard against a gross error in the analysis of a single aliquot. The uncertainty of a measurement is as important as the measurement itself, because it tells us how reliable a measurement is. If necessary, use different analytical methods on similar samples to make sure that each method gives the same result and that the choice of analytical method is not biasing the result. You may also wish to construct and analyse several different bulk samples to see what variations arise from your sampling procedure. Deliver a clearly written, complete report of your results, highlighting any special limitations that you attach to them. Your report might be written to be read only by a specialist (such as your instructor), or it might be written for a general audience (such as your mother). Be sure the report is appropriate for its intended audience. Once a report is written, the analyst might or might not be further involved in what is done with the information, such as modifying the raw material supply for a factory or creating new laws to regulate food additives. The more clearly a report is written, the less likely it is to be misinterpreted by those who use it. The analyst should at least have the responsibility to ensure that conclusions drawn from his or her data are consistent with the data.
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Introduction to Chemical Equilibrium Introduction A chemical specie will always exist in equilibrium with other forms of itself. The other forms may exist in undetectable amounts but they are always present. These other forms arise due to the natural disorder of nature that we call entropy (it's impossible to be perfect). As an example, pure water consists of the molecular compound and dissociated ions that exist together in equilibrium: H2O(l) H+(aq) + OH-(aq) The (l) subscript refers to the liquid state, and the (aq) subscript refers to ions in aqueous solution.
Equilibrium Constant The equilibrium between reactants and products is described by an equilibrium constant. For the balanced reaction: aA + bB cC + dD The equilibrium constant, Keq is defined as: Keq
[C]c [D]d = --------[A]a [B]b
where the [] brackets indicate the concentration of the chemical species. For the example of water, H2O
H+ + OH-, the equilibrium constant is:
[H+] [OH-] Keq = ---------[H2O]
The concentration of water in a water solution is constant and this expression simplifies to: Kw = (55.56 M)*Keq = [H+] [OH-] where Kw is called the dissociation constant of water and equals 1.00x10-14 at room temperature. The concentrations of [H+] and [OH-] therefore equal 1.00x10-7 M.
Rules for Writing K Expressions
1. Products are always in the numerator. 2. Reactants are always in the denominator. 3. Express gas concentrations as partial pressure, P, and dissolved species in molar concentration, [].
4. The partial pressures or concentrations are raised to the power of the stoichiometric coefficient for the balanced reaction. 5. Leave out pure solids or liquids and any solvent. Example: Zn (s) + 2 H+(aq)
Zn2+(aq) + H2 (g)
PH2 [Zn2+] K = ----------[H+]2
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Gravimetry Introduction Gravimetry is the quantitative measurement of an analyte by weighing a pure, solid form of the analyte. Since gravimetric analysis is an absolute measurement, it is the principal method for analyzing and preparing primary standards. A typical experimental procedure to determine an unknown concentration of an analyte in solution is as follows: • • • • •
quantitatively precipitate the analyte from solution collect the precipitate by filtering and wash it to remove impurities dry the solid in an oven to remove solvent weigh the solid on an analytical balance calculate the analyte concentration in the original solution based on the weight of the precipitate
Examples of Gravimetric Lab Procedures
Gravimetric Determination of Iron 1. Determine constant weight of the crucibles 2. Oxidation of iron sample 3. Precipitation of iron hydroxide 4. Ignition of iron hydroxide to iron oxide 5. Determine constant weight of the crucibles plus iron oxide 6. Calculation of iron in the sample
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Titration Introduction Titration is the quantitative measurement of an analyte in solution by completely reacting it with a reagent. The point at which all of the analyte is consumed is called the endpoint and is determined by some type of indicator that is also present in the solution. For acid-base titrations, indicators are available that change color when the pH changes. When all of the analyte is neutralized, further addition of the titrant causes the pH of the solution to change causing the color of the indicator to change. The analyte concentration is calculated from the reaction stoichiometry and the amount of reagent that was required to react with all of the analyte.
