MOLECULAR THERMODYNAMIC MODEL FOR THE SOLUBILITY OF NOBLE-GASES IN WATER

The thermodynamic model based on the distributions of molecular populations among energy levels has been employed for the analysis of the solubility of noble gases in water at different temperatures. The solubility is expressed as the polynomial {1n x(2)}(T) = (1n x(2))theta + (-Delta H-app/R)(theta)(1/T - 1/theta) + (1/2)(Delta C*(p,app)/R)(theta)(1/T - 1/theta)(2) + (1/6){partial derivative(Delta C*(p,app)/R)/partial derivative(1/T)}(theta)(1/T - 1/theta)(3) + (1/24){partial derivative(2)(Delta C*(p,app)/R)/partial derivative(1/T)(2)}(theta)(1/T - 1/theta)(4). The apparent thermodynamic quantities of this expression are obtained from the coefficients of the polynomial fitting the experimental data. The whole system is considered as the convoluted ensemble (gc*c)e formed by a grand canonical ensemble, gee, 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 thermodynamic functions can be decomposed into the contributions of the separate partition functions. In particular, the apparent enthalpy {-Delta H-app}(T) = -Delta H-0 - n(w)C(p,w)T is the sum of the enthalpy change due to the reaction between gas and water, -Delta H-0, and the heat absorbed by the water molecules involved in the reaction Delta H-w = n(w)C(p,w)T. The enthalpy term Delta H-w, which varies linearly with the temperature, has been calculated by using the relationship of thermal equivalent dilution valid for the canonical ensemble, ce. By plotting the apparent enthalpy {-Delta H-app}(T) versus T, the value n(w) can be obtained from the slope of the line. Sets of data from different sources have been analyzed and yield congruent values of -Delta H-0 and n(w). The values n(w) 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 molecules in the solvent.