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Binary Liquid-Vapor Phase Diagrams

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Chem 374-005

Group #6


Performed: 11/17/96, 11/24/96

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This experiment attempted to determine the relationship between vapor pressure and composition of solutions of cyclohexanone and tetrachloroethane at various concentrations. This was achieved through distillation and analysis of (condensed) vapor and liquid vapor samples by measuring their indices of refraction. This mixture has a strong negative deviation from Raoult's law, resulting in a maximum boiling point and an azeotrope.

Introduction & Theory

Raoult's law states that, in an ideal mixture, the partial pressure of a component is proportional to its molar percentage-where an ideal mixture is a mixture that obeys Raoult's law throughout its ranges of composition(1). While some mixtures do obey Raoult's law (especially those similar in nature), many do not. Mixtures that have temperatures where the vapor pressure of a component is higher than that predicted by Raoult's law are said to show a positive deviation, while mixtures with components with lower vapor pressures are said to show negative deviations. Often, these deviations are large enough to cause maxima or minima in vapor-pressure and boiling-point curves.

At a maximum or minimum, the plot of the temperature or pressure of L, the liquid phase, and V, the vapor phase become tangent. The mixtures defined by these tangent points are called azeotropes. As a result, azeotropes are mixtures that cannot be separated by simple distillation, as the liquid and vapor phases are of the same composition.


The procedure from Experiments in Physical Chemistry(2) pages 212-214 was followed, with the only change of procedure being an interruption of the experiment after step 6, and the experiment being restarted at step 7 one week later.

Ambient temperature for steps 1-6 was 26C, and 23C for steps 7-10. Ambient pressure was 738 mm Hg for steps 1-6 and 746 mm Hg for steps 7-10 (corrected for temperature).


Table 1 - Raw Data

Sample #

Vapor Phase


Starting Temperature (C) Ending Temperature (C) Index of Refraction (nD20) Temperature (C) Index of Refraction (nD20)
1 144.5 144.5 1.4938 144.5 1.4944
2 149.0 149.5 1.489 149.5 1.4835
3 151.0 151.0 1.488 151.5 1.4826
4 154.0 154.0 1.4835 154.0 1.4795
5 157.0 157.2 1.4749 157.5 1.4736
6 157.0 157.0 1.4694 157.0 1.4693
7 153.5 153.5 1.450 153.5 1.450
8 154.0 155.0 1.4563 155.0 1.4598
9 155.5 156.0 1.4575 156.0 1.4675
10 157.0 157.0 1.4635 157.0 1.4615

In order to improve the accuracy of the temperature readings, a stem temperature correction should be applied to all of the temperature data. Using the following formula:

the fact that the entire thermometer was not at the measured temperature may be accounted for(3). tstem is the difference between the temperature measured and ambient temperature, and Lstem is the amount of the mercury thread not at the measured temperature (expressed in degrees). Unfortunately, no notation was made of exactly how far the thermometer was pushed into the apparatus, so it will be assumed that it was pushed in to the 100C mark. As a result, Lstem will be the measured temperature minus 100C. Also, tstem would be the ambient temperature minus the measured temperature. The correction for the liquid phase of sample 1 therefore would be

making the actual temperature 145.3C.

After applying stem corrections to all of the temperature readings, the starting and ending temperature readings for the vapor phase must be averaged, giving the actual temperature at which the vapor was condensed and collected. The next step is to use the refractive indices to find the weight percent of cyclohexanone in each sample, and finally determine the molar percentage.

Table 2 - Logarithm of refractive index for cyclohexanone-tetrachloroethane mixtures(4)
Log nD20 W% C6H10O Log nD20 W% C6H10O Log nD20 W% C6H10O
0.17441 0 0.16864 40 0.16360 80
0.17298 10 0.16719 50 0.16256 90
0.17155 20 0.16582 60 0.16158 100
0.17010 30 0.16473 70

By interpolation from table 2, the weight percentage of cyclohexanone can be determined for each sample. For example, the vapor from sample 1 has a refractive index of 1.4938. The logarithm of this number is 0.17429. This is between the numbers for 0% and 10%. By subtracting the lower logarithm of refraction number and dividing by the difference between the two numbers, a percentage is obtained, in this case 72.1%. This percentage is then multiplied by the difference in weight percentages and the result is subtracted from the higher weight percentage. This final result is the extrapolated weight percentage. For some of the data points, the results are out of the range of the table. Extrapolation is not necessary for these points however, as they are known pure solutions and can be set to 0% or 100% exactly.

These weight percentages can be converted to molar percentages with the following formula:

The molecular weight of cyclohexanone is 98.1448 gram mole-1 and tetrachloroethane has a molecular weight of 165.8328 grams mole-1. So the vapor sample 1, with its weight percent of 0.839161% has a molar percentage of 0.498347%. The following table then summarizes the molar percentages for each sample.

Table 3 - Calculated Results


Vapor Phase Liquid Phase
Temperature (C) Molar % Cyclohexanone Temperature (C) Molar % Cyclohexanone
1 145.3 0.489% 144.5 0.000%
2 150.2 6.576% 149.5 14.175%
3 152.0 7.899% 151.5 15.496%
4 155.1 14.157% 154.0 20.179%
5 158.3 27.600% 157.5 29.822%
6 158.2 37.521% 157.0 37.726%
7 154.6 100.000% 153.5 100%
8 155.6 74.786% 155.0 62.619%
9 156.9 70.187% 156.0 41.436%
10 158.2 51.211% 157.0 57.257%

The graph of this data (see appendix) clearly shows an azeotrope at about 45% cyclohexanone, boiling at about 156C at about 742 mm Hg (averaged).


The fact that three of the samples had indices of refraction outside of the range of the given table is a clear indication of error. As values were found that were both too high and too low, a simple calibration problem with the refractometer does not explain this. The refractometer was checked against a known value of 1.5133 and measured 1.5124; giving an error of only 0.059%. Impure starting materials, dirty glassware, or other contamination are the most likely causes for this; of course improper reading of the instrument could cause the errors as well.

Another cause of error is the way the data was handled. The data in the table did not show a relationship between composition and index of refraction that was exactly linear. In this case, interpolation was probably more accurate than linear regression, as linear regression forces the entire data series to a straight line, where interpolation is based only on the two closest points.

The sharp drop in boiling point when the composition was near 45% cyclohexanone is a fairly clear indication of an azeotrope. Unfortunately, only two data points support the decrease, making it impossible to ascertain that the drop was not merely experimental error or to determine exactly the shape of the curve.


1. P. Atkins, Physical Chemistry, 5th ed., p. 217, W. H. Freeman and Company (1994).

2. D. P. Shoemaker, C. W. Garland, J. W. Nibler, Experiments in Physical Chemistry, 6th ed., chap. 8, experiment 14, The McGraw-Hill Companies (1996).