Explanation

(b)
For the first order reaction
$Rate\left( \frac{dx}{dt} \right) = k\lbrack A\rbrack$
[A]→concentration of reactant
K→rate constant
Given that,
$\frac{dx}{dt} = 1.5 \times 10^{- 2}mol\ L^{- 1}\min^{- 1}$
K=? and [A]=0.5 M
$1.5 \times 10^{- 2} = k \times 0.5$
$k = \frac{1.5 \times 10^{- 2}}{0.5}$ =$3 \times 10^{- 3}\min^{- 1}$
For first order reaction,
Half-life period $t_{1/2} = \frac{0.693}{k} = \frac{0.693}{3 \times 10^{- 2}}$
=23.1min