# Relation between concentration and activation energy

Will increasing the concentration of the reactants in a chemical reaction increase the proportion of molecules with an energy greater than the activation energy $$E_\mathrm{a}$$?

It seems to me that the proportion of molecules with energy greater than $$E_\mathrm{a}$$ should remain the same after increasing concentration because no extra energy is supplied. $$E_\mathrm{a}$$ is solely dependent upon the temperature of the molecules in the system, correct?

Assume that the volume $$V$$ and the temperature $$T$$ of the system is unchanged when the concentration of the molecules is increased.

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The population of an ensemble of molecules (so the molecules that would have $$E>E_\mathrm{a}$$) is determine by the Boltzmann equation (below a simplify version of it)
$$\frac{N_i}{N_\text{tot}} = g_i\exp\left(-\frac{\Delta G_i}{RT}\right),$$
where $$\Delta G$$ is the difference in energy between the molecule you're considering and the so called ground state in $$\pu{kJ mol^-1}$$, and $$g$$ is the number of states with the same energy.