Page 251 - Fundamentals of Water Treatment Unit Processes : Physical, Chemical, and Biological

206 Fundamentals of Water Treatment Unit Processes: Physical, Chemical, and Biological

9.5.3.2.1 Metal Ion Polymers 9.5.3.2.3 Aluminum=Ferric Iron Hydroxide Precipitate
In addition to the products shown in Equations Al.1 through The theory of coagulation focused first on the double layer
Al.6, examples of others include: Al 2 (OH) 34 ;Al 8 (OH) 20 ; theory. The second stage of theory delineated the chemistry of
5þ
4þ
3þ 4þ
Al 6 (OH) 15 ;Al 7 (OH) 17 (Amirtharajah and Mills, 1982, metal ion hydrolysis. In practice, however, pH > 6.0 (usu-
p. 211). These are ‘‘hydroxo metal complexes’’ that readily ally), and so aluminum hydroxide forms as an amorphous
adsorb on surfaces, and, at the same time, are polymers, that is, precipitate and is the predominant species, enmeshing colloids
include repeating units. These products result from other (Stumm and O’Melia, 1968, p. 523), which is called ‘‘sweep-
hydrolysis reactions, with about 15 identified by various authors, floc’’ (O’Melia, 1979; Amirtharajah and Mills, 1982).
for example, Stumm and Morgan (1962); Stumm and O’Melia
9.5.3.3 Species Equilibrium
(1968); O’Melia (1979); and Amirtharajah and Mills (1982).
At ‘‘equilibrium’’ in the sequence of hydrolysis reactions, a As with any reaction equation, those of Equations Al.1
distribution of aluminum-complex species results. The distri- through Al.6, may be expressed as equilibrium equations;
bution depends on the concentration of the Al 3þ (or Fe ) then, taking negative logs of each side gives p(concentration)
3þ
added and the resulting pH. The distribution of species may versus pH. Table 9.5 includes Equations Al.1 and Al.4 and
be calculated by writing the equilibrium statements for each three others as deemed important in coagulation (Amirtharajah
reaction, the mass balance equation, and imposing the condi- and Mills, 1982) in terms of the reaction, equilibrium state-
tion of electroneutrality (a topic in water chemistry). ment, and pC versus pH, respectively. Figure 9.11 illustrates
the associated equilibrium lines constructed from the respect-
9.5.3.2.2 Brevity in Writing Equations ive log-form of the equilibrium equations.
The correct depiction of the hydrolysis reactions, from the The equilibrium lines of Figure 9.11 are obtained as indi-
standpoint of accepted theory, is as indicated in Equations cated from the respective rows in Table 9.5, that is, (1) write
Al.1 through Al.6, that is, with the water ligands. Often, for the reaction expression, (2) write the associated equilibrium
brevity in equation writing, however, the water ligands are statement, and (3) take the logs of each side of the equilibrium
omitted. Thus, repeating the first two equations, that is, Equa- statement, then multiply by ‘‘ 1’’ and write the equation in
tions Al.1 and Al.2, without the water ligands gives, terms of ‘‘p,’’ and (4) plot p[concentration-of-a-given species]
versus pH. Alternatively, plot [concentration-of-a-given
Al 3þ þ H 2 O ! AlOH 2þ þ H þ (9:10)
species] on a log-scale versus pH, in which [concentration-
AlOH 2þ þ H 2 O ! Al(OH) 2 þ H þ (9:11) of-a-given species] ¼ 10 pC .
þ
Example 9.2 illustrates the method of developing the loga-
The discussion here favors retaining the water ligands in the rithmic expressions, such as given in Table 9.5, and from
equations since they are primary participants in the reactions. this constructing an equilibrium diagram. Example 9.3

TABLE 9.5
Equilibrium Relations for Hydrolysis Reactions a
Reaction Equilibrium Statement Logarithmic Form
þ 3
[H ]
Al 3þ þ 3H 2 O , Al(OH) 3 (s) þ 3H þ K o ¼ ¼ 10 þ10:4 p[Al ] ¼ 3pH þ pK o
3þ
[Al ]
3þ
pK o ¼ 10.4
[Al(OH) ][H ]
þ
2þ
Al 3þ þ H 2 O , Al(OH) 2þ þ H þ K 1,1 ¼ ¼ 10 5:55 logK 1,1 ¼ log[Al(OH) ] þ log[H ] log[Al ]
þ
2þ
3þ
[Al ]
3þ
logK 1,1 ¼ log[Al(OH) ] log[H ] þ log[Al ]
3þ
þ
2þ
pK 1,1 ¼ p[Al(OH) ] þ p[H ] p[Al ]
3þ
2þ
þ
2þ 3þ
p[Al(OH) ] p[Al ] ¼ pH þ pK 1,1
2þ 3þ
p[Al(OH) ] p[Al ] ¼ pH þ pK 1,1
pK 1,1 ¼þ5.55
þ 2
Al(OH) 3 (s) þ 2H þ ¼ > AlOH 2þ þ 2H 2 O K 5 ¼ [AlOH ]=[H ] ¼ 10 4.85 p[AlOH ] ¼ 2pH pK 5
2þ
2þ
pK 5 ¼þ4.85
Al(OH) 3 (s) þ H 2 O , Al(OH) 4 þ H þ K 4 ¼ [Al(OH) 4 ][H ] ¼ 10 12:35 p[Al(OH) 4 ] ¼ pH þ pK 4 ;pK 4 ¼ 12.35
þ

þ 20
][H ]
[Al 8 (OH) 20 4þ
8Al 3þ þ 20H 2 O , Al g (OH) 20 4þ þ 20H þ K 8,20 ¼ ¼ 10 68:7 p[Al 8 (OH) 20 ] ¼ 4pH þ pK 5
4þ
3þ 8
[Al ]
pK 5 ¼ 14.5
Source: Amirtharajah, A. and Mills, K.M., J. Am. Water Works Assoc., 74(4), 210, April 1982.
a
The water ligands are omitted for brevity. For reference, however, the second and fourth equations with the water ligands included are seen as Equations Al.1
and Al.4, respectively. Documentation that showed the water ligands for the first, third, and fifth equations was not found.