Question

A catalyst lower the activation energy of a reaction from 20 kJ mole${}^{-1}$ to 10 kJ mol${}^{-1}$. The temperature at which the uncatalysed reaction will have the same rate as that of the catalyzed at 27${}^o$ C is:

• A. $-{123}^{o}C$
• B. ${327}^{o}C$
• C. ${150}^{o}C$
• D. $+{23}^{o}C$

Answer 1

The correct option is B ${327}^{o}C$

Arrhenius equation is $k=A{e}^{-Ea/RT}$

For same rate constant and same pre exponential factor $[\frac{E_a}{T}{]}_{uncat}=[\frac{E_a}{T}{]}_{cat}$

$\frac{20000}{T}=\frac{10000}{300}$

$T=600K=600-{273}^{o}C={327}^{o}C$