Colligative properties of solutions: I. Fixed concentrations

TL;DR

This paper uses rigorous statistical mechanics to model phase separation and freezing-point depression in solutions with fixed solute concentrations, providing a theoretical foundation that aligns with heuristic formulas.

Contribution

It introduces an Ising-based model for solvent-solute systems, characterizing phase separation boundaries in fixed solute ensembles and validating heuristic formulas.

Findings

Phase separation occurs within specific chemical potential intervals.

Boundaries of phase separation match heuristic formulas asymptotically.

Model provides a rigorous theoretical framework for freezing-point depression.

Abstract

Using the formalism of rigorous statistical mechanics, we study the phenomena of phase separation and freezing-point depression upon freezing of solutions. Specifically, we devise an Ising-based model of a solvent-solute system and show that, in the ensemble with a fixed amount of solute, a macroscopic phase separation occurs in an interval of values of the chemical potential of the solvent. The boundaries of the phase separation domain in the phase diagram are characterized and shown to asymptotically agree with the formulas used in heuristic analyses of freezing point depression. The limit of infinitesimal concentrations is described in a subsequent paper.