Question

For the following parallel chain reaction

what will be that value of overall half-life of $A$ in minutes? $\left[\text{ Given that }\frac{[B{]}_t}{[C{]}_t}=\frac{16}{9}\right]$

Answer 1

Answer: 3.3

We have,
$\frac{[B{]}_t}{[C{]}_t}=\frac{4k_1}{3k_2}=\frac{16}{9}$
so, $\frac{k_1}{k_2}=\frac{4}{3}$
Now, $k=k_1+k_2=\left[2\times 10^{-3}+\frac{3}{4}\times 2\times 10^{-3}\right]{\sec }^{-1}$ $=\frac{7}{2}\times 10^{-3}se{c}^{-1}=\frac{7\times 10^{-3}\times 60}{2}{\min }^{-1}$
so, $t_{1/2}=\frac{\ln 2}{7\times 30\times 10^{-3}}min$
$=\frac{693}{7\times 30}=3.3\min$