Past exam of the year 2 of the earth sciences (geology) course of the University of Oxford / 2023 / Paper 1 / 7 / c / Solution

Under ideal independent mixing on crystallographic sites, a mineral endmember's thermodynamic activity is the product of its required site fractions, one factor per mixed site. Muscovite has one K and three Al per formula unit, sanidine has one K and one Al, and corundum has two Al. Interpreting the given Al fractions as the fractions on every relevant Al/Fe site givesThus $A_s=a_{\mathrm{san}}{a}_{\mathrm{cor}}/a_{\mathrm{mus}}=0.6237816764$. The cubic power for muscovite includes its tetrahedral Al site and two octahedral Al sites; if site-specific fractions differed, bulk Al/(Al+Fe) alone would not determine this activity. The calculation uses the uniform-site ideal-mixing interpretation intended by the given data.

At $P=5000\mathrm{bar}$ with ideal water, solvegiving $T_{\mathrm{eq}}=979.40\mathrm{K}=706.25{}^{\circ }\mathrm{C}$. Using the bulk mole fraction only once for a multisite mineral endmember would omit part of its ideal mixing chemical potential.