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

Symbol E_mathrm a

k=Aexp⁡(−EaRT),k = A\exp\left(-\frac{E_{\mathrm a}}{RT}\right),
EaE_{\mathrm a}

What this part means

EmE_mathrm a occurs above the fraction bar. The numerator is divided by the entire denominator below it.

Its job in the formula

EmE_mathrm a occurs above the fraction bar. The numerator is divided by the entire denominator below it.

The passage around this formula

Arrhenius gave the empirical form. The rate constant depends on temperature as k=Aexp⁡(−EaRT)k = A\exp\left(-\frac{E_{\mathrm a}}{RT}\right). where the exponential term is, to a good approximation, the fraction of molecular encounters carrying enough energy to clear the barrier, and the pre-exponential factor collects everything about how often encounters happen and how many of them are correctly oriented. The practical consequence of the exponential is severe. At around room temperature, lowering the activation energy by roughly six kilojoules per mole multiplies the rate by about a factor of ten. A catalyst that removes eighty kilojoules per mole from a barrier is not making the reaction somewhat faster; it is making it faster by…

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Learn the underlying idea

A subscript is a label attached below a symbol. It often selects a time step, component, category, or member of a sequence.

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