• TABLE OF CONTENTS
HIDE
 Title Page
 Acknowledgement
 Table of Contents
 List of Tables
 List of Figures
 Introduction
 Acidity of iron (III) in aqueous...
 Evaluation of literature values...
 Research plan
 Experimental
 Results
 Discussion of results
 Summary and conclusions
 Appendix
 Reference
 Biographical sketch
 Copyright














Title: hydrolysis of iron (III) in dilute aqueous solution.
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Title: hydrolysis of iron (III) in dilute aqueous solution.
Series Title: hydrolysis of iron (III) in dilute aqueous solution.
Physical Description: Book
Creator: Singley, John Edward,
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Table of Contents
    Title Page
        Page i
    Acknowledgement
        Page ii
        Page iii
    Table of Contents
        Page iv
        Page v
    List of Tables
        Page vi
        Page vii
    List of Figures
        Page viii
        Page ix
    Introduction
        Page 1
        Page 2
        Page 3
        Page 4
        Page 5
        Page 6
        Page 7
        Page 8
        Page 9
        Page 10
        Page 11
        Page 12
    Acidity of iron (III) in aqueous solution
        Page 13
        Page 14
        Page 15
        Page 16
        Page 17
        Page 18
        Page 19
        Page 20
        Page 21
        Page 22
        Page 23
        Page 24
        Page 25
        Page 26
    Evaluation of literature values of hydrolysis constants
        Page 27
        Page 28
        Page 29
        Page 30
        Page 31
        Page 32
        Page 33
        Page 34
        Page 35
        Page 36
        Page 37
        Page 38
    Research plan
        Page 39
        Page 40
        Page 41
        Page 42
        Page 43
        Page 44
        Page 45
        Page 46
    Experimental
        Page 47
        Page 48
        Page 49
        Page 50
        Page 51
        Page 52
        Page 53
        Page 54
        Page 55
        Page 56
        Page 57
    Results
        Page 58
        Page 59
        Page 60
        Page 61
        Page 62
        Page 63
        Page 64
        Page 65
        Page 66
        Page 67
        Page 68
        Page 69
        Page 70
        Page 71
        Page 72
        Page 73
        Page 74
        Page 75
        Page 76
        Page 77
        Page 78
        Page 79
        Page 80
        Page 81
        Page 82
        Page 83
        Page 84
        Page 85
        Page 86
        Page 87
        Page 88
        Page 89
        Page 90
        Page 91
        Page 92
        Page 93
        Page 94
        Page 95
        Page 96
        Page 97
        Page 98
        Page 99
        Page 100
        Page 101
        Page 102
        Page 103
        Page 104
        Page 105
    Discussion of results
        Page 106
        Page 107
        Page 108
        Page 109
        Page 110
        Page 111
    Summary and conclusions
        Page 112
        Page 113
    Appendix
        Page 114
        Page 115
        Page 116
        Page 117
        Page 118
        Page 119
        Page 120
        Page 121
        Page 122
    Reference
        Page 123
        Page 124
        Page 125
        Page 126
        Page 127
        Page 128
    Biographical sketch
        Page 129
        Page 130
        Page 131
    Copyright
        Copyright
Full Text










THE HYDROLYSIS OF IRON (III) IN
DILUTE AQUEOUS SOLUTION









By
JOHN EDWARD SINGLE

















I would like to dedicate this work to the two people who have

been most important in making it possible; Dr. A. P. Black, my com-


Liman, advise

standing an(

Black's guic

7ce of inspi:

ire to work i

life'ss contr

,ntenance of

ie has provic



daughters Gli

) job easier

sincerest ap]

Ljor contribi

stion. Dr. (

I Dr. James

ien with whon

lpeA st than


and friend, and my wi:

lelp it could not have

ice, teaching, and fri,

Aion throughout my stu(

;h THE water chemist.

ition takes many forms

ir home with little he:

1 encouragement and she



rs, Ann, Peggy, and Pa-



ciation goes to the mf

>rs to this undertaking

irge Butler, Dr. Richai

lefordner are the fine,a

: could have hoped to I

are also due to Dean [

iorgia State College, i

i, who have constantly

Is endeavor. Their fi


.e, V

been

endshj

lies.



, the

Lp fr<

>wn p.



ti hi



mberi

; thrc

,d Dr(

it grc

)e as-.

. C.

nd Di

encoi:

iends


Lnia, within

complished

have been

t has been



Lncipal of

ne during

snce and iu



done thei:



C my commi,

- their ad,

ner, Dr. F:

of scient:

Lated.

rton Burch

i. W. Mark(

;ed and im.

o and assi.










have been important factors.

Of the many other people who have helped in so many ways, I

would like to give particular thanks to Dr. Ching-lin Chen for aiding

in the preparation of the manuscript and to Mrs. Janice Larson for

typing it.

I wish to acknowledge the financial support of the Division of

Water Supply and Pollution Control, Public Health Service, through

Research Grant WP-00717.















ACKNOWLEDGMENTS . . . . . e * * ii

LIST OF TABLES . ..... . . . . . . . . vi

LIST OF FIGURES . .. . . . . . . . . viii

CHAPTER

I. INTRODUCTION . . . . * . . 1

Use of Hydrolyzing Coagulants . . . . 1

Mechanisms of Coagulation With Hydrolyzing
Coagulants . ... ... . .. ...... 2

Quantitative Mechanisms . .... .. 8

Object of Study .. . .. . . ... 12

II. ACIDITY OF IRON (III) IN AQUEOUS SOLUTION . . 13

Qualitative Relatinships .. . . . . . 13

Quantitative Relationships . . . . . 18

III. EVALUATION OF LITERATURE VALUES OF HYDROLISIS
CONSTANTS . . . . . . . . . . 27

Ionic Strength Effects . . . .. 27

Effect of Concentration ....... * 34

Kinetic Factors. . . * * * 35

SummarC. . . . . . . . . 37

IV. RESEARCH PLAN o o o e o e .... 39

Potentiometric Titrations . . . .. a 39

Calculations . . . . . . . 44

V. EXPERIMENTAL . . . 47










Page

Apparatus . . . . . 51

Procedures .. o *- .e * * * * * 55
VI. RESULTSocedures . .. . . . .. . . * 58
VI RESULTS 0a000000600 58

Effect of.Titration Parameters . . . ... 58

Titrimetric Curves ........ .... .. 63

Calculations * . . * * . . 82

VII. DISCUSSION OF RESULTS . .. . . . . 106

Comparison of Literature Values and Experimental
Results . ........ . . 106

VIII. SUMMARY AND CONCLUSIONS . . . . . . 112

APPENDICES .. .. .. .. . .. 114

AppendixI ... ................ ... 115

Appendix II . .. .... * * * 117

Appendix III ...... ..... . 119

Appendix IV ................. . . 121

LIST OF REFERENCES . . .. . . . . . . .. 123

BIOGRAPHICAL SKETCH . . . . . . . . . 129










LIST OF TABLES
Table Page

1. Iron (III) Hydrolysis Reactions . . . . 20

2. Acidity Constants of Hydroxy Complexes of Iron (III) 23

3. Analysis of Iron (III) Nitrate . . . . . . 48

4. Delivery Rate of Syringes Used .. . . .. 54

5. Titration of Sixteen Separate 25.00 ml Samples of
1 x 10-3 M Iron (III) Perchlorate Solutions With
0.01776 M NaOH . . . ....... .. .. 72
6. Titration of Eleven Separate 25.00 ml Samples of
5 x l0- M Iron (III) Perchlorate Solution With
0.01776 M NaOH .. .. . . . . . .... 77

7. Titration of Seven Separate 25.00 ml Samples of
1 x 10-4 M Iron (III) Perchlorate Solution With
0.01776 M NaOH . . . . .. . 79
8. Titration of Four Separate 50.00 ml Samples of
1 x 10-5 M Iron (III) Perchlorate Solution W&th
0.01776 M NaOH . . . . . . . . . 80

9. Formation Function Versus pH Using Biedermann's Constants
(62). Total Iron (III) Concentration = 0.10000000E-03 85

10. Literature Values of Equilibrium Constants Used in
Calculating K and CFe31) .. ..... . . 87
11. Coefficients of Terms of a Power Series Determined by
Stepwise Multiple Regression Analysis for the Titration
of a 1 x 10-4 M Fe (III) Perchlorate Solution With NaOH 96

12. Instantaneous Concentration Quotients for the Hydrolysis of
Iron (III) at Different Total Concentrations of Iron (III) 97

13. Concentration of Iron (III) Hydrolysis Species Present
as a Function of pH in a 1 x 10-3 M Solution of Iron
(III) Perchlorate . . .. . . . ... . 100
14. Concentration of Iron (III) Hyd.rlysis Species Present
as a Function of pH in a.1 x 10" M Solution of Iron
(III) Perchlorate . . o . . . . . . 101









Table Page

15. Concentration of Iron (III) Hydrolysis Species Present
as a Function of pH in a 1 x lo-5 M Solution of Iron
(III) Perchlorate . . . . . . . . 102


Table Page


(Ill) Perchlorate . 0 102










LIST OF FIGURES

Figure Page

1.. Coagulation of Organic Color ltth Fe* and A13*
Sulfates. After Blacket al.3 .. 9

2. Approximate Stoichiometry of Color-Iron (III) Interaction 11

3. Structure of the Dimer Fe2(H20)8(OH)2 After Mulay. 16

4. Effect of Ionic Strength on Formation Constant of the
UO2F0 Ion . . . . . .......... 31

5. Experimental Setup for Titrations . . * * 52

6. Representative Titration Curve Showing Initial
Buffered Zone . .. . . * * 57

7. Effect of Bicarbonate Ion on the Tiration of Fe (III) . 59

8. Effect of Bicarbonate Ion on Titration of Perchloric
Acid With NaOH . . . . . . . . . 60

9. Effect of Aging of Solution on Hydrolysis of Fe (III)
Perchlorate Solutions .. ... . ... ... 62

10. Effect of Titration Time on the Reproducibility of the
Curves in the Titration of Iron (III) Perchlorate With
Sodium Hydroxide .......... 64
-4
11. Potentiometric Titration of 25.00 ml of 5 x 10" M Iron
(III) Perchlorate Solution With 0.01776 M NaOH Showing
the Effect of Temperature .. .. 65

12. Titration of 25.00 ml of 1 x 10-3 M Iron (III)
Perchlorate Solutions With 0.01776 M NaOH . . . .. 66

13. Titration of 25.00 ml of 5 x 10-4 M Iron (III)
Perchlorate With 0.01776 M NaOH . . . . .. 67

14. Titration of 25.00 ml of 1 x 104 M Iron (III)
Perchlorate Solutions With 0.01776 M NaOH . . . .. 68

15. Titration of 50.00 ml of 1 x 10-5 M Iron (III)
Perchlorate With 0.01776 M NaOH . . ......... 69
S14 4m-t 4-4-- -4% *-- P- /TTN 111---4.L- o-n-.it --- T.= 4&u %T-nty r





ZU Gcalculated Formation Functions for the Titration of
Fe (III) With NaOH . . . . . . .. . . 89

21, Comparison of Experimental Values of R as a Function of
pH for 10-3 Molar Iron (III) With Plots Derived From
Values of the Equilibrium Constants in the Literature . 90

22. The Effect of Total Iron (III) Concentration, FeT, on
the Instantaneous Concentration Quotients, Q. . . . 98

23. Distribution Diagram for 'the Percentage of the Total
Iron (III) Present as Various Species as a Function of
pH for a Total Iron (III) Concentration of 1 x 10"3 M . 103

24. Distribution Diagram for the Percentage of the Total
Iron (III) Present as Various Species as a Function of
pH for a Total Iron (III) Concentration of 1 x 10-4 M . 104

25* Distribution Diagram for the Percentage of the Total
Iron (III) Present as Various Species as a Function of
pH for a Total Iron (III) Concentration of 1 x 10-5 M 105













I. INTRODUCTION


Use of Hydrolyzing Coagulants


The use of hydrolyzing coagulants dates to the patent of Hyatt

in 1884 which discloses the advantages of pretreating the influent water

with iron (III) chloride or sulphate prior to rapid filtration. This was

stated to prolong filter runs and produce a better quality water. This

system, employing iron (III) chloride as the coagulant, was first used

at the Sommerville and Raritan Water Company in 1885.

