SOLUBILITY OF INERT-GASES AND LIQUID HYDROCARBONS IN WATER

The thermodynamic statistical model based on the distribution of molec ular populations among energy levels has been employed for the analysi s of the solubility of hydrocarbons and other inert gases or liquids i n water at different temperatures. The statistical distribution is des cribed by a convoluted partition function Z(G) .zeta(s). The product o f a grand canonical partition function Z(G) represents the distributio n of the species in the reaction while the canonical partition functio n zeta(s) represents the properties of the solvent. The first derivati ve of the logarithm of the partition function with respect to 1/T is t he apparent enthalpy which is the result of the contributions of the s eparate partition functions, {Delta H-app}(T) = Delta H-o + n(w)C(p,w) T, where {Delta H-app}(T) refers to Z(G), n(w)C(p,w)T = -Delta H-w to zeta(s), and Delta H-o is the change in enthalpy of hydrocarbon-water reaction. The plot {Delta H-app}(T) vs. T results in a straight line w ith slope n(w) at constant C-p,C-w. The apparent enthalpy is obtained from w the coefficients of the polynomial fitting of the solubility da ta, as a function of 1/T. Alternatively, the apparent enthalpy call be determined calorimetrically. The enthalpy thus obtained is a linear f unction of the Kelvin temperature. The values of n(w) range from 1.6, 1.9, 5.6 to 5.8 for helium, hydorgen, butane and hexane, respectively. For fluorocompounds the range of n(w) is 10.1 to 11.1 indicating that n(w) is a function of the number of water molecules expelled from the cage of solvent to form a cavity to host the solute molecule. The ana lysis of several sets of calorimetric or solubility data with the pres ent molecular thermodynamic model yields values of Delta H-o and n(w) consistent with the size of the dissolved molecules.