Using statistical mechanics, the extension of an adsorption isotherm to include an arbitrary number of energetically unique adsorbed monolayers was established previously by Dutcher et al. (J. Phys. Chem. C2011, 115, 16474-16487). The main purpose of that work, although not its only application, was to represent the thermodynamic properties of solutions over very wide ranges of concentration. Here, the model is developed further to obtain expressions for the Gibbs energy, solvent and solute activities, and solute concentrations for mixtures containing arbitrary numbers of solutes. A remarkable result of this study is a novel statistical mechanical derivation of the Zdanovskii-Stokes-Robinson (ZSR) mixing rule, found in the limit of zero solute-solute interactions. The more general mixing rule derived here includes a modification of one of the energy parameters or a number of adsorption sites to represent the effects of solute-solute interactions on solution properties. The effects of this ternary solute-solute mixing term on the relationship between solvent activity and solute concentration are examined.