PHYSICAL - CHEMICAL TREATMENT OF WATER AND WASTEWATER - CHAPTER 12 ppsx

In the coagulation treatment of water and wastewater, we will be mainly interested in the solid being dispersed in water, the liquid sol orsimply sol.. The primary charges on hydrophobic

Colloids are agglomerates of atoms or molecules whose sizes are so small thatgravity has no effect on settling them but, instead, they stay in suspension Becausethey stay in suspension, they are said to be stable The reason for this stability isthe mutual repulsion between colloid particles They may, however, be destabilized

by application of chemicals Coagulation is the unit process of applying thesechemicals for the purpose of destabilizing the mutual repulsion of the particles, thuscausing the particles to bind together This process is normally applied in conjunctionwith the unit operation of flocculation The colloid particles are the cause of theturbidity and color that make waters objectionable, thus, should, at least, be partiallyremoved

This chapter applies the techniques of the unit process of coagulation to thetreatment of water and wastewater for the removal of colloids that cause turbidityand color It also discusses prerequisite topics necessary for the understanding ofcoagulation such as the behavior of colloids, zeta potential, and colloid stability Itthen treats the coagulation process, in general, and the unit process of the use ofalum and the iron salts, in particular It also discusses chemical requirements andsludge production

12.1 COLLOID BEHAVIOR

Much of the suspended matter in natural waters is composed of silica, or similarmaterials, with specific gravity of 2.65 In sizes of 0.1 to 2 mm, they settle rapidly;however, in the range of the order of 10−5 mm, it takes them a year, in the overall,

to settle a distance of only 1 mm And, yet, it is the particle of this size range thatcauses the turbidity and color of water, making the water objectionable The removal

of particles by settling is practical only if they settle rapidly in the order of severalhundreds of millimeters per hour This is where coagulation can perform its function,

by destabilizing the mutual repulsions of colloidal particles causing them to bindtogether and grow in size for effective settling Colloidal particles fall in the sizerange of 10−6 mm to 10−3 mm They are aggregates of several hundreds of atoms ormolecules, although a single molecule such as those of proteins is enough to bebecome a colloid The term colloid comes from the two Greek words kolla, meaningglue, and eidos, meaning like

A colloid system is composed of two phases: the dispersed phase, or the solute,and the dispersion medium, or the solvent. Both of these phases can have all threestates of matter which are solid, liquid, and gas For example, the dispersion mediummay be a liquid and the dispersed phase may be a solid This system is called a liquid sol, an example of which is the turbidity in water The dispersion medium may be a12

gas and dispersed phase may be solid This system is called a gaseous sol, and examplesare dust and smoke Table 12.1 shows the different types of colloidal systems Notethat it is not possible to have a colloidal system of gas in a gas, because gases arecompletely soluble in each other In the coagulation treatment of water and wastewater,

we will be mainly interested in the solid being dispersed in water, the liquid sol orsimply sol Unless required for clarity, we will use the word ‘‘sol’’ to mean liquid sol.Sols are either lyophilic or lyophobic Lyophilic sols are those that bind the solvent,while the lyophobic sols are those that do not bind the solvent When the solvent is water,lyophilic and lyophobic sols are, respectively, called hydrophilic and hydrophobic sols The affinity of the hydrophilic sols for water is due to polar functional groups thatexist on their surfaces These groups include such polar groups as −OH, −COOH, and

−NH2 They are, respectively, called the hydroxyl, carboxylic, and amine groups

polar groups are shown sticking out from the surface of the particle Because of theaffinity of these groups for water, the water is held tight on the surface This water iscalled bound water and is fixed on the surface and moves with the particle

The hydrophobic colloids do not have affinity for water; thus, they do not containany bound water In general, inorganic colloids are hydrophobic, while organiccolloids are hydrophilic An example of an inorganic colloid is the clay particlesthat cause turbidity in natural water, and an example of an organic colloid is thecolloidal particles in domestic sewage

Solid Solid Solid sol Colored glass and gems, some alloys Solid Liquid Solid emulsion Jelly, gel, opal (SiO2 and H2O), pearl

(CaCO 3 and H 2 O)

