Solvation of Inert-Gas Molecules

The simplest nontrivial solvation phenomenon is the case of a hard-sphere (HS) particle in a fluid of HS particles. This case was discussed in connection with the scaled-particle theory in section 5.11. Here we note that the solvation Gibbs energy of an HS solvaton in an HS solvent is always positive, and it increases monotonically as a function of the size of the HS solvaton or, equivalently, the radius of the corresponding cavity (see section 5.11). 

The solvation of an HS solvaton in a real fluid is important in the study of the solvation thermodynamic of any real solvaton. The solvation process of a real particle may be performed in two steps first, the creation of a suitable cavity, then turning on the other parts of the interactions between the solvaton and the (real) solvent. In order to define the size of the cavity we need to assign an effective hard-core diameter to the solvent molecules. For simple spherical molecules, such as the noble gases, a natural choice of the effective diameter might be the van der Waals or Lennard-Jones diameter of the molecules. For more complex molecules there is no universal way of defining an effective HS diameter to be assigned to the solvent molecules. 

In spite of this ambiguous concept of the effective HS diameter, a great amount of work has been carried out using the methods of the SPT to calculate the solvation thermodynamics of an HS in various real fluids, ranging from simple noble gases to water and even to ionic melts. 

Basically, the SPT is used in these cases to compute the cavity work as a first step in the solvation process. The second step consists of turning on the soft part of the interaction between the solvaton and its entire environment. The formal split of the solvation process into these two parts is discussed in section 6.14. 

The simplest real molecules for which the solvation quantities can be measured are the inert gases. Two kinds of experimental data that we can use to evaluate solvation quantities are available for these systems. First are the vapor-liquid densities of the two phases along the coexistence equilibrium line. Second are PVT data on inert-gas liquids. Both are used in the following. Let pf and be the densities of the inert gas s in the gas and liquid phases, respectively. Using our general expression (6.13.1) for the chemical potential we have 

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