We present a study of the adsorption of single molecules of volatiles, such as water, ethanol, ethyl acetate, pyridine, toluene, and n-octane, on the dry surface of a smectite clay using a series of calculations based on density functional theory. Our clay model contains both tetrahedral and octahedral substitutions, and sodium as the counterion. After establishing the accuracy of our calculations for predicting the structural features of known clays, we determine the structural features of our model clay and then characterize the changes induced by molecular adsorption and the dependence of binding on the adsorption site. In all cases, binding energies are higher in configurations bound to cations located above rings with tetrahedral substitution than for those above rings with octahedral substitutions. For molecules containing an electronegative atom, binding energies inversely correlate well with their ionization potential. Our results allow an interpretation of the trend of measured vaporization rates at low coverage and reveal that they correlate inversely with the binding energies of the molecules.