Thermodynamics of Separation Operations

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Thermodynamics of Separation Operations
Chapter2
Exercises
2
Exercise2.1

• MutuaJ solubility data for the ispOctane
  (l)/furfural(2) system "at 25C are Chem. Eng.
  ScL, 6, 116 (1957)
• Liquid Phase ? Liquid Phase?
• x1 0.0431 0.9461
• Compute
• (a) The distribution coefficients for isooctane
  and furfural
• (b) The relative selectivity for isooctane
  relative to furfural
• (c) The activity coefficient of isooctane in
  liquid phase 1 and the activity coefficient of
  furfural in liquid phase 2 assuming ?(1)2 1.0
  and ?(2)1 1.0

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Exercise2.2

• A binary ideal gas mixture of A and B undergoes
  an isothermal separation at T0, the infinite
  surroundings temperature. Starting with Eq. (4),
  Table 2.1, derive an equation for the minimum
  work of separation, Wmin, in terms of mole
  fractions of the feed and the two products. Use
  your equation to prepare a plot of the
  dimensionless group, Wmin/RTonF, as a function of
  mole fraction of A in the feed for
• (a) A perfect separation
• (b) A separation with SFA 0.98, SFB 0.02
• (c) A separation with SRA 9.0 and SRB 1/9
• (d) A separation with SF 0.95 for A and SPA.B
  361
• How sensitive is Wmin to product purities? Does
  Wmin depend on the particular separation
  operation used?
• Prove, by calculus, that the largest value of
  Wmin occurs for a feed with equimolar quantities
  of A and B.

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Exercise2.3

• A hydrocarbon vapor-liquid mixture at 250F and
  500 psia contains N2, H2S, CO2, and all the
  normal paraffins' from methane to heptane. Use
  Figure 2.8 to estimate the K-value of each
  component in the mixture. Which components will
  have a tendency to be present to a greater extent
  in the equilibrium vapor?

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Exercise2.4

• Use the R-K equation of state to estimate the
  partial fugacity coefficients of propane and
  benzene in the vapor mixture of Example 2.5.

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Exercise2.5

• Use a computer-aided, steady-state simulation
  program to estimate the k-values, using the P-R
  or S-R-K equation of state, of an equimolar
  mixture of the two butane isomers and the four
  butene isomers at 220F and 276.5 psia. Compare
  these values with the following experimental
  results J. Chem. Eng. Data, 7, 331 (1962)
• Component K-value
• Isobutane 1.067
• Isobutene 1.024
• n-Butane 0.922
• 1-Butene 1.024
• trans-2-Butene 0.952
• cis-2-Butene 0.876

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Exercise2.6

• For the binary system ethanol(l)/isooctane(2) at
  50C, the infinite-dilution, liquid-phase
  activity coefficients are
• ?1 21.17 and?2 9.84.
• (a) Calculate the constants A12and A21in the van
  Laar equations.
• (b) Calculate the constants andin the Wilson
  equations.
• (c) Using the constants from (a) and (b),
  calculated ?1 and ?2 over the entire composition
  range and plot the calculated points as log?
  versus x1.
• (d) How well do the van Laar and Wilson
  predictions agree with the azeotropic point where
  x1 0.5941,?1 1.44, and ?2 2.18?
• (e) Show that the van Laar equation erroneously
  predicts separation into two liquid phases over a
  portion of the composition range by calculating
  and plotting a y-x diagram like Figure 2.22.