Liquid Solid Liquid sol Turbidity in water, starch suspension,

ink, paint, milk of magnesia Liquid Liquid Liquid emulsion Oil in water, milk, mayonnaise, butter Liquid Gas Foam Whipped cream, beaten egg whites

Gas Liquid Gaseous emulsion Mist, fog, cloud, spray

The electrical forces are produced due to the charges that the particles possess

at their surfaces These charges called primary charges are, in turn, produced fromone or both of two phenomena: the dissociation of the polar groups and preferentialadsorption of ions from the dispersion medium The primary charges on hydrophobiccolloids are due to preferential adsorption of ions from the dispersion medium.The primary charges on hydrophilic colloids are due chiefly to the polar groupssuch as the carboxylic and amine groups The process by which the charges on thesetypes of colloids are produced is indicated in Figure 12.2 The symbol R representsthe colloid body First, the colloid is represented at the top of the drawing, without theeffect of pH Then by a proper combination of the H+ and OH− being added to thesolution, the colloid attains ionization of both carboxylic and the amine groups Atthis point, both ionized groups neutralize each other and the particle is neutral Thispoint is called the isoelectric point, and the corresponding ion of the colloid is calledthe zwitter ion Increasing the pH by adding a base cause the added OH− to neutralizethe acid end of the zwitter ion (the ); the zwitter ion disappears, and the wholeparticle becomes negatively charged The reverse is true when the pH is reduced bythe addition of an acid The added H+ neutralizes the base end of the zwitter ion(the COO−); the zwitter ion disappears, and the whole particle becomes positivelycharged From this discussion, a hydrophilic colloid can attain a primary charge ofeither negative or positive depending upon the pH

The primary charges on a colloid which, as we have seen, could either be positive

or negative, attract ions of opposite charges from the solution These opposite chargesare called counterions This is indicated in Figure 12.3 If the primary charges are

FIGURE 12.1 (a) Hydrophilic colloid encased in bound water; (b) interparticle forces as a function of interparticle distance.

COOH

COOH HOOC

NH3+

sufficiently large, the attracted counterions can form a compact layer around theprimary charges This layer is called the Stern layer The counterions, in turn, canattract their own counterions, the coions of the primary charges, forming anotherlayer Since these coions form a continuous distribution of ions into the bulk of thesolution, they tend to be diffused and form a diffused layer The second layer iscalled the Gouy layer Thus, the Stern and Gouy layers form an envelope of electricdouble layer around the primary charges

All of the charges in the Stern layer move with the colloid; thus, this layer is afixed layer In the Gouy layer, part of the layer may move with the colloid particle

by shearing at a shear plane This layer may shear off beyond the boundary of thefixed Stern layer measured from the surface of the colloid Thus, some of the charges

in the layer move with the particle, while others do not This plane is indicated inFigure 12.3

The charges are electric, so they possess electrostatic potential As indicated onthe right-hand side of Figure 12.3, this potential is greatest at the surface and decreases

to zero at the bulk of the solution The potential at a distance from the surface atthe location of the shear plane is called the zeta potential Zeta potential meters arecalibrated to read the value of this potential The greater this potential, the greater

is the force of repulsion and the more stable the colloid

FIGURE 12.2 Primary charges of a hydrophilic colloid as a function of pH.

Zeta potential

Fixed layer

Diffuse layer

Solution bulk

Distance from particle surface

© 2003 by A P Sincero and G A Sincero

550 Physical–Chemical Treatment of Water and Wastewater

The force of repulsion, as we have seen, is due to the charges on the surface.Inherent in any body is a natural force that tends to bind particles together Thisforce is exactly the same as the force that causes adsorption of particles to anadsorbing surface This is caused by the imbalance of atomic forces on the surface Whereas atoms below the surface of a particle are balanced with respect to forces

of neighboring atoms, those at the surface are not Thus, the unbalanced force at thesurface becomes the van der Waal’s force of attraction By the presence of the primarycharges that exert the repulsive force, however, the van der Waal’s force of attraction

is nullified until a certain distance designated by a −a′ is reached The distance can

be shortened by destabilizing the colloid particle

The use of chemicals to reduce the distance to a − a′ from the surface of thecolloid is portrayed in Figure 12.4 The zeta potential is the measure of the stability

of colloids To destabilize a colloid, its zeta potential must be reduced; this reduction

is equivalent to the shortening of the distance to a − a′ and can be accomplishedthrough the addition of chemicals

