Question

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

• A. $23.1$ min
• B. $8.73$ min
• C. $7.53$ min
• D. $0.383$ min

Answer 1

The correct option is A $23.1$ min

We know that for a first order reaction:-

Rate$=k\left[R\right]$

$\therefore 1.5\times {10}^{-2}Mmi{n}^{-1}=k\left[0.5M\right]$

$\Rightarrow k=\frac{1.5\times {10}^{-2}M/min}{0.5M}$

$\Rightarrow k=0.03{min}^{-1}$

We also know that, half life of a first order reaction:-

$t1/2=\frac{\ln \left(2\right)}{k}$

$=\frac{0.693}{k}$

$=\frac{0.693}{0.03{min}^{-1}}$

$=23.1$ min

$\therefore$ Correct answer is an option $A=23.1$ min is the half-life of the reaction.