Chapter 3. Chemical Principles, Source Water Composition, and Watershed Protection

3.2



CHAPTER three



INTRODUCTION

Chapters 1 through 5 serve as a foundation for the book. This foundation chapter has three

goals. One goal is to summarize basic water chemistry principles. A second goal is to provide the reader with background on the composition of source waters with respect to their

bulk water chemistry and on naturally occurring contaminants. Contaminants that enter

water supplies through human activity are also summarized. Because protecting the quality

of source waters is an important strategy in the drinking water field, principles and some

practical material on watershed protection are presented as a third goal.

The chapter is organized in the following way. We start with a summary of chemical

principles because chemical reactions affect the composition of source waters as well as

treatment processes and the quality of water in distribution systems. Next, we address the

composition of surface and groundwaters. Hydrogeochemical and biological geochemical

cycles and their effects on the composition of water quality are described. Ranges and

typical concentrations for chemical species, particles, and natural organic matter (NOM)

are presented for rivers and streams, reservoirs and lakes, and groundwaters. The chapter

examines the bulk chemical composition and naturally occurring contaminants in water.

It also examines the presence of anthropogenic chemicals that are present in some water

sources. Particles and NOM are important contaminants that affect source water quality

and many treatment processes, and so they are given extensive coverage. The last section reviews important principles related to the selection and protection of drinking water

sources with respect to water quality.



CHEMICAL PRINCIPLES AND CONCEPTS

The composition of source waters and water treatment processes are affected greatly by

various chemical reactions such as acid-base (e.g., inorganic carbon chemistry, alkalinity,

chlorination) complexation (e.g., Fe and NOM in source waters and coagulation), solubility

(e.g., the occurrence of metals in source waters, softening, and coagulation), and oxidation–

reduction (redox) (e.g., oxidation of Fe and Mn, disinfection, and corrosion). Kinetics of

chemical reactions are not covered here but in Chap. 4. Mass transfer kinetics for describing movement or transport of gases and particles are covered in the chapters dealing with

these processes.

Here, these topics are briefly summarized for use in this and other chapters. The reader

should refer to primary textbooks on water chemistry such as Stumm and Morgan (1996),

Snoeyink and Jenkins (1980), and Benjamin (2002) for extensive theory and applications

of the topics covered in this section. Note that these water chemistry references are listed

separately in the References section.

Water Properties

Polar Nature.  Water is a polar molecule, and although electrically neutral it has a polar

nature meaning the molecule has a region of negative charge near the O atoms and positive

charge near the H atom. This dipolar nature gives water important properties such as its

ability to act as a solvent. We therefore find substances (solutes) dissolved in water to varying degrees, depending on specific chemical properties. For example, simple salts such as

Na+ and Cl- are found at high concentrations such as in the oceans, while Al is found at low

concentrations at typical pH conditions of water supplies because it is insoluble. The polar

nature of water leads to H bonding of water molecules and other molecules. It also affects

the chemical speciation of dissolved substances.



CHEMICAL PRINCIPLES, SOURCE WATER COMPOSITION, AND WATERSHED PROTECTION



3.3



Physical Properties.  The dipolar nature of water also affects important physical properties. Compared to other liquids, water has a high boiling point (100°C) and a high freezing

point (0°C). Water density depends on water temperature with a maximum value at 4°C of

1000 kg/m3. Water density as a function of temperature explains the cause of lake stratification, which is addressed later in this chapter. Water viscosity is another important physical

property. Water density and viscosity affect various water treatment processes, as presented

in individual chapters. Appendix D contains values as a function of water temperature.

The conductivity of water is affected by the concentration of dissolved salts. The dissolved salt concentration affects corrosion reactions and chemical reactions in general. This

is addressed later in this chapter.

Water Dissociation, pH, and pX Notation

Water dissociates and is in equilibrium with H3O+ (hydronium ion) and OH-, as shown in

Eq. 3-1. Writing the hydronium ion recognizes that free H+ does not exist in water, it is

bound through H bonding to the water molecule. We should be aware of this fact when we

write a shorthand version of Eq. 3-1 as Eq. 3-2.







