Two separate gaseous equilibria are established at the same total pressure P : (i) A(g) B(g) + C(g) , K_ p₁ = 8 10⁻⁴ atm (ii) X(g) 2Y(g) , K_ p₂ = 2 10⁻⁴ atm If the degrees of dissociation ₁ and ₂ for the two reactions are very small compared to 1 , the ratio ₁ ₂ is ________.

Step-by-step solution

For the reaction A(g) B(g) + C(g) , the equilibrium constant is given by: K_ p₁ = ₁^2 P 1 - ₁^2 Since ₁ 1 , 1 - ₁^2 1 . Thus, K_ p₁ ₁^2 P . For the reaction X(g) 2Y(g) , the equilibrium constant is: K_ p₂ = 4 ₂^2 P 1 - ₂^2 Since ₂ 1 , 1 - ₂^2 1 . Thus, K_ p₂ 4 ₂^2 P . Dividing the two expressions: K_ p₁ K_ p₂ = ₁^2 P 4 ₂^2 P = 1 4 ( ₁ ₂ )^2 Substitute the given values of K_ p₁ and K_ p₂ : 8 10⁻⁴ 2 10⁻⁴ = 1 4 ( ₁ ₂ )^2 4 = 1 4 ( ₁ ₂ )^2 ( ₁ ₂ )^2 = 16 ₁ ₂ = 4 Answer: 4