The chemicals to be added should be the counterions of the primary charges.Upon addition, these counterions will neutralize the primary charges reducing thezeta potential This process of reduction is indicated in Figures 12.4a and 12.4b; thepotential is reduced in going from Figure 12.4a to 12.4b Note that destabilization

is simply the neutralization of the primary charges, thus reducing the force ofrepulsion between particles The process is not yet the coagulation of the colloid

FIGURE 12.4 Reduction of zeta potential to cause destabilization of colloids.

Fixed layer

Fixed layer

Diffuse layer

Diffuse layer

Zeta potential

Zeta potential

551 12.4 COAGULATION PROCESS

The destabilization of colloids through the addition of counterions should be done

in conjunction with the application of the complete coagulation process Four ods are used to bring about this process: double-layer compression, charge neutral-ization, entrapment in a precipitate, and intraparticle bridging

meth-When the concentration of counterions in the dispersion medium is smaller, thethickness of the electric double layer is larger Two approaching colloid particlescannot come close to each other because of the thicker electric double layer, there-fore, the colloid is stable Now, visualize adding more counterions When the con-centration is increased, the attracting force between the primary charges and theadded counterions increases causing the double layer to shrink The layer is thensaid to be compressed As the layer is compressed sufficiently by the continuedaddition of more counterions, a time will come when the van der Waals force exceedsthe force of repulsion and coagulation results

The charge of a colloid can also be directly neutralized by the addition of ions

of opposite charges that have the ability to directly adsorb to the colloid surface.For example, the positively charged dodecylammoniun, C12H25 , tends to behydrophobic and, as such, penetrates directly to the colloid surface and neutralize

it This is said to be a direct charge neutralization, since the counterion has penetrateddirectly into the primary charges Another direct charge neutralization method would

be the use of a colloid of opposite charge Direct charge neutralization and thecompression of the double layer may compliment each other

A characteristic of some cations of metal salts such as Al(III) and Fe(III) is that

of forming a precipitate when added to water For this precipitation to occur, acolloidal particle may provide as the seed for a nucleation site, thus, entrapping thecolloid as the precipitate forms Moreover, if several of this particles are entrappedand are close to each other, coagulation can result by direct binding because of theproximity

The last method of coagulation is intraparticle bridging A bridging moleculemay attach a colloid particle to one active site and a second colloid particle to anothersite An active site is a point in the molecule where particles may attach either bychemical bonding or by mere physical attachment If the two sites are close to eachother, coagulation of the colloids may occur; or, the kinetic movement may loop thebridge assembly around causing the attached colloids to bind because for now theyare hitting each other, thus bringing out coagulation

12.4.1 C OAGULANTS FOR THE C OAGULATION P ROCESS

Electrolytes and polyelectrolytes are used to coagulate colloids Electrolytes arematerials which when placed in solution cause the solution to be conductive toelectricity because of charges they possess Polyelectrolytes are polymers possessingmore than one electrolytic site in the molecule, and polymers are molecules joinedtogether to form larger molecules Because of the charges, electrolytes and poly-electrolytes coagulate and precipitate colloids The coagulating power of electrolytes

is summed up in the Schulze–Hardy rule that states: the coagulation of a colloid

is affected by that ion of an added electrolyte that has a charge opposite in sign to

NH3+

that of the colloidal particle; the effect of such an ion increases markedly with the

number of charges carried Thus, comparing the effect of AlCl3 and Al2(SO4)3 in

coagulating positive colloids, the latter is 30 times more effective than the former,

since sulfate has two negative charges while the chloride has only one In coagulating

negative colloids, however, the two have about the same power of coagulation

The most important coagulants used in water and wastewater treatment are alum,

copperas (ferrous sulfate), ferric sulfate, and ferric chloride Later, we will

specifi-cally discuss the chemical reactions of these coagulants at greater lengths Other

coagulants have also been used but, owing to high cost, their use is restricted only

to small installations Examples of these are sodium aluminate, NaAlO2; ammonia

The reactions of sodium aluminate with aluminum sulfate and carbon dioxide are:

