= Solution
An activity model is required in addition to the two compositions. Use \b[<ideal multisite mineral activity>]: independent ideal Fe–Mg mixing on the three relevant sites per formula unit gives
$$
a_{\mathrm{phlogopite}}=(0.80)^3=0.512,\qquad
a_{\mathrm{pyrope}}=(0.20)^3=0.008.
$$
The <garnet>/<biotite> activity ratio is $0.008/0.512=1/64$. All other solids are pure, so the dimensionless <reaction quotient> is
$$
Q=\frac{a_{\mathrm{pyrope}}}{a_{\mathrm{phlogopite}}}\frac{f_{\mathrm{H_2O}}}{P^\circ}
=\frac{6000}{64}=93.75.
$$
With the same pressure-corrected numerator as in part b,
$$
\boxed{T=\frac{127442.28}{170.7-8.3145\ln93.75}=958.60\ \mathrm K=685.45^\circ\mathrm C.}
$$
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.
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