Instrumentation Manual titration is done with a burette, which is a long graduated tube to hold the titrant. The amount of titrant used in the titration is found by reading the volume of titrant in the burette before beginning the titration and when the endpoint is reached, and taking the difference. The most important factor for making accurate titrations is to read the burette volumes reproducibly. The figure shows how to do so by using the bottom of the meniscus to read the reagent volume in the burette. For repetitive titrations, autotitrators with microprocessors are available that deliver the titrant, stop at the endpoint, and calculate the concentration of the analyte. The endpoint is usually
detected by some type of electrochemical measurement. Some examples of titrations for which autotitrators are available include: • • •
Acid or base determination by pH measurement with potentiometric detection. Determination of water by Karl Fischer reagent (I2 and SO2 in methyl alcohol and pyridine) with coulometric detection. Determination of Cl in aqueous solution with phenylarsene oxide using amperometric detection.
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Electrochemistry Introduction Electrochemistry can be broadly defined as the study of charge-transfer phenomena. As such, the field of electrochemistry includes a wide range of different chemical and physical phenomena. These areas include (but are not limited to): battery chemistry, photosynthesis, ion-selective electrodes, coulometry, and many biochemical processes. Although wide ranging, electrochemistry has found many practical applications in analytical measurements.
Electroanalytical chemistry A good working definition of the field of electroanalytical chemistry would be that it is the field of electrochemistry that utilizes the relationship between chemical phenomena which involve charge transfer (e.g. redox reactions, ion separation, etc.) and the electrical properties that accompany these phenomena for some analytical determination. This relationship is further broken down into fields based on the type of measurement that is made. Potentiometry involves the measurement of potential for quantitative analysis, and electrolytic electrochemical phenomena involve the application of a potential or current to drive a chemical phenomenon, resulting in some measurable signal which may be used in an analytical determination.
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Potentiometry Introduction Potentiometry is the field of electroanalytical chemistry in which potential is measured under the conditions of no current flow. The measured potential may then be used to determine the analytical quantity of interest, generally the concentration of some component of the analyte solution. The potential that develops in the electrochemical cell is the result of the free energy change that would occur if the chemical phenomena were to proceed until the equilibrium condition has been satisfied.
This concept is typically introduced in quantitative analysis courses in relation to electrochemical cells that contain an anode and a cathode. For these electrochemical cells, the potential difference between the cathode electrode potential and the anode electrode potential is the potential of the electrochemical cell.
If the reaction is conducted under standard state conditions, this equation allows the calculation of the standard cell potential. When the reaction conditions are not standard state, however, one must utilize the Nernst equation to determine the cell potential.
Physical phenomena which do not involve explicit redox reactions, but whose initial conditions have a non-zero free energy, also will generate a potential. An example of this would be ion concentration gradients across a semi-permeable membrane. This can also be a potentiometric phenomena, and is the basis of measurements that use ion-selective electrodes.
Instrumentation See the documents on ion-selective electrodes and pH meters.
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Coulometry Introduction Coulometry is an analytical method for measuring an unknown concentration of an analyte in solution by completely converting the analyte from one oxidation state to another. Coulometry is an absolute measurement similar to gravimetry or titration and requires no chemical standards or calibration. It is therefore valuable for making absolute concentration determinations of standards. Coumetry uses a constant current source to deliver a measured amount of charge. One mole of electrons is equal to 96,485 coulombs of charge, and is called a faraday. Schematic of a coulometric cell
Coulometric Titration Due to concentration polarization it is very difficult to completely oxidize or reduce a chemical species at an electrode. Coulometry is therefore usually done with an intermediate reagent that quantitatively reacts with the analyte. The intermediate reagent is electrochemically generated from an excess of a precursor so that concentration polarization does not occur. An example is
the electrochemical oxidation of I- (the precursor) to I2 (the intermediate reagent). I2 can then be used to chemically oxidize organic species such as ascorbic acid. The point at which all of the analyte has been converted to the new oxidation state is called the endpoint and is determined by some type of indicator that is also present in the solution. For the coulometric titration of ascorbic acid, starch is used as the indicator. At the endpoint, I2 remains in solution and binds with the starch to form a dark purple complex. The analyte concentration is calculated from the reaction stoichiometry and the amount of charge that was required to produce enough reagent to react with all of the analyte.
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Spectroscopy Absorption | Emission | Scattering
Introduction Spectroscopy is the use of the absorption, emission, or scattering of electromagnetic radiation by atoms or molecules (or atomic or molecular ions) to qualitatively or quantitatively study the atoms or molecules, or to study physical processes. The interaction of radiation with matter can cause redirection of the radiation and/or transitions between the energy levels of the atoms or molecules. A transition from a lower level to a higher level with transfer of energy from the radiation field to the atom or molecule is called absorption. A transition from a higher level to a lower level is called emission if energy is transfered to the radiation field, or nonradiative decay if no radiation is emitted. Redirection of light due to its interaction with matter is called scattering, and may or may not occur with transfer of energy, i.e., the scattered radiation has a slightly different or the same wavelength.
