Unformatted text preview: m on the next page. Analysis: (a) (continued) Exercise 7.55 (continued) Exercise 7.55 (continued)
(b) From the diagram below, the enthalpy of the feed, F , of 60 mol% nC6 at 260oF is
equal to HF = 27,700 Btu/lbmol. Upon cooling, the point P, in the two-phase region, is reached
at 200oF. From the tie line through point P, the equilibrium vapor and liquid phases are shown at
points V and L. The enthalpy of the two-phase mixture at point P = HP = 17,700 Btu/lbmol.
Therefore, the energy that must be removed = Q = 27,700 - 17,700 = 10,000 Btu/lbmol mixture.
The composition of the equilibrium vapor at point V is 77 mol% nC6. The composition of
equilibrium liquid at point L is 38 mol% nC6 . The amounts of vapor and liquid can be obtained
by material balances or by the inverse lever arm rule using the plot below. By the latter, the
molar percent vapor = 53%.
(c) In the diagram below, the equilibrium vapor from part (b), shown at F, is cooled to
180oF to point M in the two-phase region. This mixture splits into equilibrium vapor, V, and
equilibrium liquid, L. The composition of V is 92 mol% nC6. The composition of L is 60 mol%
nC6. By the lever arm rule, the mole % of equilibrium vapor = 60%. Analysis: (b) (continued) Exercise 7.55 (continued) Analysis: (c) (continued) Exercise 7.55 (continued) Exercise 7.56
Development of an enthalpy-concentration diagram for methanol-water at 1 atm.
Use of diagram to obtain minimum stages.
Given: Enthalpy and vapor-liquid equilibrium data in Table 7.8. Feed of 100 lbmol/h
containing 60 mol% methanol. Liquid distillate to contain 98 mol% methanol. Liquid bottoms
to contain 96 mol% water.
Find: (a) Enthalpy-concentration diagram.
(b) Minimum number of stages.
(c) Temperatures of distillate and bottoms.
Analysis: (a) Use a spreadsheet to plot an enthalpy-concentration diagram, using the supplied
data. The result is shown below, where the dashed lines are tie lines for the vapor-liquid
equilibrium compositions at the temperatures indicated and a pressure of 1 atm. Exercise 7.56 (continued)
(b) and (c) For the condition of total reflux, passing vapor and liquid streams have the
same compositions and are saturated vapor and liquid, respectively. Therefore, while vapor and
liquid streams at equilibrium are related by tie lines extending from the saturated liquid curve to
the saturated vapor curve, passing vapor and liquid streams are related by vertical operating lines
extending from the saturated liquid curve to the saturated vapor curve. By alternating between
the equilibrium and operating lines, from the bottoms composition to the distillate composition,
the minimum number of stages is determined by the number of tie lines used, as shown in the
diagram below for the example of a methanol bottoms mole fraction of 0.04 and a methanol
distillate mole fraction of 0.98, where the construction lines are solid lines and the equilibrium
lines are numbered from the top. The minimum number of stages...
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