Question

In a binary solution, specify ln (γ_B) as a function of XB.

If known:

ln (γ_A) = M (X_A)²

Answer 1

The Margules activity model is a simple thermodynamic model for the excess Gibbs free energy of a liquid mixture. It introduced the concept of the activity coefficient, the model could be used to derive an expression for the activity coefficients of a compound i in a liquid, a measure for the deviation from ideal solubility, also known as Raoult's law.

The activity coefficient of component i is found by differentiation of the excess Gibbs energy towards x_i. This yields, when applied only to the first term and using the Gibbs–Duhem equation.

In here A₁₂ and A₂₁ are constants which are equal to the logarithm of the limiting activity coefficients: and respectively.

When , which implies molecules of same molecular size but different polarity, the equations reduce to the one-parameter Margules activity model:

Accordingly, in the given problem,

ln (_A) = M (X_A²)

and therefore,

ln (_B) = M (X_B²)