2H 2 O  H 3 O + + OH -

H 2 O  H + + OH -



(3-1)

(3-2)



The equilibrium constant for the dissociation of water (Kw) and using Eq. 3-2 describes

the following concentration relationships. The activity or active concentrations (aH+ and

aOH –) is the formal and proper way to describe the equilibrium constant relationship—more

on activities later in this chapter. For dilute solutions, the molar concentrations (the brackets

[ ] indicate molar) are approximately equal to the activities yielding Eq. 3-4.





K w = aH + aOH -



(3-3)







K w = [H + ][OH - ]



(3-4)



At standard temperature of 298 K or 25°C, Kw is 10-14. Because chemical reactions

including the dissociation of water are temperature dependent, it is often essential to adjust

Kw. Equation 3-5 allows calculation for other water temperatures where T is the absolute

temperature. As an example of the significance of water temperature on Kw, consider that

we measure pH to control processes in water treatment so the [H+] is known or fixed for

that particular pH value; consequently, the [OH-] varies with water temperature for that

particular pH. Many precipitation reactions such as in coagulation depend on the metal

precipitating with OH-. For example, if you carried out a precipitation reaction at pH 6 in

the summer at say 25°C, the [OH-] is 10-8 M, but in winter months at the same pH 6 and say

5°C (where the Kw is 1.86 × 10-15 ), the [OH-] is 0.19 × 10-8 M about five times less OH- for

precipitation. Higher pH conditions are required in the winter for effective precipitation.







- 4471

-3

log K w = 

 - 1.71 × 10 (T ) + 6.09

 T 





(3-5)



pX Notation.  In water treatment chemistry, the pX notation is often used to describe concentrations and equilibrium constants on a log (base 10) basis. We are most familiar with

pH as minus the base 10 log [H+]. A summary of other pX notation is given in Table 3-1 for

reference. This notation is used here and in several chapters throughout the book.



3.4



CHAPTER three



Table 3-1  Guide to pX Notation Used in This Chapter and

throughout the Book

pX

pC

pH

pK

pe°



Definition

- log [C]

- log [H+]

- log K

1/n log K



Comments

molar concentration of C

molar concentration of H+

equilibrium constant

standard oxidation reduction potential, where K

  the equilibrium constant for the half reaction

is

and n is the number of electrons transferred



Concentrations

Moles and Mass.  We use various measures of concentration in evaluating water quality

and in water treatment process chemistry. A fundamental chemical measure of concentration is moles per liter, which is expressed as M. At low concentrations, it may be expressed

as millimolar (mM). One mole of a substance is the gram atomic weight of a substance.

We usually describe concentrations of substances in water on a mass basis (e.g., the alum

or chlorine dose at a water plant is expressed on a mass concentration basis). To convert

from moles to mass concentrations, our conversion factor is the gram atomic weight of the

substance. We usually express mass concentrations as g/L, mg/L, or mg/L, depending on

the relative concentration.

Equivalents: Charge and Alkalinity Concentrations.  We also use equivalent concentrations to describe the charge concentration of ions—more on this under the principle of

electroneutrality—and to describe alkalinity. The concept of alkalinity is addressed later in

the chapter. Fundamentally, alkalinity is measured in units of eq/L (equivalents per liter) or

meq/L (milliequivalents per liter), and it is the concentration of H+ that can be neutralized

or the acid neutralizing capacity of water. In our field, it is reported in terms of an equivalent concentration as CaCO3. CaCO3 has an equivalent weight of 50, so the conversion is

1 meq/L of alkalinity is 50 mg/L as CaCO3.

Other Cases.  Some other cases of interest in describing concentrations are for hardness

and in reporting nitrogen and phosphorus concentrations. Water hardness is caused by divalent and trivalent cations in water, but because calcium and magnesium are much higher in

concentrations compared to others, these are the two cations we attribute to hardness. Total

hardness is the sum of Ca2+ and Mg2+, both expressed in terms of equivalent concentrations

as CaCO3. The equivalent concentration of Ca2+ is its mass concentration times the atomic

weight of CaCO3 divided by the atomic weight of Ca2+, i.e., 1 mg/L of Ca2+ equals 100/40

or 2.5 mg/L as CaCO3. Likewise, 1 mg/L of Mg2+ equals 100/24.31 or 4.11 mg/L as CaCO3.

