1. Phase Change Reactions Precipitation-Dissolution of Inorganic Species
Bruce Herbert
Geology & Geophysics

2. Precipitation-Dissolution and Metal-Ligand Properties
Generally, species exhibit similar precipitation-dissolution reactions as complexation reactions in that
The more stable solid phases of a hard metal will be precipitates with a hard base (all other factors being equal).
The more stable solid phases of a soft metal will be precipitates with a soft base (all other factors being equal).

3. Thermodynamics of Precipitation-Dissolution
General formula for two component dissolution
(6.1)
where M is a metal, L a ligand, a and b are stoichiometric coefficients, m and n are the charges of the ions, and Kdis is the equilibrium dissolution constant.

4. Thermodynamics of Precipitation-Dissolution
The solubility product constant, Kso is defined as
(6.2)
If the solid is in its Standard State, as is commonly assumed, then Kdis=Kso. If the solid is not in its Standard State, the IAP will be a function of all of the thermodynamic variables that affect the activity of the solid.
Precipitation-dissolution reactions often occur over much longer time scales than complexation reactions in solution. Species in the solution phase will come to equilibration among themselves before they reach equilibration with the solid phase.

5. Thermodynamics of Precipitation-Dissolution
We can use this fact to define two useful criteria for precipitation-dissolution reactions:
The ion activity product, IAP is defined as
(6.3)
The relative saturation, , is defined as
(6.4)

6. Thermodynamics of Precipitation-Dissolution
The relative saturation can be monitored over time to assess the degree of equilibration in a system.
If < 1, then the system is undersaturated with respect to the solid phase as defined by the reaction in 6.1.
If > 1, then the system is oversaturated with respect to the solid phase as defined by the reaction in 6.1.
If = 1, then the system is in equilibration with respect to the solid phase as defined by the reaction in 6.1.

7. Thermodynamics of Precipitation-Dissolution
MINTEQA2 and PHREEQ calculates a saturation index, SI
SI = log [IAP/Kso] (6.5)
If the SI < 0, then the system is undersaturated
If the SI > 0, then the system is oversaturated
IF the SI ≈ 0, then the system is at equilibrium

8. Thermodynamics of Precipitation-Dissolution
If SI ≠ 0, then we can make one of three conclusions concerning the system of interest:
The reaction is not in equilibrium
No solid phase corresponding to the reaction as written exists in the system
The reaction is at (possibly metastable) equilibrium, but the solid phase is not in the Standard State assumed in computing Kso

9. Example: The Dissolution of Gibbsite
The value of Kdis can be calculated with Standard-State chemical potentials.
Assuming that gibbsite is in its Standard State, then Kdis = Kso and
Al(OH)3(s) = Al3+(aq) + 3OH-(aq) (6.6)
Check calcs

10. Thermodynamics of Precipitation-Dissolution
The central problem with precipitation-dissolution reactions, as environmental geologist, is to predict which solid phase controls aqueous activities of a metal or ligand.
The controlling phase at equilibrium will be the one which results in the smallest value of the aqueous activity of the ion.
The corollary is also true: the chemical potential, m(aq), is smallest whenever the aqueous activity is at a minimum. At that time the chemical potential of a species in the solid and aqueous phases will be equal.

11. Example: Does Cd(OH)2 or CdCO3 control (Cd2+) in solution?
Background Data: pH = 7.6; (HCO3-) = 10-3
For the Hydroxide Phase:
*Kso is the dissolution equilibrium constant for cadmium hydroxide by adding the ionization of water.
Assume both Cd(OH)2(s) and H2O(l) are in their Standard States. Then:
log (Cd2+) = log *Kso + 2 log (H+) = log *Kso -2 pH
since *Kso = (Cd2+)/(H+)2
Then log (Cd2+) = if Cd(OH)2(s) is the controlling phase

12. Example: Does Cd(OH)2 or CdCO3 control (Cd2+) in solution?
Background Data: pH = 7.6; (HCO3-) = 10-3
For the Carbonate Phase:
Assume CdCO3(s) is in its Standard State. Then:
log (Cd2+(aq)) = log Kso - pH - log (HCO3-)
then log (Cd2+) = -5.47
therefore CdCO3(s) is the controlling phase

13. Reverse experimental procedure
Determine (Cd2+) in solution using a Cd-sensitive electrode
Determine (CO32-) and calculate IAP
Compare IAP to published values of Kso.
If the two are not equal then either:
Equilibrium with the solid phase does not exist
Solid phase controlling ion activity is not the one suspected
Solid is not in the Standard State.

