Molecular thermodynamic model for the solubility of noble gases in water

The thermodn. model based on the distributions of mol. populations among energy levels was employed for the anal. of the soly. of noble gases in water at different temps. The soly. is expressed in polynomial form. The apparent thermodn. quantities are obtained from the given expression. The whole system is considered as the convoluted ensemble (gc*c)e formed by a grand canonical ensemble, gce, and a canonical ensemble, ce, the latter corresponding to the solvent. The statistical distribution is described by a convoluted partition function, (GC*C)PF, which is the product of a grand canonical partition function, GCPF, and a canonical partition function, CPF. The apparent thermodn. functions can be decompd. into the contributions of the sep. partition functions. In particular, the apparent enthalpy {-ΔHapp}T = -ΔH° - nwCp,wT is the sum of the enthalpy change due to the reaction between gas and water, -ΔH°, and the heat absorbed by the water mols. involved in the reaction ΔHw = NwCp,wT. The enthalpy term ΔHw, which varies linearly with the temp., was calcd. by using the relation of thermal equiv. diln. valid for the canonical ensemble. By plotting the apparent enthalpy{-ΔHapp}T vs. T, the value nw can be obtained from the slope of the line. Sets of data from different sources were analyzed and yield congruent values of -ΔH° and nw. The values nw ranging from 1.5 for helium to 3.3 for xenon clearly depend on the size of the atoms of the noble gas and can be related to the formation of a cavity of water mols. in the solvent.