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$\mathrm{A\: and \: B}$ are two different Chemical species Undergoing first order decomposition with rate constants $\mathrm{K_A\: and \: K_B}$ which are in the ratio of $3: 2$ respectively. If the initial Concentration of $\mathrm{A\: and \: B}$ are in the ratio $\mathrm{[A]_0:[B]_0\Rightarrow 3: 2}$ , what would be the ratio $\mathrm{[A]:[B]}$ after three half lives of $\mathrm{A}$ ?

Option: 1
$2:4$

Option: 2
$3:4$

Option: 3
$1:2$

Option: 4
$2:1$

Answers (1)

best_answer

$\mathrm{k_A: K_B}$ When A complete three half lives B complete two half lives.

$\mathrm{3:2}$

$\mathrm{ \left(t 1/2\right)_A:\left(t1/2\right)_B }$

$2:3$

1st half life 2nd half life 3rd half life

$\mathrm{ [A]=\frac{[A]_0}{2} \Rightarrow \frac{[A]_0}{2 \times 2} \Rightarrow \frac{[A]_0}{2 \times 2 \times 2} }$

1st half life 2ns half life

$\mathrm{{[B]=\frac{[B]_0}{2} \Rightarrow \frac{[B]_0}{4}} }$

$\mathrm{{[A]:[B] \Rightarrow \frac{[A]_0}{8}: \frac{[B]_0}{4}} }$

$\mathrm{\Rightarrow \frac{3}{8}:\frac{2}{4}}$

$\Rightarrow 3:4$

Hence option 2 is correct.

Posted by

SANGALDEEP SINGH

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