Expt-1-postlab.docx

Camino, Carmelli Fiel M.

3ChE-D

Group No. 5

Date Performed: April 13, 2017 Date Submitted: April 27, 2018

PARTIAL MOLAR VOLUME AND REFRACIVE INDEX OF SOLUTIONS Experiment No. 1

INTRODUCTION Due to intermolecular interactions, the total volume measured when two real liquids (e.g. ethanol and water) are mixed deviates from the total volume calculated from the individual volumes of the two liquids (volume contraction). To describe this non-ideal behaviour in the mixing phase, one defines partial molar quantities which are dependent on the composition of the system [1]. The partial molar volumes of the components of a mixture vary with the composition of the mixture, because the environment of the molecules in the mixture changes with the composition [2]. Part of this experiment is the determination of the relationship of partial molar volumes to its concentration in a binary mixture because partial molar (or molal) quantities relate changes in extensive properties of the solution (such as V, G, H, S and A) to changes in concentration [3].

For a two component system of A and B, the partial molar volumes are defined as 𝜕𝑉

𝑉𝐴 = (

)

(1)

)

(2)

𝜕𝑛𝐴 𝑛 𝐵

and

𝑉𝐵 = (

𝜕𝑉

𝜕𝑛𝐵 𝑛 𝐴

The total differential statement for volume changes in a two component mixture is therefore

𝑑𝑉 = 𝑉𝐴 𝑑𝑛𝐴 + 𝑉𝐵 𝑑𝑛𝐵

(3)

Integration of equation (3) gives the Euler relation

𝑉 = 𝑛𝐴 𝑉𝐴 + 𝑛𝐵 𝑉𝐵

(4)

indicating that partial molar quantities are indeed additive [3].

Refractometers measure the degree to which the light changes direction, called the angle of refraction. A refractometer takes the refraction angles and correlates them to refractive index (nD) values that have been established [4]. Refractive Index (Index of Refraction) is a value calculated from the ratio of the speed of light in a vacuum to that in a second medium of greater density [5]. The refractive index of methanol and toluene solution of different concentrations will also be determined in this experiment and their relationship with its mole fraction as a binary mixture. By measuring the index of refraction of a mixture of a known composition, one may estimate its molar volume. Partial molar volumes of the components may be calculated from the molar volume as a function of composition using standard methods [6].

METHODOLOGY The refractometer was cleansed by placing drops of acetone on them and gently wiping it with cotton. To rinse the refractometer, few drops of water are placed on them and then wiped with cotton. The refractive index of pure methanol and pure toluene was measured using the refractometer. The pycnometer was filled with water, then the outside surface of the pycnometer was dried and then it was weighed. For more accurate measurements, the pycnometer was calibrated thrice and then the average of its mass multiplied to the density of water (1g/mL) to obtain its volume. Ten(10) percent methanol solution was prepared and then its refractive index was measured. The empty pycnometer was constantly weighed before the solution is placed and then

the density of the solution was determined. Twenty(20) percent methanol solution was prepared from the ten(10) percent solution and the same procedure was done. The volume percentages of the solutions from 10% - 50% methanol and toluene was prepared in 10% increments serially.

SET UP OF THE EXPERIMENT

Calibration of the pycnometer.

Preparation of the solution.

Reading of the refractive index.

Weighing the pycnometer containing the solution.

Weighing of the empty pycnometer.

RESULTS AND DISCUSSION The mass of the solution is calculated by subtracting the mass of the empty pycnometer by the mass of the pycnometer containing the solution. Using the volume of the pycnometer which is 9.9779mL, the densities of solutions 10%-90% methanol is calculated as shown below: 𝑚𝑎𝑠𝑠 𝑣𝑜𝑙𝑢𝑚𝑒 8.5151𝑔 𝜌= 9.9779𝑐𝑚3 g 𝜌 = 0.8534 3 cm 𝜌=

while the densities of 100% toluene solution and 100% methanol was retrieved from textbooks.

