Property Measurement The Osmotic Coefficient

As we saw in Section 17.5, the activity coefficient of a nonelectrolyte solute can be calculated from the activity coefficient of the solvent, which, in turn, can be obtained from the measurement of colligative properties such as vapor pressure lowering, freezing point depression, or osmotic pressure. We used the Gibbs-Duhem equation in the form [Equation (17.33)] 

The activity coefficients of solute and solvent are of comparable magnitudes in dilute solutions of nonelectrolytes, so that Equation (17.33) is a useful relationship. But the activity coefficients of an electrolyte solute differ substantially from unity even in very dilute solutions in which the activity coefficient of the solvent differs from unity by less than 1 x 10 . The data in the first three columns of Table 19.3 illustrate the situation. It can be observed that the calculation of the activity coefficient of solute from the activity coefficient of water would be imprecise at best. 

To deal with this problem, Bjermm [4] suggested that the deviation of solvent behavior from Raoult s law be described by the osmotic coefficient g rather than by the activity coefficient 71. The osmotic coefficient is defined by the relationships 

The greater sensitivity, and hence usefulness, of g over 71, for solutions of electrolytes can be observed from the values in the third and fourth columns of Table 19.3. 

Equating the expressions for pi from Equation (16.1) and Equation (19.42) we obtain 

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