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  • A flask contains a mixture of compounds A and B, both compounds decompose by first order kinetics. The halflives for A and Bare 450 s and 200 s respectively. If concentrations of A and B&

A flask contains a mixture of compounds A and B, both compounds decompose by first order kinetics. The halflives for A and Bare 450 s and 200 s respectively. If concentrations of A and B are equal initially, the time required for the concentration of A to be four times that of B

Option: 1

720 sec


Option: 2

580 sec


Option: 3

1000 sec


Option: 4

422 sec


Answers (1)

best_answer

\mathrm{\begin{aligned} & C_t=C_0 e^{-k t} ; k=\frac{\ln 2}{t_{1 / 2}} \\\\ & \left(C_t\right)_A=\left(C_0\right)_A e^{-k_A t} ; k_A=\frac{\ln 2}{0} \\\\ & (C t)_B=\left(C_0\right)_B e^{-k_B t} ; k_B=\frac{\ln 2}{200} \\\\ & \frac{\left(C_t\right)_B}{(C t)_A}=\frac{\left(C_0\right)_B}{\left(C_0\right)_A} \times e^{(K B-k A) t} \end{aligned}}

\mathrm{\begin{aligned} & 4=e^{(K B-K A) t} \\ \\& 2 \ln 2=\left[\frac{\ln 2}{200}-\frac{\ln 2}{450}\right] t \\\\ & 2 \ln 2=\ln 2\left[\frac{1}{200}-\frac{1}{450}\right] t \\ \\& 2=\left[\frac{9-4}{1800}\right] t \\ \\& 720 \mathrm{sec}=t \end{aligned}}

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Devendra Khairwa

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