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ENGR5002 / Week 9
ENGR271 2026 Q3Past paperCurrent spec2:130 marks36 min

ENGR271 Summer 2026 Q3[VALID]

Oxygen is diffusing through a stagnant gas mixture containing 50% methane, 30% hydrogen and 20% carbon dioxide by volume. The total pressure is 2×105 N/m22 \times 10^5\ \mathrm{N/m^2} and the temperature is 20 deg C. The partial pressures of oxygen at two planes 25 mm apart are 23×10323 \times 10^3 and 9×103 N/m29 \times 10^3\ \mathrm{N/m^2} respectively. Estimate the rate of diffusion of oxygen.

Given: at 0 deg C and 1 atm, the diffusivities of oxygen with respect to methane, hydrogen and carbon dioxide are DO2−CH4=0.184 cm2/sD_{O_2-CH_4} = 0.184\ \mathrm{cm^2/s}, DO2−H2=0.69 cm2/sD_{O_2-H_2} = 0.69\ \mathrm{cm^2/s} and DO2−CO2=0.139 cm2/sD_{O_2-CO_2} = 0.139\ \mathrm{cm^2/s}.

Formulas you may need
  • Pressure and temperature correction: DAB,T2,P2=DAB,T1,P1(P1P2)(T2T1)3/2ΩD,T1ΩD,T2D_{AB,T_2,P_2} = D_{AB,T_1,P_1} \left(\dfrac{P_1}{P_2}\right)\left(\dfrac{T_2}{T_1}\right)^{3/2} \dfrac{\Omega_{D,T_1}}{\Omega_{D,T_2}} (take the Ω\Omega ratio as 1 when no collision data are given) (on the formula sheet)
  • Multicomponent mixture: 1D1−mix=∑j≠1yj′D1−j\dfrac{1}{D_{1-mix}} = \sum_{j \ne 1} \dfrac{y'_j}{D_{1-j}}, yj′=yj∑j≠1yjy'_j = \dfrac{y_j}{\sum_{j \ne 1} y_j} (on the formula sheet)
  • Diffusion through a stagnant gas: NA=PDABRTδpA1−pA2pB,lmN_A = \dfrac{P D_{AB}}{R T \delta} \dfrac{p_{A1} - p_{A2}}{p_{B,lm}}, pB,lm=pB2−pB1ln⁡(pB2/pB1)p_{B,lm} = \dfrac{p_{B2} - p_{B1}}{\ln(p_{B2}/p_{B1})} (equivalent to the ln⁡\ln form used in the solution) (on the formula sheet)
  • Unit conversions: 1 cm2/s=10−4 m2/s1\ \mathrm{cm^2/s} = 10^{-4}\ \mathrm{m^2/s}; R=8314 J kmol−1 K−1R = 8314\ \mathrm{J\,kmol^{-1}\,K^{-1}} (learn this)