The rate constant for a first order reaction is 20 . The time required for the initial concentration of the reactant to reduce to its level is ______ min. (Nearest integer) (Given: ln 10 = 2.303, log 2 = 0.3010) [2023]

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Solution

Q.
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) [2023]

Ans.
(17)

$t_{1 / 2} = \frac{0.693}{k} = \frac{0.693}{20} = 0.03465 min$

${(\frac{1}{2})}^{n} = (\frac{1}{32}) = {(\frac{1}{2})}^{5}$

$No. of half-life = 5$

$Time required = 0.03465 \times 5 = 0.17325 min$

$= 17.325 \times 10^{- 2} min$

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