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For two gaseous reactions, the rate constants are given by: A -> B: k1 = 10¹⁵ * e^(-3000/T) C -> D: k2 = 10¹⁴ * e^(-1000/T) Find the temperature at which k1 = k2.
- 434.2 K
- 2000 K
- 868.43 K
- None of these
Correct answer: 868.43 K
Solution
k1 = k2: 10¹⁵ * e^(-3000/T) = 10¹⁴ * e^(-1000/T). Dividing: 10 = e^(-1000/T + 3000/T) = e^(2000/T). Taking ln: ln(10) = 2000/T. T = 2000/ln(10) = 2000/2.3026 = 868.6 K. So T ≈ 868.43 K.
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