The rate constant for a first order reaction | vedclass

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Question

(C) For a first order reaction,the rate constant $k$ is given by $k = \frac{2.303}{t} \log \frac{[A]_0}{[A]_t}$.Given $[A]_t = \frac{[A]_0}{32}$ and $

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$17$

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(C) For a first order reaction,the rate constant $k$ is given by $k = \frac{2.303}{t} \log \frac{[A]_0}{[A]_t}$.Given $[A]_t = \frac{[A]_0}{32}$ and $k = 20 \, min^{-1}$.Substituting the values: $20 = \frac{2.303}{t} \log \frac{[A]_0}{[A]_0 / 32} = \frac{2.303}{t} \log 32$.Since $32 = 2^5$,$\log 32 = 5 \log 2 = 5 	imes 0.3010 = 1.505$.$t = \frac{2.303 	imes 1.505}{20} = \frac{3.466}{20} = 0.1733 \, min$.Converting to $10^{-2} \, min$: $0.1733 \, min = 17.33 	imes 10^{-2} \, min$.The nearest integer is $17$.

The rate constant for a first order reaction is $20 \, min^{-1}$. The time required for the initial concentration of the reactant to reduce to its $\frac{1}{32}$ level is $........ \times 10^{-2} \, min$. (Nearest integer) (Given: $\ln 10 = 2.303, \log 2 = 0.3010$)

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