GATE 2025 AG – Question 61
An $N_2$–He mixture in a pipe is at 1 atm and 298 K. Nitrogen partial pressures at points .22 m apart are 60.80 and 20.31 kPa. The diffusivity is $.612\times10^{-4}$ m²/s. Use $R=8314\,\mathrm{m^3\,Pa/(kg\,mol\,K)}$. Find steady nitrogen flux as $n\times10^{-6}$ kg mol/(s·m²),reporting n to two decimals.
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Correct answer: 4.50 to 4.60
Explanation
For equimolar counterdiffusion at constant pressure and temperature, Fick’s law gives $N_A=D_{AB}(p_{A1}-p_{A2})/(RTL)$. Convert kPa to Pa: $$N_A=\frac{.612\times10^{-4}(60800-20310)}{8314(298)(.22)}=4.54622\times10^{-6}.$$ Hence **n=4.55**. The equimolar-diffusion interpretation is implicit in the keyed answer; stagnant-helium diffusion would require the logarithmic correction.