Consider the following chemical equilibrium of the gas phase reaction at a constant temperature :
$$A(g) \rightleftharpoons B(g) + C(g)$$

If p being the total pressure, $$K_p$$ is the pressure equilibrium constant and $$\alpha$$ is the degree of dissociation, then which of the following is true at equilibrium ?

For the gas-phase equilibrium $$A(g)\;\rightleftharpoons\;B(g)+C(g)$$ consider that one mole of $$A$$ is initially present at total pressure $$p$$. Let $$\alpha$$ be the degree of dissociation at equilibrium.

Moles present at equilibrium:
  • $$A$$ : $$1-\alpha$$
  • $$B$$ : $$\alpha$$
  • $$C$$ : $$\alpha$$

Total moles $$n_{\text{tot}} = 1-\alpha+\alpha+\alpha = 1+\alpha$$.

Because total pressure is $$p$$, the partial pressures are obtained from mole fractions:

$$p_A = \frac{1-\alpha}{1+\alpha}\,p,\qquad p_B = \frac{\alpha}{1+\alpha}\,p,\qquad p_C = \frac{\alpha}{1+\alpha}\,p$$

The pressure equilibrium constant is

$$K_p = \frac{p_B\,p_C}{p_A} = \frac{\left(\dfrac{\alpha p}{1+\alpha}\right) \left(\dfrac{\alpha p}{1+\alpha}\right)} {\dfrac{(1-\alpha)p}{1+\alpha}} = \frac{\alpha^{2}p}{(1-\alpha)(1+\alpha)} = \frac{\alpha^{2}p}{1-\alpha^{2}} \;-(1)$$

Rearrange $$-(1)$$ to express $$\alpha$$ in terms of $$K_p$$ and $$p$$:

$$\alpha^{2}p = K_p(1-\alpha^{2})$$
$$\alpha^{2}(p+K_p) = K_p$$
$$\alpha^{2} = \frac{K_p}{p+K_p} \;-(2)$$
$$\alpha = \sqrt{\frac{K_p}{p+K_p}}$$

Now study how $$\alpha$$ depends on the total pressure $$p$$ while temperature (hence $$K_p$$) remains constant.

When $$p$$ increases:
From $$-(2)$$ the denominator $$p+K_p$$ increases, so the fraction $$\dfrac{K_p}{p+K_p}$$ decreases. Therefore $$\alpha^{2}$$ and hence $$\alpha$$ decrease.

Thus, “When $$p$$ increases $$\alpha$$ decreases” is correct (Option B).

Check the other statements:

Case $$p \gg K_p$$:
$$\alpha^{2} \approx \dfrac{K_p}{p}\ll 1\;\Rightarrow\;\alpha\ll 1$$, not $$\alpha\approx 1$$. Hence Option A is wrong.

Case $$K_p \gg p$$:
$$\alpha^{2} \approx \dfrac{K_p}{K_p}=1\;\Rightarrow\;\alpha\approx 1$$, not “much less than unity”. Hence Option C is wrong.

Option D is opposite to the correct trend, so it is also wrong.

Therefore, the only true statement is Option B.