Classifications of waters with respect to water hardness are: soft < 75, moderately hard 75

to 150, hard 150 to 300, and very hard > 300 mg/L as CaCO3 (Sawyer et al.,1994).

Phosphorus (P) can occur in water as dissolved organic P or inorganic P. Within the

inorganic form, it can exist as polyphosphates and orthophosphate. The phosphorus con+

centration is usually reported as P. Likewise, nitrogen compounds such as NH4 , NH3, and

NO3 are reported as N. For example, in chloramination 1 mg/L of NH3 added to water is

reported as N, i.e., 1 mg/L of NH3 equals 1 mg/L times the atomic weight of N divided by

the molecular weight of NH3 or 1 mg/L times 14/17 or 0.82 mg/L as N.

Gas Phase.  Gas phase concentrations are expressed in terms of pressures, partial pressures, or vapor pressures, and they are addressed in the following chapters depending on

the application. Units are in atmosphere, Pa (Pascal) or kPa, and bar.



3.5



CHEMICAL PRINCIPLES, SOURCE WATER COMPOSITION, AND WATERSHED PROTECTION



Ionic Strength, Conductivity, and Dissolved Solids

Chemists describe the ion concentration of water in terms of the ionic strength. Ionic

strength affects the active concentrations (activities) participating in chemical reactions.

It affects acid-base reactions, solubility of solids and gases in water, scaling of solids, corrosion chemistry, and colloidal particle double layer theory and stability. Ionic strength

effects are covered in Chap. 8 for colloidal particle stability and in other chapters dealing

with specific applications. Here it is defined, and expressions for estimating it from conductivity and dissolved solids measurements are presented.

The ionic strength (I) is defined by Eq. 3-6 where Ci is the ion molar concentration of

ion i, and Zi is the charge of ion i.

I=





1 n

∑Ci Z i2

2 1



(3-6)





A complete water analysis of all ions is required to use Eq. 3-6. Because this is often

impractical, correlations have been developed relating the ionic strength to more practical measurements (Snoeyink and Jenkins, 1980). Equation 3-7 is a correlation equation

between I and conductivity (κ), and Eq. 3-8 relates I to total dissolved solids (TDS).

I = 1.6 × 10 -5 (κ )







(3-7)



-5



I = 2.5 × 10 (TDS )







(3-8)



Values for I, κ, and TDS are given in Table 3-2. Most natural fresh waters have ionic

strengths between 5 × 10-4 M and 10-2 M, corresponding to estimated conductivities of

about 30 to 625 mS/cm and TDS of 20 to 400 mg/L.

Principle of Electroneutrality

Water is electrically neutral, meaning the cations must equal the anions on an equivalent

charge basis. This is expressed as Eq. 3-9 where i and j refer to cations and anions.



∑C Z = ∑C Z

i







i



i



j



j



(3-9)



j







Table 3-2  Ionic Strength (I ), Conductivity (κ), and Total Dissolved Solids (TDS ) for Several

Water Types

I (M)

1.2 × 10-5

5 × 10-4

10-3

5 × 10-3

10-2

10-1*

0.68†



κ (mS/cm) TDS (mg/L)

0.75

31

63

312

625

7000

~50,000



0.5

20

40

200

400

5000

35,000



Comments

dimineralized water open to atmospheric CO2(g) of 380 ppm

soft groundwater

low to moderate hardness surface or groundwater

high hardness surface or groundwater

very hard and brackish water

estuarine water

seawater at salinity of 35.2 parts per thousand



*Outside of correlation range of data

†

Seawater values vary with salinity but are well-known



3.6



CHAPTER three



The principle of electroneutrality has useful applications. These are (1) to determine the

accuracy of a reported chemical composition and (2) to determine an anion or cation that

was not measured. Example 3-1 shows use of the principle in evaluating the composition

of a bottled spring water.