14. Solubility of Oxides and Hydroxides
Oxides and hydroxides are often the most common precipitates of trace metals. Their precipitation-dissolution is strongly affected by pH.
Solubility of oxides and hydroxides can be expressed as:
M(OH)2(s) = M2+(aq) + 2OH-(aq) Kso = (M2+)(OH-)2
MO(s) + H20(l) = M2+(aq) + 2OH-(aq) Kso = (M2+)(OH-)2

15. Solubility of Oxides and Hydroxides
We can rewrite the reaction in order to include protons
M(OH)2(s) + 2H+(aq) = M2+(aq) + 2H2O(l)
*Kso = (M2+)/(H+)2 = Kso/Kw2 (6.15)
MO(s) + 2H+(aq) = M2+(aq) + H2O(l)
*Kso = (M2+)/(H+)2 = Kso/Kw2 (6.16)
where Kw is the hydrolysis constant for water
H2O(l) = H+(aq) + OH-(aq)
Kso = (H+)(OH-)/(H2O) (6.17)
This gives
log[Mz+] = log Kso + z pKw - z pH (6.18)

16. Graphical representation of ZnO (s)
The dissolution of zinc oxide as a function of pH is governed by the following reactions
Reaction, Logarithmic Form, log *Kso
ZnO(s) + 2H+(aq) = Zn2+(aq) + 2H2O(l)
log (Zn2+) = log *Kso - 2pH, log *Kso = 11.2
ZnO(s) + H+(aq) = ZnOH+(aq)
log (ZnOH+) = log *Kso - pH, log *Kso = 2.2
ZnO(s) + 2H2O(l) = Zn(OH)3-(aq)+ H+(aq)
log (Zn(OH)3-) = log *Kso + pH, log *Kso = -16.9
ZnO(s) + 3H2O(l) = Zn(OH)42-(aq)+ 2H+(aq)
log (Zn(OH)42-) = log *Kso + 2pH, log *Kso = -29.7

17. Graphical representation of ZnO (s)
The logarithmic equations are equations of straight lines and can be plotted (using Excel) where pH forms the independent variable:

18. Graphical representation of ZnO (s)

19. Log Activity Zn Species
This figure shows the results of the calculations for the solubility of zincite. We see the same general type of U-shaped curve with a minimum solubility. For Zn, the minimum occurs at a considerably higher pH than for Al, but the solubilities at the minima for zincite and gibbsite are roughly the same. Also, for Zn the solubility increases with decreasing pH on the left limb of the plot, but less drastically than was the case for Al (a slope of -2 for Zn vs. -3 for Al). The solubility of zincite over the range of pH commonly found for natural waters ( ) is considerably higher than the solubility of gibbsite over the same pH range. Thus, Zn concentrations can potentially be much higher than Al concentrations in many natural waters, all other things being equal.
The solubilities depicted in this slide, and slides 10 and 19, tell only part of the solubility story. The solubilities of the minerals could be much higher than shown here if additional ligands are available, and these ligands can form strong complexes with the metal ions. On the other hand, if it turns out that other phases are more stable, these other phases will, by definition, be less soluble. For example, in the case of Zn, smithsonite (ZnCO3), sphalerite (ZnS) or willemite (Zn2SiO4) could be more stable than zincite, depending on the composition of the natural water in question. The solubilities of these phases could be orders of magnitude less than that of zincite. However, the U-shape of the solubility curve with respect to pH is often preserved, even when phases other than oxides and hydroxides are more stable.
Concentrations of dissolved Zn species in equilibrium with ZnO as a function of pH.

