Definitions based on molalities

When the concentration of a multicomponent system is expressed in terms of the molalities of the solutes, the expression for the chemical potential of the individual solutes and for the solvent are somewhat different. For dilute solutions the molality of a solute is approximately proportional to its mole fraction. (The molality, m, is the number of moles of solute per kilogram of solvent. When two or more substances, pure or mixed, may be considered as solvents, a choice of solvent must be clearly stated.) In conformity with Equation (8.68), we then express the chemical potential of a solute in a solution at a given temperature and pressure as 

These two equations are useful only to change from one reference state to another. As described in Section 8.8 for mole fractions, the compositions of the standard states of the fcth solute for the chemical potential and for the entropy can only be determined by the solution of such equations as 

The chemical potential of the solvent is a function of the molalities of all the solutes at each temperature and pressure, and, for the present, is written as 

When the infinitely dilute solution with respect to all solutes is chosen as the reference state for the solvent, the first two terms on the right-hand side of Equation (8.102) become zero at the reference state and 

the standard state of the solvent is the pure solvent and is identical to the reference state for the solvent in all of its thermodynamic properties. 

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