Also in 1885, Professors P. T. Austen and F. A. Wilber2 of Rutgers

published the results of the first studies of coagulation based on sound

scientific principles. They limited their studies to alum, the common

name for aluminum sulfate in water treatment plants, as the coagulant.

The classical studies of George Warren Fuller and co-workers3 at

Louisville, Kentucky in the period 1895-97, contributed significantly to

the technology of the use of coagulants with rapid sand filtration for

the removal of turbidity from Ohio River water.

Chlorinate copperas, iron (III) chloro sulfate, was first used at

Quincy, Illinois by W. B. Bull in 1912 and was reported again in 1928

by Hedgepeth, Olsen and Olsen5 as superior to alum for the removal of

organic color from the soft, highly colored surface water used as a raw

water source at Elizabeth City, North Carolina. The lower pH range of

effectiveness of iron (III) salts as compared to aluminum salts was

discussed in some detail.


-1-





- 2-


Two papers in 19466,7 pointed out the advantages and disadvantages

of the use of iron (III) salts, particularly iron (III) sulphate, and

presented plant data to substantiate claims of lower dosages and more

efficient removal of turbidity. Data were given for specific results at

various water treatment plants throughout the country that were employing

iron (III) salts as coagulants.

The use of iron (III) salts as coagulants in the treatment of

potable water has increased to somewhat less than 100,000 tons per year

in 1965. This compares with an annual consumption of approximately

600,000 tons per year for alum.


Mechanisms of Coagulation With Hvdrolyzina Coagulants


Many of the impurities in untreated water supplies that are

removed by coagulation and filtration .exist in the natural state as

colloids. Filtration alone will not satisfactorily remove these impuri-

ties, for example, essentially no color is removed from a colored surface

water by sand filtration alone, although filtration will remove larger

particles of clay, silt, algae, and possibly some bacteria. The use of

coagulation as a preliminary step in agglomerating these particles

results in almost complete removal by subsequent filtration.

The earliest mechanisms proposed to explain the destabilization of

these colloids was borrowed from the field of colloid chemistry. The
8,9
well known Schultze-Hardy rule'9 was invoked whereby it was stated that

a trivalent ion was 700-1000 times as effective as a monovalent ion in

destabilizing a colloid of opposite charge. This explanation fitted the






-3-


experimental fact that the most effective salts studied to that time were

the trivalent iron and aluminum ions.

It is interesting to observe that-the choice of iron (III) and

aluminum salts as coagulants was not based on predicted efficiency as

colloidal destabilizers-but rather on attempts to chemically duplicate

the slimy, gelatinous organic "schmutzdecke" that coated and significantly

increased the efficiency of the slow sand filters that were in use at the

time. The initial motivation was therefore to produce a coating on the

rapid sand filters and not to agglomerate and settle the particles ahead

of filtration, which is the process that has evolved from the early

practice.

Sante Mattson, a soil chemist, was the first to point out in 1922

and again in 192811 that the hydrolysis products of iron and aluminum

were more important than the trivalent ions themselves. He attributed

maximum charge neutralization to the maximum formation of electropositive

colloidal oxychlorides of iron (III) and aluminum. This approach laly

dormant for over 25 years before it was accorded its proper position of

importance in coagulation chemistry.

The Schultze-Hardy explanation was supported by Thierault and

Clarkl2 and Miller 1316 in the interesting series of papers issued from

the United States Public Health Service Laboratories in Cincinnati, Ohio,

during the period 1923-25 in which the precipitates of aluminum and iron

(III) hydroxides were carefully analyzed at various pH's. These authors

further emphasized the complex nature and the importance of the anions

present in determining the composition of the precipitates.










In 1923, Thomas and Friedenly proposed the "solution link" theory
18
to explain the stability of iron (III) oxide sols, see Sorum.
19-21
Black and co-workers 21 in the period 1933-34, conducted a series

of studies on the effect of pH and various anions on the time of floe

formation and referred to the Schultze-Hardy effect as important in

colloidal destabilization.

For the next few years, the principal research emphasis in water

treatment was on mechanical methods of producing better flos22 and a
23
search for better coagulant aids. Among these evaluated were bentonite,23

silicates,24 and limestone.25 During this time no new data were presented

nor theories proposed to further the understanding of coagulation itself.

The paper of Langelier and Ludwig26 in 1949 entitled "The Mecha-

nism of Flocculation in the Clarification of Turbid Waters" introduced

many of the concepts of colloidal destabilization that are accepted today.

They compared hydrolyzing and non-hydrolyzing coagulants and proposed that

the much greater efficiency of the hydrolyzing coagulants could be

attributed to the formation of a flocculant precipitate composed of the

hydrolysis products of the metal ion.

They distinguished two mechanisms for the removal of colloidal

impurities; (a) perikinetic coagulation -- the compression of the double

layer to a low enough level to allow the particles to overcome the repul-

sive forces of like charges and thus agglomerate and precipitate, and (b)

orthokinetic coagulation -- a filtering action whereby small particles

are physically enmeshed by larger flocculant particles. These two mecha-










by LaMer and Healy 27 who proposed the terms "coagulation" and "floccu-

lation." Coagulation follows the same mechanism as the perikinetic

coagulation of Langeleir and Ludwig whereas flocculation is similar to

orthokinetic coagulation with the exact mechanism modified to involve a

bridgingaction by adsorption.of long-chain polymeric materials on the

colloidal particles.

A series of articles by Pokras2 in 1956 discussed the properties

of polyvalent cations in considerable detail. Whereas no discussion of

mechanisms of coagulation is included, the discussions of the chemical

properties of the hydrolysis products of cations leads to an appreciation

of the importance of the chemical factors involved in coagulation and

flocculation with hydrolyzable metal salts.

A significant step in the development of a comprehensive theory

of coagulation was the introduction of microelectrophoresis to the study

of colloidal destabilization in systems of concern to the chemist by

Black and his co-workers. The first paper was published in 1958 and the

series now includes over 20 papers. Representative examples are refer-

ences 29-33. These pointed out the effect of chemical factors such as

pH, ionic environment and the properties of the contaminant to be removed

on the charge of the colloidal particle. The direct result of this

approach was a reemphasis of the importance of hydrolysis products, as

originally proposed by Mattson. This has resulted in widespread accep-

tance of microelectrophoresis as a method of measuring the effect of

coagulation parameters and, more important to this discussion, an even






-6


mechanisms on the formation of specific hydrolysis products. In most of

the studies reported in this series, the conditions for optimum destabil-

ization and removal of colloidal impurities coincided closely with the

conditions required to produce a neutral system. These data generally

substantiate the physical mechanism of' destabilization of colloids by

neutralization of the negative charge on the colloidal particles followed

by agglomeration to particles of adequate size for precipitation.

These papers also presented some anomalies that were only explained

on the basis of specific interactions with hydrolysis products.

Two papers in 1962 by Mackrle34 and by Stumm and Morgan35 pointed

out that the concentration of the simple trivalent iron (III) or alumi-

num ions is very low in the pH range of interest in coagulation. They

further emphasized the importance of the hydrolysis products in coagula-

tion. Stumm and Morgan focused attention on the chemical factors that

should be considered in coagulation mechanisms. They presented alka-

limetric titration curves that showed the interaction of iron (III) and

aluminum ions with various anions and listed various equilibria,together

with available constants, that could be involved in coagulation reactions.

The first paper to show a stoichiometric relationship in coagula-

tion was by Black and co-workers36 in 1963, in which it was shown that

the optimum conditions for the coagulation of the organic, color-causing

compounds in natural colored waters could be accurately predicted from a

property of the raw water itself, the color. This led to renewed interest

in the search for stoichiometry of reactions in water treatment and con-

firmed the importance of chemical factors.










A paper by Hall and Packham in 1965,7 dealing with the coagula-

tion of organic color with hydrolyzing coagulants, proposes a mechanism

purely chemical in nature. The data presented are explained by a mecha-

nism involving the direct interaction of the anionic color particles with

cationic hydrolysis products of iron (III) and aluminum to precipitate

basic humates and fulvates (the two fractions obtained in analysis of

organic color are arbitrarily called the humic and fulvic acid fractions.)

A continuation of the previous studies on stoichiometry of color

removal using iron CtX) sulfate by Singley and co-workers in 196538

further emphasized the importance of specific hydrolysis products. It

was shown that the simple attainment of zero mobility was not adequate

for efficient color-iron interaction. In fact, it was pointed out that

optimum coagulation conditions were infrequently the conditions that

corresponded to production of zero charge on the color floe resulting

from coagulation. It had been customary in the literature up to this

time to overlook the fact that although the optimum conditions were close

to those producing zero mobility, they were almost never those producing

exactly zero. The majority of the data showed optimum color removal at

slightly negative mobilities. Certainly, it would be difficult to

resolve these anomalies utilizing a purely physical model for the coagu-

lation mechanism as it seems axiomatic that this model would require

optimum coagulation when the particles were neutral and the repulsive

forces at a minimum.

A paper by Packham39 in 1963 presented an ancient, simplified

mechanism, that of a'"sweep" action by the gelatinous metal hydroxides










whereby the colloidal impurities, in this case turbidity, would be

physically enmeshed as the flocculated mass settled.

Quantitative Mechanisms


The requirement that unambiguous mechanisms for the coagulation i

various dispersed impurities in water treatment incorporate chemical

effects becomes obvious when the data cited above are carefully consider:

Particularly important are the data showing the stoichiometric relation

ship between iron (III) and organic color36 and the data showing that t

quantities of iron (III) and aluminum required for destabilization of

color colloids are not stoichiometrically equivalent. This is shown in

Figure 1, as recalculated and replotted from reference 36, Figure 16.

