Question

Sulfur dioxide (SO\(_2\)) gas diffuses through a stagnant air-film of thickness \( 2 \, \text{mm} \) at \( 1 \, \text{bar} \) and \( 30^\circ \text{C} \). The diffusion coefficient of SO\(_2\) in air is \( 1 \times 10^{-5} \, \text{m}^2/\text{s} \). The SO\(_2\) partial pressures at the opposite sides of the film are \( 0.15 \, \text{bar} \) and \( 0.05 \, \text{bar} \). The universal gas constant is \( 8.314 \, \text{J}/\text{mol} \cdot \text{K} \). Assuming ideal gas behavior, the steady-state flux of SO\(_2\) in \( \text{mol}/\text{m}^2 \cdot \text{s} \) is:

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

Hint:

In diffusion problems, use Fick's law and the ideal gas law to calculate concentration differences across the film. Ensure consistent units.

Answer 1

The Correct Option is B

Given: \[ \text{SO}_2 \text{ is diffusing through a stagnant air film.} \] \[ \text{Thickness} = z_2 - z_1 = 2 \times 10^{-3} \, \text{m}, \] \[ \text{Total pressure} = P_T = 10^5 \, \text{Pa}, \] \[ \text{Temperature} = T = 30^\circ \text{C} = 303 \, \text{K}. \] At Location (1): \[ z_1, \quad P_{A1} = 0.15 \, \text{bar}, \quad P_{B1} = P_T - P_{A1} = 0.85 \, \text{bar}. \] At Location (2): \[ z_2, \quad P_{A2} = 0.05 \, \text{bar}, \quad P_{B2} = P_T - P_{A2} = 0.95 \, \text{bar}. \] Steady-state flux of \(\text{SO}_2\): The steady-state flux of \(\text{SO}_2\) can be expressed as: \[ N_A|_{\text{SO}_2} = \frac{D_{AB} P_T}{RT} \cdot \frac{(P_{A1} - P_{A2})}{P_{B\text{lm}}} \cdot \frac{1}{z_2 - z_1}. \] Log mean partial pressure of \( \text{B} \): The logarithmic mean partial pressure of \( \text{B} \) is: \[ P_{B\text{lm}} = \frac{P_{B1} - P_{B2}}{\ln\left(\frac{P_{B1}}{P_{B2}}\right)}. \] Substituting the given values: \[ P_{B\text{lm}} = \frac{0.10}{\ln\left(\frac{0.95}{0.85}\right)}. \] Substitute into the flux equation: \[ N_A|_{\text{SO}_2} = \frac{10^{-3} \cdot 10^5}{8.314 \cdot 303 \cdot 2 \times 10^{-3}} \cdot \frac{0.10}{\ln\left(\frac{0.95}{0.85}\right)}. \] Simplify step-by-step: \[ N_A|_{\text{SO}_2} = 0.022 \, \text{mol/m}^2\text{sec}. \] Final Answer: The steady-state flux of \( \text{SO}_2 \) is: \[ N_A|_{\text{SO}_2} = 0.022 \, \text{mol/m}^2\text{sec}. \]