Page 243 - Physical chemistry understanding our chemical world

210 PHASE EQUILIBRIA

of sodium chloride (NaCl) in water is large, so a saturated solution has a concentration
−3
of about 4 mol dm ; a saturated solution of NaCl in ethanol contains less than
0.01 mol dm −3 of solute.
An alternative way of expressing the partition constant of a spar-
Strictly, we should ingly soluble salt is to define its ‘solubility product’ K sp (also called
speak in terms of ionic the ‘solubility constant’ K s ). K s is defined as the product of the ion
activities rather than activities of an ionic solute in its saturated solution, each raised to
concentrations; see its stoichiometric number ν i . K s is expressed with due reference to
p. 312 ff. the dissociation equilibria involved and the ions present.
We saw above how the extent of partition is temperature depen-
dent; in that example, excess air was expelled from solution during freezing, since
the solubility of air was exceeded in a cold freezer box, and the gas left solution in
order for the value of K (partition) to be maintained.
Like all equilibrium constants, K (partition) is a function of temper-
The improved purity ature, thereby allowing the preparative chemist to recrystallize a
of precipitated solute freshly made compound. In practice, we dissolve the compound in
a solvent that is sufficiently hot so that K (partition) is large, as shown
implies that K (partition)
for the impurities is by the high solubility. Conversely, K (partition) decreases so much on
different from that for cooling that much of the solute undergoes a phase change from
the major solute. the solution phase to solid in order to maintain the new, lower
value of K (partition) . The preparative chemist delights in the way
that the precipitated solid retrieved is generally purer than that initially added to the
hot solvent.
The energy necessary to dissolve 1 mol of solute is called the ‘enthalpy of solution’
H O (cf. p. 125). A value of H can be estimated by analysing the solubility
(solution)
s of a solute (which is clearly a function of K (partition) ) with temperature T .
The value of K (partition) changes with temperature; the temperature dependence of
an equilibrium constant is given by the van’t Hoff isochore:

H 1 1
O
K (partition)2 (solution)
ln =− − (5.10)
K (partition)1 R T 2 T 1
O
H O is sometimes so an approximate value of H (solution) may be obtained from the
(solution)
called ‘heat of solu- gradient of a graph of an isochore plot of ln s (as ‘y’) against
tion’, particularly in 1/T (as ‘x’). Since s increases with increased T , we predict that
older books. The word H O will be positive.
(solution)
‘heat’ here can mislead,
and tempts us to ignore O
the possibility of pres- Worked Example 5.5 Calculate the enthalpy of solution H (solution)
sure–volume work. from the following solubilities s of potassium nitrate as a function of
temperature T .Valuesof s were obtained from solubility experiments.

T /K 354 347.6 342 334 329 322 319 317
s/g per 100 g of water 140.0 117.0 100.0 79.8 68.7 54.6 49.4 46.1