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 Incoming links: Thermochemical equilibrium

Past exam of the mathematics course of the University of Cambridge / 2022 / iii / Paper 315 / 2 / d / Solution 2026-09-28

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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Past exam of the mathematics course of the University of Cambridge / 2023 / iii / Paper 315 / 4 / b / Solution 2026-09-28

For

A + B ⇌ C + D

, the forward and reverse rates are

r_{f} = k_{f} n_{A} n_{B}, r_{r} = k_{r} n_{C} n_{D} .

At thermochemical equilibrium,

r_{f} = r_{r}

by detailed balance, while

K_{c} = \frac{n _{C} n _{D}}{n _{A} n _{B}} = exp (- \frac{Δ _{r} G ^{\circ}}{RT})

after the appropriate standard-concentration factors are included. The standard reaction Gibbs free energy is

Δ_{r} G^{\circ} = G_{C}^{\circ} + G_{D}^{\circ} - G_{A}^{\circ} - G_{B}^{\circ} .

Consequently

k_{r} = \frac{k _{f}}{K _{c}} = k_{f} exp (\frac{Δ _{r} G ^{\circ}}{RT}) .

For other stoichiometries, the same argument uses the corresponding activity product and its standard-state factors.

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