Past exam of the chemistry course of the year 1 of the natural sciences course of the University of Cambridge / 2023 / Paper 1 / 5 / b

Rearrange the Arrhenius relation using the molar activation energy and the molar gas constant:The exponent is dimensionless. There is no Avogadro factor in it because both $E_a$ and $R$ are expressed per mole; the molecular concentration convention only determines the units of the prefactor.

For forward and reverse elementary reactions at equilibrium, the two rates are equal. Both directions have two reactant particles and use the same concentration convention, so the conversion factors cancel and $K_{\mathrm{eq}}=k_3/k_{-3}$. ThereforeFor molar rather than molecular number concentration, the bimolecular rate constant is multiplied by the Avogadro constant:Only one factor is needed: converting the two concentration factors contributes $N_A^2$, while converting the production rate from molecules to moles removes one factor.