Past exam of the year 2 of the earth sciences (geology) course of the University of Oxford / 2022 / Paper 1 / 7 / c / Solution

An activity model is required in addition to the two compositions. Use ideal multisite mineral activity: independent ideal Fe–Mg mixing on the three relevant sites per formula unit givesThe garnet/biotite activity ratio is $0.008/0.512=1/64$. All other solids are pure, so the dimensionless reaction quotient isWith the same pressure-corrected numerator as in part b,Diluting the magnesian product endmember more strongly than the reactant favors the forward dehydration and lowers its equilibrium temperature. The powers of three count Fe–Mg mixing sites, not three formula units of either mineral. Nonideal site interactions or site partitioning would change these activities. If ideal mixing of whole formula units rather than sites were intended, activities would instead be $0.8$ and $0.2$; composition alone does not select that different model. The calculation explicitly adopts the conventional ideal-site interpretation.