1. Tardigrade
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  3. Chemistry
  4. A flask contains a mixture of compounds A and B. Both compounds decompose by first-order kinetics. The half-lives for A and B are 300 s and 180 s , respectively. If the concentrations of A and B are equal initially, the time required for the concentration of A to be four times that of B ( in s ): (Use ln 2=0.693)

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Q. A flask contains a mixture of compounds $A$ and B. Both compounds decompose by first-order kinetics. The half-lives for $A$ and $B$ are $300 \,s$ and $180 \,s $, respectively. If the concentrations of A and $B$ are equal initially, the time required for the concentration of A to be four times that of B ( in s ): (Use ln $2=0.693)$

JEE MainJEE Main 2020Chemical Kinetics

Solution:

$[ A ]_{ t }=4[ B ]_{ t }$

$[ A ]_{0} e ^{-\left(\ln ^{2} / 300\right)^{4}}=4[ B ]_{0} e ^{(-\ln 2 / 180) t}$

$e ^{\left(\frac{\ln ^{2}}{180}-\frac{\ln ^{2}}{300}\right)}=4$

$\left(\frac{\ln ^{2}}{180}-\frac{\ln ^{2}}{300}\right) t =\ln 4$

$\left(\frac{1}{180}-\frac{1}{300}\right) t =2$

$ \Rightarrow t =\frac{2 \times 180 \times 300}{120}=900\, sec$