Question

For the reaction $A B(g) \rightleftharpoons A(g)+B(g), A B$ is $33 \%$ dissociated at a total pressure of $p$. Therefore, $p$ is related to $K_{p}$ by one of the following options

• A. $P = K_{p}$
• B. $P = 3K_{p}$
• C. $P = 4K_{p}$
• D. $P = 8K_{p}$

Answer 1

Answer: (D)

Total pressure at equilibrium,
$=1-0.33+0.33+0.33$
$=1+0.33=1.33$
$p_{A} =\frac{0.33}{1.33} p$
$p_{B} =\frac{0.33}{1.33} p$
$p_{A B} =\frac{0.67}{1.33} p$
(Where, $p_{A}, p_{B}$ and $p_{A B}$ are partial pressures of $A, B$ and $A B$.)
$K_{p} =\frac{p_{A} \cdot p_{B}}{p_{A B}}$
$=\frac{\frac{0.33}{1.33} p \cdot \frac{0.33}{1.33} p}{\frac{0.67}{1.33} p}$
$=\frac{(0.33)^{2} p}{1.33 \times 0.67}$
$=\frac{0.1089 \times p}{0.8911}$
$K_{p} =0.122\, p$
$p =\frac{K_{p}}{0.122}=8\, K_{p}$