# 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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## 1 Answer

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.

So, increasing the number of molecules will change the frequency of the molecules with that energy, but the ration over the whole population will remain the same.