# Concentration Scales and Solvation Thermodynamics: Some Theoretical and Experimental Observations Regarding Spontaneity and the Partition Ratio

## TL;DR

This paper compares different concentration scales in solvation thermodynamics using experiments and theory to understand how they affect solvation energy and partition ratios.

## Contribution

The study experimentally validates the solvation thermodynamics formalism using diethylamine in a water/hexadecane system.

## Key findings

- The solvation Gibbs energy and partition ratio of diethylamine align with the ST formalism.
- Experimental data supports the ST formalism over the Fowler–Guggenheim approach.
- Choice of concentration scale remains arbitrary in classical thermodynamics.

## Abstract

The solvation thermodynamics (ST) formalism proposed by A. Ben-Naim is a mathematically rigorous and physically grounded theory for describing properties related to solvation. It considers the solvation process as the transfer of a molecule (“solute”) from a fixed position in the ideal gas phase to a fixed position within the solution. Thus, it removes any contribution to the solvation process that is not related to the interactions between this molecule and its environment in the solution. Because ST is based on statistical thermodynamics, the natural variable is number density, which leads to the amount (or “molar”) concentration scale. However, this choice of concentration scale is not unique in classical thermodynamics and the solvation properties can be different for commonly used concentration scales. We proposed and performed experiments with diethylamine in a water/hexadecane heterogeneous mixture to confront the predictions of the ST, based on the amount (or “molar”) concentration scale, and the Fowler–Guggenheim formalism, based on the mole fraction scale. By means of simple acid–base titration and 1H NMR measurements, it was established that the predictions of differences in the solvation Gibbs energy and the partition ratio (or “partition coefficient”) of diethylamine between water and hexadecane are consistent with the ST formalism. Additionally, with current literature data, we have shown additional experimental support for the ST. However, due to the arbitrariness of the relative amount of solvents in the partition ratio, the choice of a single concentration scale within the classical thermodynamics is still not possible.