Chapter 13. Precipitation, Coprecipitation, and Precipitative Softening

13.2



CHAPTER Thirteen



This chapter begins with a discussion of the principles of precipitation and coprecipitation and then describes practical applications of these principles in drinking water treatment. The major focus of this chapter is on precipitative softening, which is employed at

approximately 15 percent of water treatment plants in the United States. Other applications

of precipitative processes are briefly summarized. Precipitation and coprecipitation are also

involved in other processes addressed in this handbook, including coagulation with metal

salts, which involves precipitation of aluminum and iron hydroxides and coprecipitation of

various dissolved contaminants (Chap. 8); precipitation of iron and manganese after their

dissolved forms have been oxidized (Chap. 7); and scale formation, which is important in

filters (Chap. 10), membrane processes (Chap. 11), and distribution systems (Chap. 20).



PRINCIPLES

Precipitation

Precipitation occurs when dissolved constituents in a supersaturated solution interact to

form a solid. The dissolved constituents and solids may be ionic or nonionic, but further discussion will be limited to those that are ionic, since precipitative processes are used in water

treatment applications to remove ionic contaminants. An ionic contaminant can be removed

if the concentration of another (oppositely charged) ion can be increased sufficiently to

precipitate the contaminant ion out of solution, forming an ionic solid. It is also possible

for ionic contaminants present in concentrations below the point of supersaturation to be

removed by being incorporated into a precipitate formed by other ions. This process, known

as coprecipitation, is described below. Treatment processes that remove contaminants by

precipitation or coprecipitation are referred to as precipitative processes.

Precipitation of an ionic solid is both a physical and chemical process. It is commonly

viewed as occurring in three stages, nucleation, crystal growth, and aging, in which ions

in a supersaturated solution join together to form three-dimensional coordination compounds that develop into a solid phase. Coordination is the binding of a central atom (the

cation in an ionic solid) by molecules (known as ligands) containing free pairs of electrons.

Coordination is a fundamental phenomenon involved in complex formation, precipitation

of ionic solids, chemisorption of ions, and coprecipitation. The ions that react to form an

ionic solid (or crystal lattice) are referred to as the lattice ions; and other ions incorporated

into an ionic solid by coprecipitation are referred to as impurities.

Nucleation is the coordination of lattice ions to form clusters (nuclei) of sufficiently

large size that spontaneous deposition of additional lattice ions (crystal growth) can occur,

which is possible only if the solution is supersaturated with respect to the solid being formed.

Nucleation can occur through random collisions of lattice ions in solution (homogeneous

nucleation) or through adsorption (accumulation at an interface) and nucleus formation on

the surfaces of foreign particles (heterogeneous nucleation). Homogeneous and heterogeneous nucleation both require supersaturated solutions, but a higher degree of supersaturation is required for homogeneous nucleation. For this reason, and because foreign particles

are present even in relatively clear water supplies, heterogeneous nucleation is expected to

occur in precipitative drinking water treatment processes. But, if a high degree of supersaturation is achieved, for example, by adding a relatively large dose of lime or alum, then

homogeneous nucleation may also occur.

Nucleation typically occurs instantly in highly supersaturated solutions. In solutions

that are only slightly supersaturated, an extended period of time, referred to as an induction

period, may pass before solids visibly appear. When precipitation is not desired, for example in the concentrate stream in a membrane process, the induction period can be extended,







PRECIPITATION, COPRECIPITATION, AND PRECIPITATIVE SOFTENING



13.3



perhaps indefinitely, by adding a chemical that interferes with nucleation or crystallization.

Such chemicals, commonly referred to as antiscalants or threshold inhibitors, can adsorb

onto nuclei or small crystals and interfere with adsorption of lattice ions, slowing or halting

crystal growth. Solids formed in the presence of an antiscalant will contain antiscalant molecules as impurities; such impurities usually affect the properties of the solids, sometimes

dramatically, and may interfere with options for their disposal, use, or reuse.

Crystallization involves (1) transport (diffusion) of lattice ions to the crystal-solution interface, (2) adsorption of lattice ions on the surface, and (3) incorporation of lattice ions into the

lattice. Hence, the rate of crystallization can be diffusion controlled or interface controlled.

For precipitation of CaCO3(s) in a lime softening process, the reaction may be diffusion controlled during the initial moments of the reaction, for example, in the rapid mixing unit; but

the reaction soon becomes interface controlled with the rate of crystallization being proportional to the degree of supersaturation. This can be expressed mathematically as follows:





d (Ca +2)

2

= - k S [({Ca 2+}×{CO3-}) - K s 0 ]

dt



(13-1)



where

k = rate constant



S = available surface area



{Ca2+} = calcium ion activity

2−



{CO3 } = carbonate ion activity



Ks0 = solubility product constant for CaCO3

Solids recirculation increases the surface area available for crystallization, favoring

crystallization over nucleation. This results in the formation of larger particles, which may

be of significant benefit if the solids are to be removed by sedimentation or if they will be

dewatered prior to disposal or reuse.

