Question

For the reaction,
$AB\left(g\right)\rightleftharpoons A\left(g\right)+B\left(g\right)$, $AB$ is $33$%, dissociated at a total pressure of $P$. Therefore, $P$ is related to $K_p$ by one of the following option:

• A. $P=K_p$
• B. $P=3K_p$
• C. $P=4K_p$
• D. $P=8K_p$

Answer 1

The correct option is D $P=8K_p$

33% dissociation means out of one mole of AB, $\frac{1}{3}$ mole is dissociated. So $1-\frac{1}{3}=\frac{2}{3}$ mole is present.
$AB\left(g\right)\rightleftharpoons A\left(g\right)+B\left(g\right)$
Number of moles at $t_0$ $1$ $0$ $0$
Number of moles at $t_{eq.}$ $1-\frac{1}{3}=\frac{2}{3}$ $\frac{1}{3}$ $\frac{1}{3}$
After dissociation, total number of moles $\frac{2}{3}+\frac{1}{3}+\frac{1}{3}=\frac{4}{3}$
p is the total pressure.
The partial pressure of AB
$p_{AB}=\frac{2/3}{4/3}\times p=\frac{p}{2}$;
The partial pressures of A and B are
$p_A=p_B=\frac{1/3}{4/3}\times p=\frac{p}{4}$
$K_p=\frac{p_A{p}_B}{p_{AB}}$
$K_p=\frac{\frac{p}{4}\times \frac{p}{4}}{\frac{p}{2}}$
$K_p=\frac{p}{8}$
$p=8K_p$