The Scatchard-Hildebrand model can be extended to multicomponent mixtures in the following manner. Setting a_ij = (a_iia_jj)½ and a_ii/V_i = V_iδ² Eqn. 12.7 can be rewritten as

Recognizing that the quadratic term is separable and simplifying the square-root of the square:

This result can be made even simpler by adding and subtracting V² and rearranging to obtain:

where we have substituted the definition of in the second term and the definition of V in the third.

Collecting all terms in a common summation, we obtain:

This is a remarkably simple result. Derive an equally simple expression for the activity coefficient of a component in a multicomponent mixture.

Transcribed Image Text:

UE = Συν- ΣΣν.δ. δυ V.δ. 12.64