Table 1 (see Appendix) shows that the decreasing density also decreases the refractive index. The index of refraction value of a material is a number that indicates the number of times slower that a light wave would be in that material than it is in a vacuum. The density of a material relates to the sluggish tendency of the atoms of a material to maintain the absorbed energy of an electromagnetic wave in the form of vibrating electrons before reemitting it as a new electromagnetic disturbance [7]. The denser the material is, the slower that a wave will move through the material, therefore, the index of refraction value increases.

Table 2 (see Appendix) shows the partial molar volumes of each methanol solutions. Using the average molecular weight and the density calculated from the previous table, the PMV was computed as shown below: 𝑃𝑀𝑉𝑚𝑒 =

𝑃𝑀𝑉𝑚𝑒

𝑃𝑀𝑉𝑚𝑒

𝑀𝑊𝑎𝑣𝑒 𝜌𝑠𝑜𝑙𝑛

𝑔 𝑚𝑜𝑙 = 𝑔 0.8534 3 𝑐𝑚 77.1198

𝑐𝑚3 = 90.36768767 𝑚𝑜𝑙

As seen in Table 2 (see Appendix) ate higher densities the partial molar volume of the solution increases, this is due to solute-solvent interactions, density augmentation and negative PMV occur. Under the high-density conditions, the distances between solvent molecules or clusters are not enough to incorporate solute molecules, so their penetration into fluid leads to increasing of solution volume (positive PMV) independently of nature of solvent-solute interactions [12]. It can also be observed that even if a small amount toluene was added to the methanol solution, the partial molar volume decreases rapidly. This is because toluene and methanol are both hydrocarbons. Hydrocarbons have very weak intermolecular forces called dispersion forces. Intermolecular forces hold molecules together. Because of their weak intermolecular forces, hydrocarbons are volatile. This means that many of the molecules evaporate at room temperature [13]. Thus, volume and its partial molar volume decreases in an instant. In Figures 1 and 2, the relationship of mole fraction and partial molar volume is illustrated. Figure 1 shows the inverse proportionality of the mole fraction of methanol and the partial molar volume of the solution. Figure 2 shows the direct proportionality of the mole fraction of toluene and the partial molar volume of the solution. This is because toluene has larger compound size than methanol. That’s why as the quantity of toluene increases in the solution, some methanol compounds shrink, thus, its contribution of volume to the solution decreases. Figure 1. Plot of Partial Molar Volume vs. Mole Fraction (Methanol). 120

Partial Molar Volume

100

y = -60.446x + 103.62 R² = 0.9994

80 60 40 20 0 0

0.1

0.2

0.3

0.4

0.5

Mole Fraction of Methanol

0.6

0.7

0.8

Figure 2. Plot of Partial Molar Volume vs. Mole Fraction (Toluene). 120 y = 60.446x + 43.175 R² = 0.9994

Partial Molar Volume

100 80 60 40 20 0 0

0.2

0.4

0.6

0.8

1

1.2

Mole Fraction of Toluene

Table 3 (see Appendix) shows the specific and molecular refractive indices of the solutions. The speficic refractive index was calculated using the electromagnetic theory, Lorenz and Lorentz as shown below: 𝑅𝑠 = [

𝜂2 − 1 1 ]× 2 𝜂 +2 𝜌

1.49992 − 1 1 𝑅𝑠 = [ ] × 𝑔 1.49992 + 2 0.8534 3 𝑐𝑚 𝑅𝑠 = 0.344584

𝑐𝑚3 𝑔

And the molecular refractive index was calculated by multiplying Rs with the average molecular weight as shown below: 𝜂2 − 1 𝑀𝑊𝑎𝑣𝑒 𝑅𝑚 = [ 2 ] 𝜂 +2 𝜌 𝑔 77.11978 1.49992 − 1 𝑚𝑜𝑙 𝑅𝑚 = [ ]× 𝑔 1.49992 + 2 0.8534 3 𝑐𝑚

𝑐𝑚3 𝑅𝑠 = 26.57423 𝑚𝑜𝑙 where ɳ is the refractive index measured from the pycnometer, ρ is the density and MWave is the average molecular weight of the corresponding solution. In Figures 3 and 4 it was shown that the specific and molecular refractivities were both decreasing as the mole fraction of methanol was increasing, thus, the specific and molecular refractivities of solutions are both inversely proportional with mole fraction. A non-linear relationship between the mole fraction and specific and refractive index can be seen.