Further, the pH dependence of coagulation strongly indicates that it is

the existence of a specific hydrolysis product that causes a specific

interaction to take place, resulting in removal of the impurity and

simultaneous precipitation of the metal ions. The fact that the optimum

pH for the destabilization of organic color colloids by iron (III) is

between 3.5 and 4.0 and that of aluminum is between 4.5 and 5.536 fourth

indicates the chemical nature of the coagulant-colloid interaction.

Polyelectrolytes were shown to be relatively ineffective in de-

stabilizing color colloids when used in conjunction with iron (III) sul

fate, although they were effective in neutralizing the charge.3 It wa

further observed by Singley, et. al. in the same paper that there were

two pH values at which the mobility was zero and yet effective destabil













120

10 Initial Color 446



100- Fe





80-

\


fl














ows the approximate stoich


lets per liter of the color solids was calculated from the data given
40
by Black and Christman, (Figure 2) showing total organic content as a

function of color value, and the average equivalent weight of the fulvi

acid fraction. The minimum dosage of iron (III) sulfate as a function
36 -
of color value was taken from Black, et al.,3 Figure 13. It is intere

ing to note that the number of equivalents of the two substances are of

the same order of magnitude and, in fact, coincide rather closely over

the entire range studied.

Stumm and Morgan35 presented titrimetric curves that demonstrate

the interaction of aluminum ions and various anions to form aluminum

complexes. They pointed out that similar reactions would occur for irc

(III) and further emphasized the importance of the formation of such cc

plexes in coagulation chemistry.

The development of comprehensive, quantitative mechanisms of

coagulation by hydrolyzing metal coagulants depends upon the availabili

of reasonable values for the extent of reaction between competing ligar

for the coordination sites on the metal ions in the very dilute solutic

that are normally encountered in water purification. The data required

are the equilibrium constants or concentration quotients for the variot

reactions that may take place in the time available for the treatment
---- tm.. -. 1k11 +V>^. l 1ha iAnw+4-,4 +4 t h +V e-nanv caS +hV+ Tnnil





S11 -


400










200 Color solids




100 -

Iron (III) sulfate dosage
required to coagulate
0 I I I I
0 0.02 0.04 0.06 0.08 0.3
Meqs per Liter

Fig. 2 Approximate Stoichiometry of Color-Iron (III) Interaction.





predominate under a given set of conditions. These data, along with a

knowledge of the properties of the contaminant to be removed, would allow

formulation of a consistent coagulation mechanism.


Object of Study


The overall object, of which this study is a part, is to answer

the basic question "What are the predominant species of iron (III) present

under the conditions applying in water treatment processes?"

The object of the study to be reported here was concerned with the

hydrolysis of iron (III) in dilute aqueous solution, in the absence of

completing ligands other than perchlorate and hydroxide. Experimentally,

this involved the determination of instantaneous activity quotients in

solutions ranging in iron (III) concentration from 10"3 to 10-5 molar,

the extremes of the concentration used in color and turbidity removal,

respectively.

The concentrations of specific hydrolysis species could then be

calculated at various pH's and total iron (III) concentrations.












II. ACIDITY OF IRON (III) IN AQUEOUS SOLUTION


Qualitative Relationships

It is well known that metallic cations are hydrated in aqueous
solution, with the number of water molecules coordinated to each metal

ion a function of such factors as the ionic potential, i.e. charge to

radius ratio, and steric relationships. By analogy with other iron (III)

complexes it is assumed that six water molecules are coordinately bound

to each iron (III) in the "inner sphere"88 to produce a hexaaquoiron (III)

octahedral complex ion. The acidity exhibited by this complex in aqueous

solution may be explained by the Bronsted definition of an acid as a pro-

ton donor,83 by the equations:

Fe(H20)6 H H20 7 Fe(H20)50H2 + H30 ()

Fe(H20)50H2 + H20 = Fe(H20) (OHR)2 H 0 (2)


Fe(H20)4(OH) H20 H Fe(H20)3(OH)3 + H? (3)

Fe(H20)3(OH) + H20 Fe(H2O)2(OH) H+ O (4)

where the increased acidity of the water molecules attached to the iron

(III) ion compared to the very weakly acidic solvent water molecules may

be explained on the basis of the repulsion of the protons by the positive

charge on the metal ion or by the distortion of the electron distribution

of the water molecule toward the more electrophilic metal ion and


- 13 -






'1 1.


subsequent weakening of the hydrogen-oxygen bond. Phenomenologically

these are equivalent.

The tendency of a coordinately bound water to donate a proton will

be influenced by the environment. The pH then will be an important fac-

tor in determining the species of hydroxylated aquo iron (III) ions that

will be present.

It is obvious that an isolated charged entity cannot exist in solu-

tion as the charge will -be neutralized by such oppositely charged species

as are available in the immediate vicinity. In the cas.eof the positively

charged iron (III) species shown in reactions (1) and (2), the required

negative charge could be provided by the negative end of the abundant

water dipoles or by the negative ions that were added with the iron (III)

ions. Depending upon how closely these are bound to the iron complex,

additional positively charged entities may be closely associated with the

complex. Since there is no convenient method of differentiating between

unbound ions or solvent species and those bound in the complex, the

general formula for such a complex normally neglects these species. As

an example, the addition of iron (III) perchlorate to water containing

Na ions would produce complexes of the general form


CFep(H20)q(OH)r(C104) (Na)t (3p-q-rFt)

which is usually simplified to

F(ep(oH) (3p-r)

Another factor that must be considered is the tendency for the

simple hydrolysis products to polymerize to yield polynuclear complexes.





- 15 -


41
This was first discussed by Bjerrum for the formation of the dimer

Fe2(H20)8(OH)2 by the reaction


2Fe(H20)5OH2- Fe (H 0)8(OH)4 + 2H 0 (5)

Thomas and co-workers8485 discussed in detail the formation of

polymeric sols with hydroxide bridges first being formed between metal

ions, a reaction termed "olation," followed by further loss of protons

at higher pH's to produce irreversible M-O-M bonds by "oxolation"

reactions.

The structure for the dimer Fe2(H20)8(OH)2 shown in Figure 3,
86
was proposed by Mulay in 1961, supports this mechanism.

The existence of such a dimer was also supported by the spectre-
81
photometric equilibrium studies of Mulay and Selwood, Milburn and

Vosburgh,5 and Milburn.57 In addition, the potentiometric equilibrium

studies of Hedstrom53 compared the structure to that of the dimeric solid

phenanthroline complex of Gaines, et al.89

Further olation and oxolation reactions could be predicted to lead
to the formation of insoluble long chain polymers. This process can be

accelerated by increasing the pH, aging the solution, or increasing the

temperature. It was shown by Lengweiler, Buser and Feitknecht87 in 1961

that essentially all of the Fe (III) could be removed from dilute, aged

solutions in the pH range from 5 to 10 by ultracentrifugation at 93,000 G

for 180 minutes. The average size of the Fe(OH)3 particles was estimated

to be 100 Ao and was shown to vary with pH and age of the solution. This

indicated polymerization had taken place.

The number of possible complexes of the general form(Fep(OH)3pq)+










SyH




F ; Fe Fe -
\ I \



H H H



Fig. 3 Structure of the Dimer Fe2(H20)(OH)24+. After Mula86


- *1









is very large. The problem of determining the concentration of each

species and the constants for the various steps in its formation is

obviously a formidable one. Several simplifications have been suggested

for treatment of data relating to the specific species present. The

nost useful has been the "core and links" structure proposed by Sillen
90
and co-workers.9 The polymers are represented by the general formula

(Me(OH )te)n

with t an integral constant indicating the number of hydroxides in a link,

and n an integer. indicating the number of links in the complex. For

iron (III) their titrimetric data was explained using the formula

(Fe(OH)2)nFe3+n with n = 1 for the principal species present.
15
The work by Miller showed the complexity of the precipitate

formed from iron (III) sulfate and the competition between OH- and SO20

Lons. The precipitate formed below pH 7.5 contained sulfate ion, with

the amount decreasing with increasing hydroxide ion concentration. Sykes9

explained the spectrophotometric data of Olsen and Simonso47 on the basis

)f association of perchlorateion withiron (III). This interaction had

been suggested previously by Sutton.50

This type of reaction would certainly be expected on purely sta-

tistical grounds as the positive charge residing on the hydrated iron (III)

complex ion could be satisfied by any negative ion present in sufficient

concentration to compete for positions in the crystal lattice being

formed. The ratio of the anions in the product will depend upon their

mucleophilicity as well as their concentration.





nQ


Quantitative Relationships


Historical

The development of a quantitative understanding of chemical

equilibria was initiated by the independent expression of the classical

"Law of Mass Action" by Guldberg and Waage92 and van't Hoff93 in the

late 1870's. They related the rates of both the forward and reverse

.reactions with the "active masses" of the reactants and products. In

both cases their research efforts were concerned with heterogenous

equilibria and it was not until the studies of Ostwald' in 1889 that

the concept was used to explain ionic equilibria in aqueous solution.

He utilized the "Law of Mass Action" and Arrhenius' electrolyte disso-

ciation theory to calculate the first ionization constants for a series

of organic acids.

The first application to the calculation of stability constants

of complex ions was by Morse95 in 1902 who determined the first two con

stants for the mercury (II)-chloride ion system and by Bodlander and

co-workers 7 for many complex systems.

The methods currently used for the interpretation of equilibrium

data for systems in which several complex species coexist have been

developed by the Swedish school under Niels Bjerrum. His early work on

the chromium (III) thiocyanate system98 accomplished the determination

of stability constants for six separate species. This was made possibi

by the unique inertness of the individual species which allowed the

direct analytical determination of their respective concentrations.





- 10


of determining the concentration of the species that do not disturb the

position of the equilibrium have been utilized. These are usually based
on physical measurements, such as spectrophotometry, potentiometry,
magnetic susceptibility, and conductivity.

Hydrolysis Reactions and Equilibrium Constants

The hydrolysis of iron (III) can be represented by a series of

-reactions as shown in Table 1. This is a simplified representation with

the coordinated water molecules not shown. The mathematical relationship

between the concentrations of the reactants and products for the first

step in the hydrolysis

Fe3 + H20 FeOH2+ +

may be expressed as an acidity constant

k, = AFeOH 2- AH+/A^Fe3. = [Fe(7 H+ fFe0H+ fH+=
SFe Fe3* fFe3

fFeOH3+ fH
k, (6)
k Fe-

where k0 is the thermodynamic acidity or stability constant, A is the

activity of the species x, [x)is the analytical concentration of the

species x, fx is the activity coefficient of x, and k1 is the stoich-

iometric or concentration equilibrium constant.

