At temperature, T, a compound A B_ 2 ( g ) dissociates according to the reaction; 2A B_ 2 ( g ) 2A B_ ( g ) + B_ 2 ( g ) with a degree of dissociation x, which is small compared with unity. The expression for K_p, in terms of x and the total pressure, P is

At temperature, T, a compound A B_ 2 ( g ) dissociates according …

MCQ

At temperature, $T$, a compound $A{B_{2\left( g \right)}}$ dissociates according to the reaction; $2A{B_{2\left( g \right)}} \rightleftharpoons 2A{B_{\left( g \right)}} + {B_{2\left( g \right)}}$ with a degree of dissociation $x$, which is small compared with unity. The expression for $K_p$, in terms of $x$ and the total pressure, $P$ is

✓
$\frac{{P{x^3}}}{2}$
B
$\frac{{P{x^2}}}{3}$
C
$\frac{{P{x^3}}}{3}$
D
$\frac{{P{x^2}}}{2}$

✓

Answer

Correct option: A.

$\frac{{P{x^3}}}{2}$

a
$\mathop {\mathop {2A{B_{2(g)}}}\limits_1 }\limits_{1 - x} \rightleftharpoons \mathop {\mathop {2A{B_{(g)}}}\limits_0 }\limits_x + \mathop {\mathop {{B_{2(g)}}}\limits_0 }\limits_{x/2} $

$\therefore {{\text{K}}_{\text{p}}} = \frac{{{{\text{x}}^2} \cdot {\text{x}}}}{{2{{(1 - {\text{x}})}^2}}} \times {\left[ {\frac{{\text{P}}}{{1 + \frac{{\text{x}}}{2}}}} \right]^1}$