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Chemistry · Glossary

What is Activation energy?

Also known as: pre-exponential factor

Definition 8.15 University Chemistry — Year 1 · Chapter 8 — Chemical Kinetics: Rate Laws

The activation energy EaE_a of a reaction of rate constant k(T)k(T) is defined by

 ⁣dln⁡k ⁣dT=EaRT2,\frac{\dd \ln k}{\dd T} = \frac{E_a}{RT^2} ,

in J/mol\mathrm{J}/\mathrm{mol}. When EaE_a is independent of TT, integrating gives k=A e−Ea/RTk = A\,\eu^{-E_a/RT}, where the constant AA, of the unit of kk, is the pre-exponential factor.

Examples

Example 8.19 (A rule of thumb)

For Ea=53 kJ/molE_a = 53\,\mathrm{kJ}/\mathrm{mol}, going from 25 to 35 ∘C35\,{}^{\circ}\mathrm{C} multiplies kk by exp⁡ ⁣(530008.314(1298.15−1308.15))=2.0\exp\!\big(\frac{53000}{8.314}(\frac{1}{298.15} - \frac{1}{308.15})\big) = 2.0. The familiar rule “ten degrees more, twice as fast” holds near room temperature for reactions of activation energy around 50 kJ/mol50\,\mathrm{kJ}/\mathrm{mol}; for larger EaE_a the factor is larger.

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