Question

The following data were obtained for a given reaction at $300K$.

Reaction	Energy of activation $\left(kJ{mol}^{-1}\right)$
Uncatalysed	$76$
Catalysed	$57$

The factor by which rate of catalysed reaction is increased, is:

• A. $21$
• B. $2100$
• C. $2000$
• D. $1200$

Answer 1

The correct option is C $2000$

Using Arrhenius equation:
$K=A{e}^{\frac{E_a}{Rt}}$, we get-

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

$\log k_1=\log A-\frac{E_{a_{\left(1\right)}}}{2.303RT}.....\left(i\right)$

and $\log k_2=\log A-\frac{E_{a_{\left(2\right)}}}{2.303RT}$

or $\log \frac{k_2}{k_1}=\frac{1}{2.303RT}[E_{a_{\left(1\right)}}-E_{a_{\left(2\right)}}]$ (from $\left(i\right)$ and $\left(ii\right)$)

$=\frac{1}{2.303\times 8.314\times 300}(76000-57000)$

or $\log \frac{k_2}{k_1}=\frac{19000}{2.303\times 8.314\times 300}=\frac{190}{6.9\times 8.314}$

On taking antilog-

or $\frac{k_2}{k_1}=2000$

Hence, option C is correct.