Question

The activation energy for a reaction at the temperature TK was found to be 2.303 $RTJmo{l}^{-1}$. The ratio of the rate constant to Arrhenius factor is ___

• A. ${10}^{-2}$
• B. ${10}^{-1}$
• C. $2\times {10}^{-2}$
• D. $2\times {10}^{-3}$

Answer 1

The correct option is B ${10}^{-1}$

$k=A{e}^{\frac{-E_a}{RT}}$
$E_a=2.303RT$
$\therefore \frac{k}{A}=e^{-\left(\frac{2.303RT}{RT}\right)};\frac{k}{A}=e^{-2.303}$
$lo{g}_e\left(\frac{k}{A}\right)=lo{g}_e{e}^{-2.303}$
$lo{g}_e\left(\frac{k}{A}\right)=-2.303$ or $2.303lo{g}_{10}\left(\frac{k}{A}\right)=-2.303$
$log\left(\frac{k}{A}\right)=-1;log\left(\frac{A}{K}\right)=1$
$\therefore \frac{A}{k}=antilog1=10$ or $\frac{k}{A}=\frac{1}{10}={10}^{-1}$