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Mineral—solution equilibria in sparingly soluble mineral systems
Colloids and Surfaces, 15 (1985) Elsevier Science Publishers B.V.,
MINERAL-SOLUTION MINERAL SYSTEMS
J. OFORI
School of Engineering (U.S.A.)
and Applied
7 May 1984;
-Printed
EQUILIBRIA
P. SOMASUNDARAN,
(Received
309
309-333 Amsterdam
accepted
IN SPARINGLY
AMANKONAH Science,
in The Netherlands
and K.P. ANANTHAPADMABHAN
Columbia
in final form
SOLUBLE
University,
22 March
New
York,
NY
10027
1985)
ABSTRACT Recent solubility, electrokinetic, spectroscopic and flotation studies in our laboratory on apatite and calcite in aqueous electrolytes indicate complex mineral-solution interactions which can alter surface characteristics of these minerals markedly in the presence of each other. In the case of systems containing such sparingly soluble minerals, understanding of the mineral-solution chemical equilibria under different physico-chemical conditions becomes important for developing schemes for processing them. The chemical equilibria in heterogeneous systems involving salt-type minerals are investigated in this work. Stability relations have been analysed on the basis of bulk equilibria for calcite, apatite, magnesite, calcite-apatite, calcite-dolomite, apatitedolomite, gypsum-anhydrite, calcite--gypsum, calcite-apatite-dolomite and calcite-magnesitedolomite systems. The role of atmospheric carbon dioxide, which under most laboratory experimental conditions cannot be avoided, has been emphasised. Theoretical results have been correlated with experimental data reported in the literature.
INTRODUCTION
Difficulties are often encountered in processing heterogeneous mineral systems under conditions predicted on the basis of single mineral tests. In systems containing minerals such as calcite and apatite which dissolve to a significant extent in water, the effect of dissolved species on the behavior of these minerals can be severe. In this study, chemical equilibria in selected single and mixed mineral systems are examined in order to determine the role of the dissolved species. The dissolution characteristics that take place in calcite-water [l-3] and apatite-water [4-71 single mineral systems have been studied in detail in the past. The results for the solubility of apatites [8, 91 and other phosphates are, however, not in agreement with each other [ 8-10 ] . Much of the work on the apatite-aqueous solution system has been centered upon obtaining reliable solubility constants for hydroxyapatite, fluorapatite and other phosphates. Difficulties encountered in this have been attributed to the existence of a non-stoichiometric solid phase. Several authors,
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Elsevier
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Publishers
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310
being unable to get a constant solubility product for apatite, were even led to suggest various surface complexes such as Ca,(HPO,)(OH), [B, 111. Careful experimentation by Saleeb and de Bruyn [12] has, however, revealed that hydroxyapatite and fluorapatite have stoichiometric composition and well-defined stability constants. They have shown that one can get a constant solubility product if precautions are taken during the preparation to obtain a stoichiometric compound. The discrepancies between the data obtained-by various workers [ 131 can also be attributed to the crystal structure modifications and the presence of impurities, including added electrolytes that can influence the solution equilibria [ 81 . Whereas a chemical that complexes with dissolved mineral species would enhance the dissolution, chemicals that would adsorb on the solid can be expected to decrease the dissolution kinetics. It has been shown that the flotation of certain minerals such as tenorite and chrysocolla using oximes as collectors decreases with increase in mineral solubility [ 141 . Interactions of the dissolved mineral species with the collector have been speculated to be responsible for this effect. There are five sparingly soluble calcium phosphates that are of importance in aqueous systems. It is generally considered that hydroxyapatite is the least soluble of these salts. Brown [9] and Nancollas et al. [15] have shown that, although hydroxyapatite is the most stable salt under conditions found in nature, it becomes less stable (i.e. more soluble) than CaHPO, and CaHPO,. 2H20 if the solution is sufficiently acidic. As described in a later section, the pH at which the relative stability of Ca10(P04)6(OH)2 and CaHPO, is reversed (i.e. the singular point) is 4.8 and is shown to depend markedly on the presence and concentration of other chemical components [B, 91 . When apatite is exposed at normal temperature and pressure to a solution at a pH below the singular point, its surface can be covered by a coating of monetite (CaHP04). This can lead to apparent low solubilities for apatite. On the other hand, precipitation of a particular calcium phosphate from solution is markedly dependent on, in addition to pH, the concentrations of calcium, phosphate and other species in the system. Modifications in the precipitation process due to the presence of different mineral components have not, however, been investigated in detail in the past and consequently not adequately taken into account in the correlation of experimental results with theoretical predictions. The resulting apparently anomalous behavior may have led several investigators to the conclusion that the properties of calcium phosphates in general, and apatite in particular, are rather variable [B, 91. Another factor that can influence mineral stability is the particle size. Particle size and surface energy considerations appear to suggest that, in the case of the CuO/Cu(OH), system, tenorite (CuO) which is the stable phase when present as coarse size particles can change its chemical form to Cu(OH), if the size is reduced below a critical value [2, 31 . An aspect needing greatest attention is perhaps the interaction between
311
dissolved mineral species and surfactants. Adsorption of surfactants on particulates is the governing parameter in a number of interfacial processes such as flotation, flocculation, tertiary oil recovery using surfactant flooding, lubrication, detergency, comminution, chromatography and clarification for waste treatment, etc. The role of dissolved mineral species in surfactant abstraction (depletion) in these systems can be influenced significantly, in addition to solution properties such as pH, salinity and temperature, also by the mineral type [16]. Minerals such as calcite, gypsum, magnesite and limestone can be present in most reservoir rocks and systems, and recent experiments [17] have shown their predominating influence on sulfonate depletion in these systems. A knowledge of the equilibria in salt-type minerals is also important for the understanding of the interfacial processes in enhanced oil recovery. The role that dissolved mineral species play in determining the surface charge generation and thereby adsorption has been discussed by several investigators [4--8, 18, 191. An understanding of the influence of the factors discussed above on the solubility and hence the chemical equilibria in heterogeneous mineral/aqueous system will therefore prove beneficial in developing capabilities to predict and control the behavior of minerals during interfacial processes such as adsorption, flotation and flocculation. The chemical equilibria in heterogeneous systems involving salt-type minerals are examined in this work. Stability relations have been discussed on the basis of bulk equilibria. MINERAL-SOLUTION
EQUILIBRIA
The equilibria in selected salt-type mineral systems with special reference to calcite and apatite are examined below. Theoretical results are correlated with experimental data. Calcite equilibria
The following are the major situations in which calcite equilibria could be considered [ 2, 31: (1) Closed system: system closed to atmospheric CO3. (2) Open system: system open to atmospheric CO3. Although these are two extreme cases most often realized in practice, other intermediate conditions can also be obtained. When calcite is brought in contact with water, its dissolution will be followed by pH-dependent hydrolysis and complexation of the dissolved species. The following are the equilibria that will control the system [ 1, 181. CaCO,( s) CO;- + H’ HCO; + H+ COz(g) + Hz0
2 f + 2
Ca*+ + CO:HCO; H&O3 H3CO3
KS,
10-8.4 1010.3
106.3 10-1.5
312
Ca2’ + Ca2+ + Ca2+ + Ca” +
HCO; CO’,H,O 2H20
z f 2 2
CaHCO: CaCO,(aq) CaOH’+H’ Ca(OH), + 2H’
loo.8 103.3 10-12.9 10-22.8
While the activities can fairly easily be calculated in the case of the open systems due to the fixation of the partial pressure of atmospheric CO* at 10U3.’ atm, calculations for the closed systems are relatively tedious. The use of computer programs is therefore generally required in such calculations. During this investigation, a computer program is developed to calculate the activities of various dissolved species from available thermodynamic data, taking into consideration the effects of other dissolved species and solid phases in equilibrium with the system. Figures l(a) and l(b) show the distribution of various species as a function of pH for the closed and open systems, respectively. The marked effect of atmospheric COz on the solubility of calcite can be seen by comparing the data in these diagrams. This effect is particularly noticeable for Ca2’, HCO; and CO:- activities. Since Ca2’ plays a very important role in calcite flotation systems, the possible role of CO2 on flotation as well as other interfacial processes due to this effect should be noted. Beck’s theory on solubility [20] is examined using the data in these diagrams. This theory suggests that, when a solution is in equilibrium with the solid phase, the isoelectric point (IEP) will correspond to the pH of minimum solubility. Figure 2(a) shows a plot of total carbonate, total calcium and total solubility” as a function of pH. By applying Beck’s theory, an IEP of 8.4 is obtained for the calcite open system. Somasundaran and Agar [l] obtained a value of 8.2 for the IEP of calcite by measuring the pH of minimum solubility (Fig. 2(b)). The close agreement between the theoretical and the experimental IEP values suggests that the experiments were conducted under near equilibrium conditions, and that the thermodynamic data used in these calculations best describes the calcite open system. A value of 8.4 obtained by Garrels and Christ [3] from similar theoretical considerations and also results reported in literature [21] confirm the thermodynamic description given here for the calcite system. However, it must be mentioned that numerous data in the literature on the IEP of calcite are not in agreement with each other, this being possibly the result of non-equilibrium and differences in solution conditions under which the experiments were conducted [6, 181. Also, the source of the minerals used in the various experiments can be expected to play a significant role in this discrepancy [ 181. In order to further assess the effects of CO2 on the calcite system, the results for total calcium and total solubility are presented in Fig. 3 for the closed system. The levels of total solubility in the two systems (compare Figs 2 and 3) clearly show the magnitude of the CO, effect on the calcite *The total solubility is defined given solution conditions.
here as the sum of the activities
of dissolved
species
under
313
-10
-12
-4
4
6
I
1
CALCITE
I
4
Fig. 1. Species
PH
1
I
10
12
I
I
14
I
(OPEN)
I
-12
0
6
distribution
I
I
I
8
PH
10
diagrams
I
I 12
for calcitewater
(b)
1 14
systems:
(a) closed,
(b) open.
