Question

Rate of a catalysed and an uncatalysed reaction can be equal if

• A. Both reaction temperature are equal
• B. Temperature of the uncatalysed reaction is more than the catalysed reaction
• C. Temperature of the uncatalysed reaction is less than the catalysed reaction
• D. Rate of catalysed reaction cannot be equal to uncatalysed reaction in any case.

Answer 1

The correct option is B Temperature of the uncatalysed reaction is more than the catalysed reaction

Consider a rate of reaction with catalysed and uncatalysed condition.
$k=A{e}^{-E_a/RT}......eqn\left(1\right)$
$k_{cat}=A{e}^{-E_a^{\prime }/RT}.......eqn\left(2\right)$
$k$ : Rate constant without catalyst
$k_{cat}$ : Rate constant with catalyst
$E_a$ : Activation energy without catalyst
$E_a^{\prime }$ : Activation energy with catalyst

Assuming the rate of reaction of catalysed and the uncatalysed reactions are equal,
$A{e}^{-E_a/R{T}_1}=A{e}^{-E_a^{\prime }/R{T}_2}$

$T_1$ : Temperature at which uncatalysed reaction occurs
$T_2$ : Temperature at which catalysed reaction occur

$e^{-E_a/R{T}_1}=e^{-E_a^{\prime }/R{T}_2}$
Taking natural logarithm on both side
$\frac{-E_a}{R{T}_1}=\frac{-E_a^{\prime }}{R{T}_2}$

$\frac{E_a}{T_1}=\frac{E_a^{\prime }}{T_2}$

Since, $E_a>E_a^{\prime }$
$T_1>T_2$

Therefore, option (b) is correct.