Question

A certain reaction is 50 % complete in 20 min at 300 K and the same reaction is again 50 % complete in 5 min at 350 K. The activation energy is, if it is a first order reaction:

• A. $23.091kJmo{l}^{-1}$
• B. $24.093kJmo{l}^{-1}$
• C. $21.059kJmo{l}^{-1}$
• D. $Noneofthese$

Answer 1

The correct option is B $24.093kJmo{l}^{-1}$

$k_1=\frac{0.693}{20min}$ at 300 K $=0.03465mi{n}^{-1}$
$k_2=\frac{0.693}{5min}$ at 350 K $=0.1386mi{n}^{-1}$
$\therefore \frac{k_2}{k_1}=\frac{E_a}{2.3R}\left[\frac{350-300}{350\times 300}\right]$
log $\left(\frac{0.693/5}{0.693/20}\right)=\frac{E_a}{2.3\times 8.314J{k}^{-1}mo{l}^{-1}}\left(\frac{50}{350\times 300}\right)K$
log $4=\frac{E_a}{40156.6}$
$E_a=40156.6\times 2\times 0.3\approx 24093.9Jmo{l}^{-1}$
$\approx 24.093kJmo{l}^{-1}$