Example 3-1  Principle of Electroneutrality

A bottled water company gives the following chemical composition for their spring

water: pH 7.1; calcium, 91 mg/L; magnesium, 4.0 mg/L; sodium, 4.0 mg/L; sulfate,

170 mg/L; bicarbonate, 63 mg/L; fluoride, 0.4 mg/L; and nitrate, 0.26 mg/L. Check on

whether the reported composition satisfies the principle of electroneutrality.

Solution  Equation 3-9 is applied to solve the problem. The results are presented in

the table.

Cations

Ion

2+



Ca

Mg2+

Na+

H+

Sum



mg/L

91

4

4



Atomic Wgt

40

24.31

23

1



Ci (mM)



Zi



Ci Zi (meq/L)



2.275

0.164

0.173

<10-4



2

2

1

1



4.550

0.329

0.174

<10-4

5.053



Anions

Ion

HCO3

2SO4

FNO3

OH

Sum



mg/L



Atomic Wgt



Cj (mM)



Zj



Cj Zj (meq/L)



63

170

0.4

0.26



61

96

19

62

17



1.033

1.770

0.021

0.004

<10-3



1

2

1

1

1



1.033

3.540

0.021

0.004

<10-3

4.598



The total cation charge is much higher (5.053 meq/L) compared to the total anion charge

(4.598 meq/L). This can mean either that there are errors in the chemical analysis or that

one or more anions were not measured and reported. The latter is most likely since all

natural waters contain chloride, which is not reported. If we assume that the reported

concentrations of cations and anions are accurate, then we can calculate the missing

chloride concentration using Eq. 3-9. The missing anion (chloride) concentration is

0.455 meq/L, which is a chloride concentration of 16 mg/L.  ▲

Stoichiometry

Stoichiometry is the subject of chemistry that allows us to make calculations of how much

of a chemical undergoes reaction and how much of a chemical is produced for known

chemical reactions. Chemical reactions actually take place in terms of numbers of ions or

molecules or atoms. However, because the numbers are so high the chemist invented the

mole concept where 1 mole is the gram atomic weight of the substance. In other words

1 mole of a substance is the gram atomic weight of a substance and it contains 6.023 × 1023

ions or molecules or atoms. A list of atomic weights is given in App. A. In using stoichiometric calculations, one assumes the reactions go to completion. This is true for many

types of reactions in water treatment such as dissolving chemicals in water. Example 3-2

illustrates stoichiometric calculations involving the use of alum as a coagulant.



CHEMICAL PRINCIPLES, SOURCE WATER COMPOSITION, AND WATERSHED PROTECTION



3.7



Example 3-2  Alum Dosing and Residuals Produced

In Part a, find the relationship between alum dosing as alum and as Al. Alum dosing in

the United States is expressed as dry alum in which alum is Al2(SO4)3 ⋅ 14H2O. In many

other countries, alum dosing is expressed as Al. Determine the relationship between

1 mg/L of alum and mg/L as Al. In Part b, determine the production of residuals (sludge)

from precipitation of Al(OH)3(s) ((s) refers to a solid phase) from use of alum.

Solution  Part a. Dissolution of alum (Al2(SO4)3 ⋅ 14H2O) follows the stoichiometric

equation below. The calculation shown equating 1 mg/L of alum to x mg/L as Al comes

from the mole concept expressed through the stoichiometry of the chemical equation.





Al 2 (SO 4 )3 ⋅ 14H 2 O → 2Al 3+ + 3SO 2- + 14H 2 O

4







mg alum mmole alum 2 mmole Al 27 mg Al

1

×

×

××

=

0.0909 mg/L Al

L

594 mg

mmole alum mmole Al









Thus, 1 mg/L of alum equals 0.0909 mg/L as Al or 1 mg/L of Al equals 11 mg/L of alum.

