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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.
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