Catalytic barriers and reaction free energy

A directional Gibbs energy of activation measures the climb from a starting state to a transition state. The net standard reaction change in Gibbs free energy measures the difference between endpoints. Changing the climb can strongly change a rate constant while leaving that endpoint difference intact. For two illustrative single-barrier routes with common endpoint levels $G_{\mathrm{A}}^{\circ }$ and $G_{\mathrm{B}}^{\circ }$,Lowering the common transition state level lowers both directional Gibbs energies of activation; it does not lower just the forward climb. The usual statement that a catalyst lowers an activation energy describes a kinetic route, not a change in the net Gibbs free energy. An activation energy inferred from an Arrhenius plot is also distinct from a Gibbs energy of activation at one temperature.

With a common prefactor in transition state theory, subtracting the directional barriers yieldswhere $R$ is the molar gas constant and $T$ is the absolute temperature. This particular rate constant ratio requires the simple compatible directional rate laws and consistent standard states; a general multistep reaction mechanism does not supply two arbitrary measured rate constants whose ratio must equal $K$. At fixed temperature a catalyst preserves $K$ for the same net conversion. The actual reaction change in Gibbs free energy, ${\Delta }_{r}G={\Delta }_r{G}^{\circ }+RT\ln Q$, is likewise unchanged at the same reaction quotient $Q$. Composition changes during the faster approach to chemical equilibrium, so comparing mixtures at the same elapsed time need not compare the same $Q$.^[ref]