Categories of liquid-liquid systems
Liquid-liquid systems are divided into two categories:
a- Complete miscible: those are liquids, which are polar, and semipolar
such as water / alcohol, glycerin/alcohol and alcohol/acetone. These
solvents are completely mixed in all proportion. In addition, nonpolar
solvents are completely miscible when mixed together such as benzene
and carbon tetrachloride.
b- Partial miscible: Those in which a mutual solubility of one in the other
is achieved, such as water/ether or water/phenol systems. This mutual
solubility is affected by many factors, from which the most important
one is the temperature.

A mixture of phenol and water at 20°C has a total composition of 50%
phenol. The tie line at this temperature cuts the binodal at points equivalent to
8.4% and 72.2% w/w phenol. What is the weight of the aqueous layer and of
the phenol layer in 500 g of the mixture and how many grams of phenol are
present in each of the two layers?

Phase equilibrium and phase rule (Gibbs' phase rule)
The description of the equilibrium state of a system can be done when we can fix as
constant some number of intensive variables. As a simple example, if an evacuated
container is filled to half its volume with pure water, we would expect the system to reach
equilibrium when the temperature, T, becomes constant and uniform throughout the
container.
The Phase Rule stated that:
At equilibrium the number of independent variables (also called thermodynamic
potentials) that must be fixed is called the number of degrees of freedom, F (The number
of intensive variables which are independent of each other). It is given by:
F = C - p + 2
Where:
C is the number of components (The number of chemically independent constituents of
the system)
p is the number of phases in the system.

The triangular diagram for three-component system
Solubility of solids in liquids
Solubility of solids in ideal solution depends on
- Temperature,
- Melting point of the solid
- Molar heat of fusion, Δ Hf

Factors affecting solubility of solids in liquids
1- Temperature
According to Gibbs free energy equation, the change accompanies dissolution is dependent on
the value and sign of the change in enthalpy, ΔH.
*If ΔH is positive, the reaction is endothermic, thus a rise in temperature leads to increase the
solubility of that solids in the solvent.
*If ΔH is negative, the reaction is exothermic, thus a rise in temperature leads to decrease the
solubility of that solids in the solvent.
*ΔH (solution of crystalline solute) = ΔH (sublimation) + ΔH (hydration)
ΔH (sublimation) is the energy required to separate one mole of crystal into ions
ΔH (hydration) is the heat liberated when the ions are hydrated
When ΔH (hydration) ˃ ΔH (sublimation), the dissolution is exothermic
When ΔH (sublimation) ˃ ΔH (hydration), the dissolution is endothermic
ΔH is the enthalpy of the system (heat of solution) and it is the amount of heat absorbed or
evolved as the system change its thermodynamic state i.e. when dissolution occur.
, that is the heat absorbed when the solid melts.
In an ideal solution, the heat of solution is equal to the heat of fusion, which is assumed to be
a constant independent of the temperature
Δ Hf T0
-T
- log Xi
2 = --------------- x ------------
2.303 R TT0
Where
Xi
2
is the ideal solubility of the solute expressed in mole fraction,
T0
is the melting point of the solid solute in absolute degrees,
T is the absolute temperature of the solution
Example
What is the solubility of naphthalene at 20°C in an ideal solution? The melting point of
naphthalene is 80°C and the molar heat of fusion is 4500 cal/mol.