Past exam of the chemistry A course of the University of Cambridge / 2024 / Paper 2 / A7 / a / i / Solution

In transition state theory, $K^{‡}$ is the dimensionless equilibrium-like constant for forming the activated complex from the reactants under the chosen standard-state convention. It is not the equilibrium constant for forming the stable product.

${\Delta }_{\mathrm{r}}{G}^{\circ ,‡}$ is the standard activation free energy, ${\Delta }_{\mathrm{r}}{H}^{\circ ,‡}$ the standard activation enthalpy, and ${\Delta }_{\mathrm{r}}{S}^{\circ ,‡}$ the standard activation entropy. Each is the activated-complex quantity minus the corresponding sum for the reactants, with the unstable reaction-coordinate motion treated by the transition-state flux construction.

$[{]}^{\circ }=c^{\circ }$ is the standard concentration, conventionally $1\mathrm{mol}\mathrm{d}{\mathrm{m}}^{-3}$ for the rate units used here. Its inverse converts the attempt frequency $k_{\mathrm{B}}T/h$ into the units of a bimolecular rate constant. The stated Eyring equation assumes unit transmission coefficient.