Freshly precipitated ionic solids may be noncrystalline (amorphous) or microcrystalline

(composed of crystals less than 1 or 2 μm in size), or they may consist of small crystallites in

a polymorphous form. As such solids age, they tend to rearrange themselves so as to achieve

a more satisfactory (stable) coordination status, forming larger, more well-formed, and less

soluble crystals. Smaller, more soluble crystals may dissolve as larger crystals grow. This

phenomenon is referred to as Ostwald ripening and results in a larger average particle size

and a decrease in the total crystal surface area. For aging to occur, the crystals must remain

in contact with the solution from which they were precipitated, referred to as the mother

liquor. Some precipitates, such as calcite crystals composed of CaCO3(s), age very rapidly,

whereas others, such as magnesium, iron, and aluminum hydroxides, age extremely slowly

and remain amorphous under water treatment conditions.

Factors influencing contaminant removal by precipitation include the concentration of

the other ion forming the solid, the solubility of the solid formed, temperature, and the presence of species able to form complexes with the contaminant ion. For example, to remove a

metal ion from solution, the ligand concentration must be high enough to induce precipitation, and the higher the ligand concentration remaining in solution, the lower the metal ion

concentration will be at equilibrium. The solubility of many solids increases as water temperature increases, but there are notable exceptions, including CaCO3(s). Complex formation increases the total solubility of a substance when the concentrations of the complexed

species are included in the total.

Coprecipitation

Coprecipitation is the contamination of a precipitate by a substance that would otherwise

have remained in solution had the precipitate not formed. Four mechanisms of coprecipitation



13.4



CHAPTER Thirteen



have been identified (Skoog and West, 1969), each involving adsorption of impurities during crystal growth.

1. Surface adsorption, whereby impurities are not incorporated into the crystal lattice but

are adsorbed on the external surfaces of the crystals, for example, due to interactions with

counter ions in the electrical double layer surrounding crystals having a surface charge

2. Isomorphic inclusion, also known as inclusion and as mixed crystal formation, in which

impurities substitute for some of the lattice ions

3. Nonisomorphic inclusion, or solid solution formation, in which impurities appear to be

dissolved in the precipitate and are not part of the crystal lattice

4. Occlusion, which occurs when impurities are adsorbed, then entrapped by growing

crystals, creating crystal imperfections as they are covered over by lattice ions

Coprecipitation may greatly retard the rate of crystallization and can significantly influence crystal morphology (shape), structure, solubility, and surface properties.

Coprecipitation differs from postprecipitation, surface precipitation, and adsorption.

Postprecipitation occurs when a second, more slowly precipitating substance precipitates

on the surface of a previously formed precipitate. Postprecipitation is not considered coprecipitation because the solution must be supersaturated with respect to the second precipitate

for postprecipitation to occur (Kolthoff, 1932; Skoog and West, 1969). Surface precipitation occurs when a substance adsorbs on a surface and accumulates to the extent that a precipitate forms on the surface (Benjamin, 2002). If a precipitate is formed and is later added

to another solution, contaminants may adsorb onto the precipitate, but this is normally

considered adsorption (Chap. 14) or ion exchange (Chap. 12) rather than coprecipitation.

If two distinct solid phases are precipitated simultaneously, it is possible for some of the

ions associated with one precipitate to become incorporated into the other precipitate. For

example, in the excess lime softening process, both CaCO3(s) and Mg(OH)2(s) are formed

simultaneously. A small amount of Mg2+ would be expected to be incorporated into the

rapidly precipitating CaCO3(s). Since the solution is also supersaturated with respect to the

Mg2+ ion, this would not fall within the classic definition of coprecipitation, but it should

nevertheless be considered as coprecipitation.

Factors influencing the removal of contaminants by coprecipitation include

• The rate of precipitation. Crystals are purer when they grow more slowly.

• The amount of precipitate formed. Coprecipitation involves adsorption, and for crystals

of a given size a larger mass of precipitate provides a larger surface on which adsorption

can take place.

• Time. Crystal purity increases during the aging process and a coprecipitated contaminant

can diffuse out of a precipitate over time, though the rate of diffusion may be negligible,

e.g., for large molecules removed by occlusion.

• Crystal size. Contaminants diffuse more slowly out of larger crystals, but recirculating solids

to grow larger crystals is expected to reduce contaminant removal because the crystals will

remain in contact with the solution longer and will grow more slowly due to the increase in

available surface area. For a given amount of solids, a smaller crystal size corresponds to a

larger surface area, which will enhance contaminant removal by surface adsorption.

• Crystal structure. Contaminants diffuse more slowly out of well-crystallized solids,

whereas a contaminant adsorbed on an amorphous solid is expected to be in equilibrium

with the concentration of the contaminant in solution.

• Crystal surface potential. As an ionic solid precipitates, it may contain an excess of

anions or cations due to differences in the initial lattice ion concentrations in solution,







PRECIPITATION, COPRECIPITATION, AND PRECIPITATIVE SOFTENING



13.5



or it may be positively or negatively charged due to the presence of certain potential

determining ions, which typically include H+ and OH−. Contaminants having a charge

opposite to that of the ion present in excess or to that of the crystal surface are expected

to be preferentially adsorbed and coprecipitated.

