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A → B (first reaction) C → D (second reaction) Consider the above two first-order reactions. The rate constant for first reaction at 500 K is double of the same at 300 K. At 500 K, 50% of the reaction becomes complete in 2 hour. The activation energy of the second reaction is half of that of first reaction. If the rate constant at 500 K of the second reaction becomes double of the rate constant of first reaction at the same temperature; then rate constant for the second reaction at 300 K is ____ × 10^-1 hour^-1 (nearest integer).

1. 1
2. 2
3. 4
4. 5

Correct answer: 5

Solution

The rate constant for the first reaction at 500 K is known, and since the second reaction's rate constant at this temperature is double that of the first, we can use the relationship between activation energy and temperature to determine the rate constant at 300 K. Given that the activation energy of the second reaction is half that of the first, this results in a higher rate constant at the lower temperature, leading to the conclusion that the rate constant for the second reaction at 300 K is 5 × 10^-1 hour^-1.

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