Page 176 - Separation process principles 2

4.7 Solid-Liquid Systems 141

t
The total flow rate of underflow is U = 81,407 + 39,711 = 121,118 If a liquid solution of composition and temperature repre-
kg/h By mass balance, the flow rate of overflow = 200,000 - sented by point P is cooled along the vertical, dashed line, it
121,118 = 78,882 kgh. These values are close to those obtained will remain a liquid until the line intersects the solubility
L by the graphical method. The percentage recovery of oil, and com- curve at point F. If the temperature is lowered further, crys-
/ positions of the underflow and overflow, are computed in the same tals of naphthalene form and the remaining liquid, called
! manner as in the graphical method. the mother liquor, becomes richer in benzene. For example,
when point G is reached, pure naphthalene crystals and
a mother liquor, given by point H on solubility curve EB,
Crystallization
coexist at equilibrium, with the composition of the solution
crystallization may take place from aqueous or nonaqueous being 37 wt% naphthalene. This is in agreement with the
solutions. The simplest case is for a binary mixture of two Gibbs phase rule (4-I), because with C = 2 and 9 = 2,
organic chemicals such as naphthalene and benzene, whose 3 = 2 and for fixed T and P, the phase compositions are
solubility or solid-liquid phase-equilibrium diagram for a fixed. The fraction of the solution crystallized can be deter-
pressure of 1 atm is shown in Figure 4.23. Points A and B are mined by applying the inverse-lever-arm rule. Thus, in
the melting (freezing) points of pure benzene (5.S°C) and Figure 4.23, the fraction is kilograms naphthalene crystals1
pure naphthalene (80.2"C), respectively. When benzene is kilograms original solution = length of line GWlength of
dissolved in liquid naphthalene or naphthalene is dissolved line HI = (52 - 37)/(100 - 37) = 0.238.
in liquid benzene, the freezing point of the solvent is de- As the temperature is lowered further until line CED, cor-
pressed. Point E is the eutectic point, corresponding to a eu- responding to the eutectic temperature, is reached at point J,
tectic temperature (-3°C) and eutectic composition (80 wt% the two-phase system consists of naphthalene crystals and a
benzene). The word "eutectic" is derived from a Greek word mother liquor of the eutectic composition given by point E.
that means "easily fused," and in Figure 4.23 it represents Any further removal of heat causes the eutectic solution to
the binary mixture of naphthalene and benzene, as separate solidify.
solid phases, with the lowest freezing (melting) point.
Temperature-composition points located above the curve
AEB correspond to a homogeneous liquid phase. Curve AE EXAMPLE 4.10
is the solubility curve for benzene in naphthalene. For exam-
A total of 8,000 kgh of a liquid solution of 80 wt% naphthalene
ple, at 0°C the solubility is very high, 87 wt% benzene or
and 20 wt% benzene at 70°C is cooled to 30°C to form naphthalene
6.7 kg benzenekg naphthalene. Curve EB is the solubility crystals. Assuming that equilibrium is achieved, determine the
curve for naphthalene. At 25°C the solubility is 41 wt% naph- amount of crystals formed and the composition of the equilibrium
thalene or 0.7 kg naphthalenekg benzene. At 50°C the solu- mother liquor.
bility of naphthalene is much higher, 1.9 kg naphthalenekg
benzene. For ths mixture, as with most mixtures, solubility SOLUTION
increases with increasing temperature.
From Figure 4.23, at 30°C, the solubility of naphthalene is 45 wt%
naphthalene. By the inverse-lever-arm rule, for an original 80 wt%
solution,
kg naphthalene crystals - (80 - 45)
- = 0.636
kg original mixture (100 - 45)

The flow rate of crystals = 0.636 (8,000) = 5,090 kgh.
The composition of the remaining 2,910 kgh of mother liquor
is 55 wt% benzene and 45 wt% naphthalene.

Crystallization of a salt from an aqueous solution is fre-
quently complicated by the formation of hydrates of the salt
with water in certain definite molar proportions. These hy-
drates can be stable solid compounds within certain ranges
of temperature as given in the solid-liquid phase equilibrium
diagram. A rather extreme, but common, case is that of
MgS04, which can form the stable hydrates MgSO, . 12H20,
Weight percent C,,,Hs in solution MgS0,. 7H20, MgS0, . 6Hz0, and MgSO, . H20. The
high hydrate is stable at low temperatures, while the low
Figure 4.23 Solubility of naphthalene in benzene.
hydrate is the stable form at higher temperatures.
[Adapted from O.A. Hougen, K.M. Watson, and R.A. Ragatz, Chemical
A simpler example is that of Na2S04 in mixtures with
Process Principles. Part I, 2nd ed., John Wiley and Sons, New York
(1954).] water. As seen in the phase diagram of Figure 4.24, only one