Figure 3. Plot of Mole Fraction of Methanol vs. Specific Refraction. 0.4

Specific Refraction

0.35 0.3 0.25

y = -0.1112x + 0.3613 R² = 0.8196

0.2 0.15 0.1 0.05 0

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

Mole Fraction of Methanol

Figure 4. Plot of Mole Fraction of Methanol vs. Molecular Refraction.

Molecular Refraction

35 30 25 20 y = -25.105x + 31.59 R² = 0.9922

15 10 5 0 0

0.1

0.2

0.3

0.4

0.5

Mole Fraction of Methanol

0.6

0.7

0.8

ANSWERS TO QUESTIONS 1. What do the refraction graphs (a) and (b) indicate? Give an interpretation of the graphs. What are the practical uses of these graphs?

Graph (a) and (b) indicates that increasing the amount of methanol solution will decrease its volume contribution in the binary mixture. These graphs can be used for phase daigrams which are used to show conditions (pressure, temperature, volume, etc.) at which thermodynamically distinct phases occur and coexist at equilibrium. It can also be used to express how miscible two liquids are to each other. If the graph from the results shows a linear relation then the liquids are miscible, but if the graph from the results is to arched then the liquids are immiscible.

2. What are the practical uses of the refractive index in chemical engineering? Explain your answer.

Refractive index has the large number of applications. It is mostly applied for identify a particular substance, confirm its purity, or measure its concentration. Generally it is used to measure the concentration of a solute in an aqueous solution. For a solution of sugar, the refractive index can be used to determine the sugar content (Brix degree) [8]. Refractive index (RI) provides valuable information about various reservoir engineering calculations, making it a key parameter for characterizing crude oils. Refractive index is an optical parameter of crude oil that provides valuable information about crude oil specific compositions. Refractive index can be used as a suitable property for predicting other crude oil properties including those controlling PVT behavior of hydrocarbon and surface tension [9].

3. Why is it necessary to note the temperature at which the reading of the refractometer is obtained? Explain your answer.

It is important to note the temperature at which the reading is done because every different type of refractometers give an accurate reading at a partivular temperature. For older refracometers, accurate readings occurs only when the temperature is at 68°F (20°C). Both the refractometer and the sample of juice must be at this temperature. When temperatures are above or below optimal, a corrections table is needed to determine actual ºBrix. Readings can be as much as 0.89 ºBrix lower when the temperature is 50°F (10°C) if the temperature of the surroundings and the sample does not correspond to the designated temperature [10].

4. From the results of the mixing volumes, what can you say about the volumes of the pure components added together theoretically and actually?

Mixing the volumes of pure components seems like an ordinary addition; when you add 1mL of pure component A to a 1mL of pure component B, their total volume would result to 2mL of A-B solution. However the increase in volume of a pure component depends on the molecules surrounding it.

5. Why is partial molar volume important?

Partial molar volume is important because it can denote the degree of non-ideality of a system. Due to molecular interactions between the species in the solution, their individual properties are modified to some degree. This implies that substances in a solution cannot have private properties, or ones that remain truly unaffected despite being in the presence of another material [11].

CONCLUSIONS AND RECOMMENDATION As the experiment was conducted, the refractive indices of different compositions of methanol mixture was determined. The specific and molecular refractilities was also calculate from the data obtained.

After the experiment, it can be concluded that the partial molar volume and mole fraction depends on the liquids in a binary mixture. The partial molar volume also depends on the density of the solution and the ionic size of the compound. At higher density conditions, the partial molar volume increases and at lower density conditions, the partial molar volume decreases.

