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I thought that activation energy depends on steric factors. By Arrhenius equation it must depend on steric factors since $A$ depends on steric factors. $$k=A\cdot\mathrm e^{-\frac{E_\mathrm a}{RT}}$$ (for bimolecular reaction)

But my book says it doesn’t.

Does it depend on steric factors or not and why?

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The Arrhenius model of a rate rate constant is very basic so has to be modified in many cases. One of these is when steric factors (generally undefined exactly) are used as an empirical multiplier to A and used as a rationale to fit experimental data.

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Steric hindrance does indeed impact activation energy.

Steric hindrance means, essentially, the electrons are locked into orbitals that force them to repel one another as reactants approach each other, and the only way to relieve such repulsion is for the electrons to rearrange into a less stable combination of orbitals. Not only is this an energy cost either way, it can impact reaction paths and mechanisms. Compare, for instance, nucleophilic substitution on primary alkyl halides with the corresponding reaction on tertiary alkyl halides.

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