Page 293 - Water and wastewater engineering

7-10 WATER AND WASTEWATER ENGINEERING

protonated anion species are common. In addition, the cations or anions may form complexes with
other materials in solution, thus, reducing their effective concentration (Sawyer et al., 2003).
Of particular importance is the effect of solution pH on the solubility of cations. For example,
assuming that there are no other compounds in solution to react with calcium hydroxide, the solu-
bility product would be

K [Ca 2 ][OH ] 2 (7-19)
sp
or

[
[
log Ca 2 ] log K sp 2 log OH ]
(7-20)

However, log [OH ] is a function of pH:

pH pK pOH pK log OH ]
[
w w (7-21)
or

log OH ] pH pK w (7-22)
[

So Equation 7-20 may be written
log Ca 2 ] log K ( 2 pH pK )
[
sp w (7-23)
The pH not only affects the solubility of metal hydroxides, it also affects other equilibria,
which in turn affects the solubility of the cation. Of particular importance is the relationship of
the carbonate buffer system to pH. As noted in Equations 6-5 and 6-6, carbonate is an anion of the
weak diprotic acid, H 2 CO 3 . The carbonate species both influence and are influenced by the pH.
The sum of the carbonate species may be specified as a total concentration of inorganic carbon:
2
C T [H CO 3 ] [HCO 3 ] [CO 3 2 ] (7-24)
2
If the pH is specified, the saturation value for [Ca ] can be estimated for a given value of C T .
This is illustrated in Figure 7-6 .
In lime-soda softening, the pH is controlled by the addition of lime. To precipitate CaCO 3 ,
the pH of the water must be raised to about 10.3. To precipitate magnesium, the pH must be
raised to a range of about 11 to 11.3 (Horsley et al., 2005).

Process Limitations and Empirical Considerations. Lime-soda softening cannot produce a
water completely free of hardness because of the solubility of CaCO 3 and Mg(OH) 2 , the physical
limitations of mixing and contact, and the lack of sufficient time for the reactions to go to com-
pletion. Thus, the minimum calcium hardness that can be achieved is about 30 mg/L as CaCO 3 ,
and the minimum magnesium hardness is about 10 mg/L as CaCO 3 . Because of the slimy condi-
tion that results when soap is used with a water that is too soft, historically the goal for final total
hardness has been set at between 75 and 120 mg/L as CaCO 3 . In recent years, many utilities have
raised the target hardness to 120 to 150 mg/L as CaCO 3 to reduce chemical costs and residuals *
production (Horsley et al., 2005).
In order to achieve reasonable removal of hardness in a reasonable time period, an extra amount
of Ca(OH) 2 beyond the stoichiometric amount usually is provided. Based on empirical experience, the
minimum extra amount is 20 mg/L of Ca(OH) 2 expressed as CaCO 3 (or 0.40 meq).
*Residuals precipitate in the lime-softening process and brine in ion exchange and reverse osmosis softening.