The specific and molecular refractivities are inversely proportional to the mole fraction of methanol and are directly proportional to the mole fraction toluene. It can also be concluded that the denser the material is, the slower that a wave will move through the material, therefore, the index of refraction value increases.

For more accurate results, the temperature at which the reading was obtained should be recorded because every different type of refractometer gives an accurate result at a particular temperature.

APPENDIX Table 1. Density of each solutions and its Indices of Refraction. Mass of pycnometer (v/v)%

contaning the solution

Mass of empty

Mass of

Density of

pycnometer

Solution

the Solution

Index of Refrcation (𝜂)

0

-

-

-

0.867

1.5026

10

27.7208

19.206

8.5148

0.853365939

1.4999

20

27.6789

19.2362

8.4427

0.846139969

1.4751

30

27.5996

19.2362

8.3634

0.838192405

1.4575

40

27.5197

19.2645

8.2552

0.82734844

1.429

50

27.4265

19.2448

8.1817

0.819982161

1.406

60

27.4748

19.2459

8.2289

0.824712615

1.4131

70

27.3739

19.2511

8.1228

0.814079115

1.3412

80

27.2854

19.2428

8.0426

0.806041351

1.372

90

27.1938

19.2428

7.951

0.796861063

1.354

100

-

-

-

0.792

1.3352

Table 2. Partial Molar Volumes of Methanol solutions. (v/v)%

ρ(g/mL)

xme

xt

MWave

PMVme

0

0.867

0

1

90

103.8062284

10

0.8534

0.222073 0.777927 77.11978466 90.36768767

20

0.8461

0.363436 0.636564 68.92070485 81.45692571

30

0.8382

0.461323 0.538677 63.24324324 75.45125655

40

0.8273

0.533118 0.466882 59.07915994 71.41201491

50

0.82

0.588026 0.411974 55.89451176 68.16403873

60

0.8247

0.631378 0.368622 53.38010204 64.72669097

70

0.8141

0.666474 0.333526 51.34448932 63.06902018

80

0.806

0.695469 0.304531 49.66280295 61.61638083

90

0.7969

0.719825 0.280175 48.25012118 60.54727216

100

0.792

0.740575 0.259425 47.04667864 59.40237201

Table 3. Specific Refractivity (Rs) and Molecular Refractivity (Rm) computed from the data. ɳ

(v/v)%

ρ(g/mL)

Xme

Mwave

Rs

Rm

0

1.5026

0.867

0

90

0.340729

30.66559

10

1.4999

0.8534

0.222073

77.11978

0.344584

26.57423

20

1.4751

0.8461

0.363436

68.9207

0.332816

22.9379

30

1.4575

0.8382

0.461323

63.24324

0.325227

20.56839

40

1.429

0.8273

0.533118

59.07916

0.311617

18.41007

50

1.406

0.82

0.588026

55.89451

0.299551

16.74323

60

1.4131

0.8247

0.631378

53.3801

0.302424

16.14343

70

1.3412

0.8141

0.666474

51.34449

0.258298

13.26219

80

1.372

0.806

0.695469

49.6628

0.281984

14.0041

90

1.354

0.7969

0.719825

48.25012

0.272792

13.16224

100

1.3352

0.792

0.740575

47.04668

0.261273

12.29202

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[10] Vasquez, S., & Mueller, S. (2018). Refractometer Calibration, Use and Maintenance. Retrieved from http://www.iv.ucdavis.edu/files/24488.pdf [11] Gies, T. (2018). The ScienceDirect accessibility journey: A case study. Learned Publishing, 31(1), 69-76. doi: 10.1002/leap.1142 [12] (2018). Retrieved from https://www.researchgate.net/post/How_can_we_explain_the_negative_partial_molar_volu me [13] Hydrocarbons: Intermolecular Forces & Safety Issues | Study.com. (2018). Retrieved from https://study.com/academy/lesson/hydrocarbons-intermolecular-forces-safety-issues.html