-10
4
6
4-
7--1-w
14
12
10
8 PH
I
,1
I
I
2-
3-
_,21’. 4
1 6
8
IO
I
I
I
12
4
PH
Fig. 2. Determination PI.
of the isoelectric
point for calcite:
(a) theoretical,
(b) experimental
315
4
r
I
I
I
CALCITE
6
6
4
Fig. 3. Solubility
1
I
I
I
I
I
(CLOSED)
of calcite
PH
10
in water (closed
14
12
system)
as function
of pH.
solubility. As seen from Fig. 3, Beck’s theory predicts an IEP of about 11.3 for the calcite closed system. This implies that values ranging from 8.2 (completely open systems) to 11.3 (completely closed systems) can be obtained for the IEP of calcite depending on the partial pressure of carbon dioxide in equilibrium with the system. Experiental values ranging from 8.0 to 10.8 reported in the literature [ 181 can at least partly be attributed to the differences in the partial pressure of carbon dioxide. Apatite
equilibria
The equilibria below [5-7,181.
that
control
the dissolution
of apatite
in water are given
KS,
Ca,,(P04)6(F,0H)2 PO:- + H’ $ HPO:- + H’ = H,P04 + H’ +Ca2+ + H,O f Ca2+ + 2H20 f F- + H+ f Ca2’ + HPOj- 2
f 10Ca” + 6PO:- + 2(F-,OH-) HPO:H,PO: H,PO‘, CaOH’ + H’ CatOH), + 2H’ HF CaHPO,(aq)
lo-“* 1012.3
1o7.2 102.2 10-12.9
:Fr
102.’
(F)
316
CaHP04( aq) Ca2+ + H,POi Ca2+ + 2FCa2+ + F-
f ? f 2
CaHPO,( s) CaH2P0i CaF,(s) CaF’
104.3 lo’.’ 1010.4
1O’JJ
As in the case of calcite, the activities of various dissolved species were calculated at different pH values by using the relevant chemical equilibria and stoichiometric restrictions (one for hydroxyapatite and two for fluorapatite*). The distribution of the activities of dissolved species is given in Figs 4(a) and 4(b) for open and closed systems, respectively. If the system is brought in equilibrium with atmospheric carbon dioxide, the distribution will follow that shown in Fig. 4(a). For the closed system, Ca*’ species are the most predominant below about pH 12.5. The predominant phosphate species are H,PO;, HPOi- and PO:- depending on pH. By comparing the data in Fig. 4, it can be seen that, below about pH 9, the effect of atmospheric CO* on Ca*’ activity is not as drastic in this case as for calcite (Fig. 1). Above this pH, marked changes are observed: while the Ca*’ activity decreases sharply with increase in pH, an increase is observed in the activities of HPOt- and PO:- species (Fig. 4(a)). The sharp decrease in the Ca2’ activity with an increase in the phosphate solubility under high pH conditions is due to the precipitation of CaC03. Figures 5(a) and 5(b) show the effect of atmospheric carbon dioxide on the total solubility of apatite. Again, the marked effect of carbon dioxide on the total solubility is seen here. If the pH of minimum solubility is taken as the IEP [l, 201, a value of 7.2 is obtained from Fig. 5(a) which is in good agreement with the experimental values obtained earlier [6, 7, 21, 221. To our knowledge, however, no data are reported in the literature to support the IEP value of about 12 for the apatite closed system as predicted using Beck’s theory (see Fig. 5(b)). STABILITY
RELATIONS
IN CALCITE-APATITEMONETITE
SYSTEMS
As mentioned earlier, of the five most important sparingly soluble calcium phosphates it is generally assumed that hydroxyapatite is the most stable [&lo, 23, 241. While this is true generally under natural conditions, this assumption could lead to erroneous interpretations under other experimental conditions. Figure 6 shows solubility isotherms for apatite, monetite and calcite at 25°C. The singular point for monetite and apatite is 4.8 and that for apatite and calcite 9.3. This shows that, below pH 4.8, monetite is more stable (i.e., less soluble) than apatite. The implication is that, if apatite is brought in contact with acidic solutions (pH < 4.8), two processes could occur: *Total calcium/total is total calcium/total
phosphate (CaT/PT) = 1.667. Additional restriction for fluorapatite fluoride (PT/FT) = 3. fluoride (CaT/FT) = 5 or total phosphate/total
317
4
I
1
I
I
1
HYDROXYAPATITE
I
I
(OPEN)
00 /
2 -
4
I
1
1
1
I
HYDROXYAPATITE
I
(a)
/;
I
I
/
I
(CLOSED)
-
I
(b)
2
4
Fig. 4. closed.
6
Species
distribution
6
PH
diagram
10
12
for
14
hydroxyapatite-water
system : (a)
(b)
318
HYDROXYAPATITE
(OPEN)
2 -
o-
* E
4
I
HYDROXYAPATITE
1
I
I
1
(b)
(CLOSED)
TOTAL
SOLUBILITY
-8
-10
-12
1
4
Fig. 5. Effect closed.
I
I
6
of carbon
1
8
dioxide
I
1
PH
L
10
on the total
I
I
12
solubility
14
of hydroxyapatite:
(a) open,
(b)
319
++G
-4
k > -6 I3 F 2 -6 :: l-10
-12
I 4
I
I
I
6
I
6
I
I
10
I
1,
12
I 14
PH
Fig. 6. Solubility
isotherms
at 25°C
for monetite
(CaHPO,),
apatite
and calcite.
(1) The more stable phase, monetite, could precipitate from solution with the formation of a coating on the surface of the apatite particles, or (2) the surface of the apatite particles could undergo appropriate chemical reactions to convert to monetite [9]. In either case, the apparent solubility behavior of apatite in a solution more acidic than the singular point may be quite different from what one would expect for apatite. The formation of the most acidic phosphate in the form of a coating on apatite surface can lead to apparent low solubilities for apatite [8, 91. It can also be seen from Fig. 6 that, above the singular point of 9.3, calcite is more stable than apatite. This implies that, if the apatite system is open to atmospheric COz, calcite can either precipitate from solution and subsequently form a surface coating on apatite, or the surface of apatite particles could be converted to calcite through surface precipitation or various surface reactions. Reactions involving organic and inorganic species leading to surface precipitation have been examined in detail elsewhere [ 251. The conditions for the conversion of apatite to calcite can be more readily identified by considering the chemical reaction responsible for the process: Ca,,(PO,),(OH),(s)
+ lOCO:-
= lOCaCO,(s)
+ 6POd3- + 20H-
It, can be seen from this reaction that, depending on the pH of the solution, apatite can be converted to calcite if the total carbonate in the solution
320
-10
-12
1
L___A__L-_:
4
6
0
10
12
14
PH
Fig. 7. Illustration
of the possibility
of the conversion
of apatite
to calcite.
is above a certain critical value. Figure 7 shows the total carbonate required for the conversion reaction (apatite + calcite) under open and closed system conditions. Also, the total carbonate in equilibrium with the calcite system under both conditions is shown. As can be seen, the amount of dissolved carbonate from atmospheric CO2 far exceeds the amount required to convert apatite to calcite under high equilibrium pH conditions (above pH 9.3). Although the kinetics of such transformations is not known, such reactions can be important in determining the surface characteristics of minerals. The implication of this in processes such as adsorption, flotation and flocculation is obvious. Most interestingly, the calcite surface can also be converted to apatite under appropriate conditions [2, 221. Figure 8 shows the amount of phosphate required to convert calcite to apatite along with the total phosphate in equilibrium with apatite. Below pH 9.3, the amount of phosphate that can be in equilibrium with apatite far exceeds the amount required to convert calcite to apatite if the system is open to atmospheric COz. If the system is closed, it is seen that the conversion is possible in the entire pH range. It is interesting to note the amount of phosphate required for this process at each pH value. For example, for the closed system, only about 10-l’ kmol mm3 of phosphate is required to produce the conversion effect around pH 13. As mentioned before (Figs 6 and 7), apatite can be converted to calcite above pH 9.3 if the system is open to atmospheric CO,. This implies that
321
CALCITE(OPEN)~HAP
t
/
-10
4
6
6
10
12
14
PH
Fig. 8. Illustration
of the possibility
of the conversion
of calcite
to apatite.
calcite supernatant prepared above this pH could contain more than enough carbonate to convert apatite to calcite. Zeta-potential measurements conducted with calcite and apatite in water and in the supernatants of each other have shown that, indeed, these processes do occur [22]. Figure 9 presents the results of zeta-potential measurements in water and in supernatants. It can be seen that the two minerals have almost interchanged their points of zero charge (PZC). Additional electrokinetic experiments in relevant organic solutions, as well as solubility [26] and spectroscopic (ESCA) [27] studies have shown the surface conversion of apatite to calcite and vice versa under appropriate solution conditions. The ESCA results in Fig. 13 (Ref. [22] ) clearly show the surface conversion process. Apatite conditioned in the supernatant of calcite at about pH 12 exhibits spectroscopic properties characteristic of both calcite and apatite, an indication of the conversion of the surface of the apatite to calcite [27]. Another aspect that is important from a surface chemical point of view is the transformation that hydroxyapatite can undergo in inorganic solutions. The solubility of various calcium minerals is shown in Fig. 10 as a function of pH. Comparison of the hydroxyapatite (HAP), fluorapatite (FAP) and fluorite (CaF,) solubilities shows that CaF2 is the most stable phase below about pH 5 and that FAP is the most stable mineral in the intermediate pH range while HAP is stable at high pH. This implies that, if systems in equilibrium with hydroxyapatite are brought in contact with a sufficiently high
322
__.__
60
---._---7---~
2 x lo-3
kmol/m3 o A A .