(12.1)(12.2)

12.4.2 C OAGULANT A IDS

Difficulties with settling often occur because of flocs that are slow-settling and are

easily fragmented by the hydraulic shear in the settling basin For these reasons,

coagulant aids are normally used Acids and alkalis are used to adjust the pH to the

optimum range Typical acids used to lower the pH are sulfuric and phosphoric acids

Typical alkalis used to raise the pH are lime and soda ash Polyelectrolytes are also

used as coagulant aids The cationic form has been used successfully in some waters

not only as a coagulant aid but also as the primary coagulant In comparison with

alum sludges that are gelatinous and voluminous, sludges produced by using cationic

polyelectrolytes are dense and easy to dewater for subsequent treatment and disposal

Anionic and nonionic polyelectrolytes are often used with primary metal coagulants

to provide the particle bridging for effective coagulation Generally, the use of

poly-electrolyte coagulant aids produces tougher and good settling flocs

Activated silica and clays have also been used as coagulant aids Activated silica

is sodium silicate that has been treated with sulfuric acid, aluminum sulfate, carbon

dioxide, or chlorine When the activated silica is applied, a stable negative sol is

produced This sol unites with the positively charged primary-metal coagulant to

produce tougher, denser, and faster settling flocs

Bentonite clays have been used as coagulant aids in conjunction with iron and

alum primary coagulants in treating waters containing high color, low turbidity, and

low mineral content Low turbidity waters are often hard to coagulate Bentonite

clay serves as a weighting agent that improves the settleability of the resulting flocs

12.4.3 R APID M IX FOR C OMPLETE C OAGULATION

Coagulation will not be as efficient if the chemicals are not dispersed rapidly

throughout the mixing tank This process of rapidly mixing the coagulant in the

volume of the tank is called rapid or flash mix Rapid mixing distributes the chemicals

immediately throughout the volume of the mixing tank Also, coagulation should

Al2(SO4)3⋅(NH4)2⋅24H2O Al2(SO4)3⋅K2SO4⋅24H2O

6NaAlO2+Al2(SO4)3⋅14.3H2O→8Al OH( )3+3Na2SO4+2.3H2O

2NaAlO2+CO2+3H2O→2Al OH( )3↓ Na+ 2CO3

be followed by flocculation to agglomerate the tiny particles formed from the ulation process.

coag-If the coagulant reaction is simply allowed to take place in one portion of thetank because of the absence of the rapid mix rather than being spread throughoutthe volume, all four mechanisms for a complete coagulation discussed above will not

be utilized For example, charge neutralization will not be utilized in all portions ofthe tank because, by the time the coagulant arrives at the point in question, the reaction

of charge neutralization will already have taken place somewhere

Interparticle bridging will not be as effective, since the force to loop the bridgearound will not be as strong without the force of the rapid mix Colloid particleswill not effectively be utilized as seeds for nucleation sites because, without rapidmix, the coagulant may simply stay in one place Finally, the compression of thedouble layer will not be as effective if unaided by the force due to the rapid mix.The force of the rapid mix helps push two colloids toward each other, thus enhancingcoagulation Hence, because of all these stated reasons, coagulation should takeplace in a rapidly mixed tank

12.4.4 THE JAR TEST

In practice, irrespective of what coagulant or coagulant aid is used, the optimumdose and pH are determined by a jar test This consists of four to six beakers (such

as 1000 ml in volume) filled with the raw water into which varying amounts of doseare administered Each beaker is provided with a variable-speed stirrer capable ofoperating from 0 to 100 rpm

Upon introduction of the dose, the contents are rapidly mixed at a speed of about

