Standard vapor equilibria, ideal solutions

In 10.1 we present the basic thermodynamic relations that are used to start phase-equilibrium calculations we discuss vapor-liquid, liquid-liquid, and liquid-solid calculations. We have seen that the most interesting phase behavior occurs in nonideal solutions, but when we describe nonidealities using an ideal solution as a basis, we must select an appropriate standard state. Common options for standard states are discussed in 10.2 they include pure-component standard states and dilute-solution standard states. 

In this treatment all of the components are treated in the same way, with no substance designated as the solvent. The standard state for each component is the pure substance at pressure P° and at the temperature of the solution, just as with an ideal solution. As before, we obtain working formulas for volatile substances by assuming that the solution is at equilibrium with an ideal gas mixture. The chemical potential of substance i in the solution is equal to its chemical potential in the vapor phase. If we write the chemical potential in the solution in terms of the activity as in Eq. (6.3-6),... 

This illustrates the statement made earlier that the most convenient choice of standard state may depend on the problem. For gas-phase problems involving A, it is convenient to choose the standard state for A as an ideal gas at 1 atm pressure. But, where the vapor of A is in equilibrium with a solution, it is sometimes convenient to choose the standard state as the pure liquid. Since /a is the same for the pure liquid and the vapor in equilibrium... 

The isopiestic (isothermal distillation) method for the determination of molecular weights is closely related to the vapor pressure depression method.10 A weighed amount of standard is introduced into one leg of an apparatus and a weighed portion of the unknown is placed in the other leg. Solvent is introduced into the apparatus, which is then evacuated and thermostated. The solvent will distill from one solution to the other until the vapor pressures (and therefore mole fractions) of the two have equalized. If the solutions are ideal, or if the deviations from ideality are similar, equilibrium will occur when the mole fraction of the known equals that of the unknown. 

When liquid and gas phases are both present in an equilibrium mixture of reacting species, Eq. (11.30), a criterion of vapor/liquid equilibrium, must be satisfied along with the equation of chemical-reaction equilibrium. There is considerable choice in the method of treatment of such cases. For example, consider a reaction of gas A and water B to form an aqueous solution C. The reaction may be assumed to occur entirely in the gas phase with simultaneous transfer of material between phases to maintain phase equilibrium. In this case, the equilibrium constant is evaluated from AG° data based on standard states for the species as gases, i.e., the ideal-gas states at 1 bar and the reaction temperature. On the other hand, the reaction may be assumed to occur in the liquid phase, in which case AG° is based on standard states for the species as liquids. Alternatively, the reaction may be written... 

In any equilibrium state, both fi, and /t are absolute, finite quantities with a fixed difference between them. If the same standard state is chosen for each of these equations, then fi, — ji° is the same in each equation, and the activity would be the same in all phases at equilibrium. This would be nice, but it would mean using a vapor pressure as the standard state for activity in solids, or an ideal one molal solution standard state for activities in a gas, or perhaps an ideal gas at one bar for an aqueous solute. This would be not only inconvenient, but impossible in many cases. So we accept the small inconvenience of having different activities for the same species in different phases. 

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