Question

The rate of first-order reaction is 1.5 × 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

The correct option is B 23.1 min

For the first-order reaction,

$\frac{dx}{dt}=k\left[A\right]$ & $t_{1/2}=\frac{0.693}{k}$
Given:
$\frac{dx}{dt}=1.5\times {10}^{-2}mol{L}^{-1}mi{n}^{-1}$
$\left[A\right]=0.5M$
$k=3\times {10}^{-2}$

$t_{1/2}=\frac{0.693}{3\times {10}^{-2}}=23.1min$
Option B is correct.