Question

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

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

Answer 1

Answer: (B)

For the first order reaction,
$ Rate \, \big(\frac{dx}{dt}\big)=k [A]$
[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
$\therefore \, \, 1.5 \times 10^{-2}=k \times 0.5$
$\therefore k=\frac{1.5 \times 10^{-2}}{0.5}$
$ =3 \times 10^{-2} \, min^{-1}$
For first order reaction,
half-life period, $t_{1/2}=\frac{0.693}{k}=\frac{0.693}{3 \times 10^{-2}}$
$ = 23.1\, min$