= Transition state theory
{title2=$k=(k_{\mathrm B}T/h)\exp[-\Delta G^{\ddagger\circ}/(RT)]$}
{wiki}
<Transition state theory> relates an <elementary reaction>'s <rate constant> to a <Gibbs energy of activation>. The Eyring expression used in the <catalyst> example assumes every passage counted at the <transition state> succeeds. More generally, a factor accounting for unsuccessful passage multiplies it. Comparing barriers alone gives the quoted speedup only when the remaining prefactors agree. Free-energy profiles can depend on <temperature>, so the example's values at $300\,\mathrm K$ do not determine a temperature curve. See the https://goldbook.iupac.org/terms/view/T06470[IUPAC Gold Book: transition state theory].
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