20. Log Activity Al Species
If we plot the functions derived in the preceding slides we obtain the graph shown in this slide. The light colored lines represent the concentrations of individual Al species. The heavy black line represents the total concentration of all Al species, i.e., the solubility of gibbsite. Solutions with compositions plotting above the heavy black line would be supersaturated, and those plotting below the line would be undersaturated. On the low-pH side of this diagram, Al3+ is the predominant species, and so the total solubility curve (in black) follows the line representing the concentration of Al3+. On the high-pH side, Al(OH)4- is the predominant species so the total solubility curve follows the blue line. The species Al(OH)2+ is predominant only over a very narrow pH range near the minimum in the solubility curve. The species Al(OH)2+ is never predominant, but it makes a significant contribution to total solubility over a very narrow range near pH = 5. The solubility curve shown here is typical of most oxides and hydroxides. It is U-shaped, with high solubilities at low pH where cationic species predominate, high solubilities at high pH where anionic species predominate, and a minimum in between. The minimum broadly corresponds to the range of pH commonly encountered in most natural waters. Thus, the Al concentration in most natural waters will be quite low. However, note that, as was pointed out earlier, the solubility on the low-pH side increases very steeply as the pH decreases, resulting in very high Al concentrations at pH < 4. This is one of the reasons why acidification of natural waters, through such processes as acid rain or acid-mine drainage, is of considerable environmental concern. Aluminum is quite toxic to fish and other organisms. As long as the pH is near neutral, Al concentrations remain low. But even slight degrees of acidification can lead to the dissolution of hazardous levels of Al.
Concentrations of dissolved Al species in equilibrium with gibbsite as a function of pH.

21. Log Activity Fe Species
Comparison of this solubility diagram with those for gibbsite and zincite brings home the very low solubility of ferric iron (Fe3+) in natural waters. According to this diagram, the solubility of Fe(OH)3(s) is less than 10-6 mol L-1 (~ 0.06 mg L-1) over a wide pH range (from pH < 4 to pH > 12). To get iron into solution, we must either reduce it to Fe2+ (something we will investigate more in future lectures) or complex it with very strong ligands. Organisms generally require iron to survive, and low solubilities of this metal present a challenge. Many organisms have met this challenge by producing strong Fe complexing agents called siderophores. These siderophores locally increase the solubility of Fe minerals and permit Fe to be mobilized into the organisms.
Concentrations of dissolved Fe species in equilibrium with Fe(OH)3 as a function of pH.

22. Log activity dissolved Si Species
This plot illustrates the principles discussed in the previous slide. The light red lines show the concentrations of the various dissolved silica species. The concentration of H4SiO40 is represented by the horizontal line. The concentration of H3SiO4- is represented by the straight line with slope +1, and that of H2SiO42- by the straight line with slope +2. The points where the lines for the concentrations of two successive species cross occur at the pK values for silicic acid. For example, the lines representing the species H4SiO40 and H3SiO4- cross at pH = pK1 = 9.9, and the lines for the species H3SiO4- and H2SiO42- cross at pH = pK2 = The heavy dark red curve represents the logarithm of the sum of the concentrations of all the species, that is, the total solubility of quartz. At pH < 9.9, H4SiO40 accounts for almost all the dissolved silica, so the curve representing the total solubility is nearly coincident with the line representing the concentration of H4SiO40. Similarly, at 9.9 < pH < 11.7, the predominant species is H3SiO4-, so the total solubility curve has a slope near +1, and at pH > 11.7, the total solubility curve follows the line representing the concentration of H2SiO42-. Near each of the pK values (i.e., the crossover points), significant and nearly equal concentrations of two species are present, so the total solubility curve rises above the lines for the individual species.
Also shown on this plot is the total solubility curve for amorphous silica (dotted green line). This curve has exactly the same shape as that for quartz, but is displaced upward by 1.3 log units (log 20 = 1.3), which is reflective of the fact that amorphous silica is 20 times more soluble than quartz.
The plot illustrates that, over the pH range of most natural waters, silica solubility is independent of pH. However, as pH rises above 9, the solubility of silica can increase dramatically.
Activities of dissolved silica species in equilibrium with quartz and amorphous silica at 25°C. Note that silica solubility is pH-independent at pH < 9, but increases dramatically with increasing pH at pH >9.

