Suppose now that we evaporate water from the initial system to reach
point B. Cooling then causes the formation of fructose?2H 2 O crystals when
point B^0 is reached, whereby the solution becomes more dilute, and the
coexistence line is followed until C is reached, when also ice starts to form.
In other words, cooling a solution of compositionc<celeads to formation
of ice (as is desired in freeze concentration), whereas sugar crystallizes forc
ce(as is desired in sugar manufacture). At temperatures belowTeonly
crystals are present; upon heating to aboveTemelting occurs.
Most water-soluble solids, like salts and sugars, show eutectic phase
behavior, which means that they have phase diagrams of the type depicted
for fructose. Some eutectic points are as in the table.
Fructose Te¼ 98 C ce¼0.48
Sucrose Te¼ 148 C ce¼0.63
NaCl Te¼ 238 C ce¼0.245BothTeandcevary widely among solutes. Further details of the phase
diagram can also vary. For instance, it is seen in the figure that fructose has
two crystalline phases (with and without water), but other systems are
different, being either simpler or having more phases. Some mixtures do not
show eutectic behavior; see Section 15.4.3.
It should be stressed that a phase diagram depicts anequilibrium
situation, and it will take time, sometimes a long time, before equilibrium is
reached after conditions are changed. These aspects are discussed below.
Cooling Curves. Figure 15.15 gives examples of the temperature
evolution resulting when heat is removed at a constant rate. The graph
would apply to a small amount of material and slow heat transfer rate, since
otherwise significant temperature gradients in the sample will result, leading
to complex relations.
We will first consider pure water (curve W). Starting at A, the
temperature will fall almost linearly with time, since the specific heat of
water hardly changes over the temperature range involved (see Figure
15.13). Cooling goes on to a point B whereTis clearly below the freezing
point (0 8 C). This is because undercooling is needed to cause ice nucleation.
It will greatly depend on the purity of the water and on the rate of cooling at
what temperature nucleation, hence freezing, will start. Because of the
release of heat of crystallization,Twill increase to 0 8 C (point C), and it will
remain at that value until all of the water is frozen (F). Subsequently, the ice
will cool at a rate about twice that of water, because of its smaller specific
heat.