Question

Consider the following reactions at 300 K: X $\to$ Y (uncatalysed reaction) & X $\to$ Y (catalysed reaction). The energy of activation is lowered by 83.14 kJmol${}^{-1}$ for the catalysed reaction.

The rate of catalysed reaction is:

• A. $3\times {10}^{14}$ times that of uncatalysed reaction
• B. $15\times {10}^{14}$ times that of uncatalysed reaction
• C. 25 times that of uncatalysed reaction
• D. 22 times that of uncatalysed reaction

Answer 1

The correct option is A $3\times {10}^{14}$ times that of uncatalysed reaction

The Arrhenius equation for the uncatalyzed reaction is $K_{mcat}=A{e}^{-E_{\iota R}/RT}.$

The Arrhenius equation for the catalyzed reaction is $K_{cat}=A{e}^{-E_R/RT}.$

Let A' be the activation energy for the uncatalyzed reaction.

The activation energy for the catalyzed reaction will be $(A^{\prime }-83.14\times {10}^3).$

Divide the two equations.

$\frac{K_{cat}}{K_{mcat}}=\frac{e^{-(A^{\prime }-83.14\times {10}^3)/RT}}{e^{-A^{\prime }/RT}}=e^{83.14\times {10}^3/RT}=e^{33.33}\approx 3\times {10}^{14}$