• The properties of the contaminant. Adsorption of a contaminant on a growing crystal

depends on the particular contaminant species actually present, its charge and degree of

hydration, its ability to coordinate with one of the lattice ions, and its size relative to the

lattice ions.

• Complex formation. Complexation can decrease coprecipitation by holding the contaminant in solution, and it can increase coprecipitation if the complex adsorbs more strongly

to the solid than the uncomplexed contaminant.

• pH. The pH of the solution usually affects the charge and speciation of the contaminant,

the surface charge of the solid (hence its ability to adsorb ionic impurities), and the behavior of complexing agents, so coprecipitation can be strongly pH dependent.

• Temperature and ionic strength. These factors influence the activity of the contaminant

ion and can influence its adsorption on charged surfaces as well as the action of other

factors listed.

Solubility Equilibria

To determine if a contaminant can potentially be removed by precipitation (or if removal is

occurring by precipitation or coprecipitation) and to better understand the factors influencing contaminant removal by precipitation or coprecipitation, it is often helpful to examine

solubility equilibria relevant to the contaminant of interest, to other ions present, and to

various solids that may be formed under a given set of conditions. The basic concepts and

nomenclature pertaining to chemical equilibria and to precipitation and dissolution of metal

solids were introduced in Chap. 3.

The dissolution reaction for a sparingly soluble ionic solid may be expressed as





A x B y (s)  xA y+ + yBx -



(13-2)



where A and B are the lattice ions and x and y are stoichiometric coefficients. This is similar

in form to the dissolution reaction for metal solids shown in Chap. 3 with Eq. 3-35. The

solubility product constant (Ks0) for the reaction shown in Eq. 13-2 is





K s 0 = [ A y+ ] x [ B x - ] y



(13-3)



where the square brackets indicate molar concentrations. Table 13-1 provides Ks0 values for

selected sparingly soluble ionic solids containing substances potentially relevant to water

treatment or analysis.

In Eq. 13-3, activities must be used instead of molar concentrations to make accurate

calculations when ionic strength effects are significant, and a temperature correction must be

applied if the actual water temperature differs from the temperature at which the value of Ks0

was determined. Corrections for ionic strength and temperature were introduced in Chap. 3 and

are described in many textbooks, including those by Snoeyink and Jenkins (1980), Stumm

and Morgan (1996), Butler (1998), Benjamin (2002), and Jensen (2003). Examples are

included in a later section of this chapter. The Davies equation (described in Chap. 3) is valid

for ionic strengths up to 0.5 M; ionic strength corrections can be made using Pitzer’s specific

ion interaction model (Plummer et al., 1988; Pitzer, 1991; Langmuir, 1997; Benjamin, 2002)

for ionic strengths up to 1.0 M (or higher if additional terms are included).



13.6



CHAPTER Thirteen



Table 13-1  Selected Solubility Product Constants

Solid

Aluminum hydroxide

Aluminum phosphate

Barium arsenate

Barium carbonate

Barium hydroxide octahydrate

Barium oxalate

Barium oxalate monohydrate

Barium sulfate

Beryllium hydroxide

Cadmium carbonate

Cadmium hydroxide

Cadmium oxalate trihydrate

Cadmium sulfide

Calcium arsenate

Calcium carbonate (calcite)

Calcium carbonate (aragonite)

Calcium carbonate (vaterite)

Calcium carbonatomagnesium

Calcium fluoride

Calcium hydroxide

Calcium oxalate monohydrate

Calcium phosphate

Calcium selenate dihydrate

Calcium sulfate

Calcium sulfate dihydrate

Chromium(III) hydroxide

Chromium(II) hydroxide

Chromium(III) arsenate

Chromium(III) hydroxide

Cobalt(II) carbonate

Cobalt(II) hydroxide

Cobalt(II) hydroxide (amorphous)

Cobalt(III) hydroxide

Copper(I) bromide

Copper(I) chloride

Copper(I) sulfide

Copper(II) arsenate

Copper(II) carbonate

Copper(II) hydroxide

Copper (II) oxalate

Copper(II) phosphate

Copper(II) sulfide

Iron(II) carbonate

Iron(II) hydroxide

Iron(III) arsenate

Iron(III) hydroxide

Iron(III) phosphate dihydrate

Iron(III) selenite

Lead(II) arsenate

Lead(II) carbonate



Formula

Al(OH)3

AlPO4

Ba3(AsO4)2

BaCO3

Ba(OH)2·8H2O

BaC2O4

BaC2O4·H2O

BaSO4

Be(OH)2

CdCO3

Cd(OH)2

CdC2O4·3H2O

CdS

Ca3(AsO4)2

CaCO3

CaCO3

CaCO3

Ca[Mg(CO3)2]

