Definitions based on molarities

The definitions based on molarities, c, are very similar to those based on molalities, and again the solvent must be considered separately from the solutes. (The molarity is defined as the number of moles per liter of solution, and is dependent on the pressure and temperature.) Molarities, like the molalities, are used primarily for solutions for which the concentration ranges are limited. For dilute solutions the molarities of the solutes are approximately proportional to their mole fractions. We thus express the chemical potential of the fcth solute in solution at a given temperature and pressure as 

The first two of these equations are useful, in addition to showing that the standard state of the kth solute for the chemical potential and the entropy are determined, only in converting from one reference state to another. If it is ever necessary, the composition of the standard state for the chemical potential and the entropy would have to be determined by solution of equations such as  

For the solvent, we must again make use of the Gibbs-Duhem equation to find a suitable function of the molarities of the solutes. We set 

Integration of Equation (8.114) after substitution of Equation (8.115) cannot be performed easily, because p is a function of the concentrations of the solutes and is generally different for each system. However, for dilute solutions lOOOp is large with respect to f=2 cMi and P approximates pu the density of the pure solvent. If these approximations are made, then 

The difference between the integral of Equation (8.114) and that of Equation 

---