Stage Compositions – Total Condenser

1. Total Condenser Equilibrium Curve Operating Line Stage 1 Stage 2 Stage 3 ∙ ∙ ∙ Stage j Stage Compositions – Total Condenser

2. McCabe-Thiele Graphical Solution – Binary Distillation • One can graphically solve a binary distillation problem using the McCabe-Thiele method on a y vs. x plot using the equilibrium curve and the operating lines (mass balances). • If one starts at one end of the column, one can take advantage of the fact that the mass balance, or operating line, provides a link, or the relationship, between molar compositions of the vapor and liquid streams passing each other between stages. • The equilibrium relationship provides the relationship between the molar compositions of the vapor and liquid streams on the stages. • One can use these relationships to sequentially solve for all of the vapor and liquid molar compositions by “stepping off” along the stages – the McCabe-Thiele method is a sequential solution of all of the internal stage compositions. Lecture 13

3. McCabe-Thiele Graphical Example – Total Condenser • If one has a total condenser, one will know that xD = xo = y1 which serves as the starting point for the solution. • This starting point lies on the intersection of the enriching section operating line and the y = x auxiliary line. • This is equivalent to starting the stepping off on the operating line at xD. Lecture 13

4. McCabe-Thiele Graphical Example – Total Condenser • The vapor molar composition coming off the first stage in the column is known since we have a total condenser – it is y1 = xD; however, one doesn’t know the liquid composition, x1, coming off stage 1 and flowing down to stage 2. • However, one can obtain x1 from the equilibrium relationship since y1 is known. • Once one has x1, one can determine y2 from the operating line since these compositions represent passing streams. Lecture 13

5. McCabe-Thiele Graphical Solution • One can continue on down the column by stepping off between the operating line and the equilibrium curve until one reaches a desired composition coming off the last stage. • The number of “step offs” obtained is the number of stages that will be needed in the column to obtain a given separation. Lecture 13

6. Equilibrium Curve Operating Line McCabe-Thiele Stage Solution Total Reboiler and Condenser – Stepping Down Lecture 13

7. Lecture 13

8. Equilibrium Curve Top Operating Line Feed Line Bottom Operating Line Complete McCabe-Thiele Solution Lecture 13