JEE Main · 2023 · 31 Jan 2023 · Shift 2 · Chemical Kinetics

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 1 0^{- 2} min

. (Nearest integer)
(Given :

ln 10 = 2.303

lo g 2 = 0.3010

)

Answer: 17

Solution

Reduction to one thirty-second of the initial concentration means

\frac{1}{32} = \frac{1}{2 ^{5}}

, that is five successive half-lives. The half-life of this first-order reaction is

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

, so the time needed is

t = 5 \times \frac{0.693}{20} = 0.173 min

. Expressed as asked, the time required is

17 \times 1 0^{- 2} min

JEE Main · 2023 · 31 Jan 2023 · Shift 2 · Integer answer