CaF2

Ca(OH)2

CaC2O4·H2O

Ca3(PO4)2

CaSeO4·2H2O

CaSO4

CaSO4·2H2O

Cr(OH)3

Cr(OH)2

CrAsO4

Cr(OH)3

CoCO3

Co(OH)2

Co(OH)2

Co(OH)3

CuBr

CuCl

Cu2S

Cu3(AsO4)2

CuCO3

Cu(OH)2

CuC2O4

Cu3(PO4)2

CuS

FeCO3

Fe(OH)2

FeAsO4

Fe(OH)3

FePO4·2H2O

Fe2(SeO3)3

Pb3(AsO4)2

PbCO3



Ks0†

2 × 10−32

9.84 × 10−21

8.0 × 10−51

2.58 × 10−9

2.55 × 10−4

1.6 × 10−7

2.3 × 10−8

1.08 × 10−10

6.92 × 10−22

1.0 × 10−12

7.2 × 10−15

1.42 × 10−8

8.0 × 10−27

6.8 × 10−19

3.31 × 10−9

4.61 × 10−9

1.22 × 10−8

1 × 10−11

3.45 × 10−11

5.02 × 10−6

2.32 × 10−9

2.07 × 10−33

9.5 × 10−4

4.93 × 10−5

3.14 × 10−5

6 × 10−31

2 × 10−16

7.7 × 10−21

6.3 × 10−31

6 × 10−12

5.92 × 10−15

1 × 10−15

4 × 10−45

6.27 × 10−9

1.72 × 10−7

2.5 × 10−48

7.95 × 10−36

6 × 10−12

2 × 10−19

4.43 × 10−10

1.40 × 10−37

6.3 × 10−36

3.13 × 10−11

4.87 × 10−17

5.7 × 10−21

2.79 × 10−38

9.91 × 10−16

2.0 × 10−31

4.0 × 10−36

7.40 × 10−14



Reference

NIST, 2004

CRC Handbook, 2008

Lange’s Handbook, 2005

CRC Handbook, 2008

CRC Handbook, 2008

Lange’s Handbook, 2005

Lange’s Handbook, 2005

CRC Handbook, 2008

CRC Handbook, 2008

CRC Handbook, 2008

CRC Handbook, 2008

Lange’s Handbook, 2005

Lange’s Handbook, 2005

Lange’s Handbook, 2005

Plummer & Busenberg, 1982

Plummer & Busenberg, 1982

Plummer & Busenberg, 1982

Lange’s Handbook, 2005

CRC Handbook, 2008

CRC Handbook, 2008

CRC Handbook, 2008

CRC Handbook, 2008

NIST, 2004

CRC Handbook, 2008

CRC Handbook, 2008

NIST, 2004

Lange’s Handbook, 2005

Lange’s Handbook, 2005

Lange’s Handbook, 2005

NIST, 2004

CRC Handbook, 2008

NIST, 2004

NIST, 2004

CRC Handbook, 2008

CRC Handbook, 2008

Lange’s Handbook, 2005

CRC Handbook, 2008

NIST, 2004

NIST, 2004

CRC Handbook, 2008

CRC Handbook, 2008

Lange’s Handbook, 2005

CRC Handbook, 2008

CRC Handbook, 2008

Lange’s Handbook, 2005

CRC Handbook, 2008

CRC Handbook, 2008

Lange’s Handbook, 2005

Lange’s Handbook, 2005

CRC Handbook, 2008

(Continued)







13.7



PRECIPITATION, COPRECIPITATION, AND PRECIPITATIVE SOFTENING



Table 13-1  Selected Solubility Product Constants (Continued)

Solid

Lead(II) fluoride

Lead(II) hydroxide

Lead(II) oxalate

Lead(II) phosphate

Lead(II) sulfate

Lead(II) sulfide

Lead(IV) hydroxide

Magnesium ammonium

  phosphate

Magnesium arsenate

Magnesium carbonate

Magnesium carbonate trihydrate

Magnesium carbonate

  pentahydrate

Magnesium fluoride

Magnesium hydroxide (brucite)

Magnesium hydroxide

  (amorphous)

Magnesium oxalate dihydrate

Magnesium phosphate

Manganese(II) arsenate

Manganese(II) carbonate

Manganese(II) hydroxide

Mercury(I) bromide

Mercury(I) carbonate

Mercury(I) chloride

Mercury(I) iodide

Mercury(I) sulfate

Mercury(II) bromide

Mercury(II) hydroxide

Mercury(II) iodide

Mercury(II) sulfide (red)

Mercury(II) sulfide (black)