Part b. The amount of solids (residuals) produced on a dry basis is calculated from the

following stoichiometric equation. Assuming all the Al precipitates, which is a good

assumption since alum coagulation is often practiced at pH conditions that maximizes the

precipitation reaction leaving little residual dissolved Al. The solid (Al(OH)3 ⋅ 3H2O(s))

has three appended waters and this is sometimes considered in sludge calculations—see

Chap. 22. Calculating for 1 mg/L alum or 0.0909 mg/L Al follows.

Al 3+ + 3OH - → Al (OH)3 ⋅ 3H 2 O (s)

0.0909 mg Al mmole Al 1 mmole Al (OH)3 ⋅ 3H 2 O (s)

×

×

L

27 mg

mmole Al

132 mg Al (OH)3 ⋅ 3H 2 O (s)

×

mmole Al(OH)3 ⋅ 3H 2 O (s)

= 0.44 mg/L Al(OH)3 ⋅ 3H 2 O (s)

Thus, we find that 1 mg/L alum (or 0.0909 mg/L Al) produces 0.44 mg/L of residuals

from the precipitation of the metal coagulant. If we did not include the three appended

waters to the solid, the sludge generated would be 0.26 mg/L. So we can estimate the

solids generated from alum would be about 0.3 to 0.4 mg/L. Additional residuals would

come from the particles (turbidity) and organic matter in the raw water that are removed

through coagulation.  ▲

Chemical Equilibrium

Chemicals in water are either at equilibrium or seeking an equilibrium condition. By equilibrium we mean there is no net change in the concentrations, they have reached a steady

state concentration. When we add an acid or base to water, the reactions are extremely

fast (<< 1 sec) because they involve only the donation of H+ (acid) or the acceptance of

H+ (base). Other reactions may take longer (many seconds or minutes or longer) such

as precipitation of solids or oxidation-reduction reactions. We use chemical equilibrium

principles to describe the speciation of chemicals in water, for example, the fraction of

hypochlorous acid (HOCl) versus hypochlorite (OCl-) in disinfection applications. Other

examples of the use of chemical equilibrium include the solubility of metal coagulants



3.8



CHAPTER three



(Al and Fe salts), water softening precipitation reactions for CaCO3(s) and Mg(OH)2(s),

oxidation of iron and manganese, and corrosion chemistry for copper and lead. In the

material that follows, some basic principles are presented that are applied in this and later

chapters.

Equilibrium Constant.  Consider the following general reaction occurring in water where

the capital letters represent chemical species, the lower case letters are the stoichiometric

coefficients, and the symbol () depicts a system at equilibrium between the reacting species and the products. In this book an equal sign is often used for an equilibrium reaction

rather than the symbol (). The reader will know it is an equilibrium reaction from the

description of the subject matter.





aA + bB  yY + zZ



(3-10)



The equilibrium constant relationship follows setting the equilibrium composition distribution of reactants and products for standard conditions of 25°C and 1 atm pressure. The

equilibrium constant depends on the activity (ai) of the species (i) raised to the power of

the stoichiometric coefficient. The activity is used in formal development because reactions

depend on an active or apparent concentration of the species.

K=





y

z

aY aZ

a

b

a A aB



(3-11)







The activities for dissolved substances are related to molar concentrations of species [i]

by use of activity coefficients (γi). The activity coefficients account for non-ideal behavior

of the solutions. Expanding Eq. 3-11, we obtain the following expression:

K=





y

y z

aY aZ γY [Y ]y γ z [ Z ]z

Z

= a

a b

a A aB γ A [ A]a γ b [ B]b

B



(3-12)





The non-ideal behavior of reactions is accounted for by use of activity coefficients for

aqueous systems that are not dilute solutions in terms of the ionic strength or dissolved

salt content. For ions, the fundamental model accounting for ionic strength effects and

their charge is the Debye-Hückel theory. The reader should consult the water chemistry

references for presentation of this model, other models, and details regarding calculation

of activity coefficients. Here, the practical Davies equation is presented and can be used for

ionic strength (I) up to ~ 0.5 M. In Eq. 3-13, zi is the charge on the ion and A depends on the

dielectric constant (ε) of water and absolute temperature (T) according to Eq. 3-14. A has a

value of 0.5 for a water temperature of 298 K (25°C).











