In steady-state equimolar counter-diffusion of gas $A$ through a stagnant gas layer of thickness $1.0\text{ mm}$ ($0.001\text{ m}$), the diffusivity is $D_{AB} = 2.0 \times 10^{-5}\text{ m}^2/\text{s}$. If the concentration difference across the film is $\Delta C_A = 0.05\text{ mol/m}^3$, calculate the molar mass flux $J_A$ in $\text{mol/(m}^2\cdot\text{s)}$.
Answer Key:
0.001
Step-by-Step Solution & Explanation
Fick's first law of diffusion:
$J_A = D_{AB} \frac{\Delta C_A}{\Delta z} = (2.0 \times 10^{-5}) \times \frac{0.05}{0.001} = (2.0 \times 10^{-5}) \times 50 = 1.0 \times 10^{-3} = 0.0010\text{ mol/(m}^2\cdot\text{s)}$