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Equation 3 · Part 9 · Lowering the Barrier: What a Catalyst Actually Does

fraction

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

What this part means

Divide the expression above the line by the one below it.

Its job in the formula

The expression above the fraction bar is divided by the complete expression below it. The denominator must not be zero.

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 fraction a/b means a divided by b. The top number is the numerator; the bottom number is the denominator, and it cannot be zero.

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