Nickel carbonate

Nickel hydroxide

Radium sulfate

Silver bromide

Silver carbonate

Silver chloride

Silver iodide

Silver sulfide

Strontium carbonate

Strontium oxalate hydrate

Strontium sulfate

Thallium(III) hydroxide

Thorium hydroxide

Thorium phosphate

Tin(II) hydroxide

Tin(II) sulfide

Tin(IV) hydroxide



Formula



Ks0†



Reference



PbF2

Pb(OH)2

PbC2O4

Pb3(PO4)2

PbSO4

PbS

Pb(OH)4

MgNH4PO4



3.3 × 10−8

1.43 × 10−20

4.8 × 10−10

8.0 × 10−43

2.53 × 10−8

8.0 × 10−28

3.2 × 10−66

2.5 × 10−13



CRC Handbook, 2008

CRC Handbook, 2008

Lange’s Handbook, 2005

Lange’s Handbook, 2005

CRC Handbook, 2008

Lange’s Handbook, 2005

Lange’s Handbook, 2005

Lange’s Handbook, 2005



Mg3(AsO4)2

MgCO3

MgCO3·3H2O

MgCO3·5H2O



2.1 × 10−20

6.82 × 10−6

2.38 × 10−6

3.79 × 10−6



Lange’s Handbook, 2005

CRC Handbook, 2008

CRC Handbook, 2008

CRC Handbook, 2008



MgF2

Mg(OH)2

Mg(OH)2



5.16 × 10−11

5.61 × 10−12

3.91 × 10−11



CRC Handbook, 2008

CRC Handbook, 2008

Loewenthal & Marais, 1976



MgC2O4·2H2O

Mg3(PO4)2

Mn3(AsO4)2

MnCO3

Mn(OH)2

Hg2Br2

Hg2CO3

Hg2Cl2

Hg2I2

Hg2SO4

HgBr2

Hg(OH)2

HgI2

HgS

HgS

NiCO3

Ni(OH)2

RaSO4

AgBr

Ag2CO3

AgCl

AgI

Ag2S

SrCO3

SrC2O4·H2O

SrSO4

Tl(OH)3

Th(OH)4

Th3(PO4)4

Sn(OH)2

SnS

Sn(OH)4



4.83 × 10−6

5.2 × 10−24

1.9 × 10−29

2.24 × 10−11

1.9 × 10−13

6.40 × 10−23

3.6 × 10−17

1.43 × 10−18

5.2 × 10−29

6.5 × 10−7

6.2 × 10−20

3.2 × 10−26

2.9 × 10−29

4 × 10−53

1.6 × 10−52

1.42 × 10−7

5.48 × 10−16

3.66 × 10−11

5.35 × 10−13

8.46 × 10−12

1.77 × 10−10

8.52 × 10−17

6.3 × 10−50

5.60 × 10−10

1.6 × 10−7

3.44 × 10−7

1.68 × 10−44

4.0 × 10−45

2.5 × 10−79

5.45 × 10−27

1 × 10−25

1 × 10−56



CRC Handbook, 2008

NIST, 2004

Lange’s Handbook, 2005

CRC Handbook, 2008

Lange’s Handbook, 2005

CRC Handbook, 2008

CRC Handbook, 2008

CRC Handbook, 2008

CRC Handbook, 2008

CRC Handbook, 2008

CRC Handbook, 2008

Lange’s Handbook, 2005

CRC Handbook, 2008

Lange’s Handbook, 2005

Lange’s Handbook, 2005

CRC Handbook, 2008

CRC Handbook, 2008

Lange’s Handbook, 2005

CRC Handbook, 2008

CRC Handbook, 2008

CRC Handbook, 2008

CRC Handbook, 2008

Lange’s Handbook, 2005

CRC Handbook, 2008

Lange’s Handbook, 2005

CRC Handbook, 2008

CRC Handbook, 2008

Lange’s Handbook, 2005

Lange’s Handbook, 2005

CRC Handbook, 2008

Lange’s Handbook, 2005

Lange’s Handbook, 2005

(Continued)



13.8



CHAPTER Thirteen



Table 13-1  Selected Solubility Product Constants (Continued)

Solid



Ks0†



Formula



Titanium(III) hydroxide

Titanium(IV) oxide hydroxide

Vanadium(IV) hydroxide

Uranyl carbonate

Uranyl hydroxide

Uranyl phosphate

Vanadium(IV) hydroxide

Zinc arsenate

Zinc carbonate

Zinc carbonate monohydrate

Zinc hydroxide

Zinc oxalate dihydrate

Zinc phosphate

Zinc sulfide (alpha)

Zinc sulfide (beta)



Ti(OH)3

TiO(OH)2

VO(OH)2

UO2CO3

UO2(OH)2

(UO2)3(PO4)2

VO(OH)2

Zn3(AsO4)2

ZnCO3

ZnCO3·H2O

Zn(OH)2

ZnC2O4·2H2O

Zn3(PO4)2

ZnS

ZnS



Reference



1 × 10−40

1 × 10−29

8 × 10−23

1.8 × 10−12

1.1 × 10−22

2 × 10−47

5.9 × 10−23

2.8 × 10−28

1.46 × 10−10

5.42 × 10−11

3 × 10−17

1.38 × 10−9

9.0 × 10−33

1.6 × 10−24

1 × 10−21



Lange’s Handbook, 2005

Lange’s Handbook, 2005

NIST, 2004

Lange’s Handbook, 2005

Lange’s Handbook, 2005

Lange’s Handbook, 2005

Lange’s Handbook, 2005

CRC Handbook, 2008

CRC Handbook, 2008

CRC Handbook, 2008

CRC Handbook, 2008

CRC Handbook, 2008

Lange’s Handbook, 2005

Lange’s Handbook, 2005

Lange’s Handbook, 2005



†

Values of Ks0­ are at 25°C and zero ionic strength, except those fromLange’s Handbook (2005), which are for 18

to 25°C. Solubility calculations that fail to consider complexation and other factors can be highly inaccurate. Since

the second ionization constant for H2S is poorly known, it is more useful to examine sulfide solubility as described

in the CRC Handbook (2008).



