ans Q2a): 6 theoretical plates plus the reboiler; feed on stage 4 b) 6 or 7 theoretical plates plus reboiler - depends on how you draw the diagram; feed on stage 4 or 5 feedback attached to help with ques We are assuming that equilibrium is reached at each stage - thus the points (x, y) should lieon the equilibrium line of the x, y diagram for each stageWe performed component balances to relate the composition of liquid leaving stage 'I' withthe composition of vapour rising from stage 'i-1' below. These are the operating linesWe know that the composition of the vapour leaving the top of the column is xa, i.e. Yn= XdFrom the equation of the rectification operating line (obtained by a component balance), weknow that it contains the point (x, x₁) and has gradient V₁/L-R/(R+1). This may help whendrawing the graph.By definition, the intersection of operating lines is on the q-line. The q-line passes the point(x,x) and has gradient q/(q-1). It may be helpful to draw the q-line and determine where itcrosses the rectification operating line; then draw the stripping operating line between thispoint and (XX).With the operating lines drawn we may begin with y₁x and successively, by equilibriumand operating lines, evaluate liquid (read across to equilibrium line) and vapour (read downto operating line) compositions moving down the column.We always read down to the lower of the two operating lines. The feed stage is the firststage for which we read down to the stripping operating line.We continue until we meet or exceed the required bottom product composition. Thenumber of equilibrium stages (aka ideal plates), n, is one fewer than the number of timeswe have read across to the equilibrium line (since the reboiler is also an equilibrium stage).0.80.60.40.2=x-Y00X₁,Y₁.Equilibrium line0.8Xa0.60402*XmYwdistillation of ethanol/water at 1 atmRequire 5 idealplates plus thereboiler0Feed on stage 2X₁, Ywstrippingoperating lineX₁, Y₁X2, Y20.2XwMurphree Efficiency:We draw a 'virtual equilibrium line' part-way between the operating line and the trueequilibrium line.If the Murphree efficiency is based on the vapour, we work vertically; if based on the liquid,we work horizontally.• e.g. for a Murphree efficiency of 80% based on the liquid, we read across 80% of the wayfrom the operating line to find each point on our virtual equilibrium lineVirtualequilibrium lineX₂X₁0.4X₁0.6x, (molefraction of ethanol in liquid)X5, XdX3. Y3X₁Y3УзX₁,Y₂X2, Y2*******to XXs. Y4distillation of ethanol/water at 1 atmRough sketch for 80% Murphree efficiency based on liquidX1, Yw0.2rectification Intercept -x/(R+1)operating line..strippingoperating lineq-line Sat. vapour feed inthis exampleXa 08X₂, X₁X5, XdX4, Y4X3, 3X5. Y4X3, Y2rectificationoperating lineXd, Xdq-lineRead across 80% of theway from operating line.to true equilibrium line0.4X₁ 0.6x, (molefraction of ethanol in liquid)Xd 0.8We then determine stages as previously, but based on this virtual equilibrium line.Note, for a Murphree efficiency based on vapour we read up vertically from theoperating line, which may give a somewhat different outcome. 2) Atmospheric air (79% N₂ and 21% O₂ on a molar basis) is to be distilled at 1 atmto produce 98% N2 (top product) and 98% O2 (bottom product). A total condenser willbe used. Assuming the reflux ratio R = 2, determine the number of theoretical stagesrequired (using the graph below) if the feed is,a) liquid at its bubble-point,b) vapour at its dew point.MOL PER CENT NITROGEN IN VAPOUR1009080706040302010MU01020304070MOL PER CENT NITROGEN IN LIQUID50608090100CONSTANT PRESSURE LIQUID - VAPOUR EQUILIBRIUM DIAGRAM for NITROGEN OXYGENPRESSURE 760mm Hg

Question

ans Q2a): 6 theoretical plates plus the reboiler; feed on stage 4 b) 6 or 7 theoretical plates plus reboiler - depends on how you draw the diagram; feed on stage 4 or 5 feedback attached to help with ques We are assuming that equilibrium is reached at each stage - thus the points (x, y) should lieon the equilibrium line of the x, y diagram for each stageWe performed component balances to relate the composition of liquid leaving stage 'I' withthe composition of vapour rising from stage 'i-1' below. These are the operating linesWe know that the composition of the vapour leaving the top of the column is xa, i.e. Yn= XdFrom the equation of the rectification operating line (obtained by a component balance), weknow that it contains the point (x, x₁) and has gradient V₁/L-R/(R+1). This may help whendrawing the graph.By definition, the intersection of operating lines is on the q-line. The q-line passes the point(x,x) and has gradient q/(q-1). It may be helpful to draw the q-line and determine where itcrosses the rectification operating line; then draw the stripping operating line between thispoint and (XX).With the operating lines drawn we may begin with y₁x and successively, by equilibriumand operating lines, evaluate liquid (read across to equilibrium line) and vapour (read downto operating line) compositions moving down the column.We always read down to the lower of the two operating lines. The feed stage is the firststage for which we read down to the stripping operating line.We continue until we meet or exceed the required bottom product composition. Thenumber of equilibrium stages (aka ideal plates), n, is one fewer than the number of timeswe have read across to the equilibrium line (since the reboiler is also an equilibrium stage).0.80.60.40.2=x-Y00X₁,Y₁.Equilibrium line0.8Xa0.60402*XmYwdistillation of ethanol/water at 1 atmRequire 5 idealplates plus thereboiler0Feed on stage 2X₁, Ywstrippingoperating lineX₁, Y₁X2, Y20.2XwMurphree Efficiency:We draw a 'virtual equilibrium line' part-way between the operating line and the trueequilibrium line.If the Murphree efficiency is based on the vapour, we work vertically; if based on the liquid,we work horizontally.• e.g. for a Murphree efficiency of 80% based on the liquid, we read across 80% of the wayfrom the operating line to find each point on our virtual equilibrium lineVirtualequilibrium lineX₂X₁0.4X₁0.6x, (molefraction of ethanol in liquid)X5, XdX3. Y3X₁Y3УзX₁,Y₂X2, Y2*******to XXs. Y4distillation of ethanol/water at 1 atmRough sketch for 80% Murphree efficiency based on liquidX1, Yw0.2rectification Intercept -x/(R+1)operating line..strippingoperating lineq-line Sat. vapour feed inthis exampleXa 08X₂, X₁X5, XdX4, Y4X3, 3X5. Y4X3, Y2rectificationoperating lineXd, Xdq-lineRead across 80% of theway from operating line.to true equilibrium line0.4X₁ 0.6x, (molefraction of ethanol in liquid)Xd 0.8We then determine stages as previously, but based on this virtual equilibrium line.Note, for a Murphree efficiency based on vapour we read up vertically from theoperating line, which may give a somewhat different outcome. 2) Atmospheric air (79% N₂ and 21% O₂ on a molar basis) is to be distilled at 1 atmto produce 98% N2 (top product) and 98% O2 (bottom product). A total condenser willbe used. Assuming the reflux ratio R = 2, determine the number of theoretical stagesrequired (using the graph below) if the feed is,a) liquid at its bubble-point,b) vapour at its dew point.MOL PER CENT NITROGEN IN VAPOUR1009080706040302010MU01020304070MOL PER CENT NITROGEN IN LIQUID50608090100CONSTANT PRESSURE LIQUID - VAPOUR EQUILIBRIUM DIAGRAM for NITROGEN OXYGENPRESSURE 760mm Hg

Accepted Answer

Atmospheric air is to be distilled in a fractionating distillation column.