Graphical Methods for 

Studies of Aqueous 

Aluminum Hydroxide, 

Fluoride, and Sulfate 

Complexes

GEOLOGICAL SURVEY WATER-SUPPLY PAPER 1827-B
Graphical Methods for 

Studies of Aqueous 

Aluminum Hydroxide, 

Fluoride, and Sulfate 

Complexes

By J. D. HEM

CHEMISTRY OF ALUMINUM IN NATURAL WATER 

GEOLOGICAL SURVEY WATER-SUPPLY PAPER 1827-B

Mathematical procedures used to prepare 

graphs by which the series of soluble 

aluminum complexes with flu or id e 

and sulfate are described

UNITED STATES GOVERNMENT PRINTING OFFICE, WASHINGTON : 1968
UNITED STATES DEPARTMENT OF THE INTERIOR 

STEWART L. UDALL, Secretary

GEOLOGICAL SURVEY 

William T. Pecora, Director

For sale by the Superintendent of Documents, U.S. Government Printing Office 

Washington, D.C. 20402 - Price 20 cents (paper cover)
CONTENTS

Abstract. ________________________________

Introduction, ____________________________

Solubility calculations.____________________

Aluminum hydroxide complexes.___________

Aluminum fluoride complexes._____________

Species distribution diagrams._________

Diagrams showing extent of complexing. 

Effects of hydroxide._____________

Aluminum sulfate complexes.______________

Mixed solute systems.____________________

Aluminum solubility._____________________

Application to natural water.__-_____-_-___

Summary. _______________________________

References.______-_-_-_-_-_-_-_-_-_-_-_-.

FIGURE

ILLUSTRATIONS

Page 

Bl

1

2

2

3

4

11

19

20

25

30

31

32

33

[All figures are graphs]

Page

1. Distribution of dissolved aluminum species as a function of

free fluoride concentration (F~). (Ionic strength 0.5)____. B4

2. Distribution of dissolved aluminum species as a function of

total dissolved fluoride and aluminum. (Zero ionic strength) _ 9

3. Ratio of free aluminum activity [A1+3] to total dissolved 

aluminum as a function of total dissolved fluoride and 

aluminum. (Zero ionic strength).............----------- 12

4. Ratio of free aluminum activity [A1+3 ] to total dissolved 

aluminum as a function of total dissolved fluoride and 

aluminum. (Ionic strength 0.001)_____________-__----_-- 17

5. Ratio of free aluminum activity [A1+3 ] to total dissolved 

aluminum as a function of total dissolved fluoride and 

aluminum. (Ionic strength 0.01)_______-_-_-_-_-_------- I7

6. Ratio of free aluminum activity [A1+3 ] to total dissolved 

aluminum as a function of total dissolved fluoride and 

aluminum. (Ionic strength 0.10)_______-_____----------- 18

7. Ratio of free aluminum activity [A1+3] to total dissolved 

aluminum as a function of total dissolved fluoride and 

aluminum. (Ionic strength 0.71) ___________--_-_------- 18

8. Ratio of free aluminum activity [A1+3 ] to total dissolved 

aluminum as a function of total dissolved fluoride and 

aluminum. This graph differs from figure 3 in that here 

the aqueous species A1OH+2 is considered (pH 5.00)______ 19

9. Distribution of dissolved aluminum species as a function of

total dissolved sulfate and aluminum. (Zero ionic strength) _ 21

in
IV CONTENTS

FIGURE 10. Ratio of free aluminum activity to total dissolved aluminum Page 

as a function of total dissolved sulfate and aluminum. 

(Zero ionic strength)..________________________________ B22

11. Ratio of free aluminum activity to total dissolved aluminum 

as a function of total dissolved sulfate and aluminum. 

(Ionic strength 0.001)____-_-__--_-____________________ 23

12. Ratio of free aluminum activity to total dissolved aluminum 

as a function of total dissolved sulfate and aluminum. 

(Ionic strength 0.01)_-----------------_---_------_-___ 23

13. Ratio of free aluminum activity to total dissolved aluminum 

as a function of total dissolved sulfate and aluminum. 

(Ionic strength 0.10)_----__-__-_--____-_--_-_________- 24

14. Ratio of free aluminum activity to total dissolved aluminum 

as a function of total dissolved sulfate and aluminum. 

(Ionic strength 0.71)--_---__-_-______-__-__-___-_.___- 24

15. Ratio of free aluminum activity to total dissolved aluminum 

as a function of the two competing ligands, fluoride and 

sulfate. (Zero ionic strength) ___________________________ 26

16. Ratio of free aluminum activity to total dissolved aluminum 

as a function of the two competing ligands, fluoride and 

sulfate. (Ionic strength 0.1)_____-_-_-_-_-_-_-_____-____ 28

17. Ratio of free aluminum activity to total dissolved aluminum

as a function of fluoride and pH. (Ionic strength 0.00) _ _ __ 29

18. Ratio of free aluminum activity to total dissolved aluminum

as a function of sulfate and pH. (Ionic strength 0.00)_____ 30

TABLES

Page 

TABLE 1. Standard free energies____________________-___-_-_--_--_- B8

2. Activity coefficients of ion (7 ion) at different ionic strengths. 16

3. Chemical analyses for two natural waters._________-__--_-- 31
CHEMISTRY OF ALUMINUM IN NATURAL WATER

GRAPHICAL METHODS FOR STUDIES OF AQUEOUS

ALUMINUM HYDROXIDE, FLUORIDE,

AND SULFATE COMPLEXES

By J. D. HEM

ABSTRACT

Published stability constants show that aluminum forms strong complexes 

with hydroxide, fluoride, and sulfate ions. Equilibrium calculations show that 

fluoride complexes probably will be the predominant form of aluminum solute 

species in natural water below neutral pH, when more than a few tenths of a part 

per million of fluoride, is present. Sulfate complexes of aluminum can be important below neutral pH if sulfate concentrations exceed 500 parts per million.

By means of graphs, the predominant complex species and proportior of uncomplexed aluminum activity to total aluminum concentration are shown as 

functions of the analytical concentration of aluminum and fluoride, or sulfate, 

for ionic strengths ranging from zero to that of sea water. In alkaline solutions 

the species A1(OH)4~ tends to predominate. The forms of aluminum complexes 

which can be expected to predominate, and extent of complexing in solutions 

containing both fluoride and sulfate, and the effects of pH on the complexing of 

aluminum by fluoride and sulfate also are shown by means of graphs.

INTRODUCTION

The chemical behavior of aluminum in aqueous systems is strongly 

influenced by the tendency of aluminum to form soluble complex 

ionic species with various ligands. Earlier work has shown (Hem and 

Roberson, 1967) that aluminum ions in solution below neutral pH 

are six-coordinated with respect to water molecules or hydroxide ions. 

In alkaline water A1(OH) 4~ predominates. Fluoride ions form a sixcoordinated series of solute complexes with aluminum. Sulfate also 

forms soluble complexes with aluminum. Some of these complexing 

effects are strong enough to interfere in analyses for aluminum.

