COMEDK · Chemistry · 19. Chemical Kinetics
The rate constants for two different reactions, \(k_1\) and \(k_2\) are \(10^{16}\cdot e^{-2000/T}\) and \(10^{15}\cdot e^{-1000/T}\) respectively. The temperature at which \(k_1 = k_2\) is
- A \(\dfrac{2000}{2.303}\ K\)
- B \(1000\ K\)
- C \(\dfrac{1000}{2.303}\ K\)
- D \(2000\ K\)
Answer & Solution
Correct Answer
(C) \(\dfrac{1000}{2.303}\ K\)
Step-by-step Solution
Detailed explanation
Given \(k_1 = 10^{16} \cdot e^{-2000/T}\) and \(k_2 = 10^{15} \cdot e^{-1000/T}\) Equating \(k_1\) and \(k_2\): \(10^{16} \cdot e^{-2000/T} = 10^{15} \cdot e^{-1000/T}\) \(\dfrac{10^{16}}{10^{15}} = \dfrac{e^{-1000/T}}{e^{-2000/T}}\) \(10 = e^{1000/T}\) Taking natural logarithm…
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