23. Case Study: Cotter U Mill Site
The Cotter/Lincoln Park site consists of a uranium processing mill located adjacent to the unincorporated community of Lincoln Park. The mill operated continuously from 1958 until 1979, and intermittently since that time. Mill operations released radioactive materials and metals into the environment. These releases contaminated soil and groundwater around the mill and the Lincoln Park area.
For more info:
Davis, A., and D.D. Runnells Geochemical Interactions between acidic tailings fluid and bedrock: Use of the computer model MINTEQ. Applied Geochemistry 2:

24. Case Study: Cotter U Mill Site

25. Case Study: Cotter Uranium Mill Site
The contaminants of most concern at the site are molybdenum and uranium. The primary exposure pathways would be drinking contaminated water and inhaling contaminated dust. Radon, a decay product in the uranium chain, is also of potential concern.
Major cleanup activities performed since 1988 include:
Connecting Lincoln Park residents to city water;
Constructing a ground-water barrier at the Soil Conservation Service (SCS) dam
to minimize migration of contaminated ground water into Lincoln Park;
Moving tailings and contaminated soils into a lined impoundment to eliminate them as a source of contamination; and
Excavating contaminated stream sediments

26. Case Study: Cotter U Mill Site

27. Case Study: Cotter U Mill Site

28. Case Study: Cotter U Mill Site

29. Case Study: Cotter U Mill Site

30. Case Study: Cotter U Mill Site

31. Case Study: Cotter U Mill Site

32. Appendix Understand the principles governing the solubility of quartz.
Understand the principles governing the solubility of Al- and Fe-oxyhydroxides.
We will spend three lectures on Chapter 4 in Kehew (2001). In this lecture, we will cover four main topics. First, we will discuss some factors that govern the rates of weathering of silicate and oxide minerals, including the relative stabilities of primary minerals as given by Goldich’s series, and the nature of incongruent dissolution. Next we will briefly discuss the nature of the most common solid products of weathering, i.e., clay minerals. We will then briefly discuss the mechanisms by which oxides and silicates dissolve. Finally, we will investigate somewhat in depth the thermodynamics of dissolution of silica, and Al and Fe oxyhydroxides.

33. SiO2(quartz) + 2H2O(l)  H4SiO40
SILICA SOLUBILITY - I
In the absence of organic ligands or fluoride, quartz solubility is relatively low in natural waters.
Below pH 9, the dissolution reaction is:
SiO2(quartz) + 2H2O(l)  H4SiO40
for which the equilibrium constant at 25°C is:
At pH < 9, quartz solubility is independent of pH.
Quartz is frequently supersaturated in natural waters because quartz precipitation kinetics are slow.
With respect to solubility, everything is relative. The solubility of silica is low relative to a salt like NaCl, but is high compared to aluminum and iron oxyhydroxides. If ligands that can form strong complexes with silicon, e.g., fluoride or organic ligands (the role of organic ligands in silica solubility is somewhat controversial) are absent, then the main form of dissolved silica in most natural waters is silicic acid or H4SiO40. As indicated by the reaction given in this slide, the concentration of silicic acid in equilibrium with quartz (one form of silica) is independent of pH. Because H4SiO40 is the predominant form of silica in solutions with pH < 9, the solubility of quartz is therefore independent of pH under these conditions. The solubility of silica is also not strongly dependent on the ionic strength, because activity coefficients of neutral species are very close to unity (see Lecture 2). However, because the equilibrium constant for the reaction shown above is dependent on temperature and pressure, silica solubility is also dependent on these factors. In fact, in geothermal systems, the solubility of silica can be used as a geothermometer to determine the temperature at which the fluid last reached equilibrium with quartz or amorphous silica.
Quartz precipitation kinetics at low temperature are quite low. On the other hand, concentrations of H4SiO40 may build up to quite high values during the weathering of aluminosilicate minerals. It is often found that H4SiO40 concentrations in natural waters exceed those dictated by quartz solubility. In other words, many natural waters are supersaturated with quartz.