Thermodynamic data are available for hydroxide, fluoride, and 

sulfate solution complexes of aluminum. The compilation of stability 

constants by Sillen and Martell (1964) contains references to some 

complexes of aluminum with orthophosphate and with organic ligands.

Bl
B2 CHEMISTRY OF ALUMINUM IN NATURAL WAT^R

These complexes may be of importance in some natural waters but 

too little is known of the occurrence of the organic ligands for the 

complexes to be considered in this paper. The Sillen and Martell 

compilation also cites studies which found no anionic chloride complexes of aluminum in strong solutions of hydrochloric acid. Whether 

cationic complexes with chloride or bicarbonate would form is not 

known, but the absence of data may suggest that such complexes are 

relatively weak.

Mathematical treatment, assuming chemical equilibrium, can be 

used to find the predominant dissolved species in systems where any 

or all of the principal complexing ligands occur; it can also be used 

to give the proportion of complexed aluminum in solution. In this 

paper both kinds of calculations have been made for systems containing hydroxide, fluoride, and sulfate. The results of the, calculations 

are presented in the form of graphs which can be used to evaluate 

directly the degree of complexing and the nature of the species present 

when total analytical concentrations of aluminum and ligand are 

known.

SOLUBILITY CALCULATIONS

The calculations and graphs presented in this report are not directly 

indicative of aluminum solubility. They are intended principally as 

guides to the type of aluminum solute species and the extent of 

aluminum complexing if the ionic concentrations that are assumed 

actually occur.

In the experiments and calculations relating to proportions of the 

various solute species, no postulations are made as to solid species 

that might precipitate. Because the graphs given in this paper show 

some rather high concentrations, it seems likely that solids would 

form and that they would prevent conditions shown in some parts of 

the diagrams from being actually attained. The identification of solid 

species and determination of aluminum solubility in a considerable 

range of conditions is the subject of continuing research, to be described 

in separate papers.

One of the purposes of the calculations and the graphs presented 

here is to ascertain the equilibrium activity of uncomplexed aluminum 

for a wide span of solution conditions. This value is useful in complicated solubility calculations.

ALUMINUM HYDROXIDE COMPLEXES

Studies described in an earlier report (Hem and Rob^rson, 1967) 

indicate that aluminum forms the simple monomeric complex A1OH+2 

and that it also may form polymeric hydroxide complexes which can 

grow to colloidal size. An illustration in that report indicated the
ALUMINUM HYDROXIDE, FLUORIDE, AND SULFATE COMPLEXES B3

equilibrium activity of free Al+3 and A1(OH) 4~ from pH 4.0 to 9.0 in 

the presence of three different solid forms of A1(OH) 3 .

This kind of illustration is a type of solubility diagram and requires 

knowledge of the specific form of solid which is present. The hydroxide 

solute species A1OH+2 and A1(OH) 4~ can be significant factors in the 

composition of dissolved forms of aluminum in some ranges of pH 

as will be shown. A complete treatment of these species is best made 

in connection with solubility diagrams and will be deferred to a later 

paper.

Polymeric A1(OH) 3 which forms at certain pH ranges is perhaps 

best thought of as a metastable structural intermediate. This species 

can evolve into a crystalline form of aluminum hydroxide, or if other 

solutes of the right kind are present, it may form a part of more 

complicated aluminum-bearing mineral species.

ALUMINUM FLUORIDE COMPLEXES

Aluminum forms a series of particularly stable complexes with 

fluoride. Although fluoride is a minor constituent of most natural 

waters, the complexing action is strong enough to have a considerable 

influence on the form of dissolved aluminum even when ver;T little 

fluoride is present.

Brosset and Orring (1943) determined the stepwise constants for 

the series of complexes from A1F+2 to A1F8~3 , at 25°C in solutions of 

0.5 ionic strength. For the equilibrium

for which the concentration equilibrium constant is Kn , for values of 

n ranging from 1 to 6, the reported constants are shown belov^. Also 

shown are values for the accumulative constants 0'n' where /3r 

represents constants for the reactions :

' = 1017.74

Because these constants include the activity coefficients for the 

various species at 0.5 ionic strength, they are concentration constants 

rather than activity equilibrium constants shown in this report as 

Kn or /? .
B4 CHEMISTRY OF ALUMINUM IN NATURAL WATER

Throughout this paper analytical concentrations are represented 

by ionic species enclosed in parentheses and activities by species 

enclosed in square brackets.

SPECIES DISTRIBUTION DIAGRAMS

There are various ways in which the distribution of the dissolved 

complex species formed in a system containing fluoride and aluminum 

can be represented graphically. One rather commonly used representation is the species distribution diagram in which the activity or 

concentration of free F~ is plotted on the x-axis and the percentage

FIGURE 1. Distribution of dissolved aluminum species as a funtion of free 

fluoride concentration (F~). (Ionic strength 0.5.)

distributions of the species are plotted on the y-axis. This gives rise 

to a series of curves bounding the domains of the species considered. 

A vertical line drawn on the graph at any desired value of (F~) will be 

divided by the curves into segments proportional to the abundance of 

the species indicated. Figure 1 is a diagram of this type showing the 

concentration of aluminum fluoride complexes at a fixed ioric strength. 

The diagram is prepared by a calculation technique shrilar to one 

described by Butler (1964) and outlined as follows:
ALUMINUM HYDROXIDE, FLUORIDE, AND SULFATE COMPLEXES B5

From the cumulative constants /3n, the amount of any of the complex 

species can be computed as a function of [Al+3] and [F~]. Thus s, series 

of 6 equations results :

= &[F-] 2 [A1+3]

= ft[F] 3 [Al+3], and so forth.

Also, the total of the activity of all dissolved aluminum species in 

the system is obtained from the summation

2[A1] = [A1+3] + [A1F+2] + [A1F2+] + [A1F3 °] + [AlFr] + [AlFr 2] + [A 1F6~ 3] .

At zero ionic strength this is equivalent to the total analytical concentration of aluminum. For the purpose of this derivation, zero ionic 

strength is assumed, but the approach requires only a different set 

of constants when it is used for other ionic strengths.

There are nine variables in these seven basic equations. Tl ~ n, diagram to be constructed assigns a value only to one of the varables. 

The interrelationships among the other variables then will be expressed in terms of the uncomplexed [F~].

Substitution of the equations for the activities of the complexes in 

the summation leads to

S[A1] = [A1+3] + ft[F] [A1+3] + &[F] 2[A1+3]

] 6 [A1+3]

The fraction of the total aluminum activity present as uncoirplexed 

Al+3 is determined by inverting and multiplying all terms by [Al+3],

[A1+3] 1

This fraction is represented as a0 - The fraction «i, of total aluminum 

present as A1F+2 is

2[A1] 

and

[A1F,+] ar

S[A1]

[A1F+2]

] 2«o, and so forth.

271-120 O - 67 - 2
B6 CHEMISTRY OF ALUMINUM IN NATURAL WATFR

The sum of the a terms will always be 1.0, or as shown in figure 1, 

100 percent.

