Q. The rate constants k₁ and k₂ for two different reactions are 10¹⁶·e^(−2000/T) and 10¹⁵·e^(−1000/T) respectively. The temperature at which k₁ = k₂ is
A) (1000/2.303) K
B) 1000 K
C) (2000/2.303) K
D) 2000 K
Explanation
[Solution from source] Setting 10¹⁶e^(−2000/T) = 10¹⁵e^(−1000/T) gives 10 = e^(1000/T), so 1000/T = ln 10 = 2.303 and T = 1000/2.303 K ≈ 434 K. 1000 K would come from wrongly taking ln 10 as 1. Answer (1).
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.