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Given, k₁ = 10¹⁶.e^(−2000/T) and k₂ = 10¹⁵.e^(−1000/T). When k₁ and k₂ are equal at any temperature T, we have:

1. 10 × 10¹⁵.e^(−2000/T) = 10¹⁵.e^(−1000/T)
2. 10.e^(−2000/T) = e^(−1000/T)
3. ln 10 − 2000/T = −1000/T
4. ln 10 = 2000/T − 1000/T

Correct answer: ln 10 = 2000/T − 1000/T

Solution

Equating k₁ and k₂, we get 10¹⁶.e^(−2000/T) = 10¹⁵.e^(−1000/T). Simplifying, we divide both sides by 10¹⁵, leading to 10.e^(−2000/T) = e^(−1000/T). Taking the natural logarithm, ln(10) = 2000/T − 1000/T.

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