Thus the fractions, or percentages, of total Al comprised by all 

seven possible aluminum species are fixed by specifying only the free 

fluoride activity. The positions of the lines bounding the species are 

calculated by determining a values for various values of [F]. Normally, 

not more than three species will be present in significant amounts at 

one time. The derivation above uses thermodynamic constants and 

activity values. It is, of course, possible to prepare diagrams for 

any desired ionic strength using concentrations and appropriate $n " 

values, and this modification in the procedure was used in preparing 

figure 1.

Figure 1 covers the range of concentration of fluoride from 10~7 to 

10° molal. The stability constants used (Brosset and Oring, 1943) 

were determined for solutions which were 0.5 molal. Therefore, this 

diagram applies only for solutions near this ionic strength. The 

experiments of Brosset and Orring were not carried to high enough 

fluoride concentrations to determine K6"', with any degree of certainty, 

and it is unrealistic to extrapolate data for ionic strergth of 0.5 

beyond 1 molar concentrations of F~.

The computations used to prepare the figure assume chemical 

equilibrium and absence of interfering substances. If the diagram is 

applied to natural water, high (relative to fluoride) concertrations of 

ions that compete with the fluoride for complexing of aluminum should 

not be present. This assumption does not impose a serious limitation 

at low pH because the fluoride complexes are the most stable of any 

likely to be present. It does mean, however, that the pH of the system 

should be below neutrality. The master variable, free fluoride concentration, is mathematically convenient but it cannot generally be 

directly measured. The only alternative is to assume that the total, or 

analytical, fluoride concentration is virtually the same as the uncomplexed fluoride. This can be true only if fluoride is present in large 

excess over the total aluminum. Thus, although the diagram is 

theoretically correct for systems where most of the fluoride is complexed, 

it cannot be practically applied to such systems unless free fuoride can 

be measured.

Even with these limitations, the diagram (fig. 1) suggests some 

interesting relationships in the chemistry of natural water. In a 

solution containing around 2 ppm (parts per million) of fluoride (10~4 

molal) the aluminum would probably be present mostly as A1F2+ and 

A1F3 °, and nearly all the aluminum would probably be complexed 

even when only a few tenths ppm of fluoride were present, provided 

the total Al is always considerably less than the total fluoride. In
ALUMINUM HYDROXIDE, FLUORIDE, AND SULFATE COMPLEXES B7

many natural waters, however, the aluminum content is relatively 

large compared to the fluoride.

A more useful type of diagram would be one in which the master 

variables would be readily measurable. Also, one would like to b^ able 

to allow for the effects of ionic strengths different from 0.50. Other 

means of graphic presentation of the behavior of fluoride complexes 

are therefore desirable. Mathematical and graphical procedures are 

given here by which one may represent the fields of dominance of the 

various species in figure 1 on a diagram having analytical concentrations of aluminum and fluoride as abscissa and ordinate. As a first 

step, some adjustment of stability constants for effects of different 

ionic strengths is required.

The equilibrium constants reported by Brosset and Orring were 

used by King and Gallagher (1959) to compute net change in fre°> energy for the stepwise formation of constants up to A1F5~ 2 in soT utions 

having an ionic strength of 0.07. These authors gave, for the cumulative constants, the following values:

0i'=106 - 61 & = 1018 - 71

02'=1011 - 97 0s =1020 - 04 

0;'=

King and Gallagher did not calculate a free energy for A1F6 3 . An 

approximate 0g value based on the trend of the other figures was 

estimated as 1Q20 - 44 for this report. In any event, the conditions required for formation of this species in major quantity are unlikely in 

any natural system.

A further calculation converting the values of King and Gallagher 

to zero ionic strength was made, using the Debye-Hiickel equation to 

compute the activity coefficients. Values for the parameter a (needed 

for the Debye-Hiickel equation) for the various species either were 

taken from Kielland (1937) or were estimated by analogy with similar 

forms. The values obtained for the constants for zero ionic strength are

Ki=lW-01 0!=107 - 01

K2 =1W-H 02 =1012 - 75

K3 = 104 - 27 ' 03= 1017 - 02

If4 =102 - 70 04= 1019 - 72

tf5 =101 - 19 05= 1020 ' 91

Table 1 contains standard free energy values for various ionic and 

other species that enter into calculations in this paper.
B8 CHEMISTRY OF ALUMINUM IN NATURAL WATER

TABLE 1. Standard free energies

[Dissolved species indicated by (aq), solid phase by (c), and liquid by (I)]

Species

Al+3 (aq)---_----__---------

A1F+2 (aq) __ ________.__.._

AlFa+ (aq)-._..__. _.____._...

AlF8°(aq) ______________ .

AlF4 -(aq) 

AlF5-2 (aq)-. _..._._.._.__..

AIF6-3 (aq). _...__..........

AlSO4+ (aq)--- ----------

Al(S04) a -(aq)-_ 

F-(aq)_ -

A1OH +2 (aq)_-_-_ ----__-_-- _

AlOH4-(aq)- - _-_

Al(OH) 3 (c) (mierocrystalline 

gibbsite) . 

SO4 -*_ _ 

OH-_.--.---._ ----_.

HaO(/)__.-- -----

Standard free energy 

of formation AG° 

(kcal/mole)

-115.0

- 190. 64

-264. 55

-336.46

-406. 22

-473. 92

-539. 93

-296. 7

-476. 6

-66. 08

- 165. 2

-311. 7

-272. 3 

-177.34

-37. 595

-56. 69

Source of data

Latimer (1952).

Calculated, from data of King

and Gallagher (If 59). 

Do.

Do.

Do.

Do.

Do.

and Wendt (1962). 

Do.

Latimer (1952).

Calculated from data of Hem and

Roberson (1967).

Hem and Roberson (1967). 

Latimer (1952).

Do.

Do.

Figure 2 was prepared using the values for ft to ft for 0.00 ionic 

strength, the 6 fundamental equilibrium relationships developed 

earlier for ft to ft and two summarizations :

S[A1] = [A1+3] + [A1F+2] + [A1F2+] + [A1F3 °] + [A1F4~] + [A1F5

and

S[F] = [F-] + [A1F+2] +2[A1F2+] + 3[A1F3 °]

Thus there are 8 equations and 10 unknowns, and if 2[A1] and S[F] 

are specified, all other species can then be evaluated.

In any single solution (one total aluminum value corresponding to 

a certain total fluoride concentration) many of the individual species 

do not contribute significantly to the total and can be ignored without 

serious errcr so that the number of equations needed can be decreased. 

The lines drawn on figure 2 represent the conditions where the activity 

of the species above the line is equal to the activity of the species 

indicated below the line.

In figure 2, for example, the position of the line whe^e [Al+3] 

[A1F+2] is calculated from the first two complexing equilibra, and the 

two summations.
ALUMINUM HYDROXIDE, FLUORIDE, AND SULFATE COMPLEXES B9

Since

[A1F+2]=[A1+3 ],

.

The total complexed will probably also include a significant rmount 

of A1F2+. The proportion of this form can be computed from

= 1012 - 75 [A1+3] X ID" 14 - 02 - 10- 1 - 27[A1+3].

Higher complex species will be negligible. The summation of Al 

species will then be

2[A1] = [A1+3] + [A1F+2] + [A1F2+]

= [A1+3] + [A1+3] +0.0536[A1+3] =2.0536[A1+3] .

