Question

For a first-order reaction; A $\to$ B, the reaction rate at a reactant concentration of 0.01 M is found to be $2.0\times {10}^{-5}$ mole L${}^{-1}$s${}^{-1}$. The half-life period of the reaction is:

• A. $300s$
• B. $30s$
• C. $220s$
• D. $347s$

Answer 1

The correct option is D $347s$

$A\to B$

Rate$\to \frac{-d\left[A\right]}{dt}=K\left[A\right]$

when $\left[A\right]$ = 0.01M, given that rate = $2\times {10}^{-5}M{s}^{-1}$

$K=2\times {10}^{-3}$

Using integrated rate law expression,

the half life $\left(t_{1/2}\right)$ is given by $\frac{0.693}{K}$

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

$t_{1/2}=\frac{0.693}{2\times {10}^{-3}}$

$\Rightarrow t_{1/2}=346.5s$

$t_{1/2}\approx 347s$