Question

A reaction is followed and found to have a rate constant of 3.36x10^4 M^-1 s^-1 at 344K and a rate constant of 7.69 M^-1 s^-1 at 219K. Determine the activation energy for this reaction.

Answer 1

$k=A e^{-E/(RT)}$

$k_1/k_2=e^{E/(RT_2)-E/(RT_1)}$

$ln \left (\frac {k_1} {k_2}\right) =\frac {ET_1 -ET_2} {RT_1T_2}$

$E=\frac{RT_1T_2} {T_1-T_2}ln\left(k_1/k_2\right)$

$E=42 kJ•mol^{-1}$