0 -1 -2 -3 -4 -5 -6 -7 -9

FIGURE 2. Distribution of dissolved aluminum species as a function of total 

dissolved fluoride and aluminum. (Zero ionic strength.)
BIO CHEMISTRY OF ALUMINUM IN NATURAL WATER

A value for total Al is now arbitrarily selected, and the equation 

solved for [Al+3]. If the value for total Al (SA1 in fig. 2) chosen is 

10~5 molal, the value for [Al+3] becomes

2.0536[A1+3] = 10-5

[Al+3 ]=0.487 Xi(T5 .

This value which also represents [A1F+2J can now be used to find the 

total of fluoride species when S[A1] = 10~5 from the second summation 

equation

S[F] = [F-] + [A1F+2]+2[A1F2+]

=0.978X10- 7 +0.487X10- 5 +0.522X10-6 

= 5.49X10-6 =l(r5 - 26

The coordinates of the points for the A1+3 =A1F+2 line can be determined by repeating this calculation for different values of S[A1] 

and solving for the corresponding values of S[F]. Similar calculations 

using the other equilibria for the higher complexes locate the points 

for the other lines.

The summation of activities for the various species is, of course, 

equivalent to the analytically determined concentration of the element here, because the system is at zero ionic strength. Admittedly, 

zero ionic strength could be approached only in that r.rea on the 

diagram where dissolved species do not exceed about 10~5 molal, but 

the error introduced by using the diagram for somewhat higher concentrations will be relatively small.

At the right side of the graph where aluminum concentrations are 

small, the intercepts of the successive lines on the fluoride axis are 

equivalent to the (F~) values at points on the lines in figure 1 where 

activities of the two principal species are equal. As total aluminum 

concentrations increase, this relationship no longer prevails. The 

species distribution diagram, figure 1, was specified to be useful only 

when fluoride was present in excess. These conditions are represented 

by that part of figure 2 in which the lines on the diagram are parallel 

to the x-axis. Thus, figure 2 is much more broadly appUcable and 

can be used to indicate the predominant form of complex for any combination of total Al and total F concentrations. This type of diagram, 

therefore, has advantages over the usual species-distribution diagram 

for multielectrolyte solutions such as natural water.

As noted previously, figure 2 is in terms of thermodynamic concentrations. Except for very dilute solutions in which the ionic strength 

is below about 10~3 or 10~4, the stoichiometric concentrat; ons will be
ALUMINUM HYDROXIDE, FLUORIDE, AND SULFATE COMPLEXES' Bll

significantly greater than the thermodynamic concentrations. Where 

several different forms of aluminum are being considered, having 

different charges and ion configurations, it is not possible to assign a 

single activity coefficient which will convert total analytical aluminum 

concentration to an activity value simply on the basis of ionic strength 

of the solution. Therefore, the measured total concentration of 

aluminum cannot be converted accurately to an activity by m^ans of 

the Debye-Hiickel equation.

The simplest method for coping with the more concentrated solutions is to base the calculations on an arbitrarily selected value of 

ionic strength, and thus to obtain a graph which will apply directly to 

solutions at or near that ionic strength. This procedure can be extended by drawing several graphs to give as many ranges of ionic 

strength as desired, subject to the limitations of accuracy imposed by 

the methods available for calculating individual ion activity coefficients.

The species-distribution diagram based on stoichiometric data is 

qualitative in that it shows only which form of dissolved species is 

predominant. To obtain specific indications as to the proportions of 

complexed to total aluminum, a modified calculation procedure is 

required, which also obtains results that can be conveniently represented graphically as functions of analytically determined date,.

DIAGRAMS SHOWING EXTENT OF COMPLEXINQ

Figure 3, again having total concentrations of aluminum and 

fluoride as abscissa and ordinate, shows the ratio of the activity of 

aluminum in uncomplexed form to the analytical total aluminum 

for the ionic strength indicated. This ratio provides a simple means 

of determining the activity of uncomplexed Al+3 (denoted by [Al+3]), 

which in turn can be used in considering the various possible equilibria 

that might control the solubility of aluminum in a system, wtere the 

term needing evaluation is [Al+3].

Figure 3 represents a system at zero ionic strength. The effect 

of different ionic strengths will be shown in other diagrairs. The 

general calculation technique is the same, regardless of ionic strength. 

Fundamentally, the equations are about the same as the ones used 

in preparing figure 2. It is necessary to calculate a set of "hybrid" 

cumulative stability constants which will be applicable at the ionic 

strengths the diagrams are to represent, and these hybrid constants 

are represented by the symbol {}'n . These are called hybrid constants 

because they are used in an equation involving both activity and 

concentration terms. In this respect these constants are different 

from those designated by a double prime superscript (for erample, 

O, discussed earlier, which involve only concentrations.
B12 CHEMISTRY OF ALUMINUM IN NATURAL WATER

-8

-9

FIGURE 3. Ratio of free aluminum activity [A1+3 ] to total dissolved aluminum 

as a function of total dissolved fluoride and aluminum. (Zero ionic strength.)

The derivation of such a constant (X) is as follows: (Where brackets 

and parentheses denote activities and concentrations, respectively.)

0 _ [A1F+2] _1A, 01

(A1F+2 )

(AlF+2) = 

(F-)=*

[A1F+2

TAlF+2

TF- 

[A1F+2 ] 

TAIF« 

a TFX

TF7A1F+2

The activity coefficients can be computed from the ioric strength 

using the Debye-Hiickel equation. The activity rathe"- than the 

concentration of the uncomplexed form is used because this is the
ALUMINUM HYDROXIDE, FLUORIDE, AND SULFATE COMPLEXES B13

species required in the final answer. The summation equations also 

are modified by dividing each activity by the appropriate rctivity 

coefficient.

In summary, the equations required are

+ (AlF+2) + (AlF2+) + (A1F3°) + (AlF4 -)+ (AlF5

A1«

sF=(F-)-KAlF+2)+2(AlF2 +)+3(AlF3°)

+4(AlF4 -1 )+5(AlF5 -2)+6(AlF5 -3 ) 

and

The fraction present as [Al+3] can be reexpressed as

, __________________[A1+3 ]____________ *°~rAi+3i

^ !+^[Al+3 ](F-)+^[Al+3 ](F-) 2+^[Al+3 ](F-) 3 and so forth

or

oo=-

The ionic strength for the diagram can then be assigned and values for 

the stability constants and TAI« calculated.

The actual plotting on the diagram of lines representing successively decreasing values of a'0 is done one point at a time. A value of 

a'0 is chosen and a convenient value for total concentration for aluminum is selected. The SF coordinate fixing the point is calculated from 

the set of equations derived above. Additional points for the same 

value of a0' are computed for as many SA1 values as necessary to 

define the location of the line. The whole series of calculations is then

271-120 O - 67 - 3
B14 CHEMISTRY OF ALUMINUM IN" NATURAL WATER

repeated for additional lines representing other values of a'0. The procedure will be illustrated by reviewing the computations required for 

the point representing 10~2 - 00 molal total Al concentration on the 

line ao=0.001.

