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

The thermodynamic model based on the distributions of molecular popula tions among energy levels has been employed for the analysis of the so lubility of noble gases in water at different temperatures. The solubi lity 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)/parti al derivative(1/T)}(theta)(1/T - 1/theta)(3) + (1/24){partial derivati ve(2)(Delta C(p,app)/R)/partial derivative(1/T)(2)}(theta)(1/T - 1/th eta)(4). The apparent thermodynamic quantities of this expression are obtained from the coefficients of the polynomial fitting the experimen tal data. The whole system is considered as the convoluted ensemble (g cc)e formed by a grand canonical ensemble, gee, and a canonical ensem ble, ce, the latter corresponding to the solvent. The statistical dist ribution is described by a convoluted partition function, (GCC)PF, wh ich is the product of a grand canonical partition function, GCPF, and a canonical partition function, CPF. The apparent thermodynamic functi ons 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 r eaction between gas and water, -Delta H-0, and the heat absorbed by th e water molecules involved in the reaction Delta H-w = n(w)C(p,w)T. Th e enthalpy term Delta H-w, which varies linearly with the temperature, has been calculated by using the relationship of thermal equivalent d ilution valid for the canonical ensemble, ce. By plotting the apparent enthalpy {-Delta H-app}(T) versus T, the value n(w) can be obtained f rom the slope of the line. Sets of data from different sources have be en analyzed and yield congruent values of -Delta H-0 and n(w). The val ues n(w) ranging from 1.5 for helium to 3.3 for xenon clearly depend o n the size of the atoms of the noble gas and can be related to the for mation of a cavity of water molecules in the solvent.