A gas A dissociates in a closed vessel of volume 16.4 L at a temperature of 400 K according to the reaction: A(g) B(g) + C(g) Initially, 4 moles of A and an unknown amount of inert Argon gas are present in the vessel. At equilibrium, the total pressure of the mixture is 20 atm . If the equilibrium constant K_p for the dissociation is 4 atm , the number of moles of Argon gas present in the vessel is ______. (Given: R

Step-by-step solution

Let the number of moles of A dissociated at equilibrium be x . A(g) B(g) + C(g) Initial moles: 4 0 0 Equilibrium moles: 4-x x x For a fixed volume and temperature, the partial pressure of any gas is p_i = n_i ( RT V ) . RT V = 0.082 400 16.4 = 2 atm mol ⁻¹ Partial pressures at equilibrium: p_A = (4-x) 2 p_B = x 2 p_C = x 2 The equilibrium constant K_p is given by: K_p = p_B p_C p_A = (2x)(2x) 2(4-x) = 2x^2 4-x Given K_p = 4 atm : 4 = 2x^2 4-x 2(4-x) = x^2 x^2 + 2x - 8 = 0 (x+4)(x-2) = 0 x = 2 Total moles of reactin