Real solutions reference and standard states

Equation (8.71) relates two undefined quantities, Apk x and p p[T, P], in one equation. The first quantity is a function of the temperature, pressure, and (C — 1) mole fractions, but the zero of the function is not defined, and the second is a function of the temperature and pressure, but the state of 

The nomenclature and symbols used by Lewis and Randall [24] are closely related to those introduced here. The activity coefficient, yk, is related to Apk by 

the reference state of a component is the state of the system for which the activity coefficient of the component is defined to be unity and the standard state is the state of the system for which the activity of the component is unity or defined to be unity. 

In this discussion the temperature and pressure of the reference state and of the standard state have been taken to be those of the solution this usage is consistent with the recommendations of the Commission on Symbols, Terminology, and Units of the Division of Physical Chemistry of the International Union of Pure and Applied Chemistry. For the standard state however, a fixed, arbitrary pressure (presumably 1 bar) might be chosen. If we define 

Similar arguments and definitions can be applied to the other partial molar thermodynamic functions and properties of the components in solution. By differentiation of Equation (8.71), the following expressions for the partial molar entropy, enthalpy, volume, and heat capacity of the kth component are obtained  

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