Liquid-vapor equilibria at constant temperature

The condition of equilibrium, in addition to the equality of the temperature and pressure of the two phases, demands that the chemical potential of a component in each phase in which it exists must be the same. The problem is to obtain expressions for the chemical potential of a component in terms of quantities that are experimentally observable. 

The particular equations developed depend upon the experimental methods that are used and on the particular reference states that are chosen. The methods are the same for either component when both components are volatile and, consequently, we consider only one component and use the subscript 1 to indicate this component. 

The values of the excess chemical potential obtained by the use of Equation (10.32) after substitution of Equation (10.33) refer to the liquid phase in equilibrium with a vapor phase. In contrast, the values obtained by the use of Equation (10.35) refer to the liquid phase alone at the temperature T and the pressure P0. The concept of an equilibrium between the liquid phase and a gas phase has been removed by Equation (10.34). 

The dynamic method of studying vapor-liquid equilibria requires the use of an inert gas that is passed over the liquid phase under conditions that equilibrium is attained. Under such conditions the total pressure is controlled and can be made the same in each experiment. The system is actually a three-component system in which the solubility of the inert gas in the liquid phase is extremely small and its effect is neglected. The chemical potential of the first component in the gas phase in equilibrium with the solution is 

1 We note that it is the quantity A/t = RT In + A/t that is obtained on elimination of the standard states. This point was simply accepted in Chapter 8. 

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