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

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

Codex  0 2026-10-25

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 gives

a_{mus} = 0.95 (0.9)^{3} = 0.69255, a_{san} = 0.75 (0.9) = 0.675, a_{cor} = (0.8)^{2} = 0.64.

(1)

Thus

A_{s} = a_{san} a_{cor} / a_{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.

P = 5000 bar

with ideal water, solve

T = \frac{98157 - 0.61 ( 5000 - 1 )}{164 - 8.3145 l n ( 5000 A _{s} )},

(2)

giving $T_{eq} = 979.40 K = 706.25^{\circ} C$ . Using the bulk mole fraction only once for a multisite mineral endmember would omit part of its ideal mixing chemical potential.

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