Question

The rate constants of reaction at $ 500\, K $ and $700\, K$ are $0.02 \, s^{-1}$ and $0.07\, s^{-1} $ respectively. The value of $ A $ is

• A. $2 $
• B. $ 4$
• C. $ 1.61 $
• D. $3.5 $

Answer 1

Answer: (C)

$log \frac{k_{2}}{k_{1} }= \frac{E_{a}}{2.303 R} \left[\frac{T_{2}-T_{1}}{T_{1}T_{2}}\right] $
$ log \frac{0.07}{0,02}=\left[\frac{E_{a}}{2.303\times8.314 Jk^{-1}mol ^{-1}}\right]\left[\frac{700-500}{700\times500}\right] $
$0.544 =E_{a}\times5.714\times10^{-4} /19.15 $
$ E_{a}=0.544\times19.15 5.714\times10^{-4} = 18231.7J $
Since $k=A e^{-E_{d} / R T}$
$0.02=A e^{-18231.7 / 8.314 \times 500}$
$A=0.02 / 0.012=1.61$