An analytical solution, COSMOSPACE, to the statistical thermodynamics of a model of pairwise interacting surfaces, is presented. This solution was initially developed for the a priori prediction model COSMO-RS in an implicit form. A comparison of COSMOSPACE with UNIQUAC and with the quasi-chemical theory of Guggenheim reveals the conditions under which the models yield similar results and when they differ very considerably. It is shown that COSMOSPACE is in extremely good agreement with Monte-Carlo simulations for some lattice fluids (where UNIQUAC is particularly poor). The ability of COSMOSPACE to provide good fits to experimental data is shown for three binary mixtures including ethanol-cyclohexane, where UNIQUAC incorrectly predicts a liquid-liquid phase separation.