 I 0.5

log γi = - Azi 

- 0 . 3I 

1 + I 0.5





A = 1 . 82 × 10 -6 (ε T )-3/ 2



(3-13)

(3-14)



Most water supplies and treatment processes are sufficiently dilute in ionic strength that

we can assume ideal solutions. In assuming ideal solutions, we set the activity coefficients

to 1, which is a reasonable approximation for ionic strength conditions of about 0.001 M

and less. These ionic strength conditions apply to many fresh waters. Some values are presented later in the chapter. For waters or processes at higher ionic strength such as brackish



CHEMICAL PRINCIPLES, SOURCE WATER COMPOSITION, AND WATERSHED PROTECTION



3.9



waters, seawater, scaling on membranes, and desalination, we must account for the ionic

strength effects on the equilibrium constant reactions.

Concentration Scales for Ideal Systems.  The following concentration scales are used

for ideal aqueous systems:

• Dissolved substances: molar concentrations

• Water: mole fraction, which is 1 for water (even for seawater it is nearly 1)

• Solid phases: mole fraction of 1 for pure solids, which is assumed

• Gas phase: partial pressure traditionally in atm or may be expressed in bar

In presenting many of the concepts regarding equilibrium chemistry and for making

approximate calculations describing the chemistry of fresh waters and water treatment

process chemistry, activities are ignored (setting activity coefficients to 1), and hence we

consider the waters as ideal solutions. For an ideal solution, Eq. 3-12 is written then as

Eq. 3-15. It is noted that in some cases, equilibrium constants are given for specified ionic

strength conditions, meaning the effect of non-ideal solutions has been accounted for in

determining the equilibrium constant.

K=





[Y]y [ Z ]z

[ A]a [ B]b



(3-15)



Effects of Temperature and Pressure.  Equilibrium constants must be adjusted for temperature in order to make equilibrium calculations for the temperature of interest. This is

done by using a form of the van’t Hoff equation as follows:

log





Δ H ro (T2 - T1 )

K2

=

K1 2 . 303( R)(T2 )(T1 )



(3-16)





where K2 is for the temperature of interest at T2 in degrees Kelvin, K1 is for standard temperature of T1 at 298 K, ΔHro is the standard enthalpy of the reaction, and R is the universal

gas constant (8.314 J/mole . K). Values for the standard enthalpy of the reaction may be

found in the books listed under water chemistry references or from chemistry handbooks.

Only pressures at 100s of atmospheres and higher affect the equilibrium constants, so

pressure effects on the equilibrium constants are ignored in this book.

Reaction Quotient.  To determine whether actual measured concentrations are at

equilibrium for the reaction of interest, the reaction quotient (Q) is used. The actual

measured concentrations are inserted into the right-hand side (RHS) of Eq. 3-17. If Q

equals K, then the system is at equilibrium; if Q is > K then the reaction will move to

the left, seeking equilibrium; and if Q is < K, then the system will proceed to the right,

seeking equilibrium.

Q=





[Y]y [ Z ]z

[ A]a [ B]b



(3-17)



Solubility and Stripping of Gases—Henry’s Law.  Henry’s law describes the equilibrium

partitioning of gases with water. In Chap. 6 the stripping of volatile organic compounds

(VOCs) is described by the following equation in which the gas phase (i.e., the VOC of

interest in the gas phase) is on the RHS of Eq. 3-18; the resulting Henry’s law expression is

shown by Eq. 3-19. The gas phase concentration is expressed in terms of its partial pressure.



3.10



CHAPTER three



In the stoichiometric description depicted by Eq. 3-18, our interest is in stripping VOCs, so

the aqueous phase concentration is shown on the left-hand side (LHS) and leaving solution

to the gas phase. Here H has units of atm/molar.

