Page 254 - Fundamentals of Water Treatment Unit Processes : Physical, Chemical, and Biological

Coagulation 209

TABLE CD9.7
Determining the Distribution of Ferric Iron Hydrolysis Species with Varying pH
1 Reactions 2 Equilibrium Statements
Reaction Equilibrium Constant Table 9.7 Equation (a) Basic Form (b) Rearranging
3 Taking logarithms of each expression
4 Calculation of data for log concentration diagram
5 Plot

Note: Only table headings are shown in text; the spreadsheet may be downloaded.

Discussion tration which is the negative log of concentration in mol=L) are
Figure 9.11 shows a plot of [Al(OH) 4 ] versus pH, along with also shown. Figure 9.11 shows the corresponding equilibrium

the equilibrium lines for the other species listed in Table 9.5. diagram as ‘‘species-concentration versus pH’’; concentrations
Table CD9.6 demonstrates, in spreadsheet form, the con-
struction of the same diagram in the form, p[Al(OH) 4 ] are in ‘‘mol Al=L’’ on the left-hand scale and in ‘‘mg Al 2 (SO 4 ) 3

14H 2 O)=L’’ on the right-hand scale. Each line in the diagram
versus pH. With respect to nomenclature, recall that the
depicts the respective equilibrium equation of Table 9.5.
brackets, ‘‘[ ],’’ represent concentration in mol=L.
The ‘‘coagulation diagram,’’ as it is known, was assimilated
into practice during the 1980s after its description
Example 9.3 Illustrate Conversion of
by Amirtharajah and Mills (1982), building on equilibrium
Concentration in mol=Ltomg=L for Alum
theory (Stumm and O’Melia, 1968). In the diagram, pH is the
‘‘master-variable,’’ shown on the x-axis, with alum species
Given concentrations on the y-axis. In the diagram, several ‘‘zones’’
Assume that hydrated aluminum sulfate is added to water
at 50 mg Al 2 (SO 4 ) 3 14H 2 O of coagulation are identified, for example, charge-neutraliza-
tion, sweep-floc, combination, and restabilization. Regarding
Required the precipitate, the pH controls the effect as follows:
Determine the concentration of [Al 2 (SO 4 ) 3 14H 2 O] in
mol=L
. pH < 7.0: ‘‘re-stabilization’’ is likely for the posi-
Solution
tively charged precipitate
1. MW[Al 2 (SO 4 ) 3 14H 2 O] ¼ 594 g=mol (Table 9.4) . 7.0 < pH < 8.0: at an alum dose of about 30 mg
2. Calculate molar concentration,
Al 2 (SO 4 ) 3 14H 2 O)=L the charge is also positive,
mg Al (SO 4 ) 3 14H 2 O which will react with negatively charged colloids
[Al 2 (SO 4 ) 3 14H 2 O] ¼ 50 2 . pH > 8.0 the precipitate is weakly negative
L
g mol Al 2 (SO 4 ) 3 14H 2 O
1000 mg 594 g Al (SO 4 ) 3 14H 2 O In practice, the diagram provides guidance on what to expect

2
with different pH and coagulant dosage combinations, and on
mol Al 2 (SO 4 ) 3 14H 2 O
¼ 0:000084 the zones to seek or avoid. Since ‘‘every water is different,’’ a
L
common expression, the zones should be confirmed by jar
On the log scale, this concentration reads, log testing and=or pilot plant.
[0.000084] ¼ 4.076, or [Al 2 (SO 4 ) 3 14H 2 O] ¼ 10 4.076
mol=L. 9.5.3.5 Spreadsheet Construction of Coagulation
Discussion Diagrams
The conversion factor is seen to be 594,000. Thus to Table CD9.6 outlines in a spreadsheet the construction of the
convert from mol=Lto mg=L, multiply mol=L by 594,000 alum coagulation diagram, adopting the equations given in
mg Al 2 (SO 4 ) 3 14H 2 O=mol Al 2 (SO 4 ) 3 14H 2 O. As noted Table 9.5. The logic of the construction of the diagram is
in Example 9.1, however, caution should be exercised displayed stepwise along the columns of the spreadsheet. The
when Al only is expressed in mol=L as there are two Al
atoms in an Al 2 (SO 4 ) 3 14H 2 O molecule. Thus, 10 4.075 starting point is to write the respective reaction equations and
mol Al 2 (SO 4 ) 3 14H 2 O=L 2 mol Al =mol Al 2 (SO 4 ) 3 14 the associated equilibrium constants. The next step is to write
3þ
H 2 O ¼ 2 10 4.075 mol Al =L ¼ 1.68 10 4 mol Al =L. the equations for equilibrium, and then their conversions to
3þ
3þ
their logarithmic ‘‘p’’ forms. Using the equations, that is, pC
9.5.3.4 Coagulation Zones versus pH, the tabular outputs of concentrations of the differ-
Table 9.5 lists five selected reaction equations for alum as a ent species as a function of pH are calculated. From the
coagulant (Amirtharajah and Mills, 1982). The respective equi- tabular output, the pC versus pH diagram is obtained as an
librium statements and their logarithmic forms (as ‘‘p’’ concen- embedded plot (located below the tabular output). The pC