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. 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

Since for a first order reactions: Rate $=K\left[R\right]$

rate given $=1.5\times {10}^{-2}M$ ${min}^{-1}$ at $0.5M$ concentration

$1.5\times {10}^{-2}M{min}^{-1}=K\left(0.5M\right)$

$K=3\times {10}^{-2}{min}^{-1}$

Half-life $=t_{1/2}=0.693/k$

$t_{1/2}=\frac{0.693}{0.03{min}^{-1}}=23.1$ minutes

$\therefore$ Half-life of reaction is $23.1$ minutes.

Hence, the correct option is $B$