,i
KNOLI
CALCITE APATITE APATITE CALCITE
IN IN IN IN
WATER WATER CALCITE APATITE
SUP SUP
d._l___i_.
6
7
8
3
10
11
I2
13
PH
Fig. 9. Illustration
of the effects
of supernatants
on the IEP of calcite
and apatite.
-6-
Fig. 10. Solubility
of various
calcium
minerals
as a function
of pH at 25°C
323
concentration of fluoride ions, the apatie acidic pH conditions. In fact, numerous 28, 291 support this conclusion. Results tial measurements presented in Fig. 11
will be converted to fluorite under data reported in the literature [7, of fluoride uptake and zeta-potenindicate the occurrence of these (a)
APATITE pH 45
-4.7
.A
10-Q
lo-
EOUiLlBRlUM
-50
FLUORIDE
3
10-2
CONCENTRATION.
moldlster
1
1
I
1
I
,
0
2
4
6
8
10
12
Hd
Fig. 11, Illustration of surface conversion of hydroxyapatite take [ 28 1, (b) electrophoretic mobility [ 7 1.
to fluorite:
(a) fluoride
up-
324
processes. Figure 11(a) [28] shows the fluoride uptake by hydroxyapatite as a function of fluoride concentration at three pH values. The steep rise in the fluoride uptake at pH 4.5-4.7 has been attributed to CaF, formation. The data in Fig. 11(b) [7] also show that the apatite surface is more positively charged in the presence of lo-’ kmol mm3 KF solutions than in KN03 alone below pH 5. Above this pH, it is more negatively charged. These observations are attributed to the formation of fluorite at low pH values and of fluorapatite at higher pH in accord with the fact that the PZC of these minerals are in the order fluorite > hydroxyapatite > fluorapatite [7]. Therefore, in such a system, hydroxyapatite is stable only in the basic pH range. However, if the system is brought to equilibrium with atmospheric carbon dioxide, the precipitation of calcite under high pH conditions will make the apatite completely unstable under all pH conditions. MAGNESITE
EQUILIBRIA
Similar to the cases examined above, CO* is expected to play a major role also in systems containing magnesite. Based on Beck’s theory, an IEP of about 8.6 is obtained for magnesite (Fig. 12) which is in good agreement with the experimental value of 8.7 obtained by Somasundaran and Viswanathan [17]. It must, however, be noted that there are large differences in reported solubility data for magnesite and the other most common carbonates 4
8
10
12
14
PH
Fig. 12. Solubility
of magnesite
(open
system)
as a function
of pH.
325
in the Mg-W-Hz0 system. Table 1 illustrates this problem by comparing the free energy and equilibrium constant values from various sources for the most common minerals in this system at 25°C. The results obtained by using Langmuir [ 301 and Latimer [ 311 data, and Stumm and Morgan [ 21 data for the closed system are given in Figs 13(a) and 13(b), respectively. Comparison of the data in the two figures shows that magnesite is not stable in the pH range examined if Langmuir and Latimer data are used. However, on the basis of Stumm and Morgan data, mangesite is the most stable solid below about pH 10.7. Furthermore, using the data reported by Robie and co-workers [32] a value of 8.2 is obtained for the solubility product (pKsp) of magnesite, which is quite different from the values reported by Stumm and Morgan [2] and Langmuir [30] (see Table 1). The problems that can arise resulting from the differences in the interpretation of system behavior due to the use of such different data are obvious. It is to be noted that the Stumm and Morgan data are in close agreement with those reported elsewhere in the literature [3] Figure 13(b) shows that, when magnesite is equilibrated with water in a ‘closed system at sufficiently high pH (> 10.7), brucite (Mg(OH),), which is the more stable phase, can form and thus convert the magnesite surface to brucite. TABLE
1
Illustration of system at 25°C Mineral
the
variance
in solubility
data
Formula
for
some
MgCO, Mg(OH): MgCO,.SH,O Mg,(CO,),(OH),*3H,O
CALCITE-APATITE-DOLOMITE
in the
[ 301
Stumm and Morgan
Mg”-C02-H,O
PKW Langmuir and Latimer
Magnesite Brucite Nesquehonite Hydromagnesite
minerals
4.9 11.6 5.4 29.5
[ 311
7.5 11.6 4.7 29.5
Robie et al. [32 ]
[2] 8.2 _ _
EQUILIBRIA
As mentioned earlier, the problem of separation of apatite from carbonates can be exemplified by the beneficiation of dolomitic phosphates in Florida where conventional flotation techniques have not been able to yield a concentrate with an acceptable MgO level of less than 1% [33]. Since dolomite is in most respects like calcite and it is found in significant ratios with apatite, dissolved species can be expected to play an important role in this system also. The stability of dolomite under various conditions can be examined in the following manner. Consider the situation in which calcite or apatite is con-
326 4
f
I
I
I
(CLOSED
++CY
-4
-
-6
-
-6
-
-J-1o
-
,
I
SYSTEM
I
1
I
-
(a)
1
k z 5 F 2 ::
(CLOSED
: r”
-4
-
-6
-
SYSTEM)
(b)
k z
>
L 5:
-0-
:: J -10
-
-12
I 4
I 6
!
1
I
6
1 10
I
I 12
I 14
PH
Fig. 13. pH ranges of stability of the common minerals in the MgZ++ZO,-H,O (a) Langmuir and Latimer data [ 30,311, (b) Stumm and Morgan data [ 21.
system:
327
--r
1.-
I
I
I
DOLOMITE
I
I
IAPATITE
(CLOSED)
’
(0)
PH 4
/
I
CALCITE
I
/
/ DOLOMITE
1
I
/APATITE
I
,
(OPEN)
’
( b)
2
0
\ -2
-6
.
4
6
8
10
14
12
PH
Fig. 14. Stability relations in calcite-apatite-dolomite 10m4 kmol rnm3, (a) closed ([carbonate] = lo-” kmol
m-“),
system at 25°C. (b) open.
[Mg’+]
= 5.0
X
328
tacted with a solution containing 5 X 10e4 kmol mW3Mg2’ under open or system conditions. The results in Fig. closed (10L3 kmol rnd3 carbonate) 14(a) indicate that, under the closed system conditions, dolomite will precipitate if the system is equilibrated with calcite above pH 8.2. The conversion of apatite to dolomite will also take place under similar conditions above pH 9.2. If the system is equilibrated in the presence of atmospheric carbon dioxide (Fig. 14(b)), the calcite-dolomite and apatite-dolomite singular points occur at pH 8.2 and 8.8, respectively. The results indicate that atmospheric carbon dioxide has minimal effect on the relative stability of calcitedolomite and apatite-dolomite systems. This rather interesting observation will be discussed later in the next section. If calcite and apatite are equilibrated together in 5 X 10e4 kmol mm3 Mg2+ under open or closed (10Y3 kmol mS3 carbonate) system conditions, apatite will be the most stable phase under pH conditions. Dolomite precipitation reaction will determine the solubility of the system at high pH. As seen from the results, calcite is the least stable of the minerals under all the pH and CO2 partial pressure conditions examined. It should be noted that both experimental and theoretical work on the apatitedolomite system is limited and reported solubility data are conflicting with each other. This is reflected in the discrepancy of solubility product values reported for dolomite by dif4
2
0
-0
-10
-8
-6
-4 LOG
-2 -
0
2
4
[co++1 rMQ++l
Fig. 15. Stability relations 1O-4 kmol me3 [2 J.
in the Ca 2+-Mgz+-C0,-H,0
system
at 25°C
for [Mg]
= 5.0
X
329
ferent investigators which range from 10-‘6.5 to 10-‘9.5 [2]. The difficulty in devising a scheme for the beneficiation of Florida dolomite phosphates and other phosphates in general can be attributed at least partly to the lack of understanding of the chemical equilibria governing the apatite--dolomite system. The surface conversion of apatite to dolomite and vice versa should be of major concern when considering such schemes. CALCITE-MAGNESITE-DOLOMITE
SYSTEM
Figure 15 shows the relative stability of calcite, magnesite, dolomite and brucite. The conversion of magnesite to dolomite and then to calcite is seen to be possible at various calcium/magnesium ratios. If dolomite is equilibrated with water in the presence of negligible amounts of CO?, brucite will precipitate in the system. From the data in Figs 14 and 15, the conversion of dolomite to magnesite or calcite has minimal dependence on the partial pressure of carbon dioxide if the level is above about 10m6 atm. Below this value, however, brucite will be the most stable phase. SYSTEMS
INVOLVING
Calcite--gypsum
GYPSUM
equilibria
Since gypsum is one of the most soluble salt-type minerals, the high level systems will lead to the precipitation of Ca” activity in the gypsum-water
_I 8
10
12
14
PH
Fig. 16. Illustration
of the possibility
of conversion
of gypsum
to calcite
[17 ]
330
of CaC03 under certain pH conditions if the system is open to atmospheric carbon dioxide. Figure 16 shows the possibility for the conversion of gypsum to calcite at 25°C. At pH values higher than 8.2, CaCO, is expected to form if the system is open to atmospheric CO*. Thus gypsum is expected to be converted to calcite, like most of the calcium minerals discussed above, under high pH conditions. Gypsum-anhydrite
equilibria
Depending upon the temperature and other solution conditions, gypsum can exist as anhydrite (CaSO.,) or hemihydrite (CaS04* 0.5H,O). Free energy considerations indicate that gypsum should be the more stable phase at temperatures lower than about 45°C while, above this temperature, anhydrite should be more stable (see Fig. 17 [17]). Even though the conversion of gypsum to anhydrite is thermodynamically possible, the kinetics of this process is not well understood. The possibility of the existence of gypsum at higher temperatures and anhydrite at lower temperatures under laboratory experimental conditions should therefore be considered. It is seen from the above data that significant alterations in the surface chemical properties can take place owing to precipitation of various salts I
z
0.3
-
0.2
-
0.1
-
GYPSUM
0
1 ,” 1 L -0.1
-
E
a
- 0.2
ANHYDRITE
-
0
20
40
Fig. 17. The free energy of temperature [ 17).
