min, however, McCabe Thiele utilizes a graphical analysis and Fenske utilizes a numerical analysis.To use McCabe Thiele graphical analysis, the condition of constant molal overflow (CMO) must be met. The assumptions behind CMO are as follows (1, 117):1.The column must be adiabatic2.The specific heat changes are negligible compared to latent heat changes3.The heat of vaporization per mole, l, is constantAn additional criterion for utilizing McCabe Thiele analysis is the existence of good equilibrium data. Ideally, empirical equilibrium data can be found in several sources, but this data was not available for isopropanol and ethanol. To determine our equilibrium curve, we had to incorporate a different method. All of the equilibrium data was found by applying the below equation:yA = (aABxA) y [1 + (aAB - 1)xA] (2)where: yA = vapor fraction of most volatile componentxA = liquid fraction of most volatile componentaAB = relative volatility of species A and BOnce these conditions are met, the minimum number of stages can be determined. To determine the minimum number of stages, an equilibrium curve is needed. The x = y line on the equilibrium diagram is used as the operating line. Stages are then stepped off starting at the distillate composition and finishing at the bottoms composition. An important criteria in the equilibrium curve is that all compositions must be in molar units instead of mass units. All experimental compositions were found through gas chromatography. An alternative to McCabe Thiele graphical analysis is the Fenske numerical analysis. The major requirement for using the Fenske equation is an accurate value for the relative volatility of the binary system. In this case, aAB is known and thus the Fenske equation can be used. The Fenske equation is listed below (1, 276):Nmin = {ln[(xA/xB)Dist] / [(xA/xB)Bot]} / (ln aAB) (3)where: xA,Dist = distillate mole fracti...
