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Consequently,
y
=
(POX)/?r
(‘4-5
)
This equation expresses the equilibrium between the vapor and the liquid of an ideal solution at any
temperature and pressure. By means
of
this equation, the dew point and the bubble point of any ideal
solution can be calculated. From data obtained, a boiling point diagram may then be constructed.
Fractionation
On vaporizing a mixture of two liquids, that component which has the higher vapor pressure tends to
concentrate in the vapor, thus producing a difference in composition between the liquid and the vapor
phases which are in equilibrium. The vapor may then be condensed. Vapor coming from this condensate
is still enriched in the more volatile component. This successive vaporization and condensation is called
fractional distillation.
Figure A-1 shows the composition of the vapor gwen off at
98.5
O
C, when boiling a mixture of
benzene and toluene at atmospheric pressure. From a charge containing
30%
benzene and
70%
toluene,
the vapor will contain
51%
benzene and
49%
toluene.
If
this vapor were condensed and then brought up
to boiling at
92”C,
a new vapor would be evolved having a composition
of
72%
benzene and
28%
toluene. Furthermore the new residue would contain proportionately less benzene than when first
condensed. By repeated condensations and re-evaporations, which
is
called redistillation, a final product
of substantially pure benzene could be obtained.
A similar result can be obtained by condensing a very small amount of the vapor by slight cooling,
drawing off this condensate, and cooling the vapor a little more.
This
condenses another small amount of
liquid containing a relatively large amount of toluene.
If
given sufficient time, this liquid must be in
equilibrium with the vapor at the existing temperature.
This
is the method
of
partial condensation.
If the vapors from an initial mixture
of
30%
benzene and
70%
toluene, boiling at
98.5
C,
are allowed
to
bubble into a liquid
of
the same composition as the vapor (i.e.,
51%
benzene and
49%
toluene), which
has been heated just to its boiling point
(92OC),
the vapor will condense, giving up latent heat and
thereby boiling off a new vapor containing
72%
benzene and
28%
toluene. At the same time, the liquid
residue from this second still, now reduced in benzene content by the removal
of
vapor containing
72%
benzene, could be allowed to flow into the first still. It would, therefore, be reduced again in benzene
content. Simultaneously, vapor containing
72%
benzene from the second still could be allowed to bubble
into a third still containing
72%
benzene at its boiling point
(86.5 C).
This
results in evolution
of
vapor
containing
86%
benzene and return of liquid containing
72%
benzene to the second still. Thus, supplying
heat to the first still only, the vapor from each still in the series is progressively richer in benzene and
poorer in toluene, until substantially pure benzene passes from the last still into a condenser. Providing
there has been no radiation
loss
from the stills, the amount
of
heat obtained by condensing this benzene
will be exactly equal to that introduced in the coils
of
the first still.
To
maintain the exact conditions
given, it is necessary to return all of the condensed benzene to the last still,
so
that the proper amount of
liquid could flow back to the preceding still and
so
on down the line. This operation is called “fractional
distillation”, which combines the methods of redistillation and that
of
partial condensation. Figure
A-4
shows this operation diagrammatically.
The following factors are found to be essential for the theoretical case given above:
(a) The vapors rising from each still must be in equilibrium with the liquid in the still, following the
temperature and composition conditions given on the boiling-point diagram.
(b)
The liquid flowing back into each lower still must equal in amount and composition the vapors
coming into the upper still from which that liquid is flowing.
(c) There must be no addition or loss
of
heat in the system except the introduction of heat in the
steam coils
of
the first still and the removal
of
exactly the same amount of heat in the final condenser.
Practical application of this method of vapor enrichment involves some modification of theory.
Actually, the purpose of such
an
operation is to take out as much pure benzene as possible. All the
condensate, therefore, cannot be returned to the last still. By taking
off
a portion of the benzene