The rate constant for a first order reaction is $20 \mathrm{~min}^{-1}$. The time required for the initial concentration of the reactant to reduce to its $\frac{1}{32}$ level is _______ $\times 10^{-2} \mathrm{~min}$. (Nearest integer)
(Given : $\ln 10=2.303$ and $\log 2=0.3010 \text { )}$
Answer (integer)
17
Solution
$K=20 \mathrm{~min}^{-1}$
<br/><br/>$\mathrm{t}_{1 / 2}=\frac{0.6932}{20}=\frac{\ln 2}{20}$
<br/><br/>Required time $=\mathrm{n} \times \mathrm{t}_{1 / 2}$
<br/><br/>$C = {{{C_0}} \over {{2^n}}} = {{{C_0}} \over {32}}$
<br/><br/>$\Rightarrow$ ${2^n} = 32$ = ${2^5}$
<br/><br/>$\Rightarrow$ n = 5
<br/><br/>$$
\begin{aligned}
\text { Required time } & =\frac{5 \times 0.6932}{20} \\\\
& =0.173 \mathrm{~min} \\\\
& =17.3 \times 10^{-2} \mathrm{~min}
\end{aligned}
$$
About this question
Subject: Chemistry · Chapter: Chemical Kinetics · Topic: Rate of Reaction
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