Figure 3 represents a solution of zero ionic strength ard therefore 

all activity coefficients have a value of 1.00. For any set of circumstances chosen there will generally not be more than three terms in 

the denominator which will require consideration. For example, when 

the value of <x'0= 0.001,

0>001 =l+107- 01 (F-) + 1012- 75 (F-) 2+1017 - 02 (F-) 3+1019- 72 (F-)4 '

A trial value of (F~) of 10~5 - 00 gives the fraction a value of 1/770 and 

the last term in the denominator is very small relative to the others. 

A somewhat larger value for (F~) is needed. When (F~) = 10~4 - 95 the 

fraction becomes 1/973 and when (F-) = 10~4 - 94, 1/1021. The last value 

is the nearest two-place exponent, and better accuracy cannot be 

shown on the diagram, although greater refinement is obviously 

possible if needed.

Using 10" ~ 4 - 94, the value of (F~) which fits the prescribed conditions, 

it is now possible to calculate the concentration of the aluminum 

fluoride complexes from the formula

where the value for [Al+3] is equal to SAlX«o, or 10~5 - 00.

(AlF+2) = 107 - 01 X10-5 - 00 X10-4 - 94=10-2 - 93 

(A1F2+) = 1012 - 75 X 10-5 -°°X 10- 9 - 88= 10~2 - 13 

30) = 1017 - 02 X10-5 - 00 X10-I4 - 82=10-2 - 80 

4-) = 1019 - 72 X10-5 -°°X10- 19 - 76=10-5 - 04
ALUMINUM HYDROXIDE, FLUORIDE, AND SULFATE COMPLEXES B15

The necessary multiples of these species are added together to obtain 

the total F, fixing a point on the line representing ao = 0.001. Similar 

computations are required for the other points.

Computations of this type are laborious, especially if diagrams 

have to be prepared for several different ionic strengths. The data for 

the series of diagrams in this paper, however, were readily obtained by 

programming the equations for solution by an electronic computer.

Figure 3 shows the high degree of complexing which can be attained 

when fluoride is present in sufficient amounts. When used together with 

figure 2, an indication of proportion of free to complexed alumHum as 

well as the predominant form of complex present is obtained. Although 

still subject to some limitations, these diagrams provide a considerably 

greater amount of useful information than the simpler speciesdistribution diagram (fig. 1). The effect of increasing ionic strength 

is to increase the percent of complexing where fluoride is present in 

excess. Where fluoride is not in excess, the effect of ionic strength 

is much less important. The closer spacing of the lines as complexing 

approaches 100 percent is interesting.

Figures 4-7 show the values of the ratio of [Al+3]/SAl for solutions 

with ionic strengths 10~3, 10~2, 10" 1 , and 0.71. The first three represent 

the range that can be covered by the Debye-Hiickel equation and 

amounts to concentrations of up to about 6,000 ppm dissolved solids. 

The value 0.71 is about the ionic strength of normal ocean water and 

activity coefficients were taken for this ionic strength partly from 

Butler's (1964, p. 438) nomograph based on the Davies equation, and 

partly from Garrels and Christ (1965, p. 103) with some interpolation 

for a few species. These values are only approximate.

The number of different ionic strengths for which computat: ons are 

made could be decreased if the contemplated application does not 

require a high degree of accuracy. The activity coefficients for the ions 

of interest at various ionic strengths are given in table 2.

Figures 3-7 are directly applicable to solutions where fluoride is 

the mam complexing species. For most natural waters, the other 

significant ions which need to be considered are hydroxide and sulfate.
B16 CHEMISTRY OF ALUMINUM IN NATURAL WATER

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ALUMINUM HYDROXIDE, FLUORIDE, AND SULFATE COMPLEXES B17

-9

FIGURE 4. Ratio of free aluminum activity [A1+3 ] to total dissolved alurrinum 

as a function of total dissolved fluoride and aluminum. (Ionic strength 

0.001.)

-9

FIGURE 5. Ratio of free aluminum activity [A1+3] to total dissolved aluminum 

as a function of total dissolved fluoride and aluminum. (Ionic strength 

0.01.)
B18 CHEMISTRY OF ALUMINUM IN NATURAL WAT^R

0 -1 -8 -9

FIGURE 6. Ratio of free aluminum activity [A1+3] to total dissolved aluminum 

as a function of total dissolved fluoride and aluminum. (Ionic strength 

0.10.)

-4 -5 -6 

log 2 Al

-9

FIGURE 7. Ratio of free aluminum activity [A1+3 ] to total dissolved aluminum 

as a function of total dissolved fluoride and aluminum. (Ionic strength 

0.71.)
ALUMINUM HYDROXIDE, FLUORIDE, AND SULFATE COMPLEXES B19 

EFFECTS OF HYDROXIDE

The principal hydroxide species which would be present in ionic 

solution below neutral pH would be A10H+2. Aluminum (Al+3) reacts 

with water to form A1OH+2 , as follows,

Al+3 +H2O=AlOH+2 +H+.

The equilibrium constant (*Ki) for this reaction is 10~4 - 75 (Hem and 

Roberson, 1967), hence

[A1OH+2]_10

[A1+3]

-4.75

[H+]

From this it is clear that at a pH of 4.75, [A1OH+2] = [A1+3], and at a 

pH of 3.75, [A1OH+2] = 0.1[A1+3]. Therefore, from a pH of 3.75 to 

neutrality, in a system where OH~ is the only complexing ligand, 

A1OH+2 becomes important relative to Al+3 . However, they both may 

be analytically unimportant when other ligands (for example, fluoride) 

are present in the system, and then it is necessary to consider all 

reactions at the same time. Figure 8 is based on computations where 

the species AlOH+? , in addition to fluoride, is considered.

-4 -5 

log S Al

-9

FIGURE 8. Ratio of free aluminum activity [A1+3 ] to total dissolved aluminum 

as a function of total dissolved fluoride and aluminum. This graph differs 

from figure 3 in that here the aqueous species A10H+2 is considered (pH 

5.00).
B20 CHEMISTRY OF ALUMINUM IN NATURAL WATER

The basic equation for a0 at zero ionic strength beconres

1

where *.K"i/[H+] represents the additional term for .A1OH+2 . The 

stoichiometric summation equation for nuoride remains the same as 

discussed in the preceding section, and the summation equation for 

aluminum now contains a term for (A1OH+2). Figure 8, based on 

electronically computed and drawn curves, shows the rat: os [Al+3]/2Al 

at a pH of 5.0 and zero ionic strength. Similar graphs (not shown) 

were prepared for pH values 3.0, 4.0, 4.5, 5.0, 5.5, 6.0, and 6.5, for 

each of the ionic strengths: 0.0000, 0.0005, 0.005, 0.07, and 0.71. 

Comparison of figure 8 with figures 3-7 shows that in the region 

where fluoride is in excess of the aluminum (that is, th?, horizontal 

portion of the curves) the calculated amount of aluminum complexed 

is increased when effects of OH~ are considered. For example, for 

SF and SA1 of 10~6 and 10~~ 7 , respectively, and at zero icnic strength, 

the ratio [A1]/SA1 decreases from 0.1 (fig. 3), where OH~ vas neglected 

to about 0.09 (fig. 8) where OH~ at a pH of 5 was considered. At a 

pH of 6.5 (figure not shown), the ratio decreases to about 0.05 as 

compared to 0.1 when OH~ is neglected (fig. 3).

