Page 713 - Fundamentals of Water Treatment Unit Processes : Physical, Chemical, and Biological

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

Required 21.2.2.3 Other Definitions of Hardness
Calculate the concentration of Ca 2þ in: (a) mol Ca =L, Several kinds of hardness definitions have been long used in
2þ
and (b) mg Ca =L.
2þ
water treatment practice. As a rule, all of the forms are
Solution expressed as CaCO 3 and include
a. The concentration of Ca 2þ in mol Ca =L, that is,
2þ
[Ca ], is . Carbonate hardness—that hardness that equals the
2þ

2 and HCO 3 .
equivalents of CO 3
33 mg Ca 2þ as CaCO 3 mol CaCO 3 . Total hardness—the sum of all hardness cations,
2þ
L 100,000 mg CaCO expressed as CaCO 3 .
[Ca ] ¼
3
. Permanent hardness—that portion of hardness not
3:3 10 4 mol Ca 2þ associated with carbonate or bicarbonate, but with
L other anions, for example, Cl ,SO 4 , etc.
¼

. Temporary hardness—that portion of hardness asso-
b. The concentration of Ca , in mol Ca =L, that is, ciated with carbonate or bicarbonate.
2þ
2þ
[Ca ], is
2þ
21.2.2.4 Softening Reactions
3:3 10 4 mol Ca 2þ 40,000 mg Ca 2þ
2þ When lime, CaO, is added to hard water, the following reac-
L mol Ca 2þ tions are typical (Babbitt and Doland, 1949, p. 507):
C(Ca ) ¼
13:2mgCa 2þ
13 mg Ca =L Ca(HCO 3 ) 2 þ H 2 O (21:4)
2þ
L lime carbonic acid calcium bicarbonate water
¼ CaO þ 2H 2 CO 3 !
insoluble soluble causes hardness
Discussion
When expressing concentration as CaCO 3 , conversion to Removal of temporary hardness, that is, the portion of Ca 2þ
the molar concentration is the basis for conversion to mg=L associated with HCO 3 :

for the ion in question.
Ca(HCO 3 ) 2 þ Ca(OH) 2 ! 2Ca(CO 3 ) þ 2H 2 O (21:5)
calcium bicarbonate lime addition calcium carbonate water
temporary hardness insoluble
Example 21.5 Conversion of Mg 2þ Concentration
Removal of permanent hardness, that is, the portion of Ca 2þ
Given 2
Magnesium ion, Mg , is a hardness component in a associated with Cl ,NO 3 ,SO 4 :
2þ
water; its concentration in the ambient raw water is
C(Mg ) ¼ 22 mg=L as CaCO 3 . CaSO 4 þ Na 2 CO 3 ! CaCO 3 þ Na 2 SO 4
2þ
calcium sulfate sodium carbonate calcium carbonate sodium sulfate
Required permanent hardness (soda ash) insoluble soluble
Calculate the concentration of Mg 2þ in: (a) mol Mg =L, (21:6)
2þ
and (b) mg Mg =L.
2þ
Explanations are
Solution
(a) The concentration of Mg 2þ in mol Mg =L, that is, . Reaction (1), that is, Equation 21.4, expresses the
2þ
[Mg ], is
2þ
reaction of lime with carbonate.
. Reaction (2), that is, Equation 21.5, expresses is the
22 mg Mg 2þ as CaCO 3 mol CaCO 3
2þ reaction that occurs when temporary hardness is
[Mg ] ¼
L 100,000 mg CaCO
3 removed by the addition of lime.
2:2 10 4 mol Mg 2þ . Reaction (3), that is, Equation 21.6, occurs when
¼
L permanent hardness is removed by the addition of
soda ash. Normally, reaction (3) would be followed
(b) The concentration of Mg , in mol Mg =L, that is, by reaction (2) in order to remove all hardness.
2þ
2þ
[Mg ], is
2þ
Magnesium, if it occurs, is removed as magnesium hydroxide,
2:2 10 4 mol Mg 2þ 24,300 mg Mg 2þ Mg(OH) 2 , which is done usually at pH 11.0. Most softening
2þ
L mol Mg 2þ
C(Mg ) ¼ reactions are done at pH 10; at this pH, the charge on
CaCO 3 is negative and is positive on Mg(OH) 2 . Therefore,
5:3mgMg 2þ
5mgMg =L coagulants are needed to charge neutralize the particles
2þ
L
¼
(Kemmer, 1979, p. 10–12).
Discussion Dosages of lime and soda ash, if needed, may be deter-
The conversion of Mg 2þ concentration as CaCO 3 is the mined stoichiometrically, knowing the concentrations of Ca 2þ
same, in principle, as for Ca , or for bicarbonate or and Mg 2þ by analytical means. Usually, however, jar testing
2þ
carbonate. is done with different lime dosages, or lime and soda dosages,