In a 10.0 L container, an equilibrium was established between SO₃, SO₂ and O₂ gases, by starting with SO₃ only. The density of equilibrium mixture was found to be 16 g/litre at a temperature of 900 /

Question

In a 10.0 L container, an equilibrium was established between SO₃, SO₂ and O₂ gases, by starting with SO₃ only. The density of equilibrium mixture was found to be 16 g/litre at a temperature of 900 / 0.0821 K. If the degree of dissociation of SO₃ is 40%, then the value of K_p (in atm) for the reaction: 2SO₃(g) ⇌ 2SO₂(g) + O₂(g), is

Prashant Kotian · Accepted Answer

Correct answer: 0016. Let initial moles of SO₃ be 1. Eq moles: SO₃ = 1 - 0.4 = 0.6, SO₂ = 0.4, O₂ = 0.2. Total moles = 1.2. Average molar mass M_avg = M_SO₃ / 1.2 = 80 / 1.2 = 200/3 g/mol. Using the ideal gas law with density d = 16 g/L: P = dRT / M_avg = 16 × 0.0821 × (900 / 0.0821) / (200/3) = 14400 / (200/3) = 216 atm. Partial pressures: P_SO₂ = (0.4 / 1.2) × 216 = 72 atm. P_O₂ = (0.2 / 1.2) × 216 = 36 atm. P_SO₃ = (0.6 / 1.2) × 216 = 108 atm. K_p = (P_SO₂² × P_O₂) / P_SO₃² = (72² × 36) / 108² = (72/108)² × 36 = (2/3)² × 36 = (4/9) × 36 = 16. Therefore, correct answer is 0016.

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