80
60
TEMPERATURE,
change
100
‘C
for the conversion
of gypsum
to anhydrite
as a function
331
when sparingly soluble minerals are contacted with water. Furthermore, the nature of the precipitate is markedly dependent in many systems upon the pressure of carbon dioxide in the environment. It is evident that many chemical alterations can take place in aqueous systems containing minerals such as calcite, apatite, magnesite, dolomite or gypsum in the presence of each other. The conversions are due not only to the presence of carbon dioxide in the system, but also to pH and pH alterations during the equilibration. It is in fact to note the serious effects of such surface conversion reactions in determining the efficiency of various interfacial processes such as adsorption, flotation, flocculation and leaching. SUMMARY
The major findings from this investigation are summarized below: (1) Atmospheric carbon dioxide affects the species equilibrium activity distribution in MeC03 systems significantly. Stability relations in calcitewater, magnesite-water and dolomite-water systems are markedly dependent on the partial pressure of carbon dioxide. (2) The theoretical points of zero charge of calcite, apatite and magnesite are in good agreement with experimentally determined values. If apatite is conditioned with water at 25°C in the presence of atmospheric carbon dioxide, calcite can precipitate in the system at pH values above 9.3. (3) If apatite is conditioned in the supernatant of calcite, calcite may reprecipitate under certain pH conditions to convert the surface of apatite to calcite. Similarly, the precipitation of apatite from apatite supernatants that are contacted with calcite is also possible under certain other pH conditions. (4) While relatively larger amounts of carbonate are required for the conversion of apatite into calcite, the conversion of calcite to apatite is possible even in the presence of micromolar concentrations of phosphate. (5) Solid phases such as fluorite or fluorapatite can precipitate from apatite-fluoride systems depending upon fluoride concentration and pH level. (6) At pH of about 8.6, if dolomite is equilibrated with excess Ca’+, CaCO, can precipitate in the system. In the presence of excess Mg2+, it may be converted to MgC03. (7) If apatite is brought in contact with solutions containing 5 X 10m4 kmol m-3 Mg2+ under open or closed ( 10m3 kmol mm3 carbonate) system conditions at the natural pH, the apatite surface can be converted to dolomite above pH 8.8 for the open systems and above pH 9.2 for closed systems. (8) The conversion of calcite to dolomite under such solution conditions is also possible above pH 8.2 for both the open and closed systems. Conditioning both calcite and apatite in high concentration of magnesium solution in the open system makes calcite unstable in the entire pH range. (9) If gypsum is present in a magnesium-carbonate system, favorable
332
conditions are created for the precipitation high solubility of gypsum.
of calcite owing to the relatively
ACKNOWLEDGEMENT
The authors greatly acknowledge support of the National Science Foundation (CPE-83-04059), Florida Institute of Phosphate Research and the Union Carbide Corp.
REFERENCES P. Somasundaran and G.E. Agar, Zero Point of Charge of Calcite, J. Colloid Interface Sci., 24 (1967) 433-440. W. Stumm and J.J. Morgan, Aquatic Chemistry, 2nd edn., Wiley-Interscience, New York, NY, 1981. R.M. Garrels and C.L. Christ, Solutions, Minerals and Equilibria, Freeman, Cooper and Co., San Francisco, CA, 1965.
8
9
10 11
12 13 14 15 16
17 18
Y. Avnimelech, E.C. Moreno and W.E. Brown, Solubility and Surface Properties of Finely Divided Hydroxyapatite, J. Res. Nat. Bur. Stand. Sect. A, 77 (1973) 149. S. Chander and D.W. Fuerstenau, On the Dissolution and Interfacial Properties of Hydroxyapatite, Colloids Surfaces, 4 (1982) 101. P. Somasundaran, Zeta Potential of Apatite in Aqueous Solutions and Its Change During Equilibration, J. Colloid Interface Sci., 27 (1968) 659. P. Somasundaran and Y.H. Wang, Surface Chemical and Adsorption Properties of Apatite, in D.N. Mishra (Ed.), Adsorption and Surface Chemistry of Hydroxyapatite, Plenum, New York, NY, 1984, pp. 129-149. W.E. Brown, in E.J. Griffith et al. (Eds), Solubility of Phosphates and Other Sparingly Soluble Compounds, Environmental Phosphorus Handbook, Wiley, New York, NY, 1973, pp. 203-239. W.E. Brown, Physicochemistry of Apatite Dissolution, Physicochimie et Cristallographie des Apatites d’Int&et Biologique: Colloques Internationaux C.N.R.S., No. 230,1975, pp. 355-368. E.C. Moreno, T.M. Gregory and W.E. Brown, Preparation and the Solubility of Hydroxyapatite, J. Res. Nat. Bur. Stand. Sect. A, 72 (1968) 773-782. S.K. Mishra, Electrokinetic Properties and Flotation Behavior of Apatite and Calcite in the Presence of Sodium Oleate and Sodium Metasilicate, Int. J. Miner. Process, 9 (1982) 59-73. F.Z. Saleeb and P.L. de Bruyn, Surface Properties of Alkaline Earth Apatites, Electrochemical and Interfacial Electrochemistry, 37 (1972) 99-- 118. S. Chander and D.W. Fuerstenau, J. Colloid Interface Sci., 70 (1979) 506-516. D.R. Nagaraj, Chelating Agents as Flotaids: Hydroxyoximes-Copper Minerals Systems, Doctoral Thesis, Columbia University, New York, NY, 1979. G.H. Nancollas, Z. Amjad and P. Koutsoukos, Calcium Phosphates: Speciation, Solubility and Kinetic Consideration, ACS Symp. Ser., 93 (1979) 475. K.P. Ananthapadmanabhan and P. Somasundaran, The Role of Dissolved Mineral Species in Calcite-Apatite Flotation, Minerals and Metallurgical Processing, SME AIME, 1 (1984) 36-42. P. Somasundaran and K.V. Viswanathan, unpublished results. H.S. Hanna and P. Somasundaran, Flotation of Salt-Type Minerals, in M.C. Fuerstenau (Ed.),
A.M. Gaudin
Memorial
Vol. 1, AIME,
New York,
NY,
1976,
pp. 197-272.
333
19 20 21 22
U. B&sing and H. Gruner,
Electrokinetic 23 24 25 26
27 28 29 30 31 32
33
The Effect
of Dissolved
Ions on Flotation
of Spar Minerals,
Freiberg. Forschungsh. A, 513 (1973) 29-43. M.T. Beck, Acta Chim. Acad. Sci. Hung., 4 (1954) 227-230. S.K. Mishra, The Electrokinetics of Apatite and Calcite in Inorganic Electrolyte Environment, Int. J. Miner. Process., 5 (1978) 69-83. J.O. Amankonah and P. Somasundaran, Effects of Dissolved Mineral Species on the Behavior
of Calcite
and
Apatite,
Colloids
Surfaces,
15 (1985)
335-
353. W.E. Brown and L.C. Chow, Chemical Properties of Bone Mineral, Annu. Rev. Mater. Sci., 6 (1976) 213-236. W.E. Brown, Behavior of Slightly Soluble Calcium Phosphates, Soil Sci., 90 (1960) 51-57. K.P. Ananthapadmanabhan and P. Somasundaran, Surface Precipitation of Inorganics and Surfactants and Its Role in Adsorption and Flotation, Colloids Surfaces, 1985. J.O. Amankonah, P. Somasundaran and K.P. Ananthapadmanabhan, Effect of Dissolved Mineral Species on the Dissolution/Precipitation Characteristics of Calcite and Apatite, Colloids Surfaces, 15 (1985) 295-307. P. Somasundaran, J.O. Amankonah and K.P. Ananthapadmanabhan, Spectroscopic Analysis of Calcite-Apatite Interactions Using ESCA, unpublished results. The Adsorption of Fluoride Ions by J. Lin, S. Raghavan and D.W. Fuerstenau, Hydroxyapatite from Aqueous Solution, Colloids Surfaces, 3 (1981) 357-370. Y.H. Wang, Zeta-Potential Studies on Hydroxyapatite, M.S. Thesis, Columbia University, New York, NY, 1975. D. Langmuir, J. Geol., 73 (1965). W.M. Latimer, Oxidation Potentials, Prentice-Hall, New York, NY, 1952. R.A. Robie, B.S. Hemingway and J.R. Fisher, Thermodynamic Properties of Minerals and Related Substances at 298.15 K, Geol. Surv. Bull., No. 1452, Washington DC, 1978. J.E. Lawver, R.L. Wiegel, R.E. Snow and C.L. Huang, Beneficiation of Dolomitic Florida Phosphate Reserves, XIVth Int. Miner. Proc. Congress, Session IV, Flotation, Paper IV (20), CIMM, Ontario, Canada, 1982.
