4. It is necessary to determine the vapor-liquid equilibrium composition for designing a separation process for a binary mixture of perfluoro-n-heptane and n-heptane at 25 ℃ At this temperature, the vapor pressure of pure perfluoro-n-heptane is 0.1101 bar, and the vapor pressure of pure n-heptane is 0.0601 bar.
(b) (10%) Please derive the expressions of the activity coefficient for both components in a binary mixture, assuming the solution obeys the regular solution theory. The excess Gibbs energy equation of the regular solution theory is as following:
, where δi is solubility parameter of component i and Φi is volume fraction of component i: