For following reactions
$A \overset{700 K}{\to} Product$
$A \to_{catalyst}^{500 K} Product$
It was found that the activation energy is decreased by 30 kJ / mol in the presence of catalyst. If the rate remains unchanged, the activation energy for catalysed reaction is (Assume pre exponential factor is same ):

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135 kJ / mol

105 kJ / mol

75 kJ / mol

198 kJ / mol

answer is C.

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Detailed Solution

Reaction-1:

$A \overset{700 K}{\to} Product$

Reaction 2:

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

$r_{1} = r_{2} & k_{1} = k_{2} A \times e^{- {Ea}_{1}} / {RT}_{1} = A \times e^{- {Ea}_{2}} / {RT}_{2} \frac{{Ea}_{1}}{T_{1}} = \frac{{Ea}_{2}}{T_{2}} and also {Ea}_{1} = 30 + {Ea}_{2}$

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

${Ea}_{2} = 75 kJ / mol$

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