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 $1.93\times {10}^{-3}$ $se{c}^{-1}$ 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

The correct option is D none of these

The expression for the rate constant for the first order reaction is $k=\frac{1}{t}\ln \left(\frac{[A{]}_0}{[A{]}_t}\right)$
For the three independent reactions, the expression becomes $k_1+k_2+k_3=\frac{1}{t}\ln \left(\frac{[A{]}_0}{[A{]}_t}\right)$
Substitute values in the above expression.
$2\times {10}^{-3}+3\times {10}^{-3}+1.93\times {10}^{-3}=\frac{1}{t}\ln \left(\frac{[A{]}_0}{[A{]}_t}\right)$
$[A{]}_t=4.00atm$.