At 30 ° C , the half life for the decomposition of AB _ 2 is 200s and is independent of the initial concentration of AB _ 2 . The time required for 80 % of the AB _ 2 to decompose is (Given: 2 = 0 . 30 ; 3 = 0 . 48 )

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Quantrex Academy · Accepted Answer

Correct answer: C. 467s

Since half life is independent of intial concentration of the reactant, it's a first order reaction
$k = \dfrac{\ln 2}{t\dfrac{1}{2}}$
$kt = 2 . 303log\dfrac{{A}_{0}}{A}$
$\dfrac{\ln 2}{t\dfrac{1}{2}}t = 2 . 303log\dfrac{{A}_{0}}{A}$
$\dfrac{2 . 303\log 2}{200}t = 2 . 303log\dfrac{100}{20}$
$t = \dfrac{200}{0 . 3} \times \log 5 = 466 . 67sec \approx 467sec$

At 30 ° C , the half life for the decomposition of AB _ 2 is 200s...

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