For the reaction A(g) 2B(g) , 5 moles of A(g) are introduced into a 1 L flask. At equilibrium, the degree of dissociation of A(g) is 0.8. Under this condition, a certain amount of B(g) is added to the flask while maintaining the temperature, such that the new equilibrium degree of dissociation of A(g) becomes 0.2. The number of moles of B(g) added is ____.

Step-by-step solution

Let the initial moles of A(g) be a = 5 mol. At the first equilibrium, the degree of dissociation ₁ = 0.8 . Moles of A(g) at equilibrium = a(1 - ₁) = 5(1 - 0.8) = 1 mol. Moles of B(g) at equilibrium = 2a ₁ = 2 5 0.8 = 8 mol. Since the volume is 1 L, the equilibrium constant is: K_c = [B]^2 [A] = 8^2 1 = 64 Let y moles of B(g) be added. The system shifts backward to a new equilibrium where the degree of dissociation of A(g) is ₂ = 0.2 . At this new equilibrium, the moles of A(g) = a(1 - ₂) = 5(1 - 0.2) = 4 mol. The m