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Equation 3 · Part 10 · Lowering the Barrier: What a Catalyst Actually Does

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

Capital delta attached to a quantity marks a difference between two values of that quantity; the article’s sign convention determines the order.

Its job in the formula

Capital delta attached to a quantity marks a difference between two values of that quantity; the article’s sign convention determines the order.

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

Addition combines quantities; subtraction measures the signed difference between them. Parentheses show what is combined before the rest of the expression is evaluated.

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