How Does Pressure Influence the Stability of Calcium Carbonate Phases?

[Sebastian]

Homework Statement

Calcium carbonate ($\mathrm{CaCO_3}$) has two common crystal forms: Calcite and Aragonite. In room temperature and atmospheric pressure, the Calcite has Gibbs energy -1128.8 kJ/mol, volume 36.93 cm^3/mol and entropy 92.9 J/K/mol, and the Aragonite has Gibbs energy -1127.8 kJ/mol, volume 34.14 cm^3/mol and entropy 88.7 J/K/mol. Under these conditions, which is the stable phase, and under what pressure in room temperature will the second phase be more stable?

Homework Equations

We study with "Thermal Physics" by Kittel.

The Attempt at a Solution

I don't even know how to start. Any help will be appreciated. Thanks!

 

[Mike Pemulis]

"Which is the stable phase?"

This one can be answered with no arithmetic. You just need to know how the Gibbs energy is related to stability. Look this up if you don't know. And remember it -- this relation is basically why we use Gibbs energy at all!

"Under what pressure in room temperature will the second phase be more stable?"

The idea here is that if you change the pressure, the Gibbs energy will change, and so the phase that was not stable before is now stable. You need to find the pressure at which the switch occurs (or in other words, the pressure at which the two Gibbs energies become equal to each other). To answer this question, look up the mathematical definition of Gibbs energy, plug in what you know, and do the algebra. You should assume that changing the pressure on a solid does not (appreciably) change the entropy or the internal energy.