Chemical reactions are central to many petrologic processes. Knowing what the possible chemical reactions are among a group of minerals can help us interpret rock textures and history. The minerals visible in a rock are commonly the best candidates for reactants and products. If the chemical compositions of those minerals are known, we can identify and balance possible chemical reactions among them. However, this can be a time-consuming project to do by hand if there are many minerals. Fortunately, if you are reading this online, you have a powerful computer at your disposal that can "do the math" quickly to idenitfy and balance chemical reactions.
There is a straightforward procedure that can be used to balance a chemical reaction if there are more minerals (phases) than there are chemical components. The procedure is based on a linear algebra method called Gaussian Elimination. To see the logic behind the method, we will walk through the steps for an example case.
Consider the five phases quartz (Qz), sillimanite (Sil), muscovite (Ms), water (Water), and microcline (Mc). The compositions of these phases can be expressed in terms of the four oxide components SiO2, Al2O3, K2O, and H2O. The relationships among phases and components can be written as equations:
| Phase | = | Components |
| Qz (SiO2) | = | 1 SiO2 |
| Sil (Al2SiO5) | = | 1 SiO2 + 1 Al2O3 |
| Ms (Al3Si3O12H2) | = | 3 SiO2 + 1.5 Al2O3 + 0.5 K2O + 1 H2O |
| Water (H2O) | = | 1 H2O |
| Mc (KAlSi3O8) | = | 3 SiO2 + 0.5 Al2O3 + 0.5 K2O |
Like all chemical equations, we can confirm their validity by checking that the number of atoms of any element on the left side of the equation equals the number of atoms of that element on the right side of the equation, as required by the law of consevation of mass. To undertake the Gaussian Elimination these equations are collected in a table or matrix like this:
| Phase | SiO2 | Al2O3 | K2O | H2O |
| Qz (SiO2) | 1 | 0 | 0 | 0 |
| Sil (Al2SiO5) | 1 | 1 | 0 | 0 |
| Ms (Al3Si3O12H2) | 3 | 1.5 | 0.5 | 1 |
| Water (H2O) | 0 | 0 | 0 | 1 |
| Mc (KAlSi3O8) | 3 | 0.5 | 0.5 | 0 |
On the next page, this table and some familiar properties of algebraic equations will be used to identify a chemical reaction among these phases.
