1. Tardigrade
  2. Question
  3. Chemistry
  4. At 30° C, the half life for the decomposition of AB 2 is 200 s and is independent of the initial concentration of AB 2. The time required for 80 % of the AB 2 to decompose is (Given: log 2=0.30 ; log 3=0.48 )

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Q. At $30^{\circ} C$, the half life for the decomposition of $AB _2$ is $200\, s$ and is independent of the initial concentration of $AB _2$. The time required for $80 \%$ of the $AB _2$ to decompose is (Given: $\log 2=0.30 ; \log 3=0.48$ )

JEE MainJEE Main 2022Chemical Kinetics

Solution:

$ T _{1 / 2}=200 s $ and $ 1^{\text {st }} $ order reaction
$ K =\frac{2.303 \log 2}{200}=\frac{2.303}{ t } \log \frac{ A _0}{0.2 A _0} $
$ \frac{\log 2}{200}=\frac{1}{ t } \log 5 $
$ t =\frac{7}{3} \times 200=466.67 s =467 s$