Question

Consider the following reactions at $300 {K}$.

$A \longrightarrow B$ (uncatalysed reaction)

$A \stackrel{\text { catalyst }}{\longrightarrow} B$ (catalysed reaction)

The activation energy is lowered by $8.314 {~kJ} {~mol}^{-1}$ for the catalysed reaction. The rate of this reaction is

(a) 15 times

(b) 38 times

(c) 22 times

(d) 28 times.

Answer 1

Correct Option : (d)

Explanation—

$k_{\text {uncat }}=A e^{-\frac{E_{\text {uncat }}}{R T}}$

$k_{\text {cat }}=A e^{-\frac{E_{\text {cat }}}{R T}}$

From $(i) and (ii)$

$\frac{k_{\text {uncat }}}{k_{\text {cat }}}=\frac{e^{-\frac{E_{\text {uncat }}}{R T}}}{e^{-\frac{E_{\text {cat }}}{R T}}}=e^{\frac{E_{\text {cat }}-E_{\text {uncat }}}{R T}}$

$\frac{k_{\text {uncat }}}{k_{\text {cat }}}=e^{\frac{-8.314 \times 10^3}{8.314 \times 300}} \text { or } \frac{k_{\text {cat }}}{k_{\text {uncat }}}=e^{3.33} \approx 28$