This reaction is sometimes shown as the formation of the hydroxo

complex according to the following:

Fe3 + OH" FeCH2*





Equation Number Equiliorium

1 Fe3+ + H20 = Fe(OH)2+ + H+

2 Fe3+ + 2H 20 Fe(OH)2+ + 2e+

3 Fe3+ + 3H20 = Fe(OH) (s) + 3H+


4 Fe3+ + 4H20 = Fe(OH)4" + 4H+


5 2Fe3' + 2H20 4 Fe (OH)24 + 2H+


6 2Fe3 + 3H20 Fe2 OH) 3++ 3H+


7 2Fe3+ + 5H20 = Fe (OH)5 + 5H+


8 3Fe3+ + 2H20 = Fe (OH)27+ + 2H+


9 3Fe3+ + 4H20 = Fe (OH)45+ 4H+
3






- 21 -


On the other hand, Yatsimurskii and Vail'tev0 prefer the use of
an instability constant defined in terms of concentrations as

K = [Fe3] [OHi / FeOH2 for the reaction as
written
Fe0H:2 Fe3 + OH"
For the second step in the hydrolysis, the reaction may be shown
as FeOH2 + H20 Fe(OH)2 + H+

with the equilibrium constant.

k2 =AFe(OH)2+ A+/I e A+ = k2 fFe(OH)2+ fH (7)
-FeOH2+
where k2 and k2 are the respective stepwise or successive acidity
constants.1
The overall reaction may be shown as
Fe3 + 2H20 Fe(OH)2+ + 2H+

with the cumulative or overall thermodynamic acidity constant defined
by o
K2 = AFe(OH)2+ A2 = k 0 (8)
2 H+/AFe3+ kk2 (8)


The equilibrium constant for the formation of a polynuclear
complex by a reaction such as

2F3+ + 2H20 Fe2(OH)24+ + 2H+

can be expressed as

K22= AFe(OH) 24+ AH+/AFe3+ (9)






- 22


The majority of the values of the equilibrium constants given

in the current literature are for stoichiometric constants in a defined

medium of high ionic strength. Occasionally these have been corrected

by extrapolation to zero ionic strength, where the activity coefficient

is equal to one, or corrected to zero-ionic strength by the application

of some empirical relationship. .This point will be discussed later.

Table 2 lists values for stoichiometric acidity constants for

the reactions in Table 1. They have all been converted from the values

given in the original references to the same basis, and are given in

terms of the cumulative or overall constants. Many more values are

given by Sillen and Martell102 and by Yatsimirskii and Vasil'ev100 in

their respective compilations of the formation constants of complex

compounds.





- 23 -


Table 2
Acidity Constants of Hydroxy Complexes of Iron (III)


Reaction Ionic References
Number- Technique Temp. C Strength pK (Year)

1 cond. -- .002-.0003 2.61 41 (1907)
kin.4 25 0(corr)5 1.74 42 (1928)
pot.6 25 O(extr)7 2.22 43 (1934)
pot. 25 O(corr) 2.46 44 (1938)
pot.&kin. 25 O(corr) 1.96 45 (1944)
pot. 25 .53(KNO )8 2.76 46 (1941)
sp. 25 ,046(c104") 2.25 47 (1949)
pot. 25 various SO04 2.90 48 (1951)
sp. 25 O(extr) 2.19 49 (1951)
sp. 25 O(corr) 1.3 50 (1952)
pot. 15 .5(NaClO4) 2.93 51 (1954)
sp. 25 .5(NaClO4) 2.80 52 (1954)
pot. 25 3(NaC104) 3.05 53 (1953)
pot.&cond. 25 --- 2.83 54 (1953)
sp. 25 3(NaC1O4) 2.89 55 (1955)
25 0(extr) 2.17 55
sp. 15 .5(NaC1l0) 2.93 56 (1956)
35 .5(NaClO4) 2.49 56
sp. 25 1(NaC1O4) 2.78 57 (1957)
25 O(corr) 2.17 57
mag.susc. 20 3(NaC104) 3.0 58 (1957)
sp.&pot. 15 .01(NaC10) 2.81 59 (1957)






- 24


Table 2 Continued


Reactin Ionic References
Number Technique Temp. C Strength pK2 (Year)


pot.
sp.
pot.
sp.&pot.


pot.
pot.
pot&cond.
mag.susc.
pot.
pot.&cond.


thermodyll
pot.
pot.
pot.
pot.
12
lit.12
pot.&sol.13
pot.
pot.
pot.
pot.
sol.
pot.
pot.
thermody.


20
20
25
21


l(NaC10 )
0(corr)
3(NaClO4)
.1(KNO3)


O(corr)
3(NaClO0)
dilute
3(NaC104)
1(NaC104)
3(NaC104)


dilute
various
various
various
O(corr)

O(corr)
dilute
various
various
O(corr)
various
O(corr)
3(NaCl04)
0(corr)


S (amorphous)14


2.74
2.30
3.05
2.63


7.16
6.31
7.42
6.3
6.05
6.31


6.04

4
4.3
5.5
4.3
to 2.8
3.4
5.65
5
6.5
4.5
4.6
6.54
3.3
2.57
5


(1959)
(1960)
(1962)
(1963)


(1938)
(1953)
(1953)
(1957)
(1959)
(1962)


64 (1908)

65 (1924)
66 (1925
67 (1933)
68 (1937)


(1938)
(1943)
(1949)
(1950)
(1951)
(1956)
(1957)
(1958)
(1961)


I






- 25 -


Table 2 Continued


Reacti n Ionic References
Number1 Technique Temp. OC Strength pK (Year)


20
25
25


20


( -Fe20 )a
( -FeOOH)1
3(NaC104)
0(corr)
3(NaclO4)


3(NaC104)


3(NaC104)
3(NaC104)

it


0(extr)
l(NaC0l4)
0(extr)
3(NaCl0 )
l(Naclok)
3(NaC104)
3(NaC104)


3(NaC104)


50.5
-2.0
7
-0.7
3.55

18.015


2.91


2.31
22.17
2.58
::2r88
.2'.72
2.85
:2?0
2.85
2.96
1.17


5.77 62 (1962)


1Reaction numbered from Table 1.

2pK = -log K, calculation from literature values shown in
Appendix I.
3
Conductivity.

Kinetics.


sol.
thermody.
pot.


sol.


77 (1961)
77
78 (1961)
79 (1963)
80 (1963)


78 (1961)


53 (1953)
81 (1955)
81
81
55 (1955)
55
57 (1957)
57
58 (1957)
60 (1959)
62 (1962)
82 (1961)


pot.
mag.susc.
mag.susc.
sp.
sp.
sp.
sp.
sp.
mag.susc.
pot.
pot.
sp.


pot.






- 26 -


TaoD.e LUonUlnua.



Corrected to zero.

6Potentiometry.

Extrapolated to zero.

Concentration of salt indicated.

Spectrophotometry.

l0agnetic susceptibility.

11Calculated thermodynamically.
12
Calculated from values in the literature.

13Solubility.
14
14Constant determined for this structure.

15Calculated using pK = 14.0, pKp = 42.5.
w sI,





Ionic Strength Effects


;orical Development

The effect of the ionic environment on equilibria was recogr

narly as 1902 by Bodlander and co-workers 96'97 who used a const,

.c medium in their studies of metal complexes, but it was not uz
103
5 that Grossman first published a paper discussing an experir

Lgn whereby the potassium ion concentration was kept constant ii

iy of mercury (II)-thiocyanate complexes. Other studies in the

Lod up to 1921 showed the effect of different electrolytes on e(

La. Lewis and Randall104 introduced the term "ionic strength" i

b year and qualitatively state that the activity coefficient of

)ng electrolyte in dilute solution should be the same at the sai

Lc strength regardless of the specific ions present. They deve:

empirical relationship between ionic strength and activity coef:


on the distribution of nharred ions in solu






28 -


limiting law (DHLL) can be expressed for aqueous solution at 250C as

-log fi = 0.509Z 2 V (10)

where fi is the activity coefficient of the ion with charge Zi and p

is the ionic strength, which is defined in terms of the concentration,

Ci, of ion i as
= C 2 (11)

The DHLL is generally considered to be a good approximation for ionic

strength less than 0.01. For solutions with 0.01<(.<0.1 the extended

Debye-Huckel equation (EDHE) is frequently used. It can be expressed

as
-log f = 0.509Zi V + 2 l (12)

At.ionic strengths above 0.1 the problem becomes increasingly difficult

and attempts to determine the effect of ionic strength on activity

coefficients have resulted in many empirical relationships. These in-

volve multiple-termed equations containing parameters such as the hydra-
106
tion numbers of Stokes and Robinson, the effect on dielectric con-

stant of Huckel.107 Diamond08 considered various ion-ion, ion-water

and water-water interactions.


Quantitative Effect of Ionic Strength on Equilibrium Constants

The thermodynamic or activity equilibrium constant, shown as Ko

or k in (6), (7), (8), and (9) above, is not affected by ionic strength.

The activities used in the calculations include this effect, as the

activity, ai, of an ion is defined by

Ai = Ci f (13)






- 29 -


or in terms of equilibrium concentrations


A = (ijfi ()

However, it is usually operationally difficult or impossible to measure

directly the activities or activity coefficients of many species so that

stoichiometric constants are usually calculated from the available

equilibrium concentration data. One common exception to this.is the

hydrogen ion activity, which can be determined potentiometrically.

Since the stoichiometric constant is subject to ionic strength

effects, the medium must be specified and quantitative comparisons be-

tween such constants made only in cases where they are determined under

the same conditions. Because of this disadvantage it is usually'

desirable to calculate thermodynamic constants. This can be done in

one of two ways: (1) calculate the activity coefficients using some

form of the Debye-Huckel equation, or (2) determine the stoichiometric

constant at several ionic strengths and extrapolate to zero ionic

strength. The first approach is useful only at ionic strengths up to

a maximum of 0.01 using the DHLL. The theoretical basis for the extra-

polation to zero ionic strength as in the second approach above, can be

shown by considering equations (1), (11) and (12). As the total con-

centration of the electrolytes approaches zero, P approaches zero and

fi approaches one. When the activity coefficient equals one, the
activity is identical with the stoichiometric concentration according to

(14) and the stoichiometric equilibrium constant is identical with the

thermodynamic constant. This approach has been used frequently but






- 30 -


suffers the serious disadvantage that it is too frequently not even a

good approximation. Stokes and Robinson106 showed that the effect of

concentration on the activity coefficients of the alkali metal and

alkaline earth metal halides not only was not linear but varied for each

salt and went through a minimum. The 'concentrations used were relatively

high, ranging from 0.3 2.0 molar. These results cast doubt on the use

of this method for the determination of thermodynamic constants. The
109
data of Day and Powers on the effect of ionic strength on the complex

formation of the UO2F ion show that the equilibrium constant goes

through a minimum as the ionic strength is decreased. This is shown in

Figure 4. The nonlinearity of the relationship between ionic strength

and equilibrium constant was shown by Milburn and Vosburgh5 for the

first acidity constant of iron (III) as

pK1 = 2.172 + 2.04 VF /(1 + 2.4 F/ ) + 0.01 O
where the equation was derived by extrapolation to zero ionic strength.

