# Variation of Arrhenius equation with concentration

In the Arrhenius equation do Arrhenius constant and activation energy depend on concentration ? (Their units do)

• To my knowledge the activation energy does not depend on concentration while the preexponential factor will depend on the concentration. The preexponential factor is a measure for the probability of two particles colliding with the proper orientation to facilitate the reaction so a higher concentration of particles will lead to a higher preexponential factor. – Philipp Jun 6 '14 at 11:35

The Arrhenius equation gives you a rate constant $k$.

For a second order reaction, $k$ has units of $1/Ms$.

For a first order reaction, $k$ has units of $1/s$.

The Arrhenius prefactor $A$ has the same units as $k$.

The rate, as opposed to the rate constant will depend upon concentration. For the first order reaction, the rate constant is multiplied by one concentration to get the rate, and for a second order reaction the rate constant is multiplied by two concentrations to get the rate.

If $k$ and $A$ do depend upon concentration, that would imply that the reaction is not accurately modeled by the rate constant (for example not really first order when you are modeling as first order or not really second order when you are modeling as second order).

As far as activation energy $E_a$, the equation can be written in terms of energy per mole divided by $RT$ or energy per molecule divided by $k_BT$ (where $k_B$ is Boltzmann constant). $E_a$ does not depend upon concentration.

• You said than activation energy is per mole doesn't that imply it relies on concentration – Jay Jun 6 '14 at 13:59
• no, it means that $E_a$ is the amount of energy needed for 1 mole, regardless of how many moles there are in an experiment and regardless of how many moles per liter (concentration) are present. – DavePhD Jun 6 '14 at 14:04
• in other words, the fact that it is energy per mole, means that is does NOT depend upon the number of moles. Energy is an extensive variable and depends upon amount of a substance, "energy per mole" is an intensive variable and does not depend upon the amount of substance. – DavePhD Jun 6 '14 at 14:09