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

Question

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 )

TestHub · Accepted Answer

Since half life is independent of intial concentration of the reactant, it's a first order reaction
$k = \frac{\ln 2}{t_{\frac{1}{2}}}$
$kt = 2.303 \log \frac{A_{0}}{A}$
$\frac{\ln 2}{t_{\frac{1}{2}}} t = 2.303 \log \frac{A_{0}}{A}$
$\frac{2.303 \log 2}{200} t = 2.303 \log \frac{100}{20}$
$t = \frac{200}{0.3} \times \log 5 = 466.67 \sec \approx 467 \sec$

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