Ix

where is the mole fraction of species i (defined in Sec. 2.10). In aqueous solutions, the solvent is water. So, XH,0 ~ 1 (this really means that [H20]/[H20]0 = 1). Here, yH,,0 = 1 for the standard reference state. Therefore, {HjO} = 1.0. This is somewhat confusing to students. However, by convention, we typically assume that {HzO} = [H20] = L0. Thus, water is left out of an equilibrium constant expression for dilute aqueous solutions. It should be noted that for seawater (contains lots of dissolved salts), ymvMl ** 0.98, which can have a significant effect on equilibrium calculations.

3. For pure solids or pure liquids in equilibrium with aqueous solution:

As with water, the concentration or activity of pure solids or pure liquids do not need to be included in equilibrium constant expressions.

4. For gases in equilibrium with aqueous solution:

where Ff is the partial pressure of gas i in atmospheres (or bars). When total pressure decreases, -ygas approaches 1.0. When reactions take place at atmospheric pressure, {;} - P, Air is about 21 percent oxygen, so F0j = 0.21 atm = {O,} = [OJ.

With gases, the concept oifugacity, which has units of partial pressure, has also been used. Morel and Bering4 describe fugacity as being to gases as activity is to ions in solution. That is, fugacity accounts for the nonxdeal behavior of gases. Mackay5 has described how fugacity might be used in environmental engineering and science. Schwarzenbach et al.6 use fugacity as a measure of the "escaping tendency" from a phase.

2 13 I VARIATIONS OF THE EQUILIBRIUM

RELATIONSHIP

Equations (2.22) and (2.23) are general forms of the equilibrium relationship. They are useful in helping to understand the various ways in which substances may be distributed in aqueous solution and methods for their control. Homogeneous chemical equilibria are characterized by all reactants and products of . the reaction occurring in the same physical state or phase, such as reactions between gases or between materials dissolved in water. Examples of homogeneous equilibria in water are the ionization of weak acids and bases, and complex formation.

Heterogeneous chemical equilibria are characterized by substances occurring in two or more physical phases. Examples are equilibria for the solubility of a gas in a liquid, the solubility of solids in water, the distribution of a material between two different solvents, the equilibrium of a substance between its liquid phase and gaseous phase, or between its liquid phase and solid phase. Examples of homogeneous and heterogeneous equilibria of particular concern to environmental engineering and science are given here. These are considered in greater detail m Chaps.

"F. M. M. Moid and J. G. Hering, "Principles and Applications of Aquatic Chemistry," Wiley, New York, 1993.

3D. Mackay, Finding Fugacity Feasible, Env. Sei. & Tech., 13: 1218-1223 (1979).

6R. P. Schwarzenbach, P. M. Gschwend, and D. M. Imboden, "Environmental Organic Chemistry-"

Ionization

The theory of ionization stems from a doctoral dissertation completed by Svante Ar-rhenius in 1887. According to the original liieory of Anhenius, all acids, bases, and salts dissociate into ions when placed in solution in water. He noted that equivalent7 solutions of different compounds often varied greatly in conductivity. This phenomenon was attributed by Arrhenius to a difference in degree of dissociation or ionization and serves today to explain many of the observed phenomena in aqueous solution.

Ion Product of Water

One of the most important equilibria of concern in dealing with aqueous solutions is the dissociation of water into a hydrogen ion, or proton, and hydroxy! ion.

A proton is a very small particle and as such would have an extremely large charge-to-volume ratio. As a result, it will attach itself to almost anything that does not have a large positive charge. In aqueous solution, it readily becomes attached to water molecules, so that the following equation is a more correct description of water dissociation than Eq. (2.26):

where H30+ is called the hydronium ion. The hydronium ion can also react with water to form other hydrated species, so even Eq. (2.27) is not a completely accurate description for the dissociation of water. For many practical purposes, the simple dissociation indicated by Eq. (2.26) can be assumed. This leads to the ion product for water, which can be written as follows (using molar concentration instead of activity):

However, by convention [H20] is taken to equal 1, so that the ion product for water in its simplest form is

In satisfying this equilibrium, the numerical values of [H+] and [OH~J include all the H+ and OH" ions present, regardless of whether these ions are produced by the water alone or are contributed by other constituents in the water.

Ionization of Acids and Bases

The classical definition of an acid is a compound that yields a proton (H+) upon addition to water. A base yields a hydroxide ion (OH"") upon addition to water. Arrhenius' theory of ionization can help explain the variation in strength of acids and bases. All strong acids and bases are considered to approach 100 percent ionization

7See Sec. 11.4 for definition.

in dilute solutions; that is, they completely ionize and dissociate. For example, consider the case of a strong acid HA:

For a strong acid, KA is very large since there will be almost no undissociated acid (HA) in solution.

The weak acids and bases, however, are so poorly ionized that in most cases it is impractical to express the degree of ionization as a percentage. The equilibrium relationship, however, can be used as will now be illustrated.

For a typical monoprotic (yields one proton) acid (acetic acid),

[i"Ir!!lA<: ] = Ka = 1.75 X 10~s at 25°C (2.30)

where Ac- is used to designate the acetate ion.

For a typical diprotic (may yield two protons) acid (carbonic acid),

(H2CO3J

For a typical base (ammonia, NH3),

The concentration of water was not included in Eq. (2.33) for the reason discussed in Sec. 2.12. Tables giving ionization constants of weak acids, bases, and salts may be found in the usual handbooks and many textbooks of quantitative analysis or physical chemistry.

EXAMPLE 2.9

Complex Ions

Complex ions consist of one or more central ions (usually metals) that are associated with one or more ions or molecules (called Mgands) which act to stabilize the central ion and keep it in solution. For example, if Hg2+ and CI" are present in water, they will combine to form the undissociated but soluble species EgCl2(aq), where (aq) is used to designate that the species is in solution. Chloride can also combine with mercury in other proportions to form a variety of complexes. Equilibrium relationships can be developed for the various mercury-chloride species from the following reactions:

Equilibrium relationships associated with the reactions of Eqs. (2,34) to (2.37) are as follows (using molar concentration instead of activity):

[Hgcy

[HgClJ]

[Hgcyfcn

[HgClM [Hgci3~j[cn

The usual convention is to write complex reactions as indicated in Eqs. (2.34) to (2.37), as formation rather than as dissociation reactions. The equilibrium constant is then called a formation or stablity constant. The subscript on the stability constant indicates the number of chloride ions in the complex formed by the reaction.

It is sometimes convenient to consider overall reactions for the formation of complexes, and these can be developed by combination of the stepwise reactions indicated above (Eqs. (2.34) to (2.37)).

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