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GATE 2024 Chemical Engineering, Q41 · Mass Transfer

The correct answer is B, 0.022.

Question

Sulfur dioxide (SO2)(SO₂) gas diffuses through a stagnant air-film of thickness 2 mm at 1 bar and 30°C.30°C. The diffusion coefficient of SO2SO₂ in air is 1×10−5m2/s.1 \times 10⁻⁵ m²/s. The SO2SO₂ partial pressures at the opposite sides of the film are 0.15 bar and 0.05 bar. The universal gas constant is 8.314 J/(mol·K). Assuming ideal gas behavior, the steady-state flux of SO2SO₂ in mol/(m2⋅s)mol/(m²\cdot s) through the air-film is

  • A. 0.077
  • B. 0.022
  • C. 0.085
  • D. 0.057

Official answer: 0.022

Why

GATE 2024 official key: (B). Diffusion of A through stagnant B: NA=[D⋅P/(RTδ)]⋅ln[(P−pA2)/(P−pA1)]=[(1e−5)(1e5)/(8.314×303×0.002)]×ln(95000/85000)≈0.1985×0.1112≈0.022mol/(m2⋅s).N_{A} = [D\cdot P/(RTδ)]\cdot ln[(P−p_{A2})/(P−p_{A1})] = [(1e-5)(1e5)/(8.314 \times 303 \times 0.002)] \times ln(95000/85000) \approx 0.1985 \times 0.1112 \approx 0.022 mol/(m²\cdot s).

Explanation cross-checked for consistency. Final answer matches the official IIT answer key.

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