If the concentrations of the lattice ions are known, their ion product (Q), also referred to

as their reaction quotient (Chap. 3), may be calculated as follows (ignoring ionic strength

effects):







Q = [ A y+ ] x [ B x - ] y



(13-4)



If Q > Ks0, the solution is supersaturated with respect to AxBy(s) and precipitation can

occur, provided that any assumptions made are correct and that all appropriate corrections

have been applied. Similarly, if Q < Ks0, precipitation of AxBy(s) is not possible. If Q = Ks0,

the solution is in equilibrium with the solid. These same relationships may also be expressed

using the saturation ratio (SR), the saturation index (SI), or the free energy of reaction

(ΔG0 ), as illustrated in Table 13-2. The Langelier saturation index (LSI) is a special case of

rxn

the saturation index that applies specifically to precipitation of CaCO3(s). It is widely used

in the field of water supply and treatment and is described in Chap. 20.

Table 13-2  Relationships Among Parameters Used to Indicate the Saturation State of

a Solution



Parameter

Q

SR

SI

ΔG0

rxn



Equivalent

expression

See Eq. 13-4

Q/Ks0

log (Q/Ks0)

2.3RT × SI†



Supersaturated

Q > Ks0

SR > 1

SI > 0

ΔG0 > 0

rxn



For a solution that is

At equilibrium

Undersaturated

Q = Ks0

SR = 1

SI = 0

ΔG0 = 0

rxn



Q < Ks0

SR < 1

SI < 0

ΔG0 < 0

rxn



†

R is the gas constant (1.987 cal/mol-K), T is absolute temperature in degrees kelvin, and the reaction

is written as a dissolution reaction as shown in Eq. 13-2.



PRECIPITATION, COPRECIPITATION, AND PRECIPITATIVE SOFTENING







13.9



It is important to recognize that the solubility of a substance in pure water may differ

greatly from its solubility in water containing other dissolved substances. Some handbooks

provide information on the solubility of various substances in pure solutions, and such

information can be quite helpful when preparing reagents in pure water in the laboratory or

when dissolving relatively soluble materials in water to prepare chemical feeding solutions.

However, when a sparingly soluble substance is added to water containing dissolved substances, its dissolution may be hindered or promoted by ions already present. For example,

if CaSO4(s) is added to water already containing 1,000 mg/L of sodium sulfate, much less

CaSO4(s) will dissolve into the water than indicated in Example 3-3. This is expected on

the basis of LeChâtelier’s principle and is referred to, in the context of precipitation and dissolution, as the common-ion effect—the suppression of the solubility of one salt by another

when they share a common ion. At equilibrium, the ion product Q will still equal Ks0 for

CaSO4(s), but the Ca2+ concentration will be relatively low because dissolution of CaSO4(s)

will be limited by the high sulfate concentration.

A contrasting example is the dissolution of CaCO3(s) in water containing a small amount

of an acid, for example, ground water containing CO2. More CaCO3(s) will dissolve into

2−

this water than into pure water because the acid will react with carbonate ions, CO3 , con−

verting them to bicarbonate ions, HCO3 . Thus, additional CaCO3(s) must dissolve before

the value of Q equals Ks0 for CaCO3(s).

In the field of water quality and treatment, questions frequently arise concerning the

solubility of a contaminant ion in a water having a given pH, alkalinity, and ionic composition. If the solid limiting the solubility of the contaminant ion is known, the maximum concentration of the contaminant ion can often be estimated as illustrated in Example 13-1.

Example 13-1  Residual Mg2+ in Lime-Treated Water

Estimate the residual Mg2+ concentration in lime-treated water assuming it is limited

by the solubility of magnesium hydroxide, Mg(OH)2(s), and that the pH is 11.0, the

temperature is 25°C, and ionic strength effects can be ignored.

Solution



1. Write the appropriate chemical reaction.







Mg(OH)2(s)  Mg2+ + 2OH−





Mg(OH)2(s) produced in a lime softening process will be amorphous; thus, from

Table 13-1, Ks0 for this reaction is 3.91 × 10−11.

2. Determine the hydroxide ion concentration using the expression for Kw (Chap. 3).

Kw = [H+] [OH−] = 10−14 at 25°C









[H+] = 10−pH = 10−11 mol/L











Since



the concentration of OH− is

[OH−] = Kw /[H+] = 10−14/10−11 = 10−3 mol/L



3. Establish the solubility product constant expression and solve for the Mg2+

concentration.





Ks0 = [Mg2+] [OH−]2 = 3.91 × 10−11



13.10







Rearranging and solving for [Mg2+],

[Mg2+] = Ks0 /[OH−]2 =











CHAPTER Thirteen



3 . 91 × 10 -11

= 3.91 × 10−5 mol/L (or 0.95 mg/L)

(10 -3 )2



Since hardness ion concentrations are frequently expressed as CaCO3, multiply the

concentration in mg/L by the ratio of the equivalent weights of CaCO3 and Mg2+.

