b-lactose can crystallize, and their (estimated) solubility curves are given in
Figure 15.17b (broken lines). The solid lines give results for total lactose
concentration, after equilibrium betweenaandbhas been reached. Notice
that the solubility curve (labeled 1) has a sharp bend at 93.5 8 C. At that point
on the line botha- andb-lactose are saturated. Since hereR¼1.39, this
means thatb-lactose is more soluble thana, as seen in the diagram. AtT>
93.5, the solubility ofaincreases more strongly with temperature than that
ofb, implying that nowb-lactose will crystallize. Below 93.5 8 C,a-lactose
monohydrate crystallizes, which is the common form.
Notice also the differences in scale between the diagrams for sucrose
and lactose, sucrose having a much higher solubility. Lactose also needs a
higher supersaturation for spontaneous crystallization to occur than
sucrose, lnb¼0.74 and 0.26, respectively. On the other hand, owing to
the marked difference in slopes of the curves, the undercooling needed is not
greatly different.
Question 1
You have a bottle containing finely crystallized lactose, but you don’t know whether
it isa-lactose hydrate orb-lactose. How can you find out? You have no other
equipment than laboratory glassware and a balance.
Answer
Add at room temperature 40 g of the lactose to 100 g of water and stir. If it isa-
lactose, it will not fully dissolve; if it isb-lactose it will, but after some time crystals
will form in the solution, sincebwill be transformed intoa, and the latter becomes
supersaturated. As a further check, you can add 15 g to 100 g of water.b-lactose will
then readily dissolve, buta-lactose only after long stirring.
Question 2
In Section 15.2.2 it was argued that the linear growth rate ofa-lactose hydrate
crystals is very much smaller than that of sucrose crystals, because in the former case
fierce competition withb-lactose occurs, and nothing like that can occur for sucrose.
Can you now give additional causes for the crystallization rate of a lactose solution
being far smaller than that of a sucrose solution at the same supersaturation,
especially at low temperature? Tip: also consult Section 2.2.