In summary, the effect of neglecting the species A1OH+2 in preparing the graphs (figs. 3-7) is usually relatively small when fluoride is 

in excess of aluminum and even less when it is not present in excess. 

This suggests that in most natural waters below neutral pH the 

A1OH+2 form is an insignificant part of the total content of aqueous 

aluminum species.

In considering the effect of hydroxide on dissolved species at 

rather low pH, however, one should not lose sight of th°, important 

solubility effects and the formation or dissolution of sol: d aluminum 

hydroxide species. This is especially important above neutral pH 

where the anion A1(OH) 4~ is likely to predominate. Solubility diagrams, in which pH is a master variable, show the influence of hydroxide to better advantage and will be given in another paper.

ALUMINUM SULFATE COMPLEXES

Behr and Wendt (1962) studied the equilibria

Al+3+S04-2 =AlS04+ 

and

A1SO4++SO4- 2 =A1(SO4 ) 2-.
ALUMINUM HYDROXIDE, FLUORIDE, AND SULFATE COMPLEXES B21

They obtained equilibrium constants for the two reactions of 103 - 2 

and 101 - 9 , respectively.

In the terms used for evaluating the fluoride complexes one may 

then write

[A1S04+] _0 _in8 .

[A1+3][SO4-2]

[Ai(so4) 2 -]

[A1+3][SO4- 2] 2 ^~^

2 [Al] = [A1+3] + [A1S04+] + [Al (S04) 2 -] 

S [SOJ = [S04 - 2] + [A1S04+] +2 [Al (S04 )rl.

If the values for S[A1] and S[SO4 ] are specified, all the other species 

can be evaluated. Figure 9 is a species distribution graph which 

shows areas of dominance for the three aluminum species as functions 

of total aluminum and sulfate. The diagram represents a solution of 

zero ionic strength.

-7

-6

-5

CO

w

&D

-2

-1

AI+3

Al SO 4+

Al (SO4

-1 -3 -4 -5 

logZAI

-6 -7 -9

FIGXJRE 9. Distribution of dissolved aluminum species as a function of total 

dissolved sulfate and aluminum. (Zero ionic strength.)
B22 CHEMISTRY OF ALUMINUM IN NATURAL WAT^R

The same set of equations was used, with a specification of the ratio 

of [A1+3] to stoichiometric total aluminum (SA1) to prepare figure 10. 

This diagram resembles figure 4 in that it represents the effect of 

complexing without taking into account the effects of ionic strength. 

A more realistic picture is given by figures 11-14 which represent the 

same kind of calculation, for solutions of ionic strength 10~3 , 10~2 , 

10" 1 , and 0.71.

The procedures used in preparing figures 11-14 are directly analogous to those used in preparing the diagrams for the fluoride species, 

and, therefore, will not be discussed in detail. The activity coefficients 

used are given in table 1.

-7

-6

-5

0-4 

CO

-2

0.9

0.5

0.1

0.01

0.001

[AI+3 ]

S Al

_ i -2 -3 -4 -5 

log S Al

-6 -7 -9

FIGTJHE 10. Ratio of free aluminum activity to total dissolved aluminum 

as a function of total dissolved sulfate and aluminum. (Zero ionh strength.)

It may be of interest to note that the value of the ratio [Al+3]/S(Al) 

cannot be greater than the value of the activity coefficient for Al+3. 

This sets an upper limit for the ratio on each diagram.

The complexing effect of sulfate is obviously much weaker than 

that of fluoride, but is still significant. For example, if the total sulfate 

concentration is 500 ppm in a solution having an ionic strength of 

0.10, only a tenth of the total aluminum will be uncomplexed. In 

systems where sulfate complexing is potentially important, there 

rarely will be enough dissolved aluminum to use up more than a small 

fraction of the available sulfate.
ALUMINUM HYDROXIDE, FLUORIDE, AND SULFATE COMPLEXES B23

-7

-6 -

FIGURE 11. Ratio of free aluminum activity to total dissolved alumirum ; a function of total dissolved sulfate and aluminum. (Ionic strength 0.001.)

-9

FIGURE 12. Ratio of free aluminum activity to total dissolved aluminum as 

a function of total dissolved sulfate and aluminum. (Ionic strength 0.01.)
B24 CHEMISTRY OF ALUMINUM IN NATURAL WATER 

-7

-6

-5

00 o -3

-2

-1

0.1

0.01

0.001

0.0001

S Al

-1 -2 -3 -4 -5 

logS Al

-7 -9

FIGURE 13. Ratio of free aluminum activity to total dissolved aluminum as 

a function of total dissolved sulfate and aluminum. (Ionic strength 0.10.)

-7

-5

0-4

CO

00 5-3

-2

-1

0.02

0.01

0.001

0.0001

0.00001 

-1

S Al

-2 -3 -4 -5 

log 2 Al

-9

FIGURE 14. Ratio of free aluminum activity to total dissolved aluminum as 

a function of total dissolved sulfate and aluminum. (Ionic strength 0.71.)
ALUMINUM HYDROXIDE, FLUORIDE, AND SULFATE COMPLEXES B25

To apply these calculations to natural systems certain assumptions 

will be needed. These include:

1. Ligands other than SO4 are absent or negligible;

2. No other ion which might complex sulfate is present ir

significant quantity.

The first assumption will not hold for many systems, except perhaps 

for some acid waters that are low in fluoride. The tendency for sulfate 

to form ion pairs with the more common cations of natural waters is 

well known and may need to be considered in relating stoichiometric 

total sulfate to actual SO4~2 activity.

MIXED SOLUTE SYSTEMS

By extension of the procedures already given, it is possible to 

evaluate all the possible dissolved species of aluminum up to p.bout 

pH 7.00 by considering simultaneously the complexing reactions involving F~, SO4~2, and OH~, and to express the results as a diagram 

like those of figures 3-8 or 10-14, provided that the concentrations of 

only two components are allowed to vary at once. To cover any 

significant range of conditions a very large number of diagrams vould 

be required, but by means of a computer program the ones of particular interest could easily be prepared. On a three-dimeneional 

diagram or model, three variables could be handled at once. Tlireedimensional plots were not used in this report because, aside from the 

difficulties in drawing and interpreting a diagram in perspective, the 

treatment would still be correct for only one ionic strength.

By making the simplifying assumption that complexing ligands are 

present in considerable excess, the activity of free ligand becomes 

nearly equal to the total concentration at zero ionic strength. It is 

now possible to evaluate the relative importance of complexes formed 

by two competing ligands over a considerable range of ligand concentration. Figure 15 was prepared in part from figures 3 and 10, by 

extending the segments of the lines representing equal [Al+3]/SAl 

ratios which are parallel to the SA1 axis. For example, the line labeled 

0.5 corresponds to log SF= 7.03 and log SSO4 = 3.23. Where these 

lines would intersect represents a point at which the fluoride complex 

species and those containing sulfate are present in equivalent amounts. 