MINERAL-SOLUTION MINERAL SYSTEMS
J. OFORI
School of Engineering (U.S.A.)
and Applied
7 May 1984;
-Printed
EQUILIBRIA
P. SOMASUNDARAN,
(Received
309
309-333 Amsterdam
accepted
IN SPARINGLY
AMANKONAH Science,
in The Netherlands
and K.P. ANANTHAPADMABHAN
Columbia
in final form
SOLUBLE
University,
22 March
New
York,
NY
10027
1985)
ABSTRACT Recent solubility, electrokinetic, spectroscopic and flotation studies in our laboratory on apatite and calcite in aqueous electrolytes indicate complex mineral-solution interactions which can alter surface characteristics of these minerals markedly in the presence of each other. In the case of systems containing such sparingly soluble minerals, understanding of the mineral-solution chemical equilibria under different physico-chemical conditions becomes important for developing schemes for processing them. The chemical equilibria in heterogeneous systems involving salt-type minerals are investigated in this work. Stability relations have been analysed on the basis of bulk equilibria for calcite, apatite, magnesite, calcite-apatite, calcite-dolomite, apatitedolomite, gypsum-anhydrite, calcite--gypsum, calcite-apatite-dolomite and calcite-magnesitedolomite systems. The role of atmospheric carbon dioxide, which under most laboratory experimental conditions cannot be avoided, has been emphasised. Theoretical results have been correlated with experimental data reported in the literature.
INTRODUCTION
Difficulties are often encountered in processing heterogeneous mineral systems under conditions predicted on the basis of single mineral tests. In systems containing minerals such as calcite and apatite which dissolve to a significant extent in water, the effect of dissolved species on the behavior of these minerals can be severe. In this study, chemical equilibria in selected single and mixed mineral systems are examined in order to determine the role of the dissolved species. The dissolution characteristics that take place in calcite-water [l-3] and apatite-water [4-71 single mineral systems have been studied in detail in the past. The results for the solubility of apatites [8, 91 and other phosphates are, however, not in agreement with each other [ 8-10 ] . Much of the work on the apatite-aqueous solution system has been centered upon obtaining reliable solubility constants for hydroxyapatite, fluorapatite and other phosphates. Difficulties encountered in this have been attributed to the existence of a non-stoichiometric solid phase. Several authors,
0166-6622/85/$03.30
0 1985
Elsevier
Science
Publishers
B.V.
310
being unable to get a constant solubility product for apatite, were even led to suggest various surface complexes such as Ca,(HPO,)(OH), [B, 111. Careful experimentation by Saleeb and de Bruyn [12] has, however, revealed that hydroxyapatite and fluorapatite have stoichiometric composition and well-defined stability constants. They have shown that one can get a constant solubility product if precautions are taken during the preparation to obtain a stoichiometric compound. The discrepancies between the data obtained-by various workers [ 131 can also be attributed to the crystal structure modifications and the presence of impurities, including added electrolytes that can influence the solution equilibria [ 81 . Whereas a chemical that complexes with dissolved mineral species would enhance the dissolution, chemicals that would adsorb on the solid can be expected to decrease the dissolution kinetics. It has been shown that the flotation of certain minerals such as tenorite and chrysocolla using oximes as collectors decreases with increase in mineral solubility [ 141 . Interactions of the dissolved mineral species with the collector have been speculated to be responsible for this effect. There are five sparingly soluble calcium phosphates that are of importance in aqueous systems. It is generally considered that hydroxyapatite is the least soluble of these salts. Brown [9] and Nancollas et al. [15] have shown that, although hydroxyapatite is the most stable salt under conditions found in nature, it becomes less stable (i.e. more soluble) than CaHPO, and CaHPO,. 2H20 if the solution is sufficiently acidic. As described in a later section, the pH at which the relative stability of Ca10(P04)6(OH)2 and CaHPO, is reversed (i.e. the singular point) is 4.8 and is shown to depend markedly on the presence and concentration of other chemical components [B, 91 . When apatite is exposed at normal temperature and pressure to a solution at a pH below the singular point, its surface can be covered by a coating of monetite (CaHP04). This can lead to apparent low solubilities for apatite. On the other hand, precipitation of a particular calcium phosphate from solution is markedly dependent on, in addition to pH, the concentrations of calcium, phosphate and other species in the system. Modifications in the precipitation process due to the presence of different mineral components have not, however, been investigated in detail in the past and consequently not adequately taken into account in the correlation of experimental results with theoretical predictions. The resulting apparently anomalous behavior may have led several investigators to the conclusion that the properties of calcium phosphates in general, and apatite in particular, are rather variable [B, 91. Another factor that can influence mineral stability is the particle size. Particle size and surface energy considerations appear to suggest that, in the case of the CuO/Cu(OH), system, tenorite (CuO) which is the stable phase when present as coarse size particles can change its chemical form to Cu(OH), if the size is reduced below a critical value [2, 31 . An aspect needing greatest attention is perhaps the interaction between
311
dissolved mineral species and surfactants. Adsorption of surfactants on particulates is the governing parameter in a number of interfacial processes such as flotation, flocculation, tertiary oil recovery using surfactant flooding, lubrication, detergency, comminution, chromatography and clarification for waste treatment, etc. The role of dissolved mineral species in surfactant abstraction (depletion) in these systems can be influenced significantly, in addition to solution properties such as pH, salinity and temperature, also by the mineral type [16]. Minerals such as calcite, gypsum, magnesite and limestone can be present in most reservoir rocks and systems, and recent experiments [17] have shown their predominating influence on sulfonate depletion in these systems. A knowledge of the equilibria in salt-type minerals is also important for the understanding of the interfacial processes in enhanced oil recovery. The role that dissolved mineral species play in determining the surface charge generation and thereby adsorption has been discussed by several investigators [4--8, 18, 191. An understanding of the influence of the factors discussed above on the solubility and hence the chemical equilibria in heterogeneous mineral/aqueous system will therefore prove beneficial in developing capabilities to predict and control the behavior of minerals during interfacial processes such as adsorption, flotation and flocculation. The chemical equilibria in heterogeneous systems involving salt-type minerals are examined in this work. Stability relations have been discussed on the basis of bulk equilibria. MINERAL-SOLUTION
EQUILIBRIA
The equilibria in selected salt-type mineral systems with special reference to calcite and apatite are examined below. Theoretical results are correlated with experimental data. Calcite equilibria
The following are the major situations in which calcite equilibria could be considered [ 2, 31: (1) Closed system: system closed to atmospheric CO3. (2) Open system: system open to atmospheric CO3. Although these are two extreme cases most often realized in practice, other intermediate conditions can also be obtained. When calcite is brought in contact with water, its dissolution will be followed by pH-dependent hydrolysis and complexation of the dissolved species. The following are the equilibria that will control the system [ 1, 181. CaCO,( s) CO;- + H’ HCO; + H+ COz(g) + Hz0
2 f + 2
Ca*+ + CO:HCO; H&O3 H3CO3
KS,
10-8.4 1010.3
106.3 10-1.5
312
Ca2’ + Ca2+ + Ca2+ + Ca” +
HCO; CO’,H,O 2H20
z f 2 2
CaHCO: CaCO,(aq) CaOH’+H’ Ca(OH), + 2H’
loo.8 103.3 10-12.9 10-22.8
While the activities can fairly easily be calculated in the case of the open systems due to the fixation of the partial pressure of atmospheric CO* at 10U3.’ atm, calculations for the closed systems are relatively tedious. The use of computer programs is therefore generally required in such calculations. During this investigation, a computer program is developed to calculate the activities of various dissolved species from available thermodynamic data, taking into consideration the effects of other dissolved species and solid phases in equilibrium with the system. Figures l(a) and l(b) show the distribution of various species as a function of pH for the closed and open systems, respectively. The marked effect of atmospheric COz on the solubility of calcite can be seen by comparing the data in these diagrams. This effect is particularly noticeable for Ca2’, HCO; and CO:- activities. Since Ca2’ plays a very important role in calcite flotation systems, the possible role of CO2 on flotation as well as other interfacial processes due to this effect should be noted. Beck’s theory on solubility [20] is examined using the data in these diagrams. This theory suggests that, when a solution is in equilibrium with the solid phase, the isoelectric point (IEP) will correspond to the pH of minimum solubility. Figure 2(a) shows a plot of total carbonate, total calcium and total solubility” as a function of pH. By applying Beck’s theory, an IEP of 8.4 is obtained for the calcite open system. Somasundaran and Agar [l] obtained a value of 8.2 for the IEP of calcite by measuring the pH of minimum solubility (Fig. 2(b)). The close agreement between the theoretical and the experimental IEP values suggests that the experiments were conducted under near equilibrium conditions, and that the thermodynamic data used in these calculations best describes the calcite open system. A value of 8.4 obtained by Garrels and Christ [3] from similar theoretical considerations and also results reported in literature [21] confirm the thermodynamic description given here for the calcite system. However, it must be mentioned that numerous data in the literature on the IEP of calcite are not in agreement with each other, this being possibly the result of non-equilibrium and differences in solution conditions under which the experiments were conducted [6, 181. Also, the source of the minerals used in the various experiments can be expected to play a significant role in this discrepancy [ 181. In order to further assess the effects of CO2 on the calcite system, the results for total calcium and total solubility are presented in Fig. 3 for the closed system. The levels of total solubility in the two systems (compare Figs 2 and 3) clearly show the magnitude of the CO, effect on the calcite *The total solubility is defined given solution conditions.
here as the sum of the activities
of dissolved
species
under
313
-10
-12
-4
4
6
I
1
CALCITE
I
4
Fig. 1. Species
PH
1
I
10
12
I
I
14
I
(OPEN)
I
-12
0
6
distribution
I
I
I
8
PH
10
diagrams
I
I 12
for calcitewater
(b)
1 14
systems:
(a) closed,
(b) open.
