Question

Make a plan for calculating the activation energy of the reaction from the rate
constant data at different temperatures?

Answer 1

The relation between rate constatnt, activation energy and the temperature is given by the formula

lnk=lnA-E_a/RT, where k=rate constant, E_a=activation energy, R= gas constant, T=temperature and A= Arrhenius constant.

Consider at two different temperatures T₁ and T_2, the rate constants will be k₁ and k₂.

Substituting the above formula, lnk₁=-E_a/RT₁+lnA

and lnk₂= -E_a/RT₂+lnA

Difference between two rate constants= lnk₁-lnk₂=(-E_a/RT₁+lnA)=(-E_a/RT₂+lnA)

After rearrangement ln(k₁/k₂)=(1/T₂-1/T₁)E_a/R

Therefore E_a=ln(k₁/k₂)R/(1/T₂-1/T₁)