Page 290 - Water and wastewater engineering

LIME–SODA SOFTENING 7-7

The product of the activity of the ions (approximated by the molar concentration) is a con-
stant for a given compound at a given temperature. In its most general form it is written as
[] a B] b
A [
K (7-6)
[ A ab B ()s ]

where [ ] molar concentration, moles/L
(s) solid state, that is the precipitate
Because the precipitate is a solid, [ A a B b (s)] 1.0 and the equation is conventionally expressed as

a
K [] [ B] b (7-7)
A
sp

where K sp solubility product constant

This expression forms the fundamental basis for lime-soda softening. K sp values are often
reported as pK sp where
pK log K (7-8)
sp sp
A selected list of K sp values is presented in Appendix A.

Le Chatelier’s Principle. The lime-soda reactions are a direct application of Le Chatelier’s prin-
ciple or the law of mass action, which states that a reaction at equilibrium will adjust itself to relieve
any force or stress that disturbs the equilibrium. To soften the water, an ion in common in the solu-
bility equilibrium is selected to react with calcium or magnesium so the reaction forms more pre-
cipitate. The solubility product equilibrium provides a starting point for selecting the common ion.
From Appendix A, it is apparent that several forms of calcium and magnesium will form a precipi-
tate. The solubility product, as well as public health and economic criteria, are used as the criteria
for selecting the form of precipitate. In the case of calcium, the desired precipitate is CaCO 3 . In the
case of magnesium, the desired precipitate is Mg(OH) 2 . The solubility equilibrium reactions are

2

2
Ca CO 3 CaCO 3 s( )
(7-9)
2
Mg 2 OH Mg OH 2 ) ( s) (7-10)
(

2
The concentration of CO 3 and/or OH is increased by the addition of chemicals, and the
chemicals drive the reactions given in Equations 7-9 and 7-10 to the right. Insofar as possible, the
2
naturally occurring bicarbonate alkalinity (HCO 3 ) is converted to carbonate (CO 3 ) by the addi-

tion of hydroxyl ions (OH ). Hydroxyl ions cause the carbonate buffer system (Equation 6-2) to
shift to the right and, thus, provide the carbonate for the precipitation reaction ( Equation 7-9 ).
The common source of hydroxyl ions is calcium hydroxide [Ca(OH) 2 ]. Many water treatment
plants find it more economical to buy quicklime (CaO), commonly called lime, than hydrated
lime [Ca(OH) 2 ]. The quicklime is converted to hydrated lime at the water treatment plant by
mixing CaO and water to produce a slurry of Ca(OH) 2 , which is fed to the water for softening.
The conversion process is called slaking:
CaO H O Ca(OH) 2 heat (7-11)
2