Mg2+ = 0.95 mg/L ×



50 mg CaCO3 /eq

= 3.9 mg/L as CaCO3   ▲

12 . 15 mg Mg/eq



A hypothetical problem, such as Example 13-1, may be straightforward and have an

exact solution. Problems encountered in practice may be complex, perhaps more so than

those addressing them realize, and simplifying assumptions are often made to facilitate

calculations. Such calculations may provide useful quantitative information, but they are

subject to a number of limitations and can produce estimates that are inaccurate or even

grossly in error. Potential sources of error include

• Temperature and ionic strength effects. These effects are commonly ignored when making preliminary estimates, but they can significantly influence contaminant solubility.

Failing to apply appropriate corrections may make little difference at low ionic strength

or at a temperature close to that at which the reported value of Ks0 was determined, but

can make a great difference when dealing with solutions of higher ionic strength, multivalent contaminants, or solids whose solubility is strongly affected by temperature. The

best way to determine whether such effects are significant is to correct for them to see

what difference the corrections make. However, most corrections are also approximate,

in that they are usually based on correlations of measured values having limited accuracy,

and they are sometimes extended, knowingly or unknowingly, beyond the range of ionic

strength or temperature for which they were developed.

• Incorrect assumptions regarding contaminant speciation. For a particular solid, the value

of Ks0 is valid only for the specific ions forming the solid, but a contaminant may be present in more than one form and many analytical methods measure only the total amount

present rather than the individual species. For example, mercury may be present as a free

0

ion (Hg1+ or Hg2+); as an inorganic complex, with HgCl2 being the dominant dissolved

form in most freshwaters (Sawyer et al., 2003); as elemental mercury, for example, if it

leaked out of an obsolete pump seal; complexed with natural organic matter; adsorbed on

particles; coprecipitated with various solids; or as a component of one or more mercury

containing solids. Furthermore, speciation can change during treatment in response to a

change in pH, oxidant concentration, temperature, or the concentrations and properties

of other dissolved species and solids. If the speciation of the contaminant is not known,

the limits of its solubility can be hypothetically estimated or experimentally measured,

but they cannot usually be calculated with a reasonable degree of certainty.

• Complex formation. Complex formation increases the total concentration of a contaminant that can be held in solution in equilibrium with a particular solid, and it can also

increase removal of a contaminant by coprecipitation if the complex is more readily

removed than the free ion. Anions commonly present in water supplies that can complex

metal ions include carbonate and bicarbonate, hydroxide, sulfate, and as noted above

for mercury, chloride and NOM. The solubility of lead in tap water can be significantly

0

influenced by formation of the carbonato-lead(II) complex, PbCO3 (Chap. 20). Trivalent

aluminum and iron form relatively insoluble hydroxides when used as coagulants (Chap. 8),

but at higher pH values their solubility can increase significantly due to tetrahydroxo

complex formation, as shown in Figs. 8-8 and 8-9. However, aluminum concentrations

as high as those shown in Fig. 8-8 are generally not observed in practice when alum is







PRECIPITATION, COPRECIPITATION, AND PRECIPITATIVE SOFTENING



13.11



added as a coagulant in the lime softening process, presumably because one or more

aluminum-containing solids of unknown composition is formed under these conditions.

0

Sulfate interacts with Ca2+ to form a sulfato-calcium(II) complex, CaSO4 , an ion pair

that can significantly influence the solubility of CaSO4(s) and CaCO3(s). For example,

the solubility of CaSO4⋅2H2O(s) at zero ionic strength was calculated in Example 3-3

at 694 mg/L (total of calcium and sulfate), but increases to about 1,500 mg/L when the

0

CaSO4 complex is taken into consideration. Rules for naming complexes can be found

in many water chemistry textbooks, such as those by Snoeyink and Jenkins (1980) and

Sawyer et al. (2003).

• The presence of threshold inhibitors (antiscalants). These substances may be present

naturally (e.g., certain types of natural organic matter) or added intentionally (e.g., polyphosphates and other commercially available antiscalants). In either case, they can retard or

prevent precipitation and, if precipitation does occur, they can greatly alter the properties

of the precipitate, including its solubility. Calculations based on the assumption that these

compounds are absent may not be valid when they are actually present.

• Incorrect assumptions regarding the solid phase. If the solid phase actually present differs in composition from the solid assumed to be present, the calculation will be void and

will need to be redone using a Ks0 value corresponding to the correct solid. Solubility can

also be significantly influenced by crystal morphology and size, and by the presence of

impurities. At least six different crystal forms of CaCO3(s) are known, each having a different solubility. It is also possible for two or more solids to precipitate simultaneously, or

for a metastable phase to form. A metastable phase is less thermodynamically stable and

more soluble than the phase that will exist at equilibrium, but it may form more rapidly

and persist for an indefinite period of time before the more stable phase forms.