The theoretical application of the EDHE to Equation 1, Table 1,

would be as follows. The expression for the thermodynamic acidity con-

stant in terms of concentrations and activity coefficients as shown in

(6) is
o f FeOH2+ f
K1 = K1 (6)
f Fe3+
fFe

taking the logarithm of (6)

log K = log K1 + log fFeOH2+ + log fH+ log Fe3+

and defining pK = -log K

pK = pKo + log f'eOE+2 + log fH+ log fFe3+




















60



50



40



S30o



20 I I I I
0 0.20 0.40 0.60 0.80 1.00
Ionic Strength

Fig. 4 Effect of Ionic Strength on Formation Constant of the U02F Ion






- 32 -


by substituting equation (12)

pK = pK- (2.036 I- + 0.059 rV 4.581 lV )/(1 + V )

pK = pKo + 2.04 /l/(l + P )

which is similar to the relationship found by Milburn and Vosburgh55

above. It was pointed out by Rossetti and Rossetti (reference 99, p.

35) that values for the thermodynamic constant "obtained by extrapola-

tion to infinite dilution are more reliable than values calculated from

measurements at a single ionic strength, for they are less dependent on

the choice of parameters in equations for activity coefficients. How-

ever, unless measurements are made in very dilute solution, the extrapo-

lation method cannot give thermodynamic constants which are entirely

independent of assumptions about activity coefficients."


Attempts to Control Activity Coefficients

The method used by Bjerrum and co-workers and in almost all other

recent studies of complex equilibria to minimize the variation in
110
activity coefficients is based upon the work of Bronsted in 1927.

In this study it was shown that only negligible changes occurred in the

activity coefficients of a solute when the concentration of the solute

was small compared to the concentration of a "background" or "swamping"

inert electrolyte. This "background" electrolyte approach was also used
111
by Bjerrum in 1941 and by his co-workers since that time. The

rationale for their choice of this technique was discussed in detail by
111 112 90
Bjerrum, Biedermann and Sillen, Heitanen and Sillen, and

Sillen.113 The procedure generally involves maintaining the total






- 33 -


concentration of the electrolyte at some high level, usually three molar.

in sodium perchlorate, while changing the concentration of the cation

and the completing anion. Theoretically, such a large excess of electro-

lyte should keep the activity coefficients of the reacting cation and

anion constant. Small changes in the concentration of the cation and

anion resulting from complexation do not change the overall ionic

strength enough to change the activity coefficients.

This procedure has been very useful in the determination of com-

plex formation constants of various metals and ligands. These constants

are useful in the comparison of the stabilities of a series of metals or

ligands under a standard set of conditions.

The background electrolyte must, of course, be inert to the

reactants or products of interest but with this limitation the technique

has produced useful information.


Application to Dilute Solutions

Several serious disadvantages are apparent when attempts are made

to apply such values to the conditions of interest in dilute solutions.

First, the concentration constants so obtained cannot be extrapo-

lated to the dilute medium of concern in water treatment or even to zero

ionic strength to obtain thermodynamic constants. This point has been

discussed above.

Second, the assumption that the activity coefficients do not

change may not be valid since in the hydrolysis of metals generally,

and iron (III) specifically, the series of hydroxy complexes have










charges that may vary from s6me relatively large positive value for some

of the polymers to a negative value for the anionic complexes at high

pH. Since the activity coefficient of an ion is a function of the square

of the charge on the.ion, the activity coefficient will vary as the

charge varies, even at constant ionic strength.

Third, Sykes91 and Sutton5 have shown that the spectral proper-

ties of iron (III) in the presence of perchlorate ions may be explained

on the basis of the formation of iron (III) perchlorate complexes. This

would lead to the determination of erroneous equilibrium constants with

the error increasing as the perchlorate ion concentration increases.

Table 2 shows that most of the values for the acidity constants

of iron (III) have been determined in the presence of relatively high

concentrations of sodium perchlorate. In most of the examples showing

correction or extrapolation to zero ionic strength, the system studied

included a relatively high concentration of perchlorate ion.

In the light of the above factors, then, it should be obvious

that the equilibrium constants available in the literature may not be

useful in the characterization of the systems of concern in water treat-

ment processes.


Effect of Concentration


An additional factor that may adversely affect the application of

the literature values to the study of coagulation mechanisms is the

difference in the concentration ranges used in the studies reported and

the concentration range used in water treatment processes. The maximum






- 35 -


concentration of iron (III) used in the coagulation of organic color-

causing compounds is about 2.5 x 104 moles per liter6 with the mini-

mum used in turbidity removal about 1 x.10-5 moles per liter. In con-

trast the minimum concentration used in the studies of equilibrium con-

stants reported in the literature was'4 x 10-2 moles per liter.81 The

ratio of the minimum studied and the maximum needed is 160:1. It is not

unreasonable to expect that such a great difference may engender gross

errors in extrapolation to the much more dilute solutions of interest

in this study.


Kinetic Factors


Equilibrium Constants Versus Concentration Quotients

It is important to remember that equilibrium formation or acidity

constants are useful for comparing stabilities of various species at

equilibrium but may not be useful for predicting the measurable change

in a reasonable period of time. For example, on the basis of the equi-

librium constant alone one would predict that the addition of excess

acid to Co(en)3+ would give Co(H 0) + quantitatively according to the

equation

Co(en)33 + 6H+* Co(H20)x3 + 3 H2(en)2+; pK230

Analysis of the reaction mixture after one month at room temperature

showed that less than one percent of the reaction product was produced.114

Stumm15 has pointed out that hydrolysis equilibria are generally

very fast for the formation of simple hydrolysis species but are fre-

quently very slow for the formation of polynuclear complexes. The data










wnicn olumm presenTea ior iron 111.. snow unar. ne rate or nyaroysis

increased as the pH was increased but analogy with data for the

hydrolysis of cadmium by Fei necht and Reinmanll6 and zirconium by

Lister and McDonald117 would indicate thattthe attainment of equilibrium

would be very slowly This concept is substantiated by the well known

behavior of solutions of iron (III) salts. Solutions of iron (III)

chloride, sulfate, nitrate or perchlorate, that are clear when prepared,

become turbid within a few days or weeks, depending upon the pH and con-

centration of the salt, and eventually form the characteristic, red-

brown, gelatinous precipitate of polymeric iron (III) hydroxo complexes.11

In order to determine "equilibrium constants" most investigators

have aged the metal ion solutions for varying periods of time, up to

several months, before reaching equilibrium. The values so obtained may

approximate true "equilibrium constants" but such values are of little

interest in the formulation of coagulation mechanisms, as the maximum

reaction time in coagulation processes is believed to be of the order of

a few minutes or less, with an absolute maximum of an hour or so. The

values needed, then, could more correctly be termed instantaneous con-

centration quotients.


Ligand Exchange Rates

One other factor that should be considered is the rate of ex-

change of ligands by the hydrolysis products of iron (III) as compared

to the rate of hydrolysis of iron (III). This is particularly important

in the formulation of coagulation mechanisms based on chemical inter-
j _*-4 k-1 2 A-, - _-1 .tA 1 _ L -L 1 _- - 1 *


- .?U -










color-causing compounds with hydrolyzing coagulants is controlled by the

reaction that occurs within the first few minutes. The exchange of the

reactive ligands for water molecules or hydroxy groups occurs much more

rapidly than the polymerization reaction and is controlled by the con-

ditions that exist at the time of initial contact between the colored

ligands and the metal ions. This was pointed out by Black, et al.36 in

the paper that also pointed out the stoichiometric relationship between

the color and the iron (III) sulfate required to react with it.

Stumm and Leel9 emphasized that the inclusion of mineral anions

in iron (III) hydroxide precipitates could be attributed to ligand

exchange reactions.

Day and Selbin120 state that the Fe(H20)3+ ion is labile and

Rxchanyn itqs i+ anris ranil-v-


- 17 -






















aing the calculation of instantaneous concentration quotients.

The concentration of iron (III) should be within the range

5t in water treatment processes.



















Any property of-the system that changes as a result of the

formation of a complex or a series of complexes may be used as a measure

of the extent of complex formation. It is particularly fortuitous if

the property varies with the concentration of one of the species in-

volved in the reaction. Such is the case with the hydrogen ion concen-

tration in the hydrolysis of. iron (III) as was shown in equations (1),

(2), (3) and (4). The situation is complicated somewhat by the fact

that each reaction postulated involves hydrogen ions.

The glass electrode has simplified the determination of the

hydrogen ion concentration. Its use has been discussed in many mono-
121
graphs and in detail in the book by Bates. Activity of hydrogen ions

can be measured with an accuracy of 0.02 pH unit by the use of the glass
122
electrode versus a saturated calomel electrode.122 The "practical pH"

measured may be defined as follows:

E -E
practical pH = -log AH+ = pHs + s
2.3RT/F

where AH+ is the activity of the hydrogen ion

pHs is the pH of the buffer solution used to standardize the pH

meter

7n A L 1- .-


~WVL~YVII LY


SrN






- 40 -


cir


F is the Faraday in appropriate units

A knowledge of the value of the activity

calculation of the hydrogen ion concentrate


pH = -log AH+ = -log CHf

Only in very dilute solution is fH+ = 1

options must be made concerning the effect

greatly affect the value of f. For this

:eep the ionic strength as low as possible.

of the standard equations for the calculate

cts gives essentially the same results.

The use of potentiometry in the study c

;s where the hydrogen ion is involved in tk

.owing advantages:

1. Simplicity.

2. Accurate measurements of the active

pH range 2-11.

3. Does not require any assumptions at

;ies present. Such assumptions are necessz

,ometry, conductivity or magnetic susceptil






- 41


ability of the data available in the literature, the study reported

here was conducted under conditions as closely approximating those

used in water treatment as possible. Information gained as a result of

the survey of the literature values served as a guide for the research.

Concentration range. The maximum concentration of iron (III)

normally used in the treatment of water for municipal use occurs for

the removal of organic, color-causing compounds and may be as high as
-4,
2.5 x 10 molar. On the other hand, the minimum concentration required

occurs in the treatment of turbid waters and may be as low as 1 x 10-5

molar. For this reason it was decided that the concentration range to

be studied should include these maximum and minimum concentrations. The

range chosen was from 1 x lO5 to 1 x lO-3 molar.

pH range. The pH values of interest in the treatment of natural

waters range from a low of about 3.5 in the coagulation of organic,

color-causing compounds to a high of 9 to 10 in stabilized waters after

treatment. For this reason the range chosen was generally from 3.5 to

10, although there were slight experimental deviations.