A (aq)  A (g)







H=





PA

[ Aaq ]



(3-18)

(3-19)







In other applications we may be interested in the saturation concentration of a gas in

water—its solubility. Examples are O2(aq) and N2(aq) in dissolved air flotation applications

(Chap. 9), O2(aq) in source waters, and CO2(aq) in source waters and in treatment processes. For these applications, the stoichiometric equation is written in the reverse direction

from Eq. 3-18. Our interest is in dissolving the gas into water. The gas phase is written on

the LHS of Eq. 3-20, while the dissolved equilibrium concentration (solubility or saturation

concentration) is written on the RHS. Henry’s law is shown as Eq. 3-21.

A (g)  A (aq)







H* =





(3-20)







[ Aaq ]

PA



(3-21)





Here, the Henry’s law constant is designated as H*, and it has units of molar/atm.

H equals 1/H. Some values are presented in Table 3-3.

*



Table 3-3  Henry’s Law Constants (H *) at 25°C

for Selected Gases (Stumm and Morgan,1996)

Gas

Ammonia (NH3)

Carbon dioxide (CO2)

Hydrogen (H2)†

Hydrogen sulfide (H2S)

Nitrogen (N2)

Oxygen (O2)

Ozone (O3)



Units of molar/atm

57

3.39 × 10-2

8.04 × 10-4

1.05 × 10-1

6.61 × 10-4

1.26 × 10-3

9.4 × 10-3



†



Benjamin (2002)



Solubility of Carbon Dioxide.  Dissolved carbon dioxide (CO2(aq)) is hydrated by

water molecules according to Eq. 3-22, forming a diprotic acid, i.e., contains 2H+. The

reaction lies far to the left, so mostly we have CO2(aq), but the almost infinite number of

water molecules provides for maintenance of equilibrium for the acid, H2CO3. To account

for both species, they are combined according to Eq. 3-23.





CO 2 (aq) + H 2 O  H 2 CO3







H 2 CO* = CO 2 (aq) + H 2 CO3

3



(3-22)





(3-23)



CHEMICAL PRINCIPLES, SOURCE WATER COMPOSITION, AND WATERSHED PROTECTION



3.11



*

The solubility of CO2(g) is defined then with respect to H2CO3 , as shown by Eq. 3-24.

*

Henry’s law is applied to give the dissolved concentration of H2CO3 as a function of the

partial pressure of CO2(g), as presented in Eq. 3-25.



CO 2 (g) + H 2 O  H 2 CO*

3







*

H CO2 =







H 2 CO* 

3



PCO2



(3-24)







(3-25)



The value for the Henry’s constant (H*CO2) at 25°C is 3.388 × 10-2 M/atm. Air at atmospheric pressure of 101.3 kPa (1 atm) contains 380 ppm CO2(g) by volume or expressed

as partial pressure (PCO2), 3.80 × 10-4 atm. Applying Eq. 3-25 for this condition yields an

*

equilibrium dissolved H2CO3 concentration of 1.29 × 10-5 M or 0.16 mg/L as C. It should

be noted that many water systems are not in equilibrium with respect to dissolved inorganic

*

carbon (H2CO3 ) because of other reactions adding CO2(aq) such as bacterial decomposition

or removing CO2(aq) from water such as algae growth. However, if equilibrium is estab*

lished between the water and air phases, then the concentration of dissolved H2CO3 is fixed

at 1.29 × 10-5 M assuming 25°C. For a colder water temperature of say 5°C, the equilibrium

*

concentration of H2CO3 is 2.39 × 10-5 M or 0.29 mg/L as C.

Acid-Base Chemistry.  Acids and bases are defined by the Brønsted-Lowrey concept. An

acid is a substance that donates a proton (H+), and the corollary is that a base is a substance

that accepts a proton. Monoprotic acids have only one proton to donate. Generically, they

are defined as HA (e.g., hypochlorous acid (HOCl)). Some acids are diprotic and have two

*

protons and are generally defined as H2A (e.g., dissolved H2CO3 ) and some are triprotic with

three protons (H3A, e.g., H3PO4). The strength of an acid has to do with the tendency of the

acid to donate the proton to water and it is quantified by acidity constants (Ka). Table 3-4

lists pKa values for several acids of interest. Acids with high acidity constants (or pKa of

low values) are called strong acids; practically, one can assume complete dissociation when

they are added to water. Examples are sulfuric, hydrochloric, and nitric acids. There are

several weak acids and bases of interest in natural waters and in water supply and treatment,

so principles regarding the equilibrium distribution of acids and their conjugate bases are

covered next, and several applications are given.

