Experimental measurement for the propane-isopentane system, at 167 and 147 psia,

Question

Experimental measurement for the propane-isopentane system, at 167 and 147 psia, show a propane liquid-phase mole fraction of 0.2900 in equilibrium with a vapour-phase mole fraction of 0.6650. Determine the following: a) the K-value for propane and isopentane from the experimental data b) the K-values of propane and isopentane from Raoult's law. Vapour pressures of propane and isopentane at 167 are 409.6 and 58.6 psia, respectively. c) Compare the results of a and b. Assuming the experimental values are correct, how could better estimates of the K-values be achieved? Hit: To compare the experimental data with Raoult's law, determine the relative volatility of propane/isopentane using the experimental data and compare with the relative volatility obtained using Raoult's law.

Explanation / Answer

Let propane --> 1 and isopentane ---> 2

a) K1 = y1/x1 = 0.665 / 0.29 = 2.2931

K2 = y2 / x2 = (1-y1) / (1-x1) = (1-0.665) / (1-0.29) = 0.47183

b) Rault's law is given by

y1P = x1P1sat

.: K1 = y1/x1 = P1sat/P = 409.6 / 147 = 2.7864

K2 = P2sat/P = 58.6/147 = 0.39864

c) Experimental relative volatity = K1/K2 = 2.2931/0.47183 = 4.86

Relative volatity by Raoult's law = K1/K2 = 2.7864/0.39864 = 6.9897

Better estimates can be achieved by considering activity coefficients of the gas phase and fugacity coefficients of the liquid phase.

This can be found by considering Van Laar or Margules model.

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