Perchlorate ion concentration. Although perchlorate ion has been

shown to complex with iron (III), it was necessary to use the perchlorate

salt of iron (III) in this study as any other anion chosen would have

completed even more strongly with the iron (III) in solution. In the










preparation of the iron (III) perchlorate some excess perchloric acid

was left in the sample. The amount involved was not considered great

enough to affect the results. The following calculation was made to

determine the extent of association:
<-3
In the 1 x 10"3 molar Fe(ClO)' solutions the association should

be at a maximum as this solution is the most concentrated in iron (III)

and perchlorate ions. The total concentration of perchlorate ion was

found by analysis to be 3.408xW-3 molar.

The association constant for the reaction:

Fe3 + C10- = FeC1042+

was calculated by Sykes91 to be, 6.7 at J = 0.0236 and 3.7 at p = 0.0437

A linear extrapolation to p = 0.0064, the approximate ~ of the 1 x 103

molar Fe3+ solution used, gives an association constant of approximately

9.3.

Using this value, the concentration of FeClO12+ can be calculate(

to be 5 x 10-5 molar. This means that a maximum of 5% of the Fe3+ is

associated with C104" in the solutions studied.

In the calculations of the concentration quotients it was assume<

that no complexation occurred between the iron (III) and the perchlorate

ions. Although this did introduce a slight error, it was certainly a

much smaller error than that for systems with perchlorate ion used as a

"swamping" inert electrolyte.

Ionic strength. As pointed out previously, it was desirable to

keep the ionic strength at a minimum in order to maintain the activity


11;0










CLUUI .WL.L11 Vn c ti-oul ..l V 3
salt.
123
The U.S.P.H.S. Drinking Water Standards3 recommends a maximum

of 500 ppm of total dissolved solids calculated as CaCO~, in potable

water. This is equivalent to an ionic strength of approximately 0.02.

A calculation based on the maximum ionic strength in the samples used

in this study gave 0.006 as the ionic strength of a 1 x 10-3 molar

iron (III) perchlorate .solution assuming no hydrolysis at a pH of

approximately 3. At the other extreme, the solution with an iron (III)

concentration of 1 x l-5 molar had an ionic strength of approximately

6 x 10-5.

Reaction time. It was pointed out above in the discussion of

the literature values, that the hydrolysis of iron (III) reaches equi-

librium slowly. Some investigators have aged the solutions as long as

several months before equilibrium was reached.

The reaction time of importance in water treatment processes is

less than one hour and the controlling reactions may take place in less

than a minute. For this reason it was decided to use a continuous titra-

tiontechnique, where the hydroxide ion was added slowly to the iron (III)

solution while the pH was continuously monitored and recorded. This

technique provided instantaneous response to the change in pH resulting'

from the hydrolysis reactions. To insure homogeneity of the sample, a

relatively high rate of agitation was maintained.

In ofder to determine whether this technique would lead to highly

sDecific. time-deoendent values, it was planned to cemnara the nM valusn


L+. -






hh. -


as many a

Alt

planned, i

average ci

mass actic

Whe

ssary to c

the hydrog

"average"

the average


i determination of instantaneous concentration quotients would






- 45 -


stability or formation constants. These have been discussed in detail

by Bjerrum:= and co-workers in many papers since 1915. The book by

Rossetti and Rossetti presents a complete discussion of the problems

and approaches used in the calculation of equilibrium constants for a

variety of systems.

The data to be collected in this study are the pH as a function

of the amount of hydroxide ion added at various constant concentrations

of iron (III).

A very useful relationship between the ligand concentration and

metal ion concentration was defined by Bjerrum.l This secondary con-

centration variable, n, will be referred to as the formation function

and is defined by the equation


n = Oound
Total

where C01Hound is the concentration of hydroxide bound and Fet is the

total iron (III) concentration. The formation constant, which gives the

average number of hydroxides bound to each iron (III), can be determined

from the experimental data for a series of points along the titration

curve as
t.OH- + OH-3 (OH-

Fet

where the subscripts i, a, and f represent "initial," "added," and

"final" respectively.

The formation function can also be defined in terms of the over-

all concentration quotients, Q for the series of reactions





- 46 -


It is well known that the hydrolysis of a metal ion .increases

the concentration of the metal ion decreases and that polymerization

creased as the concentration decreases. It was planned to use as sin

a model as possible to explain the titrimetric data.

An examination of R as a function of hydroxide ion concentrate

measured in terms of pH, at various constant iron (III) concentration

would give a satisfactory measure of the terms required in the model.

If the n -pH plots at different values of total iron (III) wer

superimposable, n would be a function of pH only and only mononuclear

complexes would be present. The model would then only have to include

mononuclear complexes. On the other hand, if they are not superimpos

polynuclear species must be included in the model.













V. EXPERIMENTAL


Materials


Iron (III) Perchlorate

Since a commercial sample of a purified iron (III) perchlorate

was found to contain an appreciable amount of nitrate ion, it was

necessary to prepare the sample used in this.study. The procedure used

was that of Schlyter.62

Preparation. A weighed sample of Fe(NO ) (H20)9 (J. T. Baker,

reagent grade) was mixed in a porcelain evaporating dish with enough 70

HC104 (G. Fredrick Smith) to cover it completely. The analysis of the

iron (III) nitrate is shown in Table 3. The mixture was heated under

an infra red lamp. As the nitrate dissolved, HB3 fumes were given off

along with HC104 fumes. As the liquid volume decreased, pink crystals

of iron (III) perchlorate crystallized from the solution. The heating

was continued until the mass of crystals was almost dry. It was essen-

tial that the crystals be stirred continuously during the later stages

of the evaporation as there was a tendency for localized overheating of

dry crystals to cause decomposition to the characteristic reddish-browr

color of Fe203.

This process was repeated four times until a negative test was

obtained for the presence of the nitrate ion. This test involved dis-

entvinc a .crnmanl znmnl of thA salt in distilled deionized water. Dre-
















Percent by Weight


99.8

0.001

1.6

0.0002

0.004

0.0003

:,(as SO4) 0.09


Chemical Co., Phillipsburg, N. J.



;ting with diphenylamine. A deep blue


relops in the presence <


if nitrate ions.

















by this preparative procedure. The analytical procedures followed are

described in Fischer.124

Stock solution. The crystalline salt prepared above was dis-

solved in distilled, deionized water to give an approximately 1 molar

solution of Fe3+. The solution was analyzed for the concentration of

iron (III) titrimetrically with standardized K2Cr207 by the method
124
described in Fischer.124 The average of five determinations was

0.9895 t 0.0108 M.

The hydrogen ion concentration was determined by exchanging the

iron (III) ions for hydrogen ions using the cation exchanger, Amberlite

IR-120 (Rohm & Haas), that was initially saturated with hydrogen ions.

The concentration of hydrogen ions in the eluate was determined by

titration with standard sodium hydroxide solution using phenolphthalein

as an indicator. The hydrogen ion concentration of the stock solution,

Ho, could then be calculated from the total hydrogen ion concentration,

Ht, from the relationship, Ho = Ht -3 Fe3 The average of five
analyses gave a value for Ho of 0.4023 t 0.0042 M.

This solution was accurately diluted to the desired concentra-

tions.







- 50 -









pH 6.855. Prepared from KH2PO4 and Na2HPO4.H20 (N.B.S.-primary

mdards) by preparing a solution exactly 0.0250 M in each salt. Dis-

Lled, deionized, freshly boiled water was used for the dilution. The

thod used was that of Hitchcock and Taylor25 who accurately determined

e pH of this solution to be 6.855 at 25 C. These buffer solutions

re stored in polyethylene containers and used to calibrate the pH

ter.


Apparatus






f* 2 -


J-













Fig. 5


I!l
































Sxperi


7 i
b



Liqui
Level










A

I











,ntal


I i
I is
I I








C





















itup


Imi
































r Tit2


A- T


B-G

C-R
D B
D -

E F

F-R

G-G

H -

I I

J A










Lons.


'lon c
Lrring

iss el

ferenc

be for

Lyethy

bber a

3 exit

) mi t

,netic

aestos


ated n
bar

ictrode

eleol

Na

.ene ne

copper

hole

11-fol

stirrE

plate










*


letio




ie



Le





meake2


NM



L, r






- 53 -


. The chart speed was calibrated several times

months and never varied measurably from the rz

ndard glass and calomel reference electrodes wc


amp

The pump employed to add the sodium hydroxide solution to the

Ltration vessel at a constant rate was composed of two parts, a con-

tant rate drive mechanism and a syringe to contain and deliver the

solution.

Drive mechanism. The drive mechanism for the syringe was a Sage
**
mnp, Model 249-2, which drives a plunger at a constant rate across

ie bed of the pump toward a clamp that is so placed that the body of

syringe can be clamped parallel to the direction of motion. The pump

Lunger can be made to drive the syringe plunger at a constant rate in

order to expel the contents of the syringe. The rate of movement of

ie plunger was measured at 2.50 mm/minute.

Syringe. The syringe first used was a common Luer syringe.

b was discovered that reproducible volumes were not delivered. There

semed to be some eccentricity in the motion of the plunger and leakage

ast it. Gas tight Hamilton syringes were then employed and



Manufactured by Heath Co., Benton Harbor, Mich.


------, -1 -


-- ----- --I


~~c*










ave good precision.


weighing and calculating the volume of. water displaced. Replicate

alibrations of each syringe used gave excellent reproducibility. The

ates are shown in Table,4. A 12 inch polyethylene needle was used.



Table 4

Delivery Rate of Syringes Used


CA -






5-


U~tU .JlU cHUlVcUKlJ UJ Vi. L1UB ^.Li.U..

A 1.00 milliliter micro burette, calibrated to read to 0.01

milliliter, was used to measure and deliver the stock iron (III) solu-

tion for dilution to the final concentration.


Procedures


The procedure followed in all of the titrations was the same

except where deviations are noted in the discussion of the results.

The sequence of events was:

1. The pH meter was calibrated at pH 4.01 and 6.86 and adjusted

to read accurately at each value.

2. The gas tight syringe was filled with standardized sodium

hydroxide solution from the polyethylene storage bottle by means of a

stainless steel hypodermic needle inserted through the side of the

storage container. In this manner the solution was not exposed to the

atmosphere. The first sample withdrawn was used to flush out the

syringe which was then refilled.

3. The syringe was attached to the pump, the polyethylene needle

attached and the. motor turned on to engage the pump plunger with the

syringe plunger. The pump was run until the polyethylene needle was

flushed out and completely full of solution.

4. The titration vessel was flushed well with N2 that was allowed

to run continuously from this point on until the titration had been

completed.

r Tpna A-r-nn tTTT) T^AV/^T^I c e-fn n tyTO c **i//^ii%"nT+ fr in+ 4-^^






56 -


into the titration vessel through the gas exit opening.

6. The initial pH was read with the recorder chart paper

stationary.