-10
4
6
4-
7--1-w
14
12
10
8 PH
I
,1
I
I
2-
3-
_,21’. 4
1 6
8
IO
I
I
I
12
4
PH
Fig. 2. Determination PI.
of the isoelectric
point for calcite:
(a) theoretical,
(b) experimental
315
4
r
I
I
I
CALCITE
6
6
4
Fig. 3. Solubility
1
I
I
I
I
I
(CLOSED)
of calcite
PH
10
in water (closed
14
12
system)
as function
of pH.
solubility. As seen from Fig. 3, Beck’s theory predicts an IEP of about 11.3 for the calcite closed system. This implies that values ranging from 8.2 (completely open systems) to 11.3 (completely closed systems) can be obtained for the IEP of calcite depending on the partial pressure of carbon dioxide in equilibrium with the system. Experiental values ranging from 8.0 to 10.8 reported in the literature [ 181 can at least partly be attributed to the differences in the partial pressure of carbon dioxide. Apatite
equilibria
The equilibria below [5-7,181.
that
control
the dissolution
of apatite
in water are given
KS,
Ca,,(P04)6(F,0H)2 PO:- + H’ $ HPO:- + H’ = H,P04 + H’ +Ca2+ + H,O f Ca2+ + 2H20 f F- + H+ f Ca2’ + HPOj- 2
f 10Ca” + 6PO:- + 2(F-,OH-) HPO:H,PO: H,PO‘, CaOH’ + H’ CatOH), + 2H’ HF CaHPO,(aq)
lo-“* 1012.3
1o7.2 102.2 10-12.9
:Fr
102.’
(F)
316
CaHP04( aq) Ca2+ + H,POi Ca2+ + 2FCa2+ + F-
f ? f 2
CaHPO,( s) CaH2P0i CaF,(s) CaF’
104.3 lo’.’ 1010.4
1O’JJ
As in the case of calcite, the activities of various dissolved species were calculated at different pH values by using the relevant chemical equilibria and stoichiometric restrictions (one for hydroxyapatite and two for fluorapatite*). The distribution of the activities of dissolved species is given in Figs 4(a) and 4(b) for open and closed systems, respectively. If the system is brought in equilibrium with atmospheric carbon dioxide, the distribution will follow that shown in Fig. 4(a). For the closed system, Ca*’ species are the most predominant below about pH 12.5. The predominant phosphate species are H,PO;, HPOi- and PO:- depending on pH. By comparing the data in Fig. 4, it can be seen that, below about pH 9, the effect of atmospheric CO* on Ca*’ activity is not as drastic in this case as for calcite (Fig. 1). Above this pH, marked changes are observed: while the Ca*’ activity decreases sharply with increase in pH, an increase is observed in the activities of HPOt- and PO:- species (Fig. 4(a)). The sharp decrease in the Ca2’ activity with an increase in the phosphate solubility under high pH conditions is due to the precipitation of CaC03. Figures 5(a) and 5(b) show the effect of atmospheric carbon dioxide on the total solubility of apatite. Again, the marked effect of carbon dioxide on the total solubility is seen here. If the pH of minimum solubility is taken as the IEP [l, 201, a value of 7.2 is obtained from Fig. 5(a) which is in good agreement with the experimental values obtained earlier [6, 7, 21, 221. To our knowledge, however, no data are reported in the literature to support the IEP value of about 12 for the apatite closed system as predicted using Beck’s theory (see Fig. 5(b)). STABILITY
RELATIONS
IN CALCITE-APATITEMONETITE
SYSTEMS
As mentioned earlier, of the five most important sparingly soluble calcium phosphates it is generally assumed that hydroxyapatite is the most stable [&lo, 23, 241. While this is true generally under natural conditions, this assumption could lead to erroneous interpretations under other experimental conditions. Figure 6 shows solubility isotherms for apatite, monetite and calcite at 25°C. The singular point for monetite and apatite is 4.8 and that for apatite and calcite 9.3. This shows that, below pH 4.8, monetite is more stable (i.e., less soluble) than apatite. The implication is that, if apatite is brought in contact with acidic solutions (pH < 4.8), two processes could occur: *Total calcium/total is total calcium/total
phosphate (CaT/PT) = 1.667. Additional restriction for fluorapatite fluoride (PT/FT) = 3. fluoride (CaT/FT) = 5 or total phosphate/total
317
4
I
1
I
I
1
HYDROXYAPATITE
I
I
(OPEN)
00 /
2 -
4
I
1
1
1
I
HYDROXYAPATITE
I
(a)
/;
I
I
/
I
(CLOSED)
-
I
(b)
2
4
Fig. 4. closed.
6
Species
distribution
6
PH
diagram
10
12
for
14
hydroxyapatite-water
system : (a)
(b)
318
HYDROXYAPATITE
(OPEN)
2 -
o-
* E
4
I
HYDROXYAPATITE
1
I
I
1
(b)
(CLOSED)
TOTAL
SOLUBILITY
-8
-10
-12
1
4
Fig. 5. Effect closed.
I
I
6
of carbon
1
8
dioxide
I
1
PH
L
10
on the total
I
I
12
solubility
14
of hydroxyapatite:
(a) open,
(b)
319
++G
-4
k > -6 I3 F 2 -6 :: l-10
-12
I 4
I
I
I
6
I
6
I
I
10
I
1,
12
I 14
PH
Fig. 6. Solubility
isotherms
at 25°C
for monetite
(CaHPO,),
apatite
and calcite.
(1) The more stable phase, monetite, could precipitate from solution with the formation of a coating on the surface of the apatite particles, or (2) the surface of the apatite particles could undergo appropriate chemical reactions to convert to monetite [9]. In either case, the apparent solubility behavior of apatite in a solution more acidic than the singular point may be quite different from what one would expect for apatite. The formation of the most acidic phosphate in the form of a coating on apatite surface can lead to apparent low solubilities for apatite [8, 91. It can also be seen from Fig. 6 that, above the singular point of 9.3, calcite is more stable than apatite. This implies that, if the apatite system is open to atmospheric COz, calcite can either precipitate from solution and subsequently form a surface coating on apatite, or the surface of apatite particles could be converted to calcite through surface precipitation or various surface reactions. Reactions involving organic and inorganic species leading to surface precipitation have been examined in detail elsewhere [ 251. The conditions for the conversion of apatite to calcite can be more readily identified by considering the chemical reaction responsible for the process: Ca,,(PO,),(OH),(s)
+ lOCO:-
= lOCaCO,(s)
+ 6POd3- + 20H-
It, can be seen from this reaction that, depending on the pH of the solution, apatite can be converted to calcite if the total carbonate in the solution
320
-10
-12
1
L___A__L-_:
4
6
0
10
12
14
PH
Fig. 7. Illustration
of the possibility
of the conversion
of apatite
to calcite.
is above a certain critical value. Figure 7 shows the total carbonate required for the conversion reaction (apatite + calcite) under open and closed system conditions. Also, the total carbonate in equilibrium with the calcite system under both conditions is shown. As can be seen, the amount of dissolved carbonate from atmospheric CO2 far exceeds the amount required to convert apatite to calcite under high equilibrium pH conditions (above pH 9.3). Although the kinetics of such transformations is not known, such reactions can be important in determining the surface characteristics of minerals. The implication of this in processes such as adsorption, flotation and flocculation is obvious. Most interestingly, the calcite surface can also be converted to apatite under appropriate conditions [2, 221. Figure 8 shows the amount of phosphate required to convert calcite to apatite along with the total phosphate in equilibrium with apatite. Below pH 9.3, the amount of phosphate that can be in equilibrium with apatite far exceeds the amount required to convert calcite to apatite if the system is open to atmospheric COz. If the system is closed, it is seen that the conversion is possible in the entire pH range. It is interesting to note the amount of phosphate required for this process at each pH value. For example, for the closed system, only about 10-l’ kmol mm3 of phosphate is required to produce the conversion effect around pH 13. As mentioned before (Figs 6 and 7), apatite can be converted to calcite above pH 9.3 if the system is open to atmospheric CO,. This implies that
321
CALCITE(OPEN)~HAP
t
/
-10
4
6
6
10
12
14
PH
Fig. 8. Illustration
of the possibility
of the conversion
of calcite
to apatite.
calcite supernatant prepared above this pH could contain more than enough carbonate to convert apatite to calcite. Zeta-potential measurements conducted with calcite and apatite in water and in the supernatants of each other have shown that, indeed, these processes do occur [22]. Figure 9 presents the results of zeta-potential measurements in water and in supernatants. It can be seen that the two minerals have almost interchanged their points of zero charge (PZC). Additional electrokinetic experiments in relevant organic solutions, as well as solubility [26] and spectroscopic (ESCA) [27] studies have shown the surface conversion of apatite to calcite and vice versa under appropriate solution conditions. The ESCA results in Fig. 13 (Ref. [22] ) clearly show the surface conversion process. Apatite conditioned in the supernatant of calcite at about pH 12 exhibits spectroscopic properties characteristic of both calcite and apatite, an indication of the conversion of the surface of the apatite to calcite [27]. Another aspect that is important from a surface chemical point of view is the transformation that hydroxyapatite can undergo in inorganic solutions. The solubility of various calcium minerals is shown in Fig. 10 as a function of pH. Comparison of the hydroxyapatite (HAP), fluorapatite (FAP) and fluorite (CaF,) solubilities shows that CaF2 is the most stable phase below about pH 5 and that FAP is the most stable mineral in the intermediate pH range while HAP is stable at high pH. This implies that, if systems in equilibrium with hydroxyapatite are brought in contact with a sufficiently high
322
__.__
60
---._---7---~
2 x lo-3
kmol/m3 o A A .
