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CHAPTER
9

Solutions

CHAPTER OUTLINE

Much of chemistry and biochemistry takes place in solution. A solution is a homoge- 9.1 Solution Composition
neous mixture; that is, a solution is a one-phase system with more than one compo-
nent. The phase may be solid, liquid, or gas. Much of this chapter deals with liquid 9.2 Partial Molar Quantities
solutions, but most of the equations of Secs. 9.1 to 9.4 apply to all solutions. 9.3 Mixing Quantities
Section 9.1 defines the ways of specifying solution composition. The thermody-
namics of solutions is formulated in terms of partial molar properties. Their defini- 9.4 Determination of Partial
tions, interrelations, and experimental determination are discussed in Secs. 9.2 and Molar Quantities
9.4. Just as the behavior of gases is discussed in terms of departures from the behav-
ior of a simple model (the ideal gas) that holds under a limiting condition (that of low 9.5 Ideal Solutions
density and therefore negligible intermolecular interactions), the behavior of liquid
solutions is discussed in terms of departures from one of two models: (a) the ideal 9.6 Thermodynamic Properties of
solution, which holds in the limit of almost negligible differences in properties be- Ideal Solutions
tween the solution components (Secs. 9.5 and 9.6); (b) the ideally dilute solution, 9.7 Ideally Dilute Solutions
which holds in the limit of a very dilute solution (Secs. 9.7 and 9.8). Nonideal solu-
tions are discussed in Chapters 10 and 11. 9.8 Thermodynamic Properties of
Ideally Dilute Solutions
9.1 SOLUTION COMPOSITION 9.9 Summary

The composition of a solution can be specified in several ways. The mole fraction x
i
of species i is defined by Eq. (1.6) as x n /n , where n is the number of moles of
i i tot i
i and n is the total number of moles of all species in the solution. The (molar) con-
tot
centration (or amount concentration) c of species i is defined by (6.21) as
i
c n >V (9.1)*
i
i
where V is the solution’s volume. For liquid solutions, the molar concentration of a
3
species in moles per liter (dm ) is called the molarity. The mass concentration r of
i
species i in a solution of volume V is
r m >V (9.2)*
i
i
where m is the mass of i present.
i
For liquid and solid solutions, it is often convenient to treat one substance (called
the solvent) differently from the others (called the solutes). Usually, the solvent mole
fraction is greater than the mole fraction of each solute. We adopt the convention that
the solvent is denoted by the letter A.
The molality m of species i in a solution is defined as the number of moles of i
i
divided by the mass of the solvent. Let a solution contain n moles of solute B (plus
B
certain amounts of other solutes) and n moles of solvent A. Let M be the solvent
A A
molar mass. From Eq. (1.4), the solvent mass w equals n M . We use w for mass, to
A A A
avoid confusion with molality. The solute molality m is
B
n n
m B B (9.3)*
B
w A n M A
A