Question

$P{Cl}_5$ is dissociating $50$% at ${250}^{o}C$ at a total pressure of $P$ atm. If equilibrium constant is $K_p$, then which of the following relation is numerically correct?

• A. $K_P=3P$
• B. $P=3K_P$
• C. $P=\frac{2K_P}{3}$
• D. $K_P=\frac{2P}{3}$

Answer 1

Answer: (B)

$P=3K_P$

$\underset{1-x}{PC{l}_5}\rightleftharpoons \underset{x}{PC{l}_3}+\underset{x}{C{l}_2}$

Given that $x=0.5$

$\therefore$ Mole fractions of the components:

$X_{PC{l}_5}=\frac{1-0.5}{3\times 0.5}=\frac{1}{3},X_{PC{l}_3}=\frac{1}{3},X_{C{l}_2}=\frac{1}{3}$

Total pressure is $P$

$K_P=\frac{\left(P_{PC{l}_3}\right)\left(P_{C{l}_2}\right)}{\left(P_{PC{l}_5}\right)}=\frac{(X_{PC{l}_3}\times P)(X_{C{l}_2}\times P)}{(X_{PC{l}_5}\times P)}$

$=\frac{\frac{1}{3}\times P\times \frac{1}{3}\times P}{\frac{1}{3}\times P}$

$\therefore P=3K_P$