The rate constant of a first order reaction is $10^{-3} \, \mathrm{min}^{-1}$ at $300 \, \mathrm{K}$. The temperature coefficient of the reaction is 2. What is the rate constant of the reaction at $350 \, \mathrm{K}$ approximately?
A$16 \times 10^{-3}$
B$64 \times 10^{-3}$
C$32 \times 10^{-3}$
D$2^{50}$
Answer & Solution
Correct answer: C. $32 \times 10^{-3}$
Temperature coefficient $2$ means the rate constant doubles for every rise of $10 \, \mathrm{K}$. From $300 \, \mathrm{K}$ to $350 \, \mathrm{K}$, the increase is $50 \, \mathrm{K}$, so there are $5$ such intervals.
$$k_2 = k_1 \times 2^5$$
$$k_2 = 10^{-3} \times 32$$
$$k_2 = 32 \times 10^{-3}$$
On checking the options, this matches option $\mathrm{(C)}$.
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