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A mica mineral with an idealized endmember composition $\mathrm{KA}{\mathrm{l}}_3\mathrm{S}{\mathrm{i}}_3{\mathrm{O}}_{10}(\mathrm{OH}{)}_2$. Its formula contains one tetrahedral Al and two octahedral Al per formula unit. Under ideal independent mixing on crystallographic sites, an endmember thermodynamic activity includes all mixed sites rather than only a bulk mole fraction.

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.

Adopt ideal independent mixing on crystallographic sites, with Mg and Fe sharing three positions per formula unit and the other endmember sites fixed. This gives the phlogopite and pyrope activitiesThe reaction quotient contains their ratio, since pyrope is a product and phlogopite a reactant. ConsequentlyThe site-mixing assumption is part of this numerical answer: compositions alone do not determine nonideal thermodynamic activities. More detailed activity coefficients or unequal site occupancies would need an additional model. The cube counts the three magnesium-bearing positions rather than three molecules of each mineral.

The compositions alone do not specify a unique thermodynamic activity model. Adopt the usual ideal, independent mixing on crystallographic sites approximation: three Mg–Fe positions per formula unit, with the other sites fixed at their stated endmember compositions. Then the mineral endmember activities areThe exponent counts the three mixing cations; treating each whole mineral formula as a single mixing site would be a different model. In particular, the magnesian biotite and garnet components here are phlogopite and pyrope.

For the written reaction, the reaction quotient iswith the other solid activities equal to one. The Gibbs energy of reaction balance therefore givesThe smaller product-endmember activity lowers the reaction chemical potential and lowers the equilibrium temperature in this model. Nonideal activity coefficients or unequal occupancies of crystallographic sites would require further information rather than a revised universal numerical answer.^[ref]