Question

What is the activation energy for the decomposition of $N_2{O}_5$ as, $N_2{O}_5\to$ 2 $N{O}_2+\frac{1}{2}{O}_2$. if the values of the rate constants are $3.45\times {10}^{-5}$ and $6.9\times {10}^{-3}$ at ${27}^{0}C$ and ${67}^{0}C$ respectively?

• A. 112.5 kJ
• B. 200 kJ
• C. 149.5 kJ
• D. 11.25 kJ

Answer 1

Answer: (A)

112.5 kJ

The expression for the relationship between the rate constants at two different temperatures is as shown below.
$\log \frac{k_2}{k_1}=\frac{E_a}{2.303R}\frac{(T_2-T_1)}{T_1{T}_2}$

Substitute values in the above expression.
$log\frac{6.9\times {10}^{-3}}{3.45\times {10}^{-5}}=\frac{E_a}{2.303\times 8.314}\frac{340-300}{300\times 340}$

$E_a=112.5kJ$.