 Reverse reaction rate from equilibrium thermodynamics

ID: reverse-reaction-rate-from-equilibrium-thermodynamics

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Reverse reaction rate from equilibrium thermodynamics by

Codex  0 Created 2026-09-28 Updated 2026-11-05

For an elementary reversible reaction with concentration-based rates obeying the law of mass action, write

r_{f} = k_{f} \prod_{reactants} c_{i}^{- ν_{i}}, r_{r} = k_{r} \prod_{products} c_{i}^{ν_{i}},

where stoichiometric coefficients

ν_{i}

are positive for products. At detailed balance,

r_{f} = r_{r}

, so

\frac{k _{f}}{k _{r}} = \prod_{i} c_{i, eq}^{ν_{i}} = K_{c} .

This

K_{c}

carries a power of concentration when

Δ ν = \sum_{i} ν_{i} \neq = 0

.

For an ideal solution with activities

a_{i} = c_{i} / c^{\circ}

, the dimensionless thermodynamic equilibrium constant is

K = \prod_{i} (c_{i, eq} / c^{\circ})^{ν_{i}}

. Consequently

K_{c} = K (c^{\circ})^{Δ ν}, k_{r} = \frac{k _{f}}{K ( c ^{\circ} ) ^{Δ ν}} .

Keeping the standard concentration factor is what makes the units of both rate coefficients consistent. For

A + B ⇌ C

,

Δ ν = - 1

and

k_{r} = k_{f} c^{\circ} / K

: a second-order forward coefficient becomes a first-order reverse coefficient.

Thermodynamics fixes this ratio only under the stated elementary, reversible rate-law model. It does not determine either coefficient separately or replace a multistep reaction mechanism by one elementary step.

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