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Equation 2 · Part 6 · Lowering the Barrier: What a Catalyst Actually Does

=

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

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

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.

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