QJEEM23Cha711: JEE Main 2023 Chemistry - Class 12 JEEM23Cha711 Solution: The rate constant for a first order reaction is . The time…

Question

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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 { )}

Accepted Answer

K=20 \mathrm{~min}^{-1}

\mathrm{t}_{1 / 2}=\frac{0.6932}{20}=\frac{\ln 2}{20}

Required time

=\mathrm{n} \times \mathrm{t}_{1 / 2}

C = {{{C_0}} \over {{2^n}}} = {{{C_0}} \over {32}}

\Rightarrow

{2^n} = 32

=

{2^5}

\Rightarrow

n = 5

\begin{aligned}\text { Required time } &amp; =\frac{5 \times 0.6932}{20} \\\\&amp; =0.173 \mathrm{~min} \\\\&amp; =17.3 \times 10^{-2} \mathrm{~min}\end{aligned}

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