Project ForgeThe vapor-liquid equilibrium curve of a binary mixture A-B may be approximated by a linear equation over a narrow range of liquid mole fractions (0.2<xA<0.3) as y*A=1.325xA+0.121. 100 moles of a feed (xA,F=0.28) is batch distilled to a final residue (xA,W=0.2). Using the Rayleigh equation, the number of moles of the residue left behind in the distillation unit, up to 2 digits after the decimal point, is _____
Explanation
Rayleigh equation: ln(F/W)=∫[xW to xF] dx/(y*−x). Here y*−x=1.325x+0.121−x=0.325x+0.121. ∫dx/(0.325x+0.121)=(1/0.325)ln(0.325x+0.121). Evaluating from 0.2 to 0.28: (1/0.325)[ln(0.212)−ln(0.186)]=(1/0.325)(0.1308)=0.4025. F/W=e^0.4025=1.4956. W=100/1.4956≈66.86≈66.8 mol.
Source: GATE CH 2013 (2013)
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