Question

The rate of 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. 0.383 min
• B. 23.1 min
• C. 8.73 min
• D. 7.53 min

Answer 1

Answer: (B)

For the first order reaction,
$Rate\left(\frac{dx}{dt}\right)=k[A]$
[A] = concentration of reactant
k - rate constant
Given that
$\frac{dx}{dt}=1.5\times 10^{-2}mol{L}^{-1}mi{n}^{-1}$
$k=$ ? and [A] = 0.5 M
$\therefore 1.5\times 10^{-2}=k\times 0.5$
$\therefore k=\frac{1.5\times 10^{-2}}{0.5}$
$=3\times 10^{-2}mi{n}^{-1}$
For first order reaction,
half-life period, $t_{1/2}=\frac{0.693}{k}=\frac{0.693}{3\times 10^{-2}}$
$=23.1min$