 Solution

ID: past-exam-of-the-year-2-of-the-earth-sciences-geology-course-of-the-university-of-oxford/2023/paper-1/7/b/solution

f / P_{0}

for water. These are separate contributions: do not also add a gas-volume pressure correction after including

RT ln (f / P_{0})

. For this reaction,

Δ_{r} G = Δ H^{\circ} - T Δ S^{\circ} + Δ V_{solids} (P - P_{0}) + RT ln (\frac{a _{san} a _{cor}}{a _{mus}} \frac{f}{P _{0}}) .

7000 bar

with pure solids and an ideal gas,

f = P

and the solid-activity ratio is one. Therefore

0 = 98157 - 164 T - 0.61 (7000 - 1) + 8.3145 T ln 7000,

and

T_{eq} = \frac{98157 - 0.61 ( 6999 )}{164 - 8.3145 ln 7000} = 1038.74 K = 765.59^{\circ} C .

The pressure unit in the solid term is bar, matching the supplied

J ba r^{- 1}

. The gas logarithm is dimensionless because

P / P_{0} = 7000

. High water chemical fugacity opposes dehydration and raises the equilibrium temperature substantially.

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