Question

A gaseous compound $A$ reacts by three independent first order processes (as shown in figure) with rate constant $2\times 10^{-3},3\times 10^{-3}$ and $1.93\times 10^{-3}$ sec${}^{-1}$ for products $B,C$ and $D$ respectively. If initially pure $A$ was taken in a closed container with $P=8$ atm, then the partial pressure of $B$ (in atm) after $100$ sec from start of experiment

• A. $0.288$
• B. $0.577$
• C. $1.154$
• D. none of these

Answer 1

Answer: (C)

Overall rate constant $k=k_1+k_2+k_3=6.93\times 10^{-3}$
$t_{1/2}=\frac{0.693}{6.93\times 10^{-3}}=100$ sec;
After half-life, $P_B+P_C+P_D=4$ atm
$\frac{P_B}{P_B+P_C+P_D}=\frac{k_1}{k_1+k_2+k_3}=\frac{200}{693}$
$P_B=4\times \frac{200}{693}=1.154$ atm