The half-life of a substance in a first-order reaction is 15 minutes.…

Give,

Half-life $= 15 min$

We know for a first order reaction,

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

or, $k = \frac{0.693}{ t_{1/2}}$

$⇒k = \frac{0.693}{ 15}$

$⇒k = 0.462$

$⇒k = 4.62 × 10^{−2} min^{−1}$