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For any two components A and B of a multicomponent mixture, if constant a values are assumed for all pairs of components, -dMA/ -dMB = yA/yB = aAB(xA /xB). When this is integrated, we obtain ln

where MA(i) and MA( f) are the moles of component A in the pot before and after distillation and MB(i) and MB(f) are the corresponding moles of component B.

A typical application of a simple batch still might be distillation of an ethanol-water mixture at 101.3 kPa (1 atm). The initial charge is 100 mol of ethanol at 18 mole percent, and the mixture must be reduced to a maximum ethanol concentration in the still of 6 mole percent. By using equilibrium data interpolated from Table 13-1,

x

y

y - x

1/(y - x)

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