The rate constant of a reaction is 1.5 × 107 s−1 at 50°C and 4.5 × 107 s−1 at 100°C. What is the activation energy of the reaction? (R = 8.314 J K−1 mol−1)
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 2.2 × 104 J mol−1
The Arrhenius equation links the rate constants at two temperatures to the activation energy Ea:
\( \displaystyle \log\frac{k_2}{k_1}=\frac{E_a}{2.303\,R}\left(\frac{T_2-T_1}{T_1T_2}\right) \)
Here \( \frac{k_2}{k_1}=\frac{4.5\times10^{7}}{1.5\times10^{7}}=3 \), T1 = 50 + 273 = 323 K and T2 = 100 + 273 = 373 K.
\( \displaystyle \log 3=\frac{E_a}{2.303\times8.314\,\mathrm{J\,K^{-1}\,mol^{-1}}}\left(\frac{373-323}{323\times373}\right) \)
\( \displaystyle E_a=\frac{2.303\times8.314\times323\times373\times0.4771}{50}\,\mathrm{J\,mol^{-1}} \)
\( \displaystyle E_a=22012\,\mathrm{J\,mol^{-1}}\approx2.2\times10^{4}\,\mathrm{J\,mol^{-1}} \)