Limiting behaviour at high dilution

Consider a solution of a single strong electrolyte whose molality is m. From equations (10 53) and (10 54) it is evident that the Debye limiting law can be written in the form 

As m approaches zero the right-hand side of this equation approaches minus infinity. Therefore if the logarithm of the activity coefficient is plotted against the molality (rather than against its root) the gradient becomes infinitely steep as the molality approaches zero. In this respect electrolytes differ sharply in their behaviour from non-electrolytes, and this is due to the long-range forces between the ions. 

Although the slope becomes infinite, the activity coefficient itself approaches imity. For this reason the result of equation (10 85) is in no way contrary to the fact that the behaviour of the solvent approaches Raoult s law a limit. Tliis may be shown in more detail by using the Gibbs-Duhem equation as developed in 10 16. 

In place of equation (10 82), the change in the chemical potential of the solvent may be expressed in terms of the change of its partial pressure 

In the extremely dilute solution where the Debye limiting law may be applied, the term on the lefb-hcmd side of this relation is given by equation (10 86). Mctking this substitution we obtain 

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