A first order reaction is $20 \%$ complete in $10 \mathrm{~min}$. The rate constant of the reaction is

A first order reaction is $20 \%$ complete in $10 \mathrm{~min}$. The rate constant of the reaction is
  1. $0.223 \mathrm{~min}^{-1}$
  2. $0.0223 \mathrm{~min}^{-1}$
  3. $2.23 \mathrm{~min}^{-1}$
  4. $22.3 \mathrm{~min}^{-1}$

Solution

$\log \frac{[\mathrm{A}]_{t}}{[\mathrm{~A}]_{0}}=-\frac{k}{2.303} t \quad$ i.e. $\quad \log 0.8 \quad=-\frac{k}{2.303}(10 \mathrm{~min})$
or $\quad k=-\frac{2.303}{10 \min } \log (0.8)=0.0223 \mathrm{~min}^{-1}$

Asked in: JEE-TOPICTESTS-CHEMISTRY

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