Chemists commonly use a rule of thumb that an increase of 10 K in temperature doubles the rate of a reaction. What must the activation energy be for this statement to be true for a temperature increase from 25 to 35°C?
The Arrhenius equation will tell us that the activation energy in this case must be 52.4 kJ/mol.
The Arrhenius equation says that the dependence of the rate constant
For the sake of this problem, let us say that
To double the reaction rate, we must double the value of k, i.e. the ratio
This will require the right hand side of the Arrhenius equation to change to
all of which can be written in ratio forms as
Taking the natural log of each side:
Using 308K for