The industrial synthesis of sulfur trioxide involves the equilibrium
2 SO₂(g) + O₂(g) ⇌ 2 SO₃(g)
For this reaction at 700 K, Kp = 1.5 × 10². A 10.0 L reactor at 700 K is loaded with 1.20 mol SO₂ and 0.800 mol O₂. Before equilibrium is established, an additional 0.600 mol of SO₃(g) is suddenly injected and the vessel is quickly resealed. No inert gases are present.
(a) Compute the reaction quotient Qp immediately after the SO₃ injection and state the direction in which the net reaction must proceed to reach equilibrium.
(b) Introduce a variable s to represent the number of moles of SO₃ that decompose as the system moves toward equilibrium. Develop expressions for the equilibrium partial pressures of SO₂, O₂, and SO₃ in terms of s.
(c) Substitute these expressions into the equilibrium-constant expression to obtain an equation in s, then solve for s numerically.
(d) Determine the equilibrium partial pressure of each gas and the total pressure in the reactor.
(e) Evaluate whether assuming O₂ to be in large excess would have simplified the calculation, and justify your conclusion quantitatively.