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JEE MainChemistryChemical Kinetics

The rate constants for two different reactions are given by k₁ = A e^ -2000/T and k₂ = A e e^ -2500/T , where the temperature T is in Kelvin. The temperature at which both reactions have the same rate constant is ____ K.

Correct answer

500

Step-by-step solution

Given the rate constants for the two reactions: k₁ = A e^ -2000/T k₂ = A e e^ -2500/T = A e^ 1 - 2500/T We need to find the temperature T at which k₁ = k₂ : A e^ -2000/T = A e^ 1 - 2500/T Cancelling the pre-exponential factor A from both sides: e^ -2000/T = e^ 1 - 2500/T Equating the exponents: - 2000 T = 1 - 2500 T Rearranging the terms: 2500 T - 2000 T = 1 500 T = 1 T = 500 K Answer: 500

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