Why does Equilibrium shifts towards more dense phase while increasing pressure for phase change Equilibrium?

Question

I recently read that when pressure of system in phase change equilibrium is increased, it shifts towards denser phase. So, in case of Melting of ice, increase in pressure results in shift towards Liquid side as liq. H2O is more dense and M.P. decreases. But what is mechanism behind this phenomena?

Answer 1

Broadly, Nature tends to proceed to minimize energy (because this maximizes total entropy, as described by the Second Law).

For a system in thermal and mechanical contact with its surroundings, the appropriate energy potential is the Gibbs free energy $G\equiv U-TS+PV$. (The Gibbs free energy of a system is the internal energy $U$ needed to create it, minus the heating $TS$ that one gets for free from the surroundings, plus the work $PV$ needed to push the surroundings out of the way.)

In differential form, the relevant fundamental relation is $$dG=-S\,dT+V\,dP,$$ or $V\,dP$ at constant temperature.

For two different phases in contact, equilibrium corresponds to the Gibbs free energy being balanced in terms of a slight phase change. (Otherwise, some matter would move to the other phase to minimize total $G$.)

(This is equivalent to saying that at the coexistence line of a phase transition, the chemical potentials are equal for the two phases. The chemical potential $\mu\equiv\left(\frac{\partial G}{\partial N}\right)_{T,P}$ is just the partial molar Gibbs free energy; differences in the chemical potential drive shifts of matter.)

Let's say we impose a pressure change on an equilibrium situation between phases at constant temperature. From $dG=V\,dP$ or $d\mu=v\,dP$, the phase with the larger molar volume $v$ experiences essentially the larger energy increase; it becomes energetically unfavorable as a result. This shifts the equilibrium point; a phase change becomes spontaneous toward the denser phase.

This and analogous behavior for other perturbations are summarized by Le Chatelier's principle, which says essentially that Nature relies on negative feedback: If you apply pressure, the denser phase is obtained, more or less yielding to the pressure. The reverse—positive feedback, in which the less dense phase is obtained—would mean that if you push something even slightly, it pushes back even more, accelerating the process and making everything explosively unstable.

Replacing pressure changes with temperature changes, the same argument (now with $G=-S\,dT$) shows that the higher-temperature phase is always the higher-entropy phase. We may be more familiar with phase changes driven by temperature changes than by pressure changes, but the same line of reasoning applies.