Question

The diffusivity of A in B is 2x10$^{-5}$ m$^2$/s. For a stagnant film of thickness 2mm with C$_{A1}$ = 0.05 mol/m$^3$ and C$_{A2}$ = 0.01 mol/m$^3$, the molar flux is ______

• A. 4x10$^{-4}$ mol/m$^2$.s
• B. 4x10$^{-5}$ mol/m$^2$.s
• C. 4x10$^{-3}$ mol/m$^2$.s
• D. 2x10$^{-4}$ mol/m$^2$.s

Hint:

Always convert physical dimensions to SI base units (such as converting mm to m) before performing any calculations to avoid decimal point errors.

Answer 1

The Correct Option is A

Step 1: Understanding the Question:
The question asks to calculate the steady-state molar flux of component A diffusing through a stagnant film of B.
We are given the diffusivity (\( D_{AB} \)), the stagnant film thickness (\( z \)), and the concentrations of A at the boundaries (\( C_{A1} \) and \( C_{A2} \)).

Step 2: Key Formula or Approach:
For a highly dilute solution or for equimolar counter-diffusion (and as an approximation for a stagnant film when concentrations are low), Fick's first law of diffusion simplifies to:
\[ N_A = \frac{D_{AB}}{z} \cdot (C_{A1} - C_{A2}) \]
where:
\( N_A \) is the molar flux of A (\( \text{mol/m}^2\cdot\text{s} \)),
\( D_{AB} \) is the diffusivity of A in B (\( \text{m}^2\text{/s} \)),
\( z \) is the path length or film thickness (m),
\( C_{A1}, C_{A2} \) are the concentrations of A at the boundaries (\( \text{mol/m}^3 \)).

Step 3: Detailed Explanation:

• Identify and convert the given values:
Diffusivity, \( D_{AB} = 2 \times 10^{-5} \text{ m}^2\text{/s} \)
Film thickness, \( z = 2 \text{ mm} = 0.002 \text{ m} = 2 \times 10^{-3} \text{ m} \)
Concentration 1, \( C_{A1} = 0.05 \text{ mol/m}^3 \)
Concentration 2, \( C_{A2} = 0.01 \text{ mol/m}^3 \)

• Set up the equation for molar flux:
\[ N_A = \frac{2 \times 10^{-5}}{2 \times 10^{-3}} \cdot (0.05 - 0.01) \]

• Perform the calculation:
\[ N_A = 10^{-2} \cdot (0.04) \]
\[ N_A = 10^{-2} \cdot 4 \times 10^{-2} = 4 \times 10^{-4} \text{ mol/m}^2\cdot\text{s} \]


Step 4: Final Answer:
The molar flux of A is \( 4 \times 10^{-4} \text{ mol/m}^2\cdot\text{s} \).