Question

A first order reaction is $50$% complete in $30$ minutes at ${27}^{o}C$ and in $10$ minutes at ${47}^{o}C$. The energy of activation of the reaction is:

• A. $43.84kJ{mol}^{-1}$
• B. $34.84kJ{mol}^{-1}$
• C. $84.00kJ{mol}^{-1}$
• D. $30.00kJ{mol}^{-1}$

Answer 1

Answer: (A)

$43.84kJ{mol}^{-1}$

$k_{{27}^{o}C}=\frac{0.693}{30}{min}^{-1}$
$k_{{47}^{o}C}=\frac{0.693}{10}{min}^{-1}$
$\frac{k_{{47}^{o}C}}{k_{{27}^{o}C}}=3$
or $\log \frac{k_{{47}^{o}C}}{k_{{27}^{o}C}}=\log 3$
$0.4771=\frac{E_a}{2.303\times 8.314}\left(\frac{20}{300\times 320}\right)$
$E_a=43.84kJ{mol}^{-1}$