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JEE MainChemistryChemical Kinetics

The temperature dependence of the rate constant k (in min ⁻¹ ) for a first order reaction is given by the equation: k = 14 - 6000 T The temperature at which the half-life of the reaction becomes 6.93 min is ________ K . (Given : 2 = 0.693 )

Correct answer

400

Step-by-step solution

For a first order reaction, the rate constant k is related to the half-life t_ 1/2 by: k = 2 t_ 1/2 Given t_ 1/2 = 6.93 min and 2 = 0.693 : k = 0.693 6.93 = 0.1 min ⁻¹ Substitute the value of k into the given Arrhenius equation: k = 14 - 6000 T (0.1) = 14 - 6000 T -1 = 14 - 6000 T 6000 T = 15 T = 6000 15 = 400 K Answer: 400

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