,i
KNOLI
CALCITE APATITE APATITE CALCITE
IN IN IN IN
WATER WATER CALCITE APATITE
SUP SUP
d._l___i_.
6
7
8
3
10
11
I2
13
PH
Fig. 9. Illustration
of the effects
of supernatants
on the IEP of calcite
and apatite.
-6-
Fig. 10. Solubility
of various
calcium
minerals
as a function
of pH at 25°C
323
concentration of fluoride ions, the apatie acidic pH conditions. In fact, numerous 28, 291 support this conclusion. Results tial measurements presented in Fig. 11
will be converted to fluorite under data reported in the literature [7, of fluoride uptake and zeta-potenindicate the occurrence of these (a)
APATITE pH 45
-4.7
.A
10-Q
lo-
EOUiLlBRlUM
-50
FLUORIDE
3
10-2
CONCENTRATION.
moldlster
1
1
I
1
I
,
0
2
4
6
8
10
12
Hd
Fig. 11, Illustration of surface conversion of hydroxyapatite take [ 28 1, (b) electrophoretic mobility [ 7 1.
to fluorite:
(a) fluoride
up-
324
processes. Figure 11(a) [28] shows the fluoride uptake by hydroxyapatite as a function of fluoride concentration at three pH values. The steep rise in the fluoride uptake at pH 4.5-4.7 has been attributed to CaF, formation. The data in Fig. 11(b) [7] also show that the apatite surface is more positively charged in the presence of lo-’ kmol mm3 KF solutions than in KN03 alone below pH 5. Above this pH, it is more negatively charged. These observations are attributed to the formation of fluorite at low pH values and of fluorapatite at higher pH in accord with the fact that the PZC of these minerals are in the order fluorite > hydroxyapatite > fluorapatite [7]. Therefore, in such a system, hydroxyapatite is stable only in the basic pH range. However, if the system is brought to equilibrium with atmospheric carbon dioxide, the precipitation of calcite under high pH conditions will make the apatite completely unstable under all pH conditions. MAGNESITE
EQUILIBRIA
Similar to the cases examined above, CO* is expected to play a major role also in systems containing magnesite. Based on Beck’s theory, an IEP of about 8.6 is obtained for magnesite (Fig. 12) which is in good agreement with the experimental value of 8.7 obtained by Somasundaran and Viswanathan [17]. It must, however, be noted that there are large differences in reported solubility data for magnesite and the other most common carbonates 4
8
10
12
14
PH
Fig. 12. Solubility
of magnesite
(open
system)
as a function
of pH.
325
in the Mg-W-Hz0 system. Table 1 illustrates this problem by comparing the free energy and equilibrium constant values from various sources for the most common minerals in this system at 25°C. The results obtained by using Langmuir [ 301 and Latimer [ 311 data, and Stumm and Morgan [ 21 data for the closed system are given in Figs 13(a) and 13(b), respectively. Comparison of the data in the two figures shows that magnesite is not stable in the pH range examined if Langmuir and Latimer data are used. However, on the basis of Stumm and Morgan data, mangesite is the most stable solid below about pH 10.7. Furthermore, using the data reported by Robie and co-workers [32] a value of 8.2 is obtained for the solubility product (pKsp) of magnesite, which is quite different from the values reported by Stumm and Morgan [2] and Langmuir [30] (see Table 1). The problems that can arise resulting from the differences in the interpretation of system behavior due to the use of such different data are obvious. It is to be noted that the Stumm and Morgan data are in close agreement with those reported elsewhere in the literature [3] Figure 13(b) shows that, when magnesite is equilibrated with water in a ‘closed system at sufficiently high pH (> 10.7), brucite (Mg(OH),), which is the more stable phase, can form and thus convert the magnesite surface to brucite. TABLE
1
Illustration of system at 25°C Mineral
the
variance
in solubility
data
Formula
for
some
MgCO, Mg(OH): MgCO,.SH,O Mg,(CO,),(OH),*3H,O
CALCITE-APATITE-DOLOMITE
in the
[ 301
Stumm and Morgan
Mg”-C02-H,O
PKW Langmuir and Latimer
Magnesite Brucite Nesquehonite Hydromagnesite
minerals
4.9 11.6 5.4 29.5
[ 311
7.5 11.6 4.7 29.5
Robie et al. [32 ]
[2] 8.2 _ _
EQUILIBRIA
As mentioned earlier, the problem of separation of apatite from carbonates can be exemplified by the beneficiation of dolomitic phosphates in Florida where conventional flotation techniques have not been able to yield a concentrate with an acceptable MgO level of less than 1% [33]. Since dolomite is in most respects like calcite and it is found in significant ratios with apatite, dissolved species can be expected to play an important role in this system also. The stability of dolomite under various conditions can be examined in the following manner. Consider the situation in which calcite or apatite is con-
326 4
f
I
I
I
(CLOSED
++CY
-4
-
-6
-
-6
-
-J-1o
-
,
I
SYSTEM
I
1
I
-
(a)
1
k z 5 F 2 ::
(CLOSED
: r”
-4
-
-6
-
SYSTEM)
(b)
k z
>
L 5:
-0-
:: J -10
-
-12
I 4
I 6
!
1
I
6
1 10
I
I 12
I 14
PH
Fig. 13. pH ranges of stability of the common minerals in the MgZ++ZO,-H,O (a) Langmuir and Latimer data [ 30,311, (b) Stumm and Morgan data [ 21.
system:
327
--r
1.-
I
I
I
DOLOMITE
I
I
IAPATITE
(CLOSED)
’
(0)
PH 4
/
I
CALCITE
I
/
/ DOLOMITE
1
I
/APATITE
I
,
(OPEN)
’
( b)
2
0
\ -2
-6
.
4
6
8
10
14
12
PH
Fig. 14. Stability relations in calcite-apatite-dolomite 10m4 kmol rnm3, (a) closed ([carbonate] = lo-” kmol
m-“),
system at 25°C. (b) open.
[Mg’+]
= 5.0
X
328
tacted with a solution containing 5 X 10e4 kmol mW3Mg2’ under open or system conditions. The results in Fig. closed (10L3 kmol rnd3 carbonate) 14(a) indicate that, under the closed system conditions, dolomite will precipitate if the system is equilibrated with calcite above pH 8.2. The conversion of apatite to dolomite will also take place under similar conditions above pH 9.2. If the system is equilibrated in the presence of atmospheric carbon dioxide (Fig. 14(b)), the calcite-dolomite and apatite-dolomite singular points occur at pH 8.2 and 8.8, respectively. The results indicate that atmospheric carbon dioxide has minimal effect on the relative stability of calcitedolomite and apatite-dolomite systems. This rather interesting observation will be discussed later in the next section. If calcite and apatite are equilibrated together in 5 X 10e4 kmol mm3 Mg2+ under open or closed (10Y3 kmol mS3 carbonate) system conditions, apatite will be the most stable phase under pH conditions. Dolomite precipitation reaction will determine the solubility of the system at high pH. As seen from the results, calcite is the least stable of the minerals under all the pH and CO2 partial pressure conditions examined. It should be noted that both experimental and theoretical work on the apatitedolomite system is limited and reported solubility data are conflicting with each other. This is reflected in the discrepancy of solubility product values reported for dolomite by dif4
2
0
-0
-10
-8
-6
-4 LOG
-2 -
0
2
4
[co++1 rMQ++l
Fig. 15. Stability relations 1O-4 kmol me3 [2 J.
in the Ca 2+-Mgz+-C0,-H,0
system
at 25°C
for [Mg]
= 5.0
X
329
ferent investigators which range from 10-‘6.5 to 10-‘9.5 [2]. The difficulty in devising a scheme for the beneficiation of Florida dolomite phosphates and other phosphates in general can be attributed at least partly to the lack of understanding of the chemical equilibria governing the apatite--dolomite system. The surface conversion of apatite to dolomite and vice versa should be of major concern when considering such schemes. CALCITE-MAGNESITE-DOLOMITE
SYSTEM
Figure 15 shows the relative stability of calcite, magnesite, dolomite and brucite. The conversion of magnesite to dolomite and then to calcite is seen to be possible at various calcium/magnesium ratios. If dolomite is equilibrated with water in the presence of negligible amounts of CO?, brucite will precipitate in the system. From the data in Figs 14 and 15, the conversion of dolomite to magnesite or calcite has minimal dependence on the partial pressure of carbon dioxide if the level is above about 10m6 atm. Below this value, however, brucite will be the most stable phase. SYSTEMS
INVOLVING
Calcite--gypsum
GYPSUM
equilibria
Since gypsum is one of the most soluble salt-type minerals, the high level systems will lead to the precipitation of Ca” activity in the gypsum-water
_I 8
10
12
14
PH
Fig. 16. Illustration
of the possibility
of conversion
of gypsum
to calcite
[17 ]
330
of CaC03 under certain pH conditions if the system is open to atmospheric carbon dioxide. Figure 16 shows the possibility for the conversion of gypsum to calcite at 25°C. At pH values higher than 8.2, CaCO, is expected to form if the system is open to atmospheric CO*. Thus gypsum is expected to be converted to calcite, like most of the calcium minerals discussed above, under high pH conditions. Gypsum-anhydrite
equilibria
Depending upon the temperature and other solution conditions, gypsum can exist as anhydrite (CaSO.,) or hemihydrite (CaS04* 0.5H,O). Free energy considerations indicate that gypsum should be the more stable phase at temperatures lower than about 45°C while, above this temperature, anhydrite should be more stable (see Fig. 17 [17]). Even though the conversion of gypsum to anhydrite is thermodynamically possible, the kinetics of this process is not well understood. The possibility of the existence of gypsum at higher temperatures and anhydrite at lower temperatures under laboratory experimental conditions should therefore be considered. It is seen from the above data that significant alterations in the surface chemical properties can take place owing to precipitation of various salts I
z
0.3
-
0.2
-
0.1
-
GYPSUM
0
1 ,” 1 L -0.1
-
E
a
- 0.2
ANHYDRITE
-
0
20
40
Fig. 17. The free energy of temperature [ 17).
