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GATE 2024 Chemical Engineering, Q17 · Mass Transfer

The correct answer is A, 6 × 10⁻⁴.

Question

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 \times 0.1 m ×0.02 \times 0.02 m as shown in the figure, with diffusion occurring along the x-direction across the 0.02 m thickness (cross-sectional area 0.2 m ×0.1 \times 0.1 m). The total molar concentration of A and B is constant at 100mol/m3.100 mol/m³. 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 DAB=1×10−5m2/s,D_{A}B = 1 \times 10⁻⁵ m²/s, the molar flow rate of A in mol/s, along the horizontal x direction, is

Figure for Q17 (Mass Transfer, Diffusion): Consider the steady, uni-directional diffusion of a binary mixture of A and B across a vertical slab…
  • A. 6×10−46 \times 10⁻⁴
  • B. 6×10−66 \times 10⁻⁶
  • C. 3×10−63 \times 10⁻⁶
  • D. 3×10−43 \times 10⁻⁴

Official answer: 6×10−46 \times 10⁻⁴

Why

GATE 2024 official key: (A). NA=DAB⋅C⋅(xA1−xA2)/L×N_{A} = D_{A}B\cdot C\cdot (x_{A1}−x_{A2})/L \times Area =(1×10−5)(100)(0.6)/(0.02)×(0.2×0.1)=0.03×0.02=6×10−4= (1 \times 10⁻⁵)(100)(0.6)/(0.02) \times (0.2 \times 0.1) = 0.03 \times 0.02 = 6 \times 10⁻⁴ mol/s.

Explanation cross-checked for consistency. Final answer matches the official IIT answer key.

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