# A van der Waals Model of Solvation Thermodynamics

## TL;DR

This paper uses the van der Waals model to explain how solvation affects thermodynamic properties like energy and entropy when a solute is added to a liquid.

## Contribution

The paper introduces a new analytical framework for solvation thermodynamics using the van der Waals model.

## Key findings

- Solvation Gibbs free energy change has two components: cavity formation cost and attraction gain.
- Solvation entropy change includes a loss from cavity formation and a gain from structural reorganization.
- The model's predictions align qualitatively with experimental results.

## Abstract

Exploiting the van der Waals model of liquids, it is possible to derive analytical formulas for the thermodynamic functions governing solvation, the transfer of a solute molecule from a fixed position in the ideal gas phase to a fixed position in the liquid phase. The solvation Gibbs free energy change consists of two contributions: (a) the high number density of all liquids and the repulsive interactions due to the basic fact that each molecule has its own body leading to the need to spend free energy to produce an appropriate cavity to contain the solute molecule; (b) the ubiquitous intermolecular attractive interactions lead to a gain in free energy for switching-on attractions between the solute molecule and neighboring liquid molecules. Also the solvation entropy change consists of two contributions: (a) there is an entropy loss in all liquids because the cavity presence limits the space accessible to liquid molecules during their continuous translations; (b) there is an entropy gain in all liquids, at room temperature, due to the liquid structural reorganization as a response to the perturbation represented by solute addition. The latter entropy contribution is balanced by a corresponding enthalpy term. The scenario that emerged from the van der Waals model is in qualitative agreement with experimental results.