Water decomposes at a high temperature according to the reaction: H ₂ O(g) H ₂ (g) + 1 2 O ₂ (g) The reaction is carried out in a vessel containing Argon gas. At equilibrium, the total pressure of the mixture is 10 bar and the mole fraction of Argon is 0.8 . If the equilibrium constant K_p for the reaction is 8 10⁻³ , the percentage of water decomposed is _____ (Nearest integer).

Step-by-step solution

According to Dalton's law of partial pressures, the effective pressure of the reacting gases ( P_ eff ) is the total pressure minus the partial pressure of the inert gas. P_ eff = P_ total (1 - X_ Ar ) = 10 (1 - 0.8) = 2 bar For the decomposition reaction: H ₂ O(g) H ₂ (g) + 1 2 O ₂ (g) Let be the degree of dissociation. Since K_p is small, 1 . Partial pressures at equilibrium: P_ H ₂ O P_ eff P_ H ₂ P_ eff P_ O ₂ 2 P_ eff The equilibrium constant K_p is: K_p = (P_ H ₂ ) (P_ O ₂ )^ 1/2 P_ H ₂ O K_p = ( P_ eff ) ( 2