The gaseous equilibrium A(g) 2B(g) is studied at a constant temperature but at two different total pressures, P₁ and P₂ . The molar mass of gas A is 120 g mol ⁻¹ . At total pressure P₁ , the equilibrium mixture has a vapour density of 40 . At total pressure P₂ , the equilibrium mixture has a vapour density of 48 . The ratio of the total pressures P₂ P₁ is ________.

Step-by-step solution

The theoretical vapour density ( D ) of gas A is: D = Molar mass 2 = 120 2 = 60 The degree of dissociation is related to vapour density by = D - d d(n-1) . For A(g) 2B(g) , n = 2 , so = D - d d . At pressure P₁ , d₁ = 40 : ₁ = 60 - 40 40 = 20 40 = 1 2 At pressure P₂ , d₂ = 48 : ₂ = 60 - 48 48 = 12 48 = 1 4 The equilibrium constant K_p for A(g) 2B(g) is given by: K_p = 4 ^2 P 1 - ^2 Since temperature is constant, K_p remains the same at both pressures: 4 ₁^2 P₁ 1 - ₁^2 = 4 ₂^2 P₂ 1 - ₂^2 Substitute the values of ₁ a