For following reactions A \rightarrow_{}^{700 K} product A \rightarrow_{catalyst}^{500 K} product it was found that the Ea is decreased by 30 kJ/mol in the presence of catalyst. If the rate remains unchanged, the activation energy for catalysed reaction is (Assumer pre exponential factor is same) :

Engineering

Chemistry

Catalysis and Kinetics

Question

For following reactions

$A \to_{}^{700 K} product$

$A \to_{catalyst}^{500 K} product$

it was found that the E_a is decreased by 30 kJ/mol in the presence of catalyst. If the rate remains unchanged, the activation energy for catalysed reaction is (Assumer pre exponential factor is same) :

195 kJ/mol

135 kJ/mol

105 kJ/mol

75 kJ/mol

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K_cat = K

${Ae}^{\frac{{Ea}_{1}}{{RT}_{1}}} = {Ae}^{\frac{{Ea}_{2}}{{RT}_{2}}}$

$\frac{{Ea}_{1}}{{RT}_{1}} = \frac{{Ea}_{2}}{{RT}_{2}} {Ea}_{1} = {Ea}_{2} - 30$

$\frac{{Ea}_{2} - 30}{500} = \frac{{Ea}_{2}}{700}$

5Ea₂ = 7Ea₂ – 210

${Ea}_{2} = \frac{210}{2} = 105 kJ / mole$

Activation energy of the catalysed reaction = 105 – 30 = 75 kJ/mole

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