# Arrhenius equation

The

**Arrhenius equation** predicts the rate of a

chemical reaction at a certain temperature, given the

activation energy and chance of successful collision of

molecules. It is named after Swedish scientist

Svante Arrhenius.

The average amount of thermal energy that molecules possess at a certain temperature is equal to *RT*, where *R* is the molar gas constant. The fraction of molecules that have enough energy to overcome the energy barrier (those with energy over the activation energy, *E*) depends exponentially on the ratio of the activation to thermal energy. This forms the Arrhenius equation:

where

*k* is the

*rate constant* for the reaction and

*A* is a constant specific to each reaction that depends on the chance the molecules will collide in the correct orientation. It can be seen that either increasing the temperature or decreasing the

activation energy (for example through the use of

catalysts) will result in an increase in rate of reaction.

Taking the natural logarithm of the Arrhenius equation yields

The modified Arrhenius equation yields an equation of the form y=mx+b, where

So, when a reaction has a rate constant which obeys the Arrhenius equation, a plot of ln(k) versus T

^{-1} gives a straight line. Slope and intercept can be used to determine E and A characteristics.

*See also:* Kinetics