In the system, LaCl3(s) + H2O (g)+heat → LaClO(s) + 2 HCl (g), equilibrium is established. More water vapour is added to reestablish the equilibrium. The pressure of water vapour is doubled. The factor by which pressure of HCl is changed is

Q: In the system, LaCl3(s) + H2O (g)+heat → LaClO(s) + 2 HCl (g), equilibrium is established. More water vapour is added to reestablish the equilibrium. The pressure of water vapour is doubled. The factor by which pressure of HCl is changed is

(A) 2

(B) √2

(C) √3

(D) √5

Solution:  LaCl3(s) + H2O(g) + heat $\rightleftharpoons $    LaClO(s) + 2HCl(g)

At eq.   P1        P2

$\large K_P = \frac{P_2^2}{P_1} $

When  pH2O = 2P1 , Let pHCl = P2

$\large K_P = \frac{P_2^2′}{2 P_1} $

$\large \frac{P_2^2′}{2 P_1} = \frac{P_2^2}{P_1} $

$\large P_2’^2 = 2 P_2^2 $

$\large P_2’ = \sqrt{2} P_2 $

Therefore pressure of HCl is changed by √2 factor.

Ans: (B)