At a temperature T, a compound ${AB}_{4} (g)$ dissociates as $2 {AB}_{4} (g) ⇌ A_{2} (g) + 4 B_{2} (g)$ with a degree of dissociationx, which is small compared with unity. The expression of $K_{p}$ in terms of x and total pressure P is :

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

$256 P^{3} x^{5}$

none of these

$4 P x^{2}$

answer is A.

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Detailed Solution

The reaction for A, B is given as;

$\begin{array}{l} \begin{aligned} 2 A B_{4} & ⇌ & A_{2} & + & 4 B_{2} \\ 1 - x & \frac{x}{2} & 2 x \end{aligned} \\ ≃ 1 \\ K_{P} = \frac{\frac{x}{2} \times (2 x)^{4} \times P^{3}}{1^{2}} \end{array}$

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