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Encyclopedia of Physical Science and Technology EN004E-182 June 8, 2001 18:16

552 Distillation

FIGURE 9 Packed column distributor.
FIGURE 7 Dumped packing. [Courtesy of Sulzer Chemtech, Ltd.]
where the equilibrium K value,
◦
K i = p i /π (5)
y i = (p i /π)x i (3) ◦
Equation (3) relates the composition of a liquid to the Mixtures that obey Eq. (5) exactly are termed ideal
composition of its equilibrium vapor at any pressure and mixtures.
temperature (since p i depends on temperature). Equa- Deviations from ideality often occur, and the K i value
◦
tion (3) is often written: depends not only on temperature and pressure but also on
the composition of the other components of the mixture.
y i = K i x i (4) A more detailed discussion of vapor–liquid equilibrium
relationships for nonideal mixtures is outside the scope of
this article.
The relative volatility α of components 1 and 2 is ob-
tained from Eq. (4) as:
◦
◦
α 12 = K 1 /K 2 = p 1 /p 2 = (y 1 /x 1 )(x 2 /y 2 ) (6)
For a binary mixture,
x 1 + x 2 = 1 and y 1 + y 2 = 1 (7)
Substituting into Eq. (6) gives:
y 1 = α 12 x 1 /[1 + (α 12 − 1)x 1 ] (8)
Figure 10 shows the relationship between y 1 and x 1
for different values of α 12 calculated from Eq. (8). When
two components have close boiling points, by implica-
tion they have similar vapor pressures, so that α 12 is close
to unity. Separation of mixtures by distillation becomes
more difficult as α 12 approaches unity. Figure 11 indicates
some of the x, y diagrams that can be obtained for distilla-
tion systems. Also shown are corresponding temperature–
composition diagrams. The saturated vapor or dewpoint
curve is determined by finding the temperature at which
liquid starts to condense from a vapor mixture. Similarly,
the saturated liquid or bubble-point curve corresponds to
the temperature at which a liquid mixture starts to boil. For
ideal mixtures, the dewpoint and bubble-point curves can
be calculated as follows. From Eq. (3), at the dew point,
since
n

x i = 1
FIGURE 8 Structured packing. [Courtesy of Koch–Glitsch, Inc.] i=1