Solubility of inert gases and liquid hydrocarbons in water

The thermodn. statistical model based on the distribution of mol. populations among energy levels has been employed for the anal. of the soly. of hydrocarbons and other inert gases or liqs. in water at different temps. The statistical distribution is described by a convoluted partition function ZG•ζs. The product of a grand canonical partition function ZG represents the distribution of the species in the reaction while the canonical partition function ζs represents the properties of the solvent. The first deriv. of the logarithm of the partition function with respect to 1/T is the apparent enthalpy which is the result of the contributions of the sep. partition functions, {ΔHapp}T = ΔH0 + nwCp,wT, where {ΔHapp}T refers to ZG, nwCp,wT = -ΔHw to ζs and ΔH0 is the change in enthalpy of hydrocarbon-water reaction. The plot {ΔHapp}T vs. T results in a straight line with slope nw at const. Cp,w. The apparent enthalpy is obtained from the coeffs. of the polynomial fitting of the soly. data, as a function of l/T. Alternatively, the apparent enthalpy can be detd. calorimetrically. The enthalpy thus obtained is a linear function of the Kelvin temp. The values of nw range from 1.6, 1.9, 5.6 to 5.8 for helium, hydrogen, butane and hexane, resp. For fluoro compds. the range of nw is 10.1 to 11.1 indicating that nw is a function of the no. of water mols. expelled from the cage of solvent to form a cavity to host the solute mol. The anal. of several sets of calorimetric or soly. data with the present mol. thermodn. model yields values of ΔH0 and nw consistent with the size of the dissolved mols.