60 to 80 rpm for a period of one minute and then allowed to flocculate at a speed

of 30 rpm for a period of 15 minutes After the stirring is stopped, the nature and

settling characteristics of the flocs are observed and recorded qualitatively as poor, fair, good, or excellent A hazy sample denotes poor coagulation; a properly coag-

ulated sample is manifested by well-formed flocs that settle rapidly with clear waterbetween flocs The lowest dose of chemicals and pH that produce the desired flocsand clarity represents the optimum This optimum is then used as the dose in theactual operation of the plant See Figure 12.5 for a picture of a jar testing apparatus

12.5 CHEMICAL REACTIONS OF ALUM

The alum used in water and wastewater treatment is Al2(SO4)3⋅ 14H2O (The ‘‘14’’actually varies from 13 to 18.) For brevity, this will simply be written without thewater of hydration as Al2(SO4)3 When alum is dissolved in water, it dissociatesaccording to the following equation (Sincero, 1968):

Because the water molecule is polar, it attracts Al3+ forming a complex ionaccording to the following:

(12.4)

In the complex ion , Al is called the central atom and the molecules of

H2O are called ligands The subscript 6 is the coordination number, the number of

ligands attached to the central atom; the superscript 3+ is the charge of the complex

ion The whole assembly of the complex forms what is called a coordination sphere.

As indicated in Equation (12.4), aluminum has a coordination number of 6 withthe water molecule This means that no more water molecules can bind with the centralatom but that any interaction would not be a mere insertion into the coordinationsphere In fact, further reaction with the water molecule involves hydrolysis of thewater molecule and exchanging of the resulting OH− ion with the H2O ligand inside

the coordination sphere This type of reaction is called ligand exchange reaction.

Some of the hydrolysis products of the ligand exchange reaction are clear, which means that only one central atom of aluminum is in the complex; andsome are polynuclear, which means that more than one central atom of aluminum

simply be written as Al3+ This is the symbol to be used in the complex reactionsthat follow Without going into details, we will simply write at once all the complexligand exchange equilibrium reactions

(12.5)(12.6)(12.7)

FIGURE 12.5 A Phipps and Bird jar testing apparatus (Courtesy of Phipps & Bird,

Richmond, VA © 2002 Phipps & Bird.)

(12.8)(12.9)(12.10)The equilibrium constants apply at 25°C:

Also, the H+ and the OH− are participants in these reactions This means that theconcentrations of each of these complex ions are determined by the pH of the solution

In the application of the previous equations in coagulation treatment of water,conditions must be adjusted to allow maximum precipitation of the solid represented

complex ions must be held to a minimum

12.5.1 D ETERMINATION OF THE O PTIMUM pH

For effective removal of the colloids, as much of alum should be converted to the

neutralize the primary charges of the colloids to effect their destabilization Overall,this means that once the solids have been formed and the complex ions haveneutralized the colloid charges, the concentrations of the complex ions standing insolution should be at the minimum The pH corresponding to this condition is calledthe optimum pH

Let spAl represent all the species that contain the aluminum atom standing in solution.Thus, the concentration of all the species containing the aluminum atom Al(III), is

(12.11)

All the concentrations in the right-hand side of the previous equation will now beexpressed in terms of the hydrogen ion concentration This will result in the express-

ing of [spAl] in terms of the hydrogen ion Differentiating the resulting equation of

[spAl] with respect to [H+] and equating the result to zero will produce the minimum

concentration of spAl and, thus, the optimum pH determined Using the equilibriumreactions, Eqs (12.5) through (12.10), along with the ion product of water, we nowproceed as follows:

(12.12)

Al(OH)3 s( )(fresh precipitate)
Al3++3OH− K sp,Al(OH)

3 = 10−33Al(OH)3 s( ) OH−
Al OH( )4

γAlK w3

activity coefficients of the aluminum ion and the hydrogen ion and the complexes

solubility product constant of the solid and K w is the ion product of

Remember that the equilibrium constants are a function of temperature To obtain

the corresponding values at other temperatures, the Van’t Hoff equation should be

used The use of this equation, however, requires the value of the standard enthalpy At present, none are available for the aluminum complexes Research istherefore needed to find these values

H+[ ]2

γAl, γH,γAl(OH) c, γAl7(OH)17c γAl13(OH)34c γAl(OH)4c, γAl2(OH)2c

Al7(OH)174+ Al13(OH)345+ Al(OH)4− Al2(OH)24+ K sp,Al(OH)

