Stage Compositions

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Stage Compositions Total Condenser
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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.

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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.

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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
  doesnt 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.

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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.

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McCabe-Thiele Stage Solution Total Reboiler and
Condenser Stepping Down
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Complete McCabe-Thiele Solution