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  • A and B decompose via first order kinetics with half lives and <img alt="20 \math

A and B decompose via first order kinetics with half lives 56.0 \mathrm{~min} and 20 \mathrm{~min} respectively. starting from equmolar non reactive mixture of A and B, the time taken for the concentration of A to becomes 16 times that of B is

Option: 1

124 min


Option: 2

180 min


Option: 3

320 min


Option: 4

150 min


Answers (1)

best_answer

Initially: \mathrm{\left[\mathrm{A}_0\right]=\left[\mathrm{B}_0\right]=a}

After time \mathrm{' t ' \min \div[A]=16[B]}

\mathrm{ \begin{aligned} & {[A]=\left[A_0\right] e^{-k_A t}} \\\\ & {[B]=\left[B_0\right] e^{-k_B t}} \\\\ & a \cdot e^{-k_A t}=16 a e^{-k_B t} \end{aligned} }

\mathrm{\begin{gathered} (k B-k A) t=\ln 16 \\ \ln 2\left(\frac{1}{20}-\frac{1}{56}\right) t=4 \ln 2 \\ \left(\frac{14-5}{280}\right) t=4 \\ \left(\frac{9}{280}\right) t=4 \\ t=\frac{4 \times 280}{9} \\ t=124 \mathrm{~min} \end{gathered}}

Posted by

manish painkra

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