Competition between the complexing ligands causes the lines to meet 

in a smooth curve.

The location of the curved part of the [Al+3]/SAl=0.5 line can be 

determined simply by a procedure described by Hem (1963), if only 

two complex species need to be considered at a time.
B26 CHEMISTRY OF ALUMINUM IN NATURAL WATFR

r-3 

-5

-9

0.0001

0.001

0.01

~ 0.1

0.5

__ -7 -6 -5 -4 

log [SO 4 ]

-3 -2

FIGURE 15. Ratio of free aluminum activity to total dissolved aluminum as a 

function of the two competing ligands, fluoride and sulfate. (Zero ionic 

strength.)

From the complexing equilibria previously considered, it can be 

shown that

[A1S04+][Fand

[AlF+2][S04-2j

[A1(S04) 2-][F-12 

[A1F2+][S04

= 10-3.81

-212 = 10-7.65 10

For the area of interest in figure 15, these two equations define a 

nearly continuous straight line for any single ratio of complexed 

sulfate species to complexed fluoride species. The diagonal line in 

figure 15 represents a ratio of 1.0. Along this line

S[A1F species] = S[A1S04 species]. 

Where the only complexed forms of importance are A1F+2 and A1S04+
ALUMINUM HYDROXIDE, FLUORIDE, AND SULFATE COMPLEXES B27

Where 50 percent of the total activity of aluminum is complexed

[AlF+2] + [AlSO4+] nf 

 2pjj =0-5

and

=2[A1F+2]. 

From the first complexing step for aluminum and fluoride we knov that

[A1F+2] F 

[A1+3 ] L J> 

Therefore

____ 2X107 - 01= i n-7- 31

This represents the intersection of the 0.5 line with the diagonal.

The curved part of this line can be plotted by drawing other diagonals for different ratios of sulfate to fluoride complex activity and 

repeating the calculations to determine the intersection of these 

diagonals with the 0.5 line.

Figure 15 represents a system at zero ionic strength where activity 

coefficients all have a value of unity. Computations for systems having 

higher ionic strength require appropriate activity coefficients and 

modification of equilibrium constants.

An approximate indication of the effects at higher ionic strength 

can be obtained by combining appropriate graphs from figures 3-7 

and 10-14. For example, figure 16 was prepared for solutions of ionic 

strength 0.10 from figures 6 and 13 by extending the lines for equal 

values of the ratio [Al+3]/SAl to their point of intersection. The dashed 

line connecting these intersections should represent equal total concentrations of aluminum species. This relationship is not the same as 

the one used for the diagonal line in figure 15, and no exact computation of the location of curved parts of the ratio lines in figure 16 was 

made.

A graphical evaluation of the competing effects of fluoride and 

hydroxide is given in figure 17. This diagram was prepared by techniques similar to those used in preparing figure 15. However, the line 

separating the areas of dominance of F and OH species takes1 into 

account all the significant forms. Below a pH of 5.00 only A1OH+2 

and A1F+2 are considered. Above a pH of 6.00 the A1(OH) 4~ form 

is the only significant hydroxide complex, but several of the fluoride 

species must be considered at a time. The location of the dividing 

line was determined by plotting its intercept with integral pH values.
B28 CHEMISTRY OF ALUMINUM IN NATURAL WATER 

_ 2

-3 -

-4 -

-5 -

1 1 1

0.0001

0.001

0.01

0.1

-

X"

^

/

/ \

/

/

-8 -7 -6 -5 -4 -3 -2 -1 C 

logSSCU

-6 -

-9

FIGURE 16. Ratio of free aluminum activity to total dissolved aluminum as a 

function of the two competing ligands, fluoride and gulfate. (Ionic strength 0.1.)

The ratio of activity of free A1+3 to A1(OH) 4~ was determined for the 

selected pH from the cumulative constant /34 and the activity of OH" 

for that pH. The ratio of free A1+3 to the total concentration of fluoride complexes (a0) was calculated by means of equations developed 

previously for computation of complexing effects. By a procedure of 

successive approximation, a value for uncomplexed F~ was determined 

which gave a0 =[Al+3]/[Al(OH)r]. This value for [F~] then represents 

the other coordinate fixing the point through the line separating 

fluoride from hydroxide domains passes. The computation is repeated 

for as many pH values as are required to locate the curved line.

Figure 17 represents a system at zero ionic strength: activity 

coefficients all are equal to 1. It would be possible to express the 

relationship for other ionic strengths with appropriate modifications 

in the stability constants. However, because pH measurements are 

direct measurements of hydrogen and hydroxide activities, there is 

less reason for using concentration values for these variables.

The proportion of free to complexed aluminum again can be expressed by means of contours drawn on the graph. The values shown 

in figure 17 were taken from the area of figure 3 where fluoride was
ALUMINUM HYDROXIDE, FLUORIDE, AND SULFATE COMPLEXES B29

-1

-2

-4 _ 0.00001

-5 

F complexes predominate 

0.000001

-7 '

0.0001 /

0.001

0.01

o.i

-7 °- 5

OH complexes predominate

4 

-10

5 

-9

7

PH

-7

log [OH]

8 

 6

9

_ C

10

-4

FIGURE 17. Ratio of free aluminum activity to total dissolved aluminum as a 

function of fluoride and pH. (Ionic strength 0.00.)

present in excess. The values shown in figure 17 therefore are valid 

only where the total fluoride exceeds total aluminum by more than an 

order of magnitude. Under these conditions, total concentration of 

fluoride is approximately equal to the concentration of uncomplexed F~.

The method used previously for locating the ratio lines near the 

intersections of the fluoride and hydroxide domains is not readily 

applicable where more than two species at a time must be considered; 

therefore, no attempt was made to refine the diagram in that area.
B30 CHEMISTRY OF ALUMINUM IN NATURAL WATER

Figure 17 demonstrates the importance of the pH effects on aluminum solute complexes. Above neutral pH only solutions containing 

more than 2X10~4 moles per liter of fluoride (about 3.8 ppm) will 

contain more fluoride-complexed aluminum than tl ^ hydroxide 

complex (Al(OH)r).

Figure 18 is a representation of competing effects between sulfate 

and hydroxide complexes and was prepared by a mettod analogous 

to that used for figure 17. It is evident that sulfate complexes of 

aluminum will predominate only in acid solutions because even in 

brines concentrations of sulfate will be unlikely to exceed 1 molar.

0

-1

SO4 complexes predominate /

|_ 0.001

-3

-4

0.01

"/'

o.io

0.5 / 

/

OH complexes predominate

7 

PH

10

FIGURE 18. Ratio of free aluminum activity to total dissolved aluminum as a 

function of sulfate and pH. (Ionic strength 0.00.)

ALUMINUM SOLUBILITY

The effects of precipitation reactions were not considered when 

preparing the illustrations for this paper. The graphs show which 

species might be expected to be predominant in solution; they also 

show proportions of one species to others over certain concentration 

ranges. The total concentration of aluminum which could be present 

in solution at equilibrium, however, cannot be determined without 

taking precipitation reactions and solid species into account.

