Statistical thermodynamic formulations based on the Bethe-Guggenheim (BG) quasi-chemical and the Bragg-Williams (BW) random-mixing approximations are applied for comparison to the retention and thermodynamic behavior of monomeric solute molecules distributed between a binary solvent mobile phase and a stationary phase consisting of a monolayer of solvent molecules sorbed on a chemically homogeneous planar support surface. For structureless monomeric solute (3) and two types of solvent molecules (1, 2), the capacity factors and the enthalpies and entropies of solute transfer between chromatographic phases are determined in both BG and BW approaches as functions of the mobile-phase composition, phi(1m), of the more favorable solvent, the corresponding solvent adsorption isotherm,a energies beta Delta W-12, beta Delta W13, and beta Delta W-23 (beta=(k(B)T)(-1)). As the difference beta(Delta W-13 - Delta W-23) increases the comparative predictions of the BG and BW approximations become more disparate for the same phi(1m) and the same set of interchange energies. For example, when -0.75 < beta Delta W-12 less than or equal to 0 and beta(Delta(13) - Delta W-23)/2 greater than or equal to 2 and the more favorable solvent for the solute is preferentially sorbed on the stationary phase surface, then the composition dependence of the enthalpies Delta H-BG and Delta H-BW and entropies Delta S-BG and Delta S-BW of solute transfer calculated in the BG and BW approximations, respectively, exhibit quite different behaviors. Specifically the composition variation (monotonic decrease) of Delta H-BG is predicted to be much smaller than that of Delta H-BW over most of the composition range (1 greater than or equal to phi(1m) > 0.1). Also Delta S-BG increases and exhibits a composition maximum, while Delta S-BW always decreases and then passes through a minimum over the same composition range (1 greater than or equal to phi(1m) > 0.1). The BG prediction of preferential solvation of the solute by the better solvent in excess of that obtained from random mixing in each chromatographic phase is physically responsible for the difference in thermodynamic behavior generated from the two models. The predictions of the present analysis are also compared with experimental measurements of the composition dependence of the enthalpies and entropies of solute transfer performed for nonpolar alkylbenzene and polycyclic aromatic hydrocarbon solutes in acetonitrile/water and methanol/water mixed mobile phases using reversed-phase liquid chromatography. Only the predicted dependences of Delta H-BG and Delta S-BG on phi(1m) achieve qualitative agreement with the corresponding experimental measurements obtained using acetonitrile/water mobile phases.