Question

The energy of activation and specific rate constant for a first order reaction at $25^{\circ }C$ are $100kJ/mol$ and $3.46\times 10^5{\sec }^1$ respectively. Determine the temperature at which half life of reaction is 2 hour.
$\underset{(inCC{l}_4)}{2N_2{O}_5}\to \underset{(inCC{l}_4)}{2N_2{O}_4}+O_2$

• A. 300 K
• B. 302 K
• C. 304 K
• D. 306 K

Answer 1

Answer: (D)

$k_1=3.46\times 10^{-5}$
$T=298K$
$T=?$
Using Arrhenius equation :
$In\frac{k_2}{k_1}=-\frac{E_a}{R}\left(\frac{1}{T_2}-\frac{1}{T_1}\right)$
$2.303\log \left(\frac{9.6\times 10^{-5}}{3.46\times 10^{-5}}\right)--\frac{100\times 10^3}{8.314}\left(\frac{1}{T}-\frac{1}{298}\right)$
$\frac{1}{298}-\frac{8.314}{10^5}\times 2.303(\log 2.77)=\frac{1}{T}$
$3.355\times 10^{-3}-8.48\times 10^{-5}=\frac{1}{T}$
$T=306K$