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GATE 2024 CH – Question 41

Mass Transfer · Fick's laws, molecular diffusion and mass transfer coefficients · 2 marks · Multiple choice

Sulfur dioxide (SO$_2$) gas diffuses through a stagnant air-film of thickness 2 mm at 1 bar and 30 °C. The diffusion coefficient of SO$_2$ in air is $1 \times 10^{-5}$ m$^2$ s$^{-1}$. The SO$_2$ 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$^{-1}$ K$^{-1}$. Assuming ideal gas behavior, the steady-state flux of SO$_2$ in mol m$^{-2}$ s$^{-1}$ through the air-film is

  1. 0.077
  2. 0.022
  3. 0.085
  4. 0.057

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Correct answer: (B) 0.022

Explanation

For diffusion through a stagnant film, $N_A = \frac{D P}{RTz}\ln\frac{P - p_{A2}}{P - p_{A1}} = \frac{10^{-5} \times 10^5}{8.314 \times 303.15 \times 0.002}\ln\frac{0.95}{0.85} = 0.1984 \times 0.1112 = 0.0221$ mol m⁻² s⁻¹.