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GATE 2024 CH – Question 17

Mass Transfer · Fick's laws, molecular diffusion and mass transfer coefficients · 1 mark · Multiple choice

Consider the steady, uni-directional diffusion of a binary mixture of $A$ and $B$ across a vertical slab of dimensions 0.2 m × 0.1 m × 0.02 m as shown in the figure. The total molar concentration of $A$ and $B$ is constant at 100 mol m$^{-3}$. The mole fraction of $A$ on the left and right faces of the slab are maintained at 0.8 and 0.2, respectively. If the binary diffusion coefficient $D_{AB} = 1 \times 10^{-5}$ m$^2$ s$^{-1}$, the molar flow rate of $A$ in mol s$^{-1}$, along the horizontal $x$ direction is

a slab with the face of 0.20 m × 0.10 m normal to the x direction, and the thickness of 0.02 m along x.
  1. $6 \times 10^{-4}$
  2. $6 \times 10^{-6}$
  3. $3 \times 10^{-6}$
  4. $3 \times 10^{-4}$

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Correct answer: (A) $6 \times 10^{-4}$

Explanation

The diffusion is across the thickness $L = 0.02$ m along $x$. With a constant total concentration, the flux is $N_A = D_{AB}C\frac{x_{A1} - x_{A2}}{L} = 10^{-5} \times 100 \times \frac{0.6}{0.02} = 0.03$ mol m$^{-2}$ s$^{-1}$. The area is $0.2 \times 0.1 = 0.02$ m², so the molar flow rate is $0.03 \times 0.02 = 6 \times 10^{-4}$ mol s$^{-1}$.