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 $k = k_{1} + k_{2} + k_{3} = 6.93 \times 10^{-3}$
$t_{1/2} = \frac{0.693}{6.93 \times10^{-3}} =100$ 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