Implicit function theorem and Jacobians in solvation and adsorption

The use of Jacobians in chemical thermodynamics has focused chiefly on explicit functions. We generalize this powerful method to incorporate implicit functions. Considering a slight deviation from equilibrium, governed by the Gibbs-Duhem equations, is demonstrated to simplify the theories of preferential solvation and adsorption significantly. Since these deviations are zero at equilibrium, implicit function theorem can be applied by postulating their differentiability. A generalization to multiple component solutions is straightforward by virtue of Jacobians and the implicit function theorem.