Question

The rate constant of a reaction is $1.5\times {10}^7{s}^{-1}$ at ${50}^{\circ }C$ and $4.5\times {10}^7{s}^{-1}$ at ${100}^{\circ }C$. The approximate value of Arrhenius parameter $logA$ and $E_a$ respectively, are:
(where, A is frequency factor)

• A. $10.72$ and $2.2\times {10}^{4}Jmo{l}^{-1}$
• B. $7.52$ and $2.2\times {10}^{4}Jmo{l}^{-1}$
• C. $3.72$ and $2.2\times {10}^{3}Jmo{l}^{-1}$
• D. $5$ and $2.2\times {10}^{-4}Jmo{l}^{-1}$

Answer 1

The correct option is A $10.72$ and $2.2\times {10}^{4}Jmo{l}^{-1}$

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

$log\frac{4.5\times {10}^7}{1.5\times {10}^7}=\frac{E_a}{2.303\times 8.314}(\frac{1}{323}-\frac{1}{373})$

$E_a=2.2\times {10}^{4}Jmo{l}^{-1}$

We know that,
$lo{g}_{10}k=lo{g}_{10}A-\frac{E_a}{2.303RT}$

$lo{g}_{10}(1.5\times {10}^7)=lo{g}_{10}A-\frac{2.2\times {10}^4}{2.303\times 8.314\times 323}$

$logA=10.72$

Hence, (a) is correct.