= Solution
In <transition state theory>, $K^\ddagger$ 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.
$\Delta_{\mathrm r}G^{\circ,\ddagger}$ is the standard <activation free energy>, $\Delta_{\mathrm r}H^{\circ,\ddagger}$ the standard <activation enthalpy>, and $\Delta_{\mathrm r}S^{\circ,\ddagger}$ 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 $1\ \mathrm{mol\,dm^{-3}}$ 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.
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