Working in the molal scale

The general Kirkwood—Buff expressions in the molal scale are very straightforward, although they can become lengthy if the number of components in solution is large. Because these equations contain cofactors of determinants of matrices, we will review their use shortly. Given a matrix A [see Eq. (26.8)] and its determinant \A\, the cofactor of \A \ with respect to element Aik is indicated by the symbol \A\ik and can be calculated as the derivative of the determinant \A \ with respect to element A^. The following example is for two dimensions

(A" A12 ^ \a\ — jl\a\- — U21 A2J |A|12 " A ~ dar

The overall correlation between components i and k (the Kirkwood—Buff integral Gik) can then be calculated by (Kirkwood and Buff, 1951)

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