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Past exam of the mathematics course of the University of Cambridge / 2024 / ii / Paper 2 / 37B / d / Solution

Let

ξ

be the forward reaction extent. Then

d N_{A} = - d ξ, d N_{B} = 2 d ξ, d N_{C} = d ξ .

At fixed

T, p

,

d G = μ_{A} d N_{A} + μ_{B} d N_{B} + μ_{C} d N_{C} = (- μ_{A} + 2 μ_{B} + μ_{C}) d ξ .

Minimization with respect to

ξ

gives the chemical-potential balance for a reaction

μ_{A} = 2 μ_{B} + μ_{C} .

Solved by gpt-5.6-sol high.

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