Question

For following reactions ${A ->[700\,K][] Product}$ ${A ->[500\,K][{\text{catalyst}}] Product}$ it was found that the $E_a$ is decreased by 30 k J/mol in the presence of catalyst. If the rate remains unchanged, the activation energy for catalysed reaction is (Assume pre exponential factor is same):

• A. $198 \,kJ/ mol$
• B. $105\, kJ/ mol$
• C. $75 \,kJ/ mol$
• D. $135 \,kJ/ mol$

Answer 1

Answer: (C)

$75 \,kJ/ mol$

Answer 2

$K_{1}=Ae \frac{E a}{R\times700}$

$K_{2}=A\times e\frac{\left(Ea-30\right)}{R\times500}$

For same rate $K_{1}=K_{2}$

$e\frac{E a}{700 R}_{=e} \frac{\left(E a-30\right)}{R\times500}$

$\frac{E a}{700 R}=\frac{E a-30}{R\times500}$

$5 Ea=7Ea-210$
$210=2E a$
$E_{a}=105 kJ/mole$
$E_{a}-30=75$

The Correct Option is (C): $75\;KJ\;/mol$