34. SILICA SOLUBILITY - II
Thus, quartz saturation does not usually control the concentration of silica in low-temperature natural waters. Amorphous silica can control dissolved Si:
SiO2(am) + 2H2O(l)  H4SiO40
for which the equilibrium constant at 25°C is:
Quartz is formed diagenetically through the following sequence of reactions: opal-A (siliceous biogenic ooze)  opal-A’ (nonbiogenic amorphous silica)  opal-CT  chalcedony  microcrystalline quartz
Quartz saturation generally does not control silica concentrations in natural waters. The precipitation rate of amorphous silica is faster than that of quartz, so natural waters are rarely supersaturated with amorphous silica. Natural waters may be saturated with amorphous silica. In other words, the solubility of amorphous silica can control the concentration of dissolved silica in natural waters. According to the equilibrium constants given in this slide and slide 3, the solubility of amorphous silica is approximately 20 times greater than that of quartz.
Quartz can precipitate directly from natural waters at low temperatures, but because the rate of this reaction is slow, it is more common for amorphous silica to precipitate first. Because quartz has a lower solubility than amorphous silica, it is the stable phase and, with time, the amorphous silica slowly transforms to quartz. It has been shown that, during the diagenesis of marine sediments, the sequence shown in this slide is followed.

35. SILICA SOLUBILITY - III
At pH > 9, H4SiO40 dissociates according to:
H4SiO40  H3SiO4- + H+
H3SiO4-  H2SiO42- + H+
The total solubility of quartz (or amorphous silica) is:
Being an acid, H4SiO40 can dissociate at elevated pH. The value of pK1 = 9.9 suggests that it is a very weak acid, and that it will only undergo significant dissociation at pH > 9. At pH = 9.9, H4SiO40 and H3SiO4- are present in equal amounts, but at pH > 9.9, the latter predominates. The pK2 value of 11.7 indicates that at pH > 11.7, H2SiO42- becomes the predominant species. The total solubility of silica is the sum of all silica species in solution. Because the concentrations of H3SiO4- and H2SiO42- pH-dependent, once these species become predominant over H4SiO40, silica solubility also becomes pH-dependent.
It should be kept in mind that, as long as quartz or amorphous silica is present, and the solution remains in equilibrium with one of these phases, then the concentration of H4SiO40 remains constant, even though this species tends to dissociate to H3SiO4- and H2SiO42- as the pH rises. As some of the H4SiO40 dissociates, more quartz or amorphous silica dissolves to replace the H4SiO40 lost to dissociation. Because H4SiO40 is constant, significant dissociation leads to increased total silica in solution, because eventually H3SiO4- and H2SiO42- make important contributions to dissolved silica on top of the constant amount of H4SiO40 always present.

36. SILICA SOLUBILITY - IV
The equations for the dissociation constants of silicic acid can be rearranged (assuming a = M ) to get:
We can now write:
To calculate the concentrations of H3SiO4- and H2SiO42- we need to rearrange the mass-action expressions for the dissociation reactions of silicic acid as shown in this slide. For simplicity we assume that activity coefficients are equal to unity. The expressions we derive for the concentrations of these species turn out to be dependent on the concentration of H4SiO40, but we have already demonstrated that this is a constant at fixed temperature and pressure, if the solution is in equilibrium with either quartz or amorphous silica. Thus, we see that the concentrations of H3SiO4- and H2SiO42- in equilibrium with quartz or amorphous silica are dependent on the activity of hydrogen ion. If we take the logarithm of both sides of the first two equations in this slide, employ the definition of pH, and rearrange the equations a bit, we obtain
log MH3SiO4- = log (K1MH4SiO40) + pH
and
log MH2SiO42- = log (K1K2MH4SiO40) + 2pH
To summarize these results, the concentration of H4SiO40 is independent of pH, the concentration of H3SiO4- increases one log unit for each unit increase in pH, and the concentration of H2SiO42- increases two log units for each unit increase in pH. If we plotted the logarithm of the concentrations of each of these species vs. pH, we would get a horizontal line for H4SiO40, a line with slope +1 for H3SiO4-, and a line with slope +2 for H2SiO42-. The slopes of the lines for the concentrations of these species will be the same irrespective of whether the solution is saturated with quartz or amorphous silica. However, the lines will all be shifted vertically for amorphous silica compared to quartz, because the former is the more soluble phase.

