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 value of Arrhenius parameters A is:

• A. $5.42\times {10}^{10}{s}^{-1}$
• B. $5.36\times {10}^{10}{s}^{-1}$
• C. $5.65\times {10}^{10}{s}^{-1}$
• D. $Noneofthese$

Answer 1

The correct option is A $5.42\times {10}^{10}{s}^{-1}$

$k=A{e}^{-E_a/RT}$

or log k = log A - $\frac{E_a}{2.303RT}$

$\therefore log\frac{k_2}{k_1}=\frac{E_a}{2.303R}[\frac{1}{T_1}-1T_2]$

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

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

$k=A{e}^{-E_a/RT}$

or log k = log A -$\frac{2.2\times {10}^4}{2.303\times 8.314\times 373}$

or A = $5.42\times {10}^{10}{s}^{-1}$