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Published equation contexts

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

Why this formula appears here

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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EaE_{\mathrm a}

Symbol E_mathrm a

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

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RR

Symbol R

R occurs below the fraction bar. The quantity above the bar is divided by this expression; zero is excluded as a denominator.

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TT

Symbol T

T occurs below the fraction bar. The quantity above the bar is divided by this expression; zero is excluded as a denominator.

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How to interpret it

With a fixed numerator, increasing a nonzero denominator reduces the fraction. Read it with the definitions, units, and assumptions supplied by the article.

Published contexts (1)

A symbol can carry a different meaning in another article. Each occurrence keeps its own guide and term definitions.

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

Equation 2 · Chemistry & Catalysis

Lowering the Barrier: What a Catalyst Actually Does

This equation states an equality: the expressions on both sides have the same value under the article’s assumptions.

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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