Physical Processes - Isoconversional Kinetics of Thermally Stimulated Processes - page 124

3.9 Mixing and Demixing

…he took the materials, of which he made a compound, mixing
them all and boiling them a good while until it seemed to him
they had come to perfection
Miguel de Cervantes Saavedra, Don Quixote

3.9.1 Background

So far we have discussed the phase transitions in single-component systems. If a
system contains more than one component, it can exist as a single mixed phase and
as several demixed phases. A transition between mixed and demixed phases is the
phase transition specific to multicomponent systems. The mixed and demixed phas-
es can coexist at equilibrium at certain temperature and pressure. A simple example
is equilibrium between a solid solute and liquid solvent. If a small amount of so-
dium chloride (solute) is put in a large volume of water (solvent), it will disappear
forming a solution, which is a single mixed phase (solution) containing sodium and
chloride ions and water molecules. However, if we keep increasing the amount of
sodium chloride, at some point the solution will saturate so that an excess of solid
sodium chloride will coexist in equilibrium with its aqueous solution as two im-
miscible phases.
The transition between the mixed and demixed phases can be stimulated by
changing temperature. Normally, the solubility of a solid solute increases with tem-
perature as follows: [ 18 ]

= −

∆ H

RT TT

11

f

(3.77)

ln x − ,

m

where x, Δ H f , and T m are respectively the mole fraction, enthalpy of fusion, and
melting temperature of the solid. This means that upon heating above certain equi-
librium temperature, T 0 , the two phases would merge into one. Conversely, the
single-phase solution can be separated in two phases by dropping its temperature
below T 0 that would force the solid solute out of solution or, in other words, would
cause crystallization of the solute. Equation 3.77 gives rise to the phase diagram
shown in Fig. 3.53 . The solid line represents temperatures at which the solutions of
different concentration can coexist at equilibrium with the solute. A solution pre-
pared at higher temperature obviously has higher equilibrium concentration. A so-
lution of the concentration x 1 prepared at T 1 , i.e., above the respective equilibrium
temperature, is a single-phase system. Dropping its temperature to T 2 would cause
the solution to separate in two phases that eventually would come to equilibrium.
The concentration of the solution would drop from x 1 to x 2 , and the excess of the
solute (i.e., x 1 − x 2 ) would fall out of solution to form the solid phase.
Something similar happens when mixing two partially miscible liquids, i.e., liq-
uids that have limited solubility in each other. The respective phase diagram for liq-