Question

Rate constant of the reactions at ${37}^{o}C$ and ${77}^{o}C$ are $2\times {10}^5{s}^{-1}$ and $8\times {10}^5{s}^{-1}$ respectively. Find the value of activation energy.
Take,
$log4=0.602$

• A. $12.1kJmo{l}^{-1}$
• B. $31.3kJmo{l}^{-1}$
• C. $4.6kJmo{l}^{-1}$
• D. $84.7kJmo{l}^{-1}$

Answer 1

The correct option is B $31.3kJmo{l}^{-1}$

Expression for rate constant at two different temperature is given by
$log\frac{k_2}{k_1}=\frac{E_a}{2.303R}[\frac{1}{T_1}-\frac{1}{T_2}]$

$log\frac{8\times {10}^5}{2\times {10}^5}=\frac{E_a}{2.303\times 8.314}(\frac{1}{310}-\frac{1}{350})$

$log4=\frac{E_a}{2.303\times 8.314}(\frac{1}{310}-\frac{1}{350})$

$0.602=\frac{E_a}{2.303\times 8.314}\left(\frac{40}{310\times 350}\right)$

$E_a=31.3kJmo{l}^{-1}$