• Failure to reach equilibrium. Precipitation can occur when Q > Ks0, but a solution can

remain supersaturated for an extended period of time. Once precipitation commences,

the system may approach equilibrium very slowly, especially if an amorphous or metastable phase precipitates first and is then slowly transformed into a more stable phase.

Precipitation and dissolution involve the physical transfer of matter (ions) from one phase

to another, which can also proceed slowly. For example, if water is left standing in a

lead service line, it can take hours or days for the lead concentration in solution to reach

equilibrium with the lead pipe (Chap. 20), especially if the lead ions must pass through

a layer of scale or a biofilm. If other reactions occur simultaneously, such as oxygen

consumption and pH changes (commonly associated with both corrosion reactions and

biofilm growth), it may take far longer to reach equilibrium.

• An inaccurate solubility product constant. Experimentally determined Ks0 values vary.

Some values have been accurately determined and then verified by later investigators,

whereas other values may be slightly in error. The most authoritative sources of Ks0 values,

for example, NIST (2004), are those whose authors have critically reviewed the available

data and selected one or more values judged to have been accurately determined.

The solubility behavior of most sparingly soluble ionic solids in natural and treated

waters is complicated due to numerous competing solubility and acid-base equilibria, complex formation, and other factors including those already noted. Simple calculations can

provide much useful information. But, when accurate results and a deeper understanding

of contaminant behavior are needed, many investigators find it helpful to conduct empirical

studies or to employ a computer-based chemical equilibrium model able to simultaneously

address a large number (perhaps hundreds or thousands) of dissolved species and numerous

solid phases. Commonly used models include MINEQL+, an updated version of MINEQL

(Westall et al., 1976); MINTEQA2 (Allison et al., 1991), a revised version of MINTEQ,

which combined MINEQL with WATEQ (Truesdell and Jones, 1973 and 1974); Visual



13.12



CHAPTER Thirteen



MINTEQ (Gustafsson, 2009); and PHREEQC, a program based on the work of Parkhurst

(1992) and Plummer et al. (1988) that includes redox equilibria and the ability to handle

high-ionic-strength environments. Cogley (1998) and Jensen (2003) have summarized the

capabilities and use of a number of computer-based chemical equilibrium models. Some

suppliers of antiscalants also provide software programs that estimate the dose required to

inhibit precipitation of a given salt under a specific set of conditions.



PRECIPITATIVE SOFTENING

Precipitative softening, commonly referred to as lime softening (since lime is the chemical

most commonly used for this purpose), is primarily used to remove calcium and magnesium

hardness from water supplies. It also removes other contaminants commonly found in hard

waters including NOM, iron and manganese, and various other inorganic contaminants,

especially metal ions. Precipitative softening processes typically include coagulation, flocculation, and sedimentation, in which case they also remove particles, as described in Chaps. 8

and 9. Softening units operated as crystallizers without coagulant addition do not remove

particles but can be followed by coagulation and filtration if particle removal is desired.

Water Hardness

Water is considered hard if it forms scale, especially on heating, if it makes soap difficult to

lather, if it precipitates soap (forming curdles or soap scum), or if it requires extra detergent

for proper cleaning action. Water hardness is caused by dissolved divalent metal cations.

In natural waters, Ca2+ and Mg2+ are the predominant cations causing hardness, since most

other divalent cations are typically present at concentrations below 1 mg/L. Trivalent cations can also contribute to water hardness, but their concentrations in drinking water supplies are usually negligible. For analytical purposes, total hardness (TH) is defined as the

sum of dissolved Ca2+ and Mg2+ (APHA, AWWA, and WEF, 2005). Other hardness-causing

cations are either ignored or are measured and reported individually.

Units of Expression.  When measured separately, Ca2+ and Mg2+ concentrations are usually reported in units of mg/L (as Ca or Mg) or mg/L as CaCO3. Total hardness, whether

determined by direct measurement (titration) or by summing the individually measured

concentrations of calcium and magnesium, is usually reported in mg/L as CaCO3. It is not

useful or appropriate to report total hardness in mg/L because the atomic weight of Ca differs

from that of Mg.

Hardness can also be reported in units of milliequivalents per liter (meq/L) or millimoles

per liter (mM). Units of meq/L are most often used when determining the types and concentrations of hardness present; and units of mM are commonly used when calculating chemical dosages. For calculations involving the use of solubility product constants or complex

stability constants, the concentrations of Ca2+ and Mg2+ must be expressed in units of moles

per liter (M), corrected for the effects of ionic strength and complex formation when appropriate. For ion exchange softening (Chap. 12), chemists typically prefer units of meq/L for

the liquid phase and units such as meq/mL, eq/L, or eq/g for the solid phase. But the units

of grains per gallon and kilograins per cubic foot are often used by practitioners.

Example 13-2  Units of Expression

A water sample is analyzed and found to contain 84.2 mg/L of Ca2+ (as Ca) and 9.7 mg/L

of Mg2+ (as Mg). What are the concentrations of calcium, magnesium, and total hardness

in mM, meq/L, and mg/L as CaCO3?