I really shouldn’t be blogging right now. I should be doing my on-line coursework for Exploring Mars, but I’m mentally exhausted and just need to give my brain a break. So, I’m just gonna dump all my thermodynamics stuff here. I’ve spent the last couple hours staring at a white board in the meteorite lab trying to figure out this problem from geochemistry:
Calculate deltar G for reaction  at a temperature of 25 oC and a pressure of 5 Kb (~5000 atm) assuming pure carbonate phases, and that deltar V = constant with pressure. The molar volumes of aragonite and calcite are Voarag = 34.150 cm3/mol and Vocalcite = 36.934 cm3/mol. 1 cm3 = 0.0239 cal/bar. At T = 25 oC and P = 5 Kb, in which direction will reaction  /proceed, and which carbonate is more stable?
Reaction 1 refers to CaCO3 (aragonite) to CaCO3 (calcite)
We calculated the Gibbs free energy equation in order to determine which direction the reaction would proceed and which mineral would be stable at standard temperature and pressure. In this case, aragonite doesn’t do so hot at 1 bar of pressure and 298 K and actually converts to calcite in about 10,000,000 years.
The question I’d been working on asked us to look at the same reaction, but at 5,000 bars of pressure instead of 1 bar. For those unfamiliar with measurements of pressure, 1 bar is basically the amount of pressure we feel at sea level. So, we had to determine in which direction the reaction would occur and which mineral was stable at 5,000 bars of pressure. That simple change in pressure resulted in this:
It’s not easy to see here, but there are actually two different sets of calculations: the massive one that takes up the entire board and that small, simple boxed one in the upper right corner. For those that haven’t ran away screaming yet, the right answer is in the latter equation. At 5,000 bars of pressure calcite becomes aragonite because it’s more stable at higher pressures. And then I realized something- the answer was in the question. Aragonite takes up less volume per mole than calcite. Aragonite has the same structure as calcite, but takes up less space. And that’s because its only stable at pressures that essentially “squish” its structure. At one bar of pressure, aragonite essentially relaxes- very slowly- and takes up a little more room and becomes calcite.
Once I saw this I had a an “a-ha” and “duh” moment all at the same time. Had I remembered that little fact about aragonite taking up less space I would have had some idea what the correct answer was. Granted, I still needed to do the work, but I would have realized that I needed a positive Gibbs value in order for the reaction to occur from the left to the right. *long exasperated sigh*
/end brain dump.