Page 288 - Water and Wastewater Engineering Design Principles and Practice

LIME–SODA SOFTENING 7-5

discrepancy between the cation and anion totals because there are other ions that were not ana-
lyzed. If a complete analysis were conducted, and no analytical error occurred, the equivalents of
cations would equal exactly the equivalents of anions. Typically, a complete analysis may vary
5% because of analytical errors.

The relationships between total hardness, carbonate hardness, and noncarbonate hardness
are illustrated in Figure 7-4 . In Figure 7-4a , the total hardness is 250 mg/L as CaCO 3 ,

the carbonate hardness is equal to the alkalinity HCO 3 200 mg/L as CaCO 3 ), and the
noncarbonate hardness is equal to the difference between the total hardness and the carbonate
hardness (NCH TH CH 250 200 50 mg/L as CaCO 3 ). In Figure 7-4b , the total

hardness is again 250 mg/L as CaCO 3 . However, because the alkalinity HCO 3 is greater than
the total hardness, and because the carbonate hardness cannot be greater than the total hard-
ness (see Equation 7-3 ), the carbonate hardness is equal to the total hardness, that is, 250
mg/L as CaCO 3 .
With the carbonate hardness equal to the total hardness, then all of the hardness is carbonate
hardness and there is no noncarbonate hardness. Note that in both cases it may be assumed that

the pH is less than 8.3 because HCO 3 is the only form of alkalinity present.
2

Example 7-2. A water has an alkalinity of 200 mg/L as CaCO 3 . The Ca concentration is
2
160 mg/L as the ion, and the Mg concentration is 40 mg/L as the ion. The pH is 8.1. Find the
total, carbonate, and noncarbonate hardness.
Solution. The molecular weights of calcium and magnesium are 40 and 24, respectively.

Because each has a valence of 2 , the corresponding equivalent weights are 20 and 12. Using
Equation 6-7 to convert mg/L as the ion to mg/L as CaCO 3 and adding the two ions as shown
in Equation 7-2 , the total hardness is

⎛ 50 mg/meq⎞ ⎛ 5 50mg/meq⎞
TH 160 mg/L ⎜ 20 mg/meq⎠ ⎟ 40 mg/L ⎜ ⎝ 12mg/meq⎠ ⎟ 567 mg/L as CaCO 3
⎝

where 50 is the equivalent weight of CaCO 3 .
By definition, the carbonate hardness is the lesser of the total hardness or the alkalinity.
Because, in this case, the alkalinity is less than the total hardness, the carbonate hardness (CH) is
equal to 200 mg/L as CaCO 3 . The noncarbonate hardness is equal to the difference

NCH TH CH 567 200 367 mg/L as CaCO 3

2 2
Note that concentrations of Ca and Mg can only be added and subtracted if they are in
equivalent units, for example, moles/L or milliequivalents/L or mg/L as CaCO 3 .
The removal of ions that cause hardness is called softening. The majority of treatment
systems that employ softening are those using a groundwater source. There are, however,
a number of surface water sources with a groundwater component that is hard that employ
softening as part of their treatment process. Softening can be accomplished by the lime-soda
process, ion exchange, nanofiltration, or reverse osmosis. Lime-soda softing is discussed in
this chapter. The other methods are discussed in chapters 8 and 9.