# At constant temperature, can the solid phase be more stable than the gas if pressure decreases?

In a phase diagram, the triple point is the point at which the three phases can coexist. If we consider, for example, CO2

If we go below the triple point by decreasing pressure and keeping temperature constant, we get to the gas phase.

My question is: Is there any substance for which, from the triple point, if the pressure is decreased by keeping the temperature constant, the solid phase is reached instead of the gaseous one?

As shown in the sketch below:

• In order for that to happen, the solid phase would need to have a larger volume (lower density) than the gas phase (and of course the liquid phase as well). While there are of course cases where the solid is less dense than the liquid (water), I can't think of a single case where the solid is less dense than the gas. Oct 5, 2021 at 3:56
• Oct 5, 2021 at 9:21

That's not really possible. To see why simply express the Gibbs' free energy for each of the phases of the homogeneous substance in differential form:

$$dG = Vdp - SdT$$

We assume constant composition.

We can identify the volume $$V$$ as the partial derivative of the free energy with respect to pressure at constant temperature:

$$V = \left( \frac {\partial G}{\partial p}\right)_T$$

Since volumes are always positive quantities, the general response of a pure substance at constant temperature to a decrease in pressure is a decrease in free energy ($$(dG)_T = Vdp$$). The only way we can have a solid with a lower free energy than the corresponding gas as we lower pressure is therefore if there is a discontinuity (break from monotonous behavior) marked by a sudden increase in the free energy at the transition point from solid to gas. But since $$V$$ is, by definition, greater in a gas than in a condensed phase such as a solid, the free energy change at the transition point from gas to solid is $$(d \Delta G)_T = \Delta Vdp >0$$ if we decrease the pressure ($$dp<0$$), so that the solid is identified as the less stable phase.

It may be difficult or impossible with a pure substance, but a solid may precipitate from a supercritical fluid when the pressure is decreased and the fluid becomes an ordinary gas.

For instance, in principle a solution of sodium chloride in water could be heated and compressed unto the supercritical range of the water. Under supercritical pressure the water would remain dense enough to solvate the ions of the salt, which therefore remains dissolved; but if the solution is decompressed and the water becomes steam, the sodium chloride loses its solubility.

• There are many ways to change the solubility, changing the ratio of solvent, evaporating the solvent, or adding common ions to name a few. What I was thinking was if there is a process where the total entropy will increase when the same substance goes from liquid/gas to solid. This may seem like a contradiction, but it is not. In the process you mention a solid is produced and the entropy of the universe increases as a net result. But... is it possible to decompress a liquid/gas and turn it into a solid? I think not, since there will be nothing else to increase the entropy. Jan 15, 2022 at 7:18