7. The amount of sodium hydroxide to be added initially was

added from the 5 milliliter micro burette, which was fitted with a dry-

ing tube filled with Ascarite. The purpose of this initial addition

was to keep the complete titration within one filling of the syringe.

A preliminary titration was used in each case to decide how much could

be added before getting to the first break in the curve. The initial

amount added was always kept well within the first buffered range. See

Figure 6.

8. The pump and the chart drive were started simultaneously and

thereafter the titration proceeded automatically.



























First buffered zone




ml NaOH solution added
titration started
I I I I I I l I I I I I

ml NaOH Added

Fig. 6 Representative Titration Curve Showing Initial Buffered Zone.













VI. RESULTS


Effect of Titration Parameters


Carbon Dioxide Absorption

In planning the procedure to be used in the alkalimetric titra-

tion of iron (III), it was assumed that the strongly acidic solutions

would not absorb CO2 from the atmosphere and that normal precautions

should be taken to protect the sodium hydroxide solution from CO2 during

storage. When this procedure was followed, the curve shown in Figure 7

(HCO03 present) resulted. The pronounced break from pH 4-6 suggested

the possibility of HCO contamination, therefore a series of titrations
3
was run using the same technique but replacing the iron (III) perchlorat

solution with HC104 solution. The results are shown in Figure 8. The

curve showing HCO 3 present was typical of those obtained. The pro-

cedure was then modified to protect the entire system from CO2. The

results were plotted in Figure 8 and are shown as "HCO absent, under
3
N2." This indicated that the presence of CO2 affected the results. The

modified procedure was used for the titration of a 1 x 10 M solution

of iron (III) perchlorate, as before. The results are shown in Figure

7 with a typical curve designated HCO3 absent, under N2. As a conse-

quence of these observations, the procedure, as modified, was adopted










i I


chlorate




03 absent


M Iron
MMols











Irn


A/ /


[


I


present


I I


I













9.c-



8.0- f I
I

I
8. /
/


/
7.0-
HCO" absent under N2 /
I

6.0- i



/1
5.0-
S.o. / 1

HC03 present ~- /

4.o-0



3.0 I I I
0 .1 .2 .3 .4 .5 .6 .7 .8 .9 1.0
Ml NaOH (.017761 N)
Fig. 8 Effect of Bicarbonate Ion on Titration of Perchloric Acid


_


I










Lg44L Ui ,.I.UU I .L.L/ LLUl.U.IOI

It had been shown by Matijevic and Tezak126 that aged aluminum

.on solutions had greater coagulating power toward silver halide sols

.han freshly prepared solutions. It was pointed out by Stumm and

[organ35 that changes in.the.ultraviolet and visible spectrum of iron

III) were due to increased hydrolysis. From these observations, it

ras decided to determine the effect of aging of the diluted solution

in the results. Figure-9 shows the results of titrating a freshly pre-

>ared 1 x 10-3 M iron (III) perchlorate solution and titrating another

liquot of the same solution after it had aged 46 hours.

The proximity of equivalent points showed that aging would not'

effectt the results. This conclusion was reaffirmed frequently through-

ut the study as no differences were noted between fresh and aged solu-

ions at any of the concentrations used. This shows that any change in

he composition of the solution that occurs as a result of aging is

:eversed or modified almost instantaneously when the pH is changed and

hat the instantaneous composition is controlled by the pH. This can

nly be stated for aging at the low pH values employed in this study.


itration Time

Although many reactions of iron (III) in dilute solution indicate

hat the initial hydrolysis reaction is rapid, it was felt that this

oint should be verified. It was particularly important to determine

whether the individual titration curves were measures of a system that

as essentially static or at least changing only slowly. In order to


V_





1..


- 62 -


o
0@


1 x 103 M Fe (III) Perchlorate

2.5 x 10"2 MMols Fe (III)
0



Solution titrated 2 O
minutes after being
diluted from stock
solution.

0
0

O Solution aged 46 hours
before being titrated.


10.0 -


9.0o-


7.0 -


6.0-


5.0-


0.06


0.09


0.07


0.08


0.10


MMols NaOH

Fig. 9 Effect of Aging of Solution on Hydrolysis
Perchlorate Solutions.


of Fe (III)















e mad

ts ar

e in

used


Lre

thoughg

,e car


this factor, a series of titrations was conducted in which the tempera.

ture was varied. The titration vessel was jacketed and water from a

constant temperature bath, held to + l1C was circulated through the

jacket. The results shown in Figure 11 indicated that the temperature

effect was not significant. The temperature, therefore, was not con-

trolled beyond allowing all the solutions to equilibrate to room tempe:

ture. A heavy asbestos plate was placed between the magnetic stirrer

and the titration vessel to shield it from heat evolved by the stirrer


Titrimetric Curves


Using the titration technique discussed previously, curves were


. ^ -





6IL -


8.0- o0


0 Average of 7 values at rate 00
0.00179 MMols/min.

7.0-
0 Average of 4 values at rate 0
0.000732 MMols/min. 0


6.0- 0

8

00

5.0- o
00
o
o


0
00
0
0 o


3.0I --
0 0.01 0.02












9.C


5 x 104 M Fe(III)

81.25 x 10-2 Mols Fe(III)
8.-


1

7- 250_ 98-32-XI ,7
27C 98-32-XII
0oC_ 98-32-XIII

6.0-









4.0-
5.0




3.0 I I I I
0 2 4 6 8 10
Time (minutes)

ig. 11 Potentiometric Titration of 25.00 ml of 5 x 10"4 M Iron (III)
Perchlorate Solution With 0.01776 M NaOH Showing the Effect
of Temperature.


W- -









10.0 Mean of 16 Titrations





9.0





8.0





7.0 -





p' 6.0 -





5.0





4.0





3.0o

0 0.06 0.07 0.8 6.b U1
MMols NaOH

Fig. 12 Titration of 25.00 ml of 1 x 10-3 M Iron (I1) Perchlorate
e--%..J.A. 1 -- I ?I. 1- fl^ ^'% Prt % ITf T


^ ^






67 -


10.0





9.0 -
Mean of 11 values




8.0





7.0





6.0-





5.0





4.0-




3 o Ii I
3.0 _________ __________ __________ _\ ________
0 0.03 0.04 0.05 0.06
MMols NaOH

Fir. 11 Titration of 25.00 ml of 5 x 10- M Trnn (TTTI PArnhinfnta






- 68 -


10.4


6.0-



5.0



4.0


0




Fig. 14 Titration of 25.00 ml of
Solutions With 0.01776 M


MMols NaOH


1 x 10"4 M Iron (III) Perchlorate
NaOH.





9.0




8.0 Average of 4 values




7.0




6.0




5.0




4.0 1 I I
0 .002 .004 .006 .008

MMols NaOH




r. 1q Titration of q0.00 ml of 1 x 10-5 M Tron (nTTT PaerhloratA






- 70 -


curves is shown in Figure 16. These curves give a semi-quantitative

picture of the effect of dilution on the extent of hydrolysis. For

example, Figure 16 shows the neutralization (to a pH of 7.0) of 2.5 x

10-2 millimoles of iron (III) at a concentration of 1 x 10-3 M iron

(III) required approximately 0.087 millimoles of sodium hydroxide or

about 3.48 millimoles of sodium hydroxide per millimole of iron (III).
-4G
The 1 x 10 M iron (III) solution required about 5.2 millimoles of

sodium hydroxide per millimole of iron (III). This increase could be

attributed to the increased acidity of the more dilute solution per

unit of iron (III). This resulted from increased hydrolysis.


Precision

In order to determine the precision of the technique used,

replicate runs were made under the same conditions for each concentra-

tion of iron (III). Several samples were taken from each of several

separate dilutions of the stock solution. The "mean values" for each

point were calculated using a computer program that also calculated

the standard deviation for each point and the overall average standard

deviation for the entire set of points in the curve. The computer pro-

gram for these calculations is shown in Appendix II. The maximum

deviation from the mean was determined for each point using a desk cal-

culator.

The data for the titration of 1 x 10- M iron (III) perchlorate

solution are shown in Table 5. The precision is shown in Figure 17 in

terms of the maximum positive or negative deviation for each point.












10 -

50 x 10o M 5 x 10"

8




6




4 1.25 x 102 MMols
2.5 x 10-3 MMols Fet
-Fe -- 2.5 x 10
"----- ~. MMols Fet

2 I I I I I I I I
0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.10
MMols NaOH


Iron (III) Perchlorate Solutions With NaOH.


Fig. 16 Titration of









Table 5
Titration of Sixteen Separate 25.00 ml Samples of
1 x 10-3 M Iron (III) Perchlorate Solutions With
0.01776 M NaOH


Mfols
NaOH pH

0.0000 2.90 2.92 3.12 2.96 2.91 2.95 3.12 2.91
0.0622 3.51 3.54 3.50 3.43 3.45 3.45 3.48 3.40
0.0658 3.52 3.52 3.50 3.43 3.43 3.43 3.50 3.40
0.0693 3.60 3.59 3.51 3.48 3.48 3.48 3.56 3.47
0.0729 3.71 3.68 3.61 3.57 3.57 3.57 3.67 3.57
0.0765 .3.83 3.82 3.74 3.71 3.71 3.71 3.82 3.71
0.0801 4.08 4.08 3.97 3.94' 3.93 3.94 4.10 3.98
0.0818 4.30 4.33 4.16 4.16 4.13 4.15 4.42 4.25
0.0836 4.77 4.90 4.56 4.62 4.51 4.65 5.24 4.82
-0.0844 5.08 5.28 4.86 4.98 4.81 5.00 5.75 5.28
0.0851 5.46 5.65 5.22 5.40 5.20 5.48 6.06 5.74
0.0858 5.82 5.91 5.62 5.76 5.58 5.82 6.24 5.98
0.0865 6.10 6.39 5.92 6.06 5.88 6.06 6.70 6.25
0.0872 6.62 7.10 6.26 6.64 6.24 6.62 7.35 6.87
0.0879 7.42 7.96 6.91 7.55 6.90 7.42 8.03 7.75
0.0886 8-29 8.81 7.80 8.51 7.80 8.40 8.80 8.65
0.0894 9.10 9.39 8.70 9.22 8.72 9.22 9.33 9.28
0.0901 9.62 9.75 9.31 9.62 9.39 9.66 9.58 9.55
0.0908 9.87 9.95 9.63 9.82 9.72 9.83 9.88 9.85
0.0915 10.00 10.06 9.81 9.93 9.86 9.94 9.98 9.93
0.0922 10.10 10.14 9.92 10.02 9.95 10.03 10.07 10.02







- 73 -


Table 5 Extended



Deviation*
pH Mean (+) (-) S2


2.90 2.91 2.90 2.71 2.90 2.99 2.96 2.94 .18 .04 0.0935
-- ^ jk J., -. A. i 1'9^ '1, il. ^ Ar~ ri


























7.C




6.c




5.C




4.C


A


~1.