3Al(OH)3(s)

K Al(OH) c KAl7(OH)17c , KAl13(OH)34c KAl(OH)4c KAl2(OH)2c

Al(OH)2+ Al7(OH)174+ Al13(OH)345+Al(OH)4−, Al2(OH)24+

∆H298

o

Equations (12.12) through (12.17) may now be substituted into Equation (12.11)

to produce

(12.18)

To obtain the optimum pH, differentiate [spAl] of Equation (12.18) with respect

to [H+] and equate the result to zero Doing the differentiation, rearranging theresulting equation, and calling the resulting solution for [ ] as [ ], obtain thefollowing equation:

[H+]2

γAl(OH) c K w

3

+

γAlK w

3

- 3 10

33 –

( ) 0.94( )3

0.56( ) 10– 14

- 8 10

6.3 –

+

-=9.62 10( 15)

- 65 0.94( )5

0.20( ) 10– 19.6

13 –

( ) 4.66 10( )– 14

–4.66 10( )– 14

2.30 10( –20)–

12.6 CHEMICAL REACTIONS OF THE FERROUS ION

The ferrous salt used as coagulant in water and wastewater treatment is copperas,FeSO4⋅ 7H2O For brevity, this will simply be written without the water of hydration

as FeSO4 When copperas dissolves in water, it dissociates according to the followingequation:

(12.21)

As in the case of alum, the ions must be rapidly dispersed throughout the tank

in order to effect the complete coagulation process The solid precipitate Fe(OH)2(s)and complexes are formed and expressing in terms of equilibrium with the solidFe(OH)2(s), the following reactions transpire (Snoeyink and Jenkins, 1980):

(12.22)(12.23)(12.24)

participant in these reactions This means that the concentrations of each of thesecomplex ions are determined by the pH of the solution In the application of theabove equations in an actual coagulation treatment of water, conditions must beadjusted to allow maximum precipitation of the solid represented by Fe(OH)2(s) Toallow for this maximum precipitation, the concentrations of the complex ions must

be held to the minimum The values of the equilibrium constants given above are

at 25°C

12.6.1 DETERMINATION OF THE OPTIMUM pH

For effective removal of the colloids, as much of the copperas should be converted

to the solid Fe(OH)2(s) Also, as much of the concentrations of the complex ionsshould neutralize the primary charges of the colloids to effect their destabilization.Overall, this means that once the solids have been formed and the complex ionshave neutralized the colloid charges, the concentrations of the complex ions standing

in solution should be at the minimum The pH corresponding to this condition isthe optimum pH for the coagulation using copperas

Let spFeII represent all the species that contain the Fe(II) ion standing in solution.Thus, the concentration of all the species containing the ion is

(12.25)All the concentrations in the right-hand side of the previous equation will now beexpressed in terms of the hydrogen ion concentration As in the case of alum, this

will result in the expressing of [spFeII] in terms of the hydrogen ion Differentiating

the resulting equation of [spFeII] with respect to [H+] and equating the result to zero

FeSO4→Fe2++SO42−

Fe(OH)2 s( )
Fe2++2OH− K sp,Fe OH( )

2 = 10–14.5Fe(OH)2 s( )
FeOH++OH− K FeOHc = 10–9.4Fe(OH)2 s( ) OH−
Fe OH( )3

−

3c = 10–5.1Fe(OH)3−

spFeII

[ ]=[Fe2+]+[FeOH+]+[Fe(OH)3−]

will produce the minimum concentration of spFeII and, thus, the optimum pH mined Using the equilibrium reactions, Eqs (12.22) through (12.24), along withthe ion product of water, we now proceed as follows:

deter-(12.26)

(12.27)

(12.28)

γFeII, γFeOHc, are, respectively, the activity coefficients of the ferrous ion

of the solid Fe(OH)2(s) K FeOHc and are, respectively, the equilibrium

Equations (12.26) through (12.28) may now be substituted into Equation (12.25)

to produce

(12.29)

Differentiating with respect to [H+], equating to zero, rearranging, and changing H+

to , the concentration of the hydrogen ion at optimum conditions,

(12.30)

