The rate of a first-order reaction is $1.5 imes 10^{-2} ext{ mol L}^{-1} ext{ min}^{-1}$ at $0.5 ext{

Question

The rate of a first-order reaction is $1.5 	imes 10^{-2} 	ext{ mol L}^{-1} 	ext{ min}^{-1}$ at $0.5 	ext{ M}$ concentration of the reactant. The half-life of the reaction is:

Accepted Answer

For a first-order reaction, the rate law is given by $	ext{Rate} = k[A]$.
Given:
$	ext{Rate} = 1.5 	imes 10^{-2} 	ext{ mol L}^{-1} 	ext{ min}^{-1}$
Concentration $[A] = 0.5 	ext{ M}$

First, we calculate the rate constant ($k$):
$k = \frac{	ext{Rate}}{[A]} = \frac{1.5 	imes 10^{-2}}{0.5} = 3.0 	imes 10^{-2} 	ext{ min}^{-1}$

The half-life ($t_{1/2}$) of a first-order reaction is related to the rate constant by the formula:
$t_{1/2} = \frac{0.693}{k}$

Substituting the value of $k$:
$t_{1/2} = \frac{0.693}{3.0 	imes 10^{-2}} = 23.1 	ext{ min}$.

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