The rate of a first order reaction is $1.5 \times 10^{-2} \mathrm{~mol} \mathrm{~L}^{-1}$ $\min ^{-1}$ at $0…

The rate of a first order reaction is $1.5 \times 10^{-2} \mathrm{~mol} \mathrm{~L}^{-1}$ $\min ^{-1}$ at $0.5 \mathrm{M}$ concentration of the reactant. The halflife of the reaction is
  1. $0.383 \mathrm{~min}$
  2. $23.1 \mathrm{~min}$
  3. $8.73 \mathrm{~min}$
  4. $7.53 \mathrm{~min}$

Solution

For a first order reaction, $\mathrm{A} ightarrow$ Products
$r=k[\mathrm{~A}]$ or $k=\frac{r}{[\mathrm{~A}]}$
$\Rightarrow k=\frac{1.5 \times 10^{-2}}{0.5}=3 \times 10^{-2}$
Further, $t_{1 / 2}=\frac{0.693}{k}=\frac{0.693}{3 \times 10^{-2}}=23.1$

Asked in: JEE-TOPICTESTS-CHEMISTRY

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