Table 3-4  Acidity Constants for Some Important Acids at 25°C (from Stumm and Morgan, 1996

and Benjamin, 2002)

Acid



Formula



pKa1



pKa2



Sulfuric



H2SO4



~  – 3



1.99



Phosphoric



H3PO4



2.16



7.20



12.3



Arsenic

Carbonic



H3AsO4

*

H2CO3



2.24

6.35



6.76

10.33



11.6



Hydrogen Sulfide

Hypochlorous

Arsenous



H2S

HOCl

H3AsO3



6.99

7.60

9.23



12.92



+

NH4



9.25



Ammonium



12.1



pKa3



13.4



Applications

Coagulation, pH control,

  membrane cleaning

Speciation in lakes, corrosion

  control

Oxidized As—in water treatment

Many; see inorganic carbon

  section

Found in some groundwaters

Chlorination

Reduced As found in some

  groundwaters

Chloramination



3.12



CHAPTER three



Acid-Base Equilibria.  We begin with monoprotic acids and consider generically the

acid HA and its conjugate base A-. The stoichiometric and equilibrium constant equations

follow:

HA  A - + H +







(3-26)



[ A - ][H + ]

[HA]



(3-27)



K a1 =







Ka1 is the acidity constant. Because there is only one proton involved, it may be written

simply as Ka. Taking base 10 logs of both sides of Eq. 3-27, invoking the pX notation for

[H+] and Ka, and rearranging, we obtain Eq. 3-28.

log





[A- ]

= pH - p K a

[HA]





(3-28)



Applying Eq. 3-28 to the equilibrium distribution of HOCl/OCl- (free chlorine), we obtain

Eq. 3-29.

log





[OCl - ]

[OCl - ]

= pH - p K a = log

= pH - 7.6

[HOCl ]

[HOCl ]





(3-29)



If we practice free chlorination at pH 7.6, then chlorine in the form of HOCl equals

OCl-. For lower pH conditions, HOCl is the dominant form of free chlorine, whereas at

pH > pKa, OCl- dominates. This simple acid (HOCl) and base (OCl-) chemistry is important in chlorination because HOCl is a far more effective disinfectant than OCl-. In Chap.

17 the chemistry of free chlorine is covered in detail.

Another important application is the use of ammonia in combined chlorination or chlo+

ramination (see Chap. 17). Equation 3-30 shows the dependence of ammonium ion (NH4 )

and dissolved ammonia (NH3) on pH. It shows that when ammonia is used in chloramination at pH < 9.25, ammonium ion dominates.

log





[ NH 3 ]

[ NH 3 ]

= pH - p K a = log

= pH - 9.25

[ NH + ]

[ NH + ]

4

4







(3-30)



Two diprotic acids of interest are hydrogen sulfide and dissolved inorganic carbon

*

(H2CO3 ). Because reduced inorganic sulfur can occur in groundwaters, the distribution

of H2S/HS-/S2- as a function of pH is important to understand. Its occurrence is presented

later in this chapter; the removal of H2S by stripping is covered in Chap. 6, and the removal

of reduced sulfur by oxidation is covered in Chap. 7. Inorganic carbon has many important

applications presented later in this chapter.

Generically, we describe the diprotic acid systems as H2A/HA-/A2-. Note that H2A

is an acid, HA- is both an acid and a base, and A2- is a base. The total molar concentration of A (CT,A) containing species must equal the sum of all species, as shown by

Eq. 3-31.





CT , A = [H 2 A] + [HA - ] + [ A 2- ]



(3-31)