The value of [Hopt] may be solved by trial error

12.7 CHEMICAL REACTIONS OF THE FERRIC ION

The ferric salts used as coagulant in water and wastewater treatment are FeCl3 and

Fe2(SO4)3 They have essentially the same chemical reactions in that both form theFe(OH)3(s) solid When these coagulants are dissolved in water, they dissociateaccording to the following equations:

(12.31)(12.32)

As in any coagulation process, these ions must be rapidly dispersed throughout thetank in order to effect the complete coagulation process The solid precipitateFe(OH)3(s) and complexes are then formed The reactions, together with the respectiveequilibrium constants at 25°C, are as follows (Snoeyink and Jenkins, 1980):

the OH− ion is a participant in these reactions This means that the concentrations

of each of these complex ions are determined by the pH of the solution

In the application of the above equations in an actual coagulation treatment ofwater as in all applications of coagulants, conditions must be adjusted to allowmaximum precipitation of the solid which in the present case is represented byFe(OH)3(s) To allow for this maximum precipitation, the concentrations of thecomplex ions must be held to a minimum

12.7.1 DETERMINATION OF THE OPTIMUM pH

For effective removal of the colloids, as much of the ferric ions should be converted

to the solid Fe(OH)3(s) Also, as much of the concentrations of the complex ionsshould neutralize the primary charges of the colloids to effect their destabilization.Overall, this means that once the solids have been formed and the complex ionshave neutralized the colloid charges, the concentrations of the complex ions standing

in solution should be at the minimum, which corresponds to the optimum pH forthe coagulation process

Let spFeIII represent all the species that contain the Fe(III) ion standing in solution.Thus, the concentration of all the species containing the ion is

Fe OH( )3 s( ) OH−
Fe OH( )4

−

4c 10= 52Fe OH( )3 s( )
Fe2(OH)2

4+

4OH−

2 ( OH )2c = 10–50.8Fe(OH)2+ Fe(OH)4− Fe2(OH)24+

spFeIII

[ ]=[Fe3+]+[FeOH2+]+[Fe(OH)2+]+[Fe(OH)4−] 2 Fe+ [ 2(OH)24+]

[spFeIII] with respect to [H+] and equating the result to zero will produce the minimum

concentration of spFeIII and, thus, the optimum pH determined Using the equilibriumreactions, Eqs (12.33) through (12.37), along with the ion product of water, we nowproceed as follows:

are, respectively, the equilibrium constants of the complexes FeOH2+,

Differentiating with respect to [H+], equating to zero, rearranging, and changing H+

to , the concentration of the hydrogen ion at optimum conditions,

(12.45)The value of [Hopt] may be solved by trial error

Example 12.2 A raw water containing 140 mg/L of dissolved solids is jected to coagulation treatment using copperas Calculate the optimum pH that theoperation should be conducted Assume the temperature of operation is 25°C

( ) 0.94( )2

0.77( ) 10– 14

( ) 0.94( )0.94

0.94( ) 0.94( ) - 8.99 10( –20)

Solving by trial and error, let

Example 12.3 A raw water containing 140 mg/L of dissolved solids is jected to coagulation treatment using a ferric salt Calculate the optimum pH thatthe operation should be conducted Assume the temperature of operation is 25°C

20 –

–3.99 10( –20) 4.05 10– 18

– -

( )

–

)(0.94)4(0.36)(10–14)4 - 2.75(106)

3K sp,Fe(OH)

3γH 3

0.56

γFeIIIK w

2

- 3(10

38 –

)(0.94)30.56(10–14)3 - 4.45(104)

)

–

)(0.94)2(0.77)(10–14)2 - 158.78

(0.94)(0.94)(10–14) - 10–2.74

12.8 JAR TESTS FOR OPTIMUM pH DETERMINATION

We may summarize the optimum pH’s of the coagulants obtained in the previousexamples: alum = 5.32, ferrous = 11.95, and ferric = 8.2 The problem with thesevalues is that they only apply at a temperature of 25°C If the formulas for thedetermination of these pH’s are reviewed, they will be found to be functions ofequilibrium constants By the use of the Van’t Hoff equation, values at other tem-peratures for the equilibrium constants can be found These, however, as mentionedbefore, also need the value of the standard enthalpy change, as discussed inthe chapter on water stabilization For the aforementioned coagulants, no values ofthe enthalpy change are available Thus, until studies are done to determine thesevalues, optimum pH values must be determined using the jar test

