Appling Calculus to Calculate the Temperature of Mineral Formation in Magma

by Jesse Scholpp

Submitted : Spring 2017

The Gibbs free energy equation is base equation which can be used to calculate a compounds chemical state and whether it is stable. The Gibbs equation also can be used to make diagrams for different chemical compounds and how they react under a variety of temperatures and pressures. In this project I used the Gibbs equation in an attempt to make a phase diagram for the mineral Olivine, which has a chemical composition of Mg₂SiO₄. In doing so I derived equations for each of the important variables and found the stability of the mineral at standard temperature and pressure (25˚C and 1 atm) and I found the point at which the mineral will form under these conditions. During this process I found that there are some problems with using this equation to make phase diagrams for geologist, partly due to the fact that in geology condition are almost never at standard temperature and pressure. Although these diagrams can still be used to help understand processes which we can test in nature.

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