Question

At a temp, $T$, a compound $A{B}_4\left(g\right)$ dissociates as $2A{B}_4\left(g\right)\rightleftharpoons A_2\left(g\right)+4B_2\left(g\right)$ with a degree of dissociation $x$, which is small compared with unity. The expression of $K_p$ in terms of $x$ and total pressure $P$ is:

• A. $8P^3{x}^5$
• B. $256P^3{x}^5$
• C. $4P{x}^2$
• D. None of these

Answer 1

The correct option is A $8P^3{x}^5$

$2A{B}_4\rightleftharpoons A_2+4B_{2}c00$

At equilibrium:

$c-cx\frac{cx}{2}2cx$

Total number of moles at equilibrium = $c(1+\frac{3x}{2})\approx c,asx<<1$

partial pressure of each specie is:

$p_{A{B}_4}=P.c(1-x)/c=P(1-x)=P{p}_{A_2}=P.\frac{cx}{2}/c=\frac{Px}{2}{p}_{B_2}=P.2cx/c=2Px$

Using the relation $K_p=\frac{{\left[A_2\right]\left[B_2\right]}^4}{{\left[A{B}_4\right]}^2}=\frac{p_{A_2}.{\left(p_{B_2}\right)}^4}{{\left(p_{A{B}_4}\right)}^2}$

Upon substituting the values we get:

$K_p=8P^3{x}^5$

Therefore option A is correct.