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Equation 3 · Part 2 · Lowering the Barrier: What a Catalyst Actually Does

Symbol kappa

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

What this part means

kappa is one of the signed contributions combined to compute the quantity on the left.

Its job in the formula

kappa is one of the signed contributions combined to compute the quantity on the left.

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

A variable is a named place for a value. Its letter is a local label: x can mean position in one formula and a data point in another.

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