Question 13.7: Calculating the Composition of Vapor in Equilibrium with a L...
Calculating the Composition of Vapor in Equilibrium with a Liquid Solution
What is the composition of the vapor in equilibrium with the benzene toluene solution of Example 13-6?
Analyze
We are being asked to find the mole fraction of benzene and of toluene in the vapor. From Example 13-6 we know the vapor pressure of pure benzene and pure toluene. We have already calculated the partial vapor pressures; now we need to apply the definition of mole fraction.
The ratio of each partial pressure to the total pressure is the mole fraction of that component in the vapor. (This is another application of equation 6.17.) The mole-fraction composition of the vapor is
\frac{n_{ A }}{n_{\text {tot }}} = \frac{P_{ A }}{P_{\text {tot }}} = \frac{V_{ A }}{V_{\text {tot }}} = x_{ A } (6.17)
x_{\text {benz }} = \frac{P_{\text {benz }}}{P_{\text {total }}} = \frac{47.6 mmHg }{61.8 mmHg } = 0.770
x_{\text {tol }} = \frac{P_{\text {tol }}}{P_{\text {total }}} = \frac{14.2 mmHg }{61.8 mmHg } = 0.230
Assess
The mole fraction of benzene in the vapor is 0.770, whereas in the liquid the mole fraction of benzene is 0.5. For toluene the mole fraction in the vapor is 0.230, whereas in the liquid the mole fraction of toluene is 0.5. This difference in mole-fraction vapor composition caused by the difference in vapor pressures of the two components is the central concept of fractional distillation, which is discussed next.