Past exam of the mathematics course of the University of Cambridge / 2022 / iii / Paper 315 / 2 / d

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- Solution d

Solution

At fixed temperature and pressure, thermochemical equilibrium minimizes the Gibbs free energy subject to elemental conservation. For every independent reaction with stoichiometric coefficients

ν_{i}

,

Δ_{r} G = i \sum ν_{i} μ_{i} = 0 .

Equivalently, forward and reverse rates satisfy detailed balance. For ideal gases,

i \prod (\frac{p _{i}}{p ^{\circ}})^{ν_{i}} = K_{p} (T) = exp [- \frac{Δ _{r} G ^{\circ} ( T )}{RT}] .

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