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For following reactions A 700 K -> Product A 500 K -> Product catalyst 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 second reaction is (Assume pre exponential factor is same):

1. 135 kJ/mol
2. 105 kJ/mol
3. 75 kJ/mol
4. 198 kJ/mol

Correct answer: 105 kJ/mol

Solution

The presence of a catalyst lowers the activation energy (E_a) required for a reaction. Since the activation energy is decreased by 30 kJ/mol, and the original activation energy for the first reaction is 135 kJ/mol (700 K), the activation energy for the second reaction at 500 K becomes 105 kJ/mol.

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