For a first order reaction $\mathrm{A} \longrightarrow \mathrm{B}$ the reaction rate at reactant…

For a first order reaction $\mathrm{A} \longrightarrow \mathrm{B}$ the reaction rate at reactant concentration of $0.01 \mathrm{M}$ is found to be $2.0 \times 10^{-5} \mathrm{~mol} \mathrm{~L}^{-1} \mathrm{~s}^{-1}$. The half life period of the reaction is
  1. $30 \mathrm{~s}$
  2. $220 \mathrm{~s}$
  3. $300 \mathrm{~s}$
  4. $347 \mathrm{~s}$

Solution

Given $[\mathrm{A}]=0.01 \mathrm{M}$
Rate $=2.0 \times 10^{-5} \mathrm{~mol} \mathrm{~L}^{-1} \mathrm{~s}^{-1}$
For a first order reaction Rate $=k[\mathrm{~A}]$
$k=\frac{2.0 \times 10^{-5}}{[0.01]}=2 \times 10^{-3}$
$t_{1 / 2}=\frac{0.693}{2 \times 10^{-3}}=347 \mathrm{sec}$

Asked in: JEE-TOPICTESTS-CHEMISTRY

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