The rate constant of a reaction at 400 K is ten times its rate constant at 200 K. What is the activation energy (Ea) of the reaction? (R = gas constant)
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 921.2 R
The Arrhenius equation written for two temperatures relates the two rate constants to the activation energy Ea:
\( \displaystyle \log\frac{k_2}{k_1}=\frac{E_a}{2.303R}\left[\frac{T_2-T_1}{T_1T_2}\right] \)
Data: T1 = 200 K, T2 = 400 K, \( \frac{k_2}{k_1}=10 \), so \( \log\frac{k_2}{k_1}=\log10=1 \).
\( \displaystyle 1=\frac{E_a}{2.303R}\times\frac{400-200}{200\times400}=\frac{E_a}{2.303R}\times\frac{1}{400} \)
\( \displaystyle E_a=2.303\times400\times R \)
\( \displaystyle E_a=921.2\,R \)