For pH's above neutrality, a consideration of hydroxide solubility 

is essential. Basic aluminum sulfates may be precipitate! from some
ALUMINUM HYDROXIDE, FLUORIDE, AND SULFATE COMPLEXES R31

solutions. Johansson (1963) reported obtaining crystals of a material 

having the composition 13Al2O3 -6SO3 -a;H2O (where x«79) from 

solutions 0.01 molar in aluminum and 0.03 molar in sulfate. The pH 

was not indicated but probably was in the vicinity of 4.5. The mineral 

alunite, KA13 (OH) 6 (SO4) 2 , occurs naturally. When aluminum and 

fluoride activities become high, in solutions which contain sodium 

ions, cryolite (Na3AlF6 ) can be precipitated (C. E. Roberson, 1966, 

oral commun.).

Laboratory and theoretical studies designed to explore the behavior of aluminum in mixed electrolyte solutions where complexes 

and various solids are formed will be described in later papers in 

this series.

In general, one would expect the solution complexes to increase 

the solubility of a given solid. In the simpler systems at least this 

expectation is realized and can be demonstrated in laboratory experiments. As the solutions increase in concentration and number of 

dissolved forms, however, some unexpected results can occur.

In mixed electrolyte solutions brought to supersaturation with 

one or more solids, the form that will be precipitated may depend 

more on reaction kinetics than on equilibrium status. Silica, which is 

present as H4SiO4 in all natural water, may depress the solubility of 

aluminum by forming co-polymer layer-type minerals, such as the 

clay minerals. Solid basic aluminum fluoride and other mixed species 

may be less soluble than simple hydroxides under some conditions.

APPLICATION TO NATURAL WATER

The graphs in this paper can be used directly for estimating the 

proportion of the total aluminum content comprised by uncomplexed 

Al and the most likely forms of aluminum in solution. The two analyses 

used here were published by White, Hem, and Waring (1963, p. F54) 

and represent samples collected in September 1957 from Mammoth 

Springs and Big Horn Spring in Wyoming. Computed values for the 

logarithms of the concentrations of fluoride, sulfate and aluminum 

and other pertinent data are given in table 3.

TABLE 3. Chemical analyses for two natural waters

pH._.. ._._.._.___

Ionic strength _ _

Al_____.___.

SO4 ________

F___ _. _

ppm

0.2

501

2.4

6.6

0.039

moles per liter

0. 7X10- 5

5.2X10-3

1. 3X10-4

log moles 

per liter

-5. 13

-2.28

-3.89

ppm

0.4

726

3. 5

6.2

0.057

moles per liter

1. 5X10- 5

7. 6X10-3

1.8X10-4

log moles 

per liter

-4.82

-2. 12

-3. 74
B30 CHEMISTRY OF ALUMINUM IN NATURAL WATSR

From the concentrations of the complexing ligands and figures 

15-18, it is evident that fluoride complexes of aluminum are the 

predominant aluminum species in these solutions. Because the water 

has an ionic strength considerably greater than zero these graphs 

cannot be used to compute [Al+3]. Figure 6, however, provides a 

means of estimating this value. For both waters [Al+3] is indicated to 

be very nearly 10~5 X total Al, or in the vicinity of 10~ 10 moles per 

liter. Figure 2 indicates the predominant complex to be A1F3 °.

Both of these waters contain moderate amounts of silica, and the 

low activity of free aluminum may be related to interactions between

aluminum and silica.

SUMMARY

Despite limitations mentioned for use of the diagrams, several 

interesting implications for natural waters appear.

1. In a solution containing fluoride in excess of aluminum, nearly all 

the latter would be associated with one or more fluoride ions. 

This is true below neutral pH. Above neutral pH the hydroxy 

complex appears to be dominant.

2. Below neutral pH, except in water containing very high sulfate 

concentrations, fluoride, if present in excess of aluminum, is 

probably the most important ligand in tying up aluminum. This 

means that OH~ also is generally unimportant in this region and 

the effect of pH can be ignored, if one keeps in irind the fact 

that only aluminum in "true" solution is being considered.

3. A unique type of distribution graph has been introduced in this 

report. This graph permits one to estimate the activity of uncomplexed aluminum in an aqueous solution, given merely the 

stoichiometric analytical data. The activity so obtained should 

be useful in studies of the factors which control aluminum 

solubility.

4. The methods for preparing these diagrams, although not new, 

have involved some unique features. Calculations like these are 

not complicated but are laborious if done by hand because of 

the potentially large number of variables and specie^. Use of an 

electronic computer, however, permits a large number of calculations to be performed so that simple two-dimensional graphs, 

each applicable to a restricted set of conditions, may readily be 

prepared.
ALUMINUM HYDROXIDE, FLUORIDE, AND SULFATE COMPLEXES B3«3

REFERENCES

Behr, Barbara, and Wendt, H., 1962, Fast ion reactions in solutions, (I) formation of the aluminum sulfate complex: Zeitschr. Elekrochemie, v. 66, 

p. 223-228.

Brosset, Cyrill, and Orring, Jonas, 1943, Studies on the consecutive formation 

of Al fluoride complexes: Svensk Kemisk Tidskr., v. 55, p. 101-116.

Butler, J. N., 1964, Ionic equilibrium, a mathematical approach: Reading, Mass., 

Addison-Wesley Pub. Co., p. 267.

Garrels, R. M., 1960, Mineral equilibria: New York, Harper & Bros., 254 p.

Garrels, R. M., and Christ, C. L., 1965, Solutions, minerals and equilibria: New 

York, Harper and Row Publishers, 450 p.

Hem, J. D., 1960, Calculation and use of ion activity: U.S. Geol. Survey WaterSupply Paper 1535-C, p. C1-C17.

 1963, Manganese complexes with bicarbonate and sulfate in natural 

water: Jour. Chem. & Engr. Data, v. 8, p. 99-101.

Hem, J. D., and Roberson, C. E., 1967, Form and stability of aluminum hydroxide complexes in dilute solution: U.S. Geol. Survey Water-fupply 

Paper 1827-A, 55 p.

Johansson, Georg, 1963, On the crystal structure of the basic aluminum sulfate 

13 Al2O3 -6SOrz H2O: Arkiv. kemi., v. 20, p. 321.

Kielland, Jacob, 1937, Individual activity coefficients of ions in aqueous solutions: Jour. Am. Chem. Soc., v. 59, p. 1675-1678.

King, E. L., and Gallagher, P. K., 1959, The thermodynamics of aluir'num, 

III. Fluoride complex ion reactions. The graphical evaluation quotients 

from n([X]): Jour. Phys. Chem., v. 63, p. 1073-1076.

Latimer, W. M., 1952, Oxidation potentials: New York, Prentice-Hall, 392 p.

Sill4n, L. G., and Martell, A. E., 1964, Stability constants of metal-ion complexes: 

Chem. Soc. [London] Spec. Pub. 17, 754 p.

White, D. E., Hem, J. D., and Waring, G. A., 1963, Data of geochemistry, Sixth 

Ed. Chap. F, Chemical composition of subsurface waters: U.S. Geol. Purvey 

Prof. Paper 440-F, p. F1-F67.

U. S. GOVERNMENT PRINTING OFFICE : 1967 O - 271-120