GATE 2022 CH – Question 31
Consider steady-state diffusion in a binary A-B liquid at constant temperature and pressure. The mole-fraction of A at two different locations is 0.8 and 0.1. Let $N_{A1}$ be the diffusive flux of A calculated assuming B to be non-diffusing, and $N_{A2}$ be the diffusive flux of A calculated assuming equimolar counter-diffusion. The quantity $\frac{(N_{A1} - N_{A2})}{N_{A1}} \times 100$ is ____________ (rounded off to one decimal place).
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Correct answer: 53.23 to 53.77
Explanation
For the same end compositions, $\frac{N_{A1}}{N_{A2}} = \frac{1}{(1 - x_A)_{lm}}$. The values of $1 - x_A$ are 0.2 and 0.9, so $(1 - x_A)_{lm} = \frac{0.9 - 0.2}{\ln 4.5} = 0.4654$. Then $\frac{N_{A2}}{N_{A1}} = 0.4654$ and $\frac{N_{A1} - N_{A2}}{N_{A1}} \times 100 = 53.5$.