Practice question
Question
For 2SO₃(g) <=> 2SO₂(g) + O₂(g) , Kp = 0.01 at 900 K. If 1 mole of SO₃ is placed in a 1 L vessel, what is the partial pressure of O₂ at equilibrium ( R = 0.0831 bar L/mol K )?
Explanation
Initial: PSO₃ = (1 × 0.0831 × 900/1) = 74.79 bar . Let 2x mol of SO₃ dissociate, so PSO₃ = 74.79(1 - 2x) , PSO₂ = 74.79 × 2x , PO₂ = 74.79x , total pressure = 74.79. Kp = ((PSO₂)² PO₂/(PSO₃)²) = ((74.79 × 2x)² (74.79x)/[74.79(1 - 2x)]²) = 0.01 . Simplifying, (4x² · 74.79x/(1 - 2x)²) = 0.01 , 299.16x³ = 0.01 (1 - 2x)² . Solving, x ≈ 0.013 , PO₂ = 74.79 × 0.013 ≈ 0.972 bar .
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