Question

For the reaction: $AB\left(g\right)\rightleftharpoons A\left(g\right)+B\left(g\right)$,
$AB$ is $25\%$ dissociated at a total pressure of P. Then,

• A. $P=K_p$
• B. $P=25K_p$
• C. $P=15K_p$
• D. $P=8K_p$

Answer 1

The correct option is C $P=15K_p$

$\begin{array}{ccccc}AB\left(g\right)& \rightleftharpoons & A\left(g\right)& +& B\left(g\right)\\ 1& & 0& & 0\\ -\frac{1}{4}& & \frac{1}{4}& & \frac{1}{4}\\ \frac{3}{4}& & \frac{1}{4}& & \frac{1}{4}\end{array}$
${\left(\sum n\right)}_{\text{Equilibrium}}=\frac{3}{4}+\frac{1}{4}+\frac{1}{4}=\frac{5}{4}$
$\therefore K_p=\frac{P_A.P_B}{P_{AB}}=\frac{\left(\frac{\frac{1}{4}}{\frac{5}{4}}P\right)\left(\frac{\frac{1}{4}}{\frac{5}{4}}P\right)}{\left(\frac{\frac{3}{4}}{\frac{5}{4}}P\right)}$
or, $K_p=\frac{1}{15}P$
$\Rightarrow P=15K_p$