37. Log activity dissolved Si Species
This plot illustrates the principles discussed in the previous slide. The light red lines show the concentrations of the various dissolved silica species. The concentration of H4SiO40 is represented by the horizontal line. The concentration of H3SiO4- is represented by the straight line with slope +1, and that of H2SiO42- by the straight line with slope +2. The points where the lines for the concentrations of two successive species cross occur at the pK values for silicic acid. For example, the lines representing the species H4SiO40 and H3SiO4- cross at pH = pK1 = 9.9, and the lines for the species H3SiO4- and H2SiO42- cross at pH = pK2 = The heavy dark red curve represents the logarithm of the sum of the concentrations of all the species, that is, the total solubility of quartz. At pH < 9.9, H4SiO40 accounts for almost all the dissolved silica, so the curve representing the total solubility is nearly coincident with the line representing the concentration of H4SiO40. Similarly, at 9.9 < pH < 11.7, the predominant species is H3SiO4-, so the total solubility curve has a slope near +1, and at pH > 11.7, the total solubility curve follows the line representing the concentration of H2SiO42-. Near each of the pK values (i.e., the crossover points), significant and nearly equal concentrations of two species are present, so the total solubility curve rises above the lines for the individual species.
Also shown on this plot is the total solubility curve for amorphous silica (dotted green line). This curve has exactly the same shape as that for quartz, but is displaced upward by 1.3 log units (log 20 = 1.3), which is reflective of the fact that amorphous silica is 20 times more soluble than quartz.
The plot illustrates that, over the pH range of most natural waters, silica solubility is independent of pH. However, as pH rises above 9, the solubility of silica can increase dramatically.
Activities of dissolved silica species in equilibrium with quartz and amorphous silica at 25°C. Note that silica solubility is pH-independent at pH < 9, but increases dramatically with increasing pH at pH >9.

38. SILICA SOLUBILITY - V
An alternate way to understand quartz solubility is to start with: SiO2(quartz) + 2H2O(l)  H4SiO40
Now adding the two reactions:
SiO2(quartz) + 2H2O(l)  H4SiO40 Kqtz
H4SiO40  H3SiO4- + H+ K1
SiO2(quartz) + 2H2O(l)  H3SiO4- + H+ K
We can derive the relationships required to make the preceding diagram in an alternate fashion. This approach depends on the fact that, if we add two chemical reactions, the equilibrium constant of the resulting reaction is equal to the product of the equilibrium constants of the two reactions that were added together.
As before, we see that the concentration of H4SiO40 in water in equilibrium with quartz is a constant, independent of pH.

39. SILICA SOLUBILITY - VI
Taking the log of both sides and rearranging we get:
Finally adding the three reactions:
SiO2(quartz) + 2H2O(l)  H4SiO40 Kqtz
H4SiO40  H3SiO4- + H+ K1
H3SiO4-  H2SiO42- + H+ K2
SiO2(quartz) + 2H2O(l)  H2SiO H+ K
The manipulations shown in this slide are pretty self-explanatory. Make sure that you know how to derive the plot in slide 7 by at least one of the two methods shown.

40. SILICA SOLUBILITY - VII
SUMMARY
Silica solubility is relatively low and independent of pH at pH < 9 where H4SiO40 is the dominant species.
Silica solubility increases with increasing pH above 9, where H3SiO4- and H2SiO42- are dominant.
Fluoride, and possibly organic compounds, may increase the solubility of silica.
Saturation with quartz does not control silica concentrations in low-temperature natural waters; saturation with amorphous silica may.

41. Appendix Understand the principles governing the solubility of quartz.
Understand the principles governing the solubility of Al- and Fe-oxyhydroxides.
We will spend three lectures on Chapter 4 in Kehew (2001). In this lecture, we will cover four main topics. First, we will discuss some factors that govern the rates of weathering of silicate and oxide minerals, including the relative stabilities of primary minerals as given by Goldich’s series, and the nature of incongruent dissolution. Next we will briefly discuss the nature of the most common solid products of weathering, i.e., clay minerals. We will then briefly discuss the mechanisms by which oxides and silicates dissolve. Finally, we will investