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For two reactions, the rate constants are given by k₁ = 10¹⁶ e⁻²⁰⁰⁰/T and k₂ = 10¹⁵ e⁻¹⁰⁰⁰/T. At what temperature do the two rate constants become equal?

1. 1000 K
2. 2000/2.303 K
3. 2000 K
4. 1000/2.303 K

Correct answer: 1000/2.303 K

Solution

10^16 e^(-2000/T) = 10^15 e^(-1000/T) -> 10 = e^(1000/T) -> ln10 = 1000/T -> T = 1000/2.303 K.

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