6
The Thermodynamics of Solutions
PRINCIPAL FACTS AND IDEAS
1. A solution is a homogeneous mixture of two or more substances.
2. An ideal solution is a model system in which every component has its
chemical potential given for all compositions by
µ i µ
∗
i + RT ln(x i )
where µ ∗
i is the chemical potential of the pure substance i, R is the ideal
gas constant, T is the absolute temperature, and x i is the mole fraction of
the substance in the solution.
3. Every component in an ideal solution at equilibrium with an ideal vapor
phase very nearly obeys Raoult’s law
P i P
∗
i x i
where P i is the partial pressure of gaseous substance i at equilibrium with
the solution and P ∗
i is the partial pressure of substance i in the gas phase
at equilibrium with pure substance i (the vapor pressure of the pure
substance).
4. Mixtures of substances with similar molecules form nearly ideal solutions.
5. Nonelectrolyte solutes in dilute solutions very nearly obey Henry’s law:
P i k i x i
where k i is a function of temperature called the Henry’s law constant and
x i is the mole fraction of substance i in the solution.
6. Activities and activity coefficients describe deviations from ideal or dilute
behavior.
7. The activities of strong electrolyte solutes require special treatment. The
Debye–Hückel theory provides an accurate limiting law for activity
coefficients of electrolyte solutes.
8. Phase diagrams can be used to show the phase equilibria of multicomponent systems and can be understood through the phase rule of Gibbs.
9. Colligative properties depend on concentrations of solutes, but not on
their identities.
237
The Thermodynamics of Solutions
PRINCIPAL FACTS AND IDEAS
1. A solution is a homogeneous mixture of two or more substances.
2. An ideal solution is a model system in which every component has its
chemical potential given for all compositions by
µ i µ
∗
i + RT ln(x i )
where µ ∗
i is the chemical potential of the pure substance i, R is the ideal
gas constant, T is the absolute temperature, and x i is the mole fraction of
the substance in the solution.
3. Every component in an ideal solution at equilibrium with an ideal vapor
phase very nearly obeys Raoult’s law
P i P
∗
i x i
where P i is the partial pressure of gaseous substance i at equilibrium with
the solution and P ∗
i is the partial pressure of substance i in the gas phase
at equilibrium with pure substance i (the vapor pressure of the pure
substance).
4. Mixtures of substances with similar molecules form nearly ideal solutions.
5. Nonelectrolyte solutes in dilute solutions very nearly obey Henry’s law:
P i k i x i
where k i is a function of temperature called the Henry’s law constant and
x i is the mole fraction of substance i in the solution.
6. Activities and activity coefficients describe deviations from ideal or dilute
behavior.
7. The activities of strong electrolyte solutes require special treatment. The
Debye–Hückel theory provides an accurate limiting law for activity
coefficients of electrolyte solutes.
8. Phase diagrams can be used to show the phase equilibria of multicomponent systems and can be understood through the phase rule of Gibbs.
9. Colligative properties depend on concentrations of solutes, but not on
their identities.
237