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Equation 3 · Part 8 · Lowering the Barrier: What a Catalyst Actually Does

=

k=κ kBThexp⁡(−ΔG‡RT),k = \kappa\,\frac{k_{\mathrm B}T}{h}\exp\left(-\frac{\Delta G^{\ddagger}}{RT}\right),
=

What this part means

The expressions on both sides represent the same quantity under the stated assumptions.

Its job in the formula

The equals sign connects the complete expression on the left with the complete expression on the right. Both sides must have compatible units.

The passage around this formula

Transition state theory recasts this in thermodynamic language. Treating the activated complex as in quasi-equilibrium with the reactants gives k=κ kBThexp⁡(−ΔG‡RT)k = \kappa\,\frac{k_{\mathrm B}T}{h}\exp\left(-\frac{\Delta G^{\ddagger}}{RT}\right). in which the universal frequency factor sets the timescale, the Gibbs energy of activation sets the barrier, and the transmission coefficient absorbs the failures of the picture — recrossing of the dividing surface, tunnelling, and the fact that the chosen reaction coordinate is rarely perfect. Splitting the activation Gibbs energy into enthalpic and entropic parts is the point of the exercise. It makes explicit that a catalyst can help either by lowering the enthalpic cost of bond reorganisation or by paying the entropic price…

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Learn the underlying idea

An equals sign says that the expression on its left and the expression on its right have the same value under the stated definitions and assumptions.

Open the illustrated equality: what the equals sign claims guide →

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