At 30°C, the half life for the decomposition of AB₂ is 200 s and is independent of the initial concentration of AB₂. The time required for 80% of the AB₂ to decompose is (Given: log 2 = 0.30; log 3 = 0.48)

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532 s

200 s

467 s

323 s

answer is C.

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Detailed Solution

$T_{1 / 2} = 200 s$ and 1^st order reaction

$\begin{array}{l} K = \frac{2 .303 \log 2}{200} = \frac{2 .303}{t} \log \frac{A_{0}}{0 .2 A_{0}} \\ \frac{\log 2}{200} = \frac{1}{t} \log 5 \\ t = \frac{7}{3} \times 200 = 466 .67 s = 467 s \end{array}$

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