Question

Consider the following parallel reactions being given by $A(t_{1/2}=$ $1.386\times 10^2$ hours), each path being $1^{\text{st }}$ order.

If distribution of $A$ in the product mixture is $50\%$, calculate partial half-life of $A$ for the conversion into $B$.

• A. 346.5 h
• B. 231 h
• C. 154 h
• D. 92.4 h

Answer 1

Answer: (B)

$\frac{2k_1}{2k_1+3k_2}=0.5$ and $k_1+k_2=\frac{0.693}{1.386\times 10^2}=5\times 10^{-3}{h}^{-1}$
Solving
$\frac{k_1}{k_2}=\frac{3}{2}$ and $k_1=3\times 10^{-3}{h}^{-1}$ and $k_2=2\times 10^{-3}{h}^{-1}$
$t_{1/2(A\to B)}=\frac{0.693}{k_1}=\frac{0.693}{3\times 10^{-3}}=231h$