The situation becomes more complicated when more solutes and
especially when particulate material is present. It is not uncommon that
crystallization of solutes does not occur within a reasonable time. We will
come back to this in Chapter 16.
Question
It is often useful to know the freezing point depression of a solution. An example is
given by the detection of adulteration of milk due to dilution with water. This is
possible because milk as it comes from the cow has a very constant freezing point
depression. Can you think of a method for accurately determining the freezing point
of a solution?
Answer
From Figure 15.15, curve S, we see that noting the temperature at the moment that
the first ice is formed (point B^0 ) gives a result that greatly differs from the equilibrium
valueTf, because of the delay involved for ice nucleation to occur. It is better to
observe the maximum temperature reached after the first ice has formed (C^0 ), but this
temperature is also too low; moreover, the deviation will depend on such
uncontrollable factors as the concentration of catalytic impurities in the sample.
Still better is it to watch the further temperature evolution, and then extrapolate the
curve C^0 –D^0 back to the line A–B^0. In practice, even that turns out to be insufficiently
accurate. However, this method can be used to obtain a first estimate ofTf.Ina
second experiment, the solution is cooled to slightly below this value and then seeded
with a tiny ice crystal. The maximum temperature observed after seeding will then be
very close toTf.
15.3.3 Crystallization of Sugars
When crystallization from solution is desired, the first thing one wants to
know is the solubility of the solute as a function of temperature. For ideal
solutions, this relation can be calculated by the Hildebrand equation (2.9)
from the heat of fusion and the fusion temperature of the solute. However,
sugar solutions are strongly nonideal, and solubilities have to be determined
experimentally.
Figure 15.16 gives somesolubility–temperature curves. The relation can
be simple, as for sucrose, but for most sugars it is more complicated.
Considerglucose: either thea- or theb-anomer can crystallize, the former as
a monohydrate or in anhydrous form. When starting with an equilibrium