Excess functions and deviation from ideality

Most real solutions cannot be described in the ideal solution approximation and it is convenient to describe the behaviour of real systems in terms of deviations from the ideal behaviour. Molar excess functions are defined as 

The excess molar Gibbs energy of mixing is thus 

The activity coefficient of component i, y(-, is now defined as a measure of the deviation from the ideal solution behaviour as the ratio between the chemical activity and the mole fraction of i in a solution. 

The partial molar Gibbs energy of mixing of a component i in a non-ideal mixture can in general be expressed in terms of activity coefficients as 

Using eq. (3.34) the excess Gibbs energy of mixing is given in terms of the mole fractions and the activity coefficients as 

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