80
60
TEMPERATURE,
change
100
‘C
for the conversion
of gypsum
to anhydrite
as a function
331
when sparingly soluble minerals are contacted with water. Furthermore, the nature of the precipitate is markedly dependent in many systems upon the pressure of carbon dioxide in the environment. It is evident that many chemical alterations can take place in aqueous systems containing minerals such as calcite, apatite, magnesite, dolomite or gypsum in the presence of each other. The conversions are due not only to the presence of carbon dioxide in the system, but also to pH and pH alterations during the equilibration. It is in fact to note the serious effects of such surface conversion reactions in determining the efficiency of various interfacial processes such as adsorption, flotation, flocculation and leaching. SUMMARY
The major findings from this investigation are summarized below: (1) Atmospheric carbon dioxide affects the species equilibrium activity distribution in MeC03 systems significantly. Stability relations in calcitewater, magnesite-water and dolomite-water systems are markedly dependent on the partial pressure of carbon dioxide. (2) The theoretical points of zero charge of calcite, apatite and magnesite are in good agreement with experimentally determined values. If apatite is conditioned with water at 25°C in the presence of atmospheric carbon dioxide, calcite can precipitate in the system at pH values above 9.3. (3) If apatite is conditioned in the supernatant of calcite, calcite may reprecipitate under certain pH conditions to convert the surface of apatite to calcite. Similarly, the precipitation of apatite from apatite supernatants that are contacted with calcite is also possible under certain other pH conditions. (4) While relatively larger amounts of carbonate are required for the conversion of apatite into calcite, the conversion of calcite to apatite is possible even in the presence of micromolar concentrations of phosphate. (5) Solid phases such as fluorite or fluorapatite can precipitate from apatite-fluoride systems depending upon fluoride concentration and pH level. (6) At pH of about 8.6, if dolomite is equilibrated with excess Ca’+, CaCO, can precipitate in the system. In the presence of excess Mg2+, it may be converted to MgC03. (7) If apatite is brought in contact with solutions containing 5 X 10m4 kmol m-3 Mg2+ under open or closed ( 10m3 kmol mm3 carbonate) system conditions at the natural pH, the apatite surface can be converted to dolomite above pH 8.8 for the open systems and above pH 9.2 for closed systems. (8) The conversion of calcite to dolomite under such solution conditions is also possible above pH 8.2 for both the open and closed systems. Conditioning both calcite and apatite in high concentration of magnesium solution in the open system makes calcite unstable in the entire pH range. (9) If gypsum is present in a magnesium-carbonate system, favorable
332
conditions are created for the precipitation high solubility of gypsum.
of calcite owing to the relatively
ACKNOWLEDGEMENT
The authors greatly acknowledge support of the National Science Foundation (CPE-83-04059), Florida Institute of Phosphate Research and the Union Carbide Corp.
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8
9
10 11
12 13 14 15 16
17 18
Y. Avnimelech, E.C. Moreno and W.E. Brown, Solubility and Surface Properties of Finely Divided Hydroxyapatite, J. Res. Nat. Bur. Stand. Sect. A, 77 (1973) 149. S. Chander and D.W. Fuerstenau, On the Dissolution and Interfacial Properties of Hydroxyapatite, Colloids Surfaces, 4 (1982) 101. P. Somasundaran, Zeta Potential of Apatite in Aqueous Solutions and Its Change During Equilibration, J. Colloid Interface Sci., 27 (1968) 659. P. Somasundaran and Y.H. Wang, Surface Chemical and Adsorption Properties of Apatite, in D.N. Mishra (Ed.), Adsorption and Surface Chemistry of Hydroxyapatite, Plenum, New York, NY, 1984, pp. 129-149. W.E. Brown, in E.J. Griffith et al. (Eds), Solubility of Phosphates and Other Sparingly Soluble Compounds, Environmental Phosphorus Handbook, Wiley, New York, NY, 1973, pp. 203-239. W.E. Brown, Physicochemistry of Apatite Dissolution, Physicochimie et Cristallographie des Apatites d’Int&et Biologique: Colloques Internationaux C.N.R.S., No. 230,1975, pp. 355-368. E.C. Moreno, T.M. Gregory and W.E. Brown, Preparation and the Solubility of Hydroxyapatite, J. Res. Nat. Bur. Stand. Sect. A, 72 (1968) 773-782. S.K. Mishra, Electrokinetic Properties and Flotation Behavior of Apatite and Calcite in the Presence of Sodium Oleate and Sodium Metasilicate, Int. J. Miner. Process, 9 (1982) 59-73. F.Z. Saleeb and P.L. de Bruyn, Surface Properties of Alkaline Earth Apatites, Electrochemical and Interfacial Electrochemistry, 37 (1972) 99-- 118. S. Chander and D.W. Fuerstenau, J. Colloid Interface Sci., 70 (1979) 506-516. D.R. Nagaraj, Chelating Agents as Flotaids: Hydroxyoximes-Copper Minerals Systems, Doctoral Thesis, Columbia University, New York, NY, 1979. G.H. Nancollas, Z. Amjad and P. Koutsoukos, Calcium Phosphates: Speciation, Solubility and Kinetic Consideration, ACS Symp. Ser., 93 (1979) 475. K.P. Ananthapadmanabhan and P. Somasundaran, The Role of Dissolved Mineral Species in Calcite-Apatite Flotation, Minerals and Metallurgical Processing, SME AIME, 1 (1984) 36-42. P. Somasundaran and K.V. Viswanathan, unpublished results. H.S. Hanna and P. Somasundaran, Flotation of Salt-Type Minerals, in M.C. Fuerstenau (Ed.),
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Memorial
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NY,
1976,
pp. 197-272.
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19 20 21 22
U. B&sing and H. Gruner,
Electrokinetic 23 24 25 26
27 28 29 30 31 32
33
The Effect
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Freiberg. Forschungsh. A, 513 (1973) 29-43. M.T. Beck, Acta Chim. Acad. Sci. Hung., 4 (1954) 227-230. S.K. Mishra, The Electrokinetics of Apatite and Calcite in Inorganic Electrolyte Environment, Int. J. Miner. Process., 5 (1978) 69-83. J.O. Amankonah and P. Somasundaran, Effects of Dissolved Mineral Species on the Behavior
of Calcite
and
Apatite,
Colloids
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15 (1985)
335-
353. W.E. Brown and L.C. Chow, Chemical Properties of Bone Mineral, Annu. Rev. Mater. Sci., 6 (1976) 213-236. W.E. Brown, Behavior of Slightly Soluble Calcium Phosphates, Soil Sci., 90 (1960) 51-57. K.P. Ananthapadmanabhan and P. Somasundaran, Surface Precipitation of Inorganics and Surfactants and Its Role in Adsorption and Flotation, Colloids Surfaces, 1985. J.O. Amankonah, P. Somasundaran and K.P. Ananthapadmanabhan, Effect of Dissolved Mineral Species on the Dissolution/Precipitation Characteristics of Calcite and Apatite, Colloids Surfaces, 15 (1985) 295-307. P. Somasundaran, J.O. Amankonah and K.P. Ananthapadmanabhan, Spectroscopic Analysis of Calcite-Apatite Interactions Using ESCA, unpublished results. The Adsorption of Fluoride Ions by J. Lin, S. Raghavan and D.W. Fuerstenau, Hydroxyapatite from Aqueous Solution, Colloids Surfaces, 3 (1981) 357-370. Y.H. Wang, Zeta-Potential Studies on Hydroxyapatite, M.S. Thesis, Columbia University, New York, NY, 1975. D. Langmuir, J. Geol., 73 (1965). W.M. Latimer, Oxidation Potentials, Prentice-Hall, New York, NY, 1952. R.A. Robie, B.S. Hemingway and J.R. Fisher, Thermodynamic Properties of Minerals and Related Substances at 298.15 K, Geol. Surv. Bull., No. 1452, Washington DC, 1978. J.E. Lawver, R.L. Wiegel, R.E. Snow and C.L. Huang, Beneficiation of Dolomitic Florida Phosphate Reserves, XIVth Int. Miner. Proc. Congress, Session IV, Flotation, Paper IV (20), CIMM, Ontario, Canada, 1982.