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At temperature, T, a compound ${AB}_{2} (g)$ dissociates ccording to the reaction $2 {AB}_{2} (g) \Leftrightarrow 2 AB (g) + B_{2} (g)$ with a degree of dissociation, x, which is small compared with unity. Deduce the expression for $K_{p}$ in terms of x and the total pressure, P.

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$\frac{{Px}^{2}}{2}$

$\frac{{Px}^{2}}{3}$

$\frac{{Px}^{3}}{2}$

$\frac{{Px}^{3}}{3}$

answer is A.

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Detailed Solution

The equilibrium reaction for A and B is given as;

$\begin{array}{lcc} 2 A B_{2} (g) & ⇌ 2 A B (g) + B_{2} (g) \\ a (1 - x) & a x & \frac{a x}{2} \\ ~ a \end{array}$

$n_{T} = a (1 + \frac{x}{2}) ~ a$

$K_{P} = x^{2} \times P \times \frac{x}{2}$

$K_{p}$ = $\frac{{Px}^{3}}{2}$

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