In addition, the optimum pH’s of 5.32, 11.95, and 8.2 were obtained at a dissolvedsolids of 140 mg/L The value of the dissolved solids predicts the values of the activitycoefficients of the various ions in solution, which, in turn, determine the activities ofthe ions, including that of the hydrogen ion It follows that, if the dissolved solidsconcentration is varied, other values of optimum pH’s will also be obtained not onlythe respective values of 5.32, 11.95, and 8.2 This is worth repeating: the values of5.32, 11.95, and 8.2 apply only at a dissolved solids concentration of 140 mg/L Inaddition, they only apply provided the temperature is 25°C In subsequent discussions,mention of these optimum pH values would mean values at the conditions of 25°C oftemperature and a solids concentration of 140 mg/L

The respective chemical reactions will first be derived From the concept ofequivalence, the number of equivalents of all the species participating in a given

19 –

)–1.82(10–19)1.82(10–19)–1.82(10–23) -

chemical reaction are equal From the reaction, the equivalent masses will then becalculated Once this is done, equations for chemical requirements can be derived.

12.9.1 CHEMICAL REQUIREMENTS IN ALUM

COAGULATION TREATMENT

The water of hydration for alum varies from 13 to 18 For the purposes of calculating

the chemical requirements, this range of values will be designated by x In actual applications, the correct value of x must be obtained from the label of the container used to ship the chemical Using x as the water of hydration, the chemical reaction

for alum is

(12.46)The rationale behind the previous reaction is explained here The bicarbonate isknown to act as a base as well as an acid As a base, its interaction is

The K sp of aluminum hydroxide is imately (10−33) This means that the hydroxide is very insoluble Thus, with the ions

approx-of the coagulant and the bicarbonate dispersed in the water, Al3+ ‘‘grabs” whatever

OH− there is to form the precipitate, Al(OH)3, and the reaction portrayed above ensues

A very important point must be discussed with respect to the previous coagulationreaction, in comparison with those found in the literature The environmental engi-neering literature normally uses the equilibrium arrows,
, instead of the singleforward arrow, → , as written previously Equilibrium arrows indicate that a particularreaction is in equilibrium, which would mean for the present case, that alum is produced

in the backward reaction Alum, however, is never produced by mixing aluminumhydroxide, carbon dioxide, calcium sulfate, and water, the species found on the right-hand side of the previous equation Once Al2(SO4)3⋅ 14H2O is mixed with Ca(HCO3)2,the alum is gone forever producing the aluminum hydroxide precipitate—it cannot berecovered After the formation of the precipitate, any backward reaction would be forthe complex reactions and not for the formation of Al2(SO4)3⋅ xH2O, as would beinferred if the above reaction were written with the equilibrium arrows

In addition, coagulation is a process of expending the coagulant In the process

of expenditure, the alum must react to produce its products This means that whatmust ‘‘exist” is the forward arrow and not any backward arrow Portraying thebackward arrow would mean that the alum is produced, but it is known that it is notproduced but expended During expenditure, no equilibrium must exist To reiterate,the coagulation reaction should be represented by the forward arrow and not by theequilibrium arrows

As shown in Equation (12.46), an alkaline substance is needed to react with thealum The bicarbonate alkalinity is used, since it is the alkalinity that is always found

in natural waters In practice, its concentration must be determined to ascertain ifenough is present to satisfy the optimum alum dose If found deficient, then lime isnormally added to satisfy the additional alkalinity requirement As we have found,the reaction is optimum at a pH of 5.32 at 25°C when the dissolved solids concen-tration is 140 mg/L

Al2(SO4)3⋅xH2O+3Ca(HCO3)2→2Al(OH)3↓+6CO2+3CaSO4+xH2O

−

H2O+

H2CO3+OH−
CO2+H2O+OH−