(a) Consider a two-phase system, where one phase is pure liquid A and the second phase is...

(a) Consider a two-phase system, where one phase is pure liquid A and the second phase is an ideal gas mixture of A vapor with inert gas B (assumed insoluble in liquid A). The presence of gas B changes  the chemical potential of liquid A, because B increases the total pressure on the liquid phase. However, since the vapor is assumed ideal, the presence of B does not affect the chemical potential of A in the vapor phase [see Eq. (6.4)]. Because of its effect on  gas B affects the liquid–vapor equilibrium position, and its presence changes the equilibrium vapor pressure of A. Imagine an isothermal infinitesimal change dP in the total pressure P of the system. Show that this causes a change dPA in the vapor pressure of A given by

 (7.38)

Equation (7.38) is often called the Gibbs equation. Because  is much less than  the presence of gas B at low or moderate pressures has only a small effect on the vapor pressure of A. (b) The vapor pressure of water at 25°C is 23.76 torr. Calculate the vapor pressure of water at 25°C in the presence of 1 atm of inert ideal gas insoluble in water.