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  3. Chemistry
  4. 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 (1/32) level is × 10-2 min. (Nearest integer) (Given: ln 10=2.303 log 2=0.3010 )

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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: $\ln 10=2.303$ $\log 2=0.3010$ )

JEE MainJEE Main 2023Chemical Kinetics

Solution:

$ C =\frac{ C _{ o }}{2^{ n }} =\frac{ C _{ o }}{32} $
$ n =5 $
$ t =5 t _{1 / 2} $
$ =\frac{5 \times 0.693}{20}=\frac{0.693}{4} $
$ =0.17325 \min =17.325 \times 10^{-2} \min $