Absorption When atoms or molecules absorb light, the incoming energy excites a quantized structure to a higher energy level. The type of excitation depends on the wavelength of the light. Electrons are promoted to higher orbitals by ultraviolet or visible light, vibrations are excited by infrared light, and rotations are excited by microwaves. An absorption spectrum is the absorption of light as a function of wavelength. The spectrum of an atom or molecule depends on its energy level structure, and absorption spectra are useful for identifying of compounds. Measuring the concentration of an absorbing species in a sample is accomplished by applying the Beer-Lambert Law.
Emission Atoms or molecules that are excited to high energy levels can decay to lower levels by emitting radiation (emission or luminescence). For atoms excited by a high-temperature energy source this light emission is commonly called atomic or optical emission (see atomic-emission spectroscopy), and for atoms excited with light it is called atomic fluorescence (see atomicfluorescence spectroscopy) or molecular fluorescence (see molecular fluorescence spectroscopy). For molecules it is called fluorescence if the transition is between states of the same spin and phosphorescence if the transition occurs between states of different spin. The emission intensity of an emitting substance is linearly proportional to analyte concentration at low concentrations, and is useful for quantitating emitting species.
Scattering When electromagnetic radiation passes through matter, most of the radiation continues in its original direction but a small fraction is scattered in other directions. Light that is scattered at the same wavelength as the incoming light is called Rayleigh scattering. Light that is scattered in transparent solids due to vibrations (phonons) is called Brillouin scattering. Brillouin scattering is typically shifted by 0.1 to 1 cm-1 from the incident light. Light that is scattered due to vibrations in molecules or optical phonons in solids is called Raman scattering. Raman scattered light is shifted by as much as 4000 cm-1 from the incident light.
Related topics Optics Descriptions of the optical components in spectroscopic instrumentation. Interaction of light with matter A qualitative quantum mechanical description. Spectroscopic techniques The spectroscopy section of the Contents.
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Electromagnetic Radiation Introduction Electromagnetic radiation is a transverse energy wave that is composed of an oscillating electric field component, E, and an oscillating magnetic field component, M. The electric and magnetic fields are orthogonal to each other, and they are orthogonal to the direction of propogation of the wave. A wave is described by the wavelength, , which is the physical length of one complete oscillation, and the frequency, , which is the number of oscillations per second. The figure shows one wavelength of a wave of light. The names we give electromagnetic radiation for different wavelength and frequency ranges are listed in the electromagnetic spectrum document.
Schematic of an electromagnetic wave
Velocity of light Electromagnetic waves travel through a vacuum at a constant velocity of 2.99792x108 m/s, which is known as the speed of light, c. The relationship between the speed of light, wavelength, and frequency is: c= When light passes through other media, the velocity of light decreases. For a given frequency of light, the wavelength also must decrease. This decrease in velocity is quantitated by the refractive index, n, which is the ratio of c to the velocity of light in another medium, v: n=c/v
Since the velocity of light is lower in other media than in a vacuum, n is always a number greater than one. The table lists the refractive index of several examples. Refractive index is an intrinsic physical property of a substance, and can be used to monitor purity or the concentration of a solute in a solution. The refractive index of a material is measured with a refractometer, and is usually made versus air. If the precision warrants, the measurements can be corrected for vacuum. Note that the difference between nair and nvacuum is only significant in the fourth decimal place. For anisotropic materials, such as quartz crystals, light of different polarizations (see below) will experience different refractive indices. These indices are called the ordinary refractive index, no, and the extraordinary refractive index, ne.
medium
n*
air
1.0003
water
1.333
50% sucrose 1.420 in water carbon disulfide
1.628
crystalline quartz
1.544 (no) 1.553 (ne)
diamond
2.417
*measured with 589.3 nm light
Polarization An incoherent light source, such as the hot filament of a light bulb, consists of multiple, randomly oriented light emitters, which produce electromagnetic waves with their electric-field vector oriented in all directions. The resulting light emission is called unpolarized light. Linearly (or plane) polarized light is light in which the electric-field vector is oscillating in only one direction. Linearly polarized light is produced by isolating one orientation of the electric field with a polarizer, or from lasers that contain polarized optical components. Circularly polarized light is light in which the electric field vector is rotating around the axis of light propogation. The electric field vector can rotate in either the right or left direction (as viewed in the direction of light propogation), and the light is called right circularly polarized or left circularly polarized, respectively.
Wave-particle duality Electromagnetic radiation shows both wave and particle characteristics depending on how the radiation is observed. Einstein first postulated that the energy of radiation is quantized and that radiation is composed of energy packets that were later named photons. The energy, E, of one photon depends on its frequency (or wavelength): E=h
= hc /
where h is Planck's constant (6.62618x10-34 Js), of light, and is wavelength.
is the frequency of the radiation, c is the speed
de Broglie equation Moving particles; such as electrons, protons, and neutrons; have wave properties as described by the de Broglie equation: =h/p
where is wavelength, h is Planck's constant, and p is the momentum of the particle. Beams of particles can therefore show wave effects such as interference.
Related topics • •
Electromagnetic Spectrum Introduction to Spectroscopy
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Electromagnetic Spectrum
Visible Spectrum
Electromagnetic Spectrum Type of Radiation gamma-rays x-rays ultraviolet visible near-infrared infrared
Frequency Range (Hz) 20 24 10 -10 1017-1020 1015-1017 4-7.5x1014 1x1014-4x1014 1013-1014
Wavelength Range -12 <10 m 1 nm-1 pm 400 nm-1 nm 750 nm-400 nm 2.5 um-750 nm 25 um-2.5 um
microwaves
3x1011-1013
1 mm-25 um
radio waves
<3x1011
>1 mm
Type of Transition nuclear inner electron outer electron outer electron outer electron molecular vibrations molecular vibrations molecular rotations, electron spin flips* nuclear spin flips*
*energy levels split by a magnetic field
Related topics • •
Electromagnetic radiation Introduction to spectroscopy
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Separations
Introduction A sample that requires analysis is often a mixture of many components in a complex matrix. For samples containing unknown compounds, the components must be separated from each other so that each individual component can be identified by other analytical methods. The separation properties of the components in a mixture are constant under constant conditions, and therefore once determined they can be used to identify and quantify each of the components. Such procedures are typical in chromatographic and electrophoretic analytical separations. A mixture can be separated using the the differences in physical or chemical properties of the individual components. As an example, dumping spaghetti and water in a colander separates the two components because the liquid water can run through the colander but the solid spaghetti cannot (assuming that it is not grossly overcooked as prepared in some university dining halls). Some water will stick to the spaghetti and some spaghetti may go down the drain because the colander is not 100% efficient. An analagous example is the filtering of a solid precipitate to separate it from a solution. These separations are based on the states of matter of the two components, other physical properties that are useful for separations are density and size. Some useful chemical properties by which compounds can be separated are solubility, boiling point, and vapor pressure.
Simple separation procedures • • • • •
Centrifugation Crystallization Distillation Extraction Filtering
Instrumental separation procedures • •
Chromatography Electrophoresis
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Extraction Introduction Extractions use two immiscible phases to separate a solute from one phase into the other. The distribution of a solute between two phases is an equilibrium condition described by partition theory. Boiling tea leaves in water extracts the tannins, theobromine, and caffeine (the good
stuff) out of the leaves and into the water. More typical lab extractions are of organic compounds out of an aqueous phase and into an organic phase. Illustration of an extraction in a separatory funnel
Analytical Extractions Elemental analysis generally requires fairly simple (not necessarily easy) sample preparation. Solids are usually dissolved or digested in caustic solution and liquids are sometimes extracted to separate the analyte from interferences. Organic analysis is often much more complicated. Real-world samples can be very complicated matrices that require careful extraction procedures to obtain the analyte(s) in a form that can be analyzed.
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Data Analysis Introduction Since analytical chemistry is the science of making quantitative measurements, understanding the difference between accuracy and precision is vital. Also, it is important that raw data is manipulated and reported correctly to give a realistic estimate of the uncertainty in a result. Presentation of data in the form of graphs is extremely useful. Simple data manipulations may only require keeping track of significant figures. More complicated calculations require propagation-of-error methods. The uncertainity in a result can be categorized into random error and systematic error. See the statistical formula document for more quantitative descriptions of describing and testing data sets.
See the statistics of sampling document for information about uncertainty involved in sampling.