6/


I





x is the mean value

t is a constant based on the number of observations, n,

and the confidence level desired

s is the standard deviation which can be calculated from


n-1
where x is the value of an individual observation

The value of t was obtained from Laitinen. This means that

here is 95% confidence that the true value lies within the interval -

pecified -- assuming only random errors.

The results show that excellent reproducibility or precision is

achieved by the technique used.

Tables 6, 7, and 8 show the same data for the other concentra-

ions studied. The curves showing the "mean value" of the pH as a

unction of millimoles of sodium hydroxide added do not include the

eviations as this would make the presentation complicated. The data

n the tables show that the precision was high in all cases.






- 76 -


10.0 -




9.0





8.0 +
S = x .533S




7.0




6.0




5.0





4.0




3.0



0 0.06 0.07

Fig. 18 Precision of Titration of Iron
Confidence Interval.


(III) With NaOH Based on 95%



















? 3.
3 3.
3 3.
3 4.


5 4.
3 4.!
3 5..
) 5.C













1 0 0 fl .'t*


u.u~u ou O.yu 0.yu 0.u .u .7 b. .94 8.85 8.88 8.

0.0537 9.03 9.01 9.00 9.09 8.92 9.05 8.96 9.00 8.

0.0544 9.13 9.09 9.10 9.19 9.03 9.16 9.05 9.08 8.

0.0562 9.32 9.31 9.31 9.36 9.25 9.35 9.26 9.25 9.


Standard deviation.






'9 -


Table 7
Titration of Seven Separate 25.00 ml Samples of 1 x 104 M Iron (III)
Perchlorate Solution With 0.01776 M NaOH


Aols 1
aOH pH Mean S

.0000 3.69 3.69 3.68 3.60 3,60 3.51 3.51 3.61 .079

.0036 3.88 3.88 3.82 3.82 3.82 3.73 3.73 3.81 .062

.0072 4.12 4.14 4.07 4.07 4.07 4.10 4110 4.10 .028

.0079 4.19 4.22 4.13 4.13 4.13 4.19 4.19 4.17 .038
.0086 4.32 4.36 4.24 4.27 4.26 4.30 4.30 4.29 .040

.0093 4.48 4.58 4.38 4.44 4.42 4.46 4.46 4.46. .062
.0100 4.78 5.00 4.62 4.75 4.70 4.80 4.80 4.78 .117

.0107 5.40 5.58 5.10 5.45 5.25 5.50 5.50 5.40 .167

.0115 5.80 5.92 5.60 5.78 5.65 5.98 5.98 5.80 .153
1.0122 6.26 6.38 5.92 6.15 6.00 6.36 .6.36 6.20 .186
'.0129 6.90 7.03 6.35 6.80 6.50 6.90 6.90 6.77 .248

.0136 7.70 7.75 6.94 7.50 7.15 7.60 7.60 7.46 .302

).0143 8.38 8.34 7.70 8.16 7.88 8.20 8.20 8.12 .246

).0150 8.74 8.72 8.30 8.62 8.42 8.62 8.62 8.58 .160
1.0158 8.90 8.92 8.78 8.85 8.76 8.85 8.85 8.84 .058
1.0165 9.00 9.06 8.90 8.98 8.94 8198 8.98 8.98 .050

1.0172 9.10 9.14 9.03 9.09 9.07 9.08 9.08 9.08 C033

1.0179 9.18 9.22 9.12 9.18 9.16 9.16 9.16 9.17 .030
1.0186 9.24 9.28 9.20 9.23 9.22 9.22 9.22 9.23 .025





80 -


Table 8

Titration of Four Separate 50.00 ml Samples of
1 x 10-5 M Iron (III) Perchlorate Solution
With 0.01776 M NaOH


MMols, NaOH pH Mean S1

0.0000 4.50 4.51 4.50 4.50 4.50 .005

0.0004 4.58 4.58 4.58 4.54 4.57 .020
0.0007 4.66 4.68 4.68 4.60 4.66 .038
0.0011 4.76 4.80 4.80 4.70 4.76 .047

0.0015 4.92 4.88 4.92 4.84 4.89 .038
0.0018 5.02 5.08 5.10 5.00 5.05 .048

0.0022 5.22 5.28 5.25 5.18 5.23 .043
0.0025 5.42 5.50 5.50 5.42 5.46 .046
0.0029 5.70 5.75 5.72 5.68 5.71 .030

0.0033 5.92 6.00 5.92 5.92 5.94 .040
0.0036 6.15 6.15 6.10 6.10 6.12 .030
0.0040 6.35 6.35 6.30 6.30 6.32 .030
0.0044 6.59 6.59 6.56 6.56 6.57 .018

0.0047 6.88 6.88 6.86 6.86 6.87 o011

0.0051 7.18 7.16 7.18 7.18 7.18 .010
0.0054 7.50 7.50 7.52 7.52 7.51 .011

0.0058 7.75 7.75 7.80 7.80 7.78 .029










Table 8 Continued



MMols, NaOH pH Mean Sl


0.0062 8.00 8.00 8.00 8.00 8.00 .000

0.0066 8.15 8.15 8.15 8.15 8.15 .000

0.0069 8.30 8.30 8.28 8.28 8.29 .011

0.0073 8.39 8.39 8.36 8.36 8.38 .018


1Standard deviation.


- 01 -









Calculations

Literature Data

The calculation of the formation function-pH dependency based
upon the literature values for the pertinent equilibrium constants could
have been a very laborious process but was simplified by the use of a
computer. The computer program used is given in Appendix III and was
based upon Newton's method of approximating the roots of polynomials.

The equilibrium constants used are shown in Table 2. They were
used in four sets. The first three sets of values were from the work
62 53 57
of Biedermann,2 Hedstrom,5 and Milburn.57 The fourth set was a com-

bination of the constants from Biedermann, above, with an average Ksp
for Fe(OH) of 1042.5 from Feitknecht77 and K41 from Lengweiler, Buser,
and Feitknecht.8

The calculation required the determination of the (Fed concen-
tration in the following manner:
From the hydrolysis equilibria discussed in Chapter II, the
definition of the equilibrium constants required can be given as

K11 = FeoH Qf)


K1 = Fe(OH)2) H) 2
21 =



CFeY3
K (Fe(OH)j ) CH) 4
(Fey3)


On





- 0. -


K22 = LFe2(OH)2') 2 H j -
K22 = . ..
(Fe3)
K = (Fe,(OH)45) (Hf 4
CFe) 3 3
Mhe total iron (III) concentration, FeT, can then be expressed as

FeT = (Fe3 + (FeOH2*) + (Fe(OH) -) + (Fe(OH)3) + (Fe(OH)4)

+ 2 Fe2(OH)2 ) + 3 (Fe (OH)
md by substituting the constants above, becomes

















pH Fe3+ Iter.2

3.00 4.0214E-05 0.7960 3
3.20 2.6152E-05 1.0623 4
3.40 1.5131E-05. 1.3188 4
3.60 7.8723E-06 1.5347 5
3.80 3.7553E-06 1.6964 6
.00 1.6803E-06 1.8073 7
4.20 7.1989 E07 1.8793 8
4.40 2.9996E-07 1.9246 9
4.60 1.2284E-07 1.9528 10
+.80 4.9772E-08 1.9705 11
5.00 2.0033E-08 1.9815 12
5.20 8.0305E-09 1.9883 13
5.40 3.2108E-09 1.9927 14
5.60 1.2817E-09 1.9954 16
5.80 5.1114E-10 1.9971 17
5.00 2.0371E-10 1.9982 18
5.20 8.1152E-11 1.9988 19
S.40 3.2321E-11 1.9993 20
5.60 1.2871E-11 1.9995 21.
5.80 5.1248E-12 1.9997 22
7.00 2.0404E-12 1.9998 24

11.00000000 x 10-4

2Number of approximations required.


--rU* -1 C V- VA












7.0


0 Hedstrom's Constan

Biedermann's Const
6.0
Total Iron (III) =

o Total Iron (III) =

5.0 Milburn's Constant:
5.0-

















Reference
tant Biedermann62 Hedstrom53 lburn57


S9 x 10- 9 x 104 6.7 x 10-3

,..- -7 .. -'7


22 1.1 x 103 1.2 x 103 1.4

43 1.7 x 10" --


1 1 x 10-5
431

.12 1 x10-18
'41

1Feitknecht77
2Lengweiler, Buser, and Feitknecht78


underflow from the control of the monitor. This allowed

nts to be calculated before truncation of the values cause

ors to be introduced. The monitor control inhibited exect

program when ten over-or underflows occurred.


erimental Data

Formation function curves. The formation function, n,

ated as a function of pH from the titration data. The cal

e carried out in the same computer program that determined


ition of


-6 A F C. U J.LA V


_(- L L










average pH and the standard deviation for the pH values. This program

is shown in Appendix II. These data are plotted in Figure 20 for the

four concentrations of iron (III) studied. The data for the 1 x 10-3

iron (III) solution are plotted in Figure 21 along with values calculated

from the literature constants.

The calculation of n utilized the relationship

= (H)bound = H)o + (OH)a OHf
FeT FeT

where the subscripts o, a, and f were defined as original, added, and

final, respectively.

The (OH)o was calculated from the hydrogen ion concentration of

the stock solution diluted to the final volume. The (OH)a was from the
nnmmn+. nr-P MnATT or1-n+ vrt rlgn n-ntl (MnUT -ri) +V1- (Atr) r.,tA4-U 4-1U-


















9.0-



H
8"0 H


H .i

7.0 4
S*<

6.0- 4 x-



5.0





4.0 -




3.0

2 3 4 5 6 7 8

Formation Function, n

Fig. 20 Calculated Formation Functions for the Titration of Fe (III)
With NaOH.






90 -













8.0--





of the units making up the polymer. The equivalent curves from this

study, Figure 20, show. neither characteristic, they are neither super-

imposable nor parallel. This, of course, does not mean that neither

mononuclear nor polynuclear species are present. It does mean that

equilibrium has not been reached* It is further suggested that the less

concentrated solutions are farther from equilibrium. This was qualita-

tively confirmed by the observation that the insoluble iron (III)

hydrous oxides agglomerated to a visible size much slower in more

dilute solution.

On the basis of consideration of these results it was decided to

determine a separate set of quotients for each curve, keeping in mind

that these would be instantaneous quotients and not necessarily even

related to the comparable equilibrium quotients.

Since the principal measurements made on the system were the

activity of the hydrogen ion and the stoichiometric concentration of

the iron (III), the values obtained were mixed activity-concentration

values. A sample calculation of the effect of ionic strength on the

activity of the hydrogen ion in the extreme case, that is 1 x 1073 M,

showed the change was less than 5% of the value of the hydrogen ion

activity. Since this error is less than other systematic errors in

the study, the activity of the hydrogen ion was substituted for the

concentration of the hydrogen ion in all calculations and




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