The rate constant for a first order reaction is 20 ^ - 1 . The time...

For a first order reaction, we know:
${t}_{1/2} = \dfrac{0 . 693}{k} = \dfrac{0 . 693}{20} = 0 . 03465min$
From the relation of half lives(where 'n' is the no. of half-lives):

$⇒ {\left(\dfrac{1}{2}\right)}^{n} = \left(\dfrac{1}{32}\right)$

$= {\left(\dfrac{1}{2}\right)}^{5}$

Thus, No. of Half life $= 5$

$∴$Time required $= 0 . 03465 \times 5 = 0 . 17325min = 17 . 325 \times {10}^{- 2}min$