Question

$A$ and $B$ are two different chemical species undergoing first order decomposition with rate constants $K_A$ and $K_B$ which are in the ratio of 3:2, respectively. If the initial concentration of $A$ and $B$ are in the ratio of $[A{]}_0:[B{]}_0=3:2$, what would be the ratio $\left[A\right]:\left[B\right]$ after three half lives of $A$?

Answer 1

Given, $A_o/B_o=3/2$

Suppose the half line of $A$ be $20$ years & that of $B$ is $30$ years.

After $3$ half lines, $\left[A\right]=\frac{\left[A_o\right]}{8}$ in $60$ years.

After $30$ years, $\left[B\right]=\left[B_o\right]/2$ & after $60$ years, $\left[B\right]=B/4$

$\therefore$ Ratio of concentration is

$\left(A_o/8\right)/\left(B_o/4\right)=\frac{A_o}{B_o}\left(\frac{4}{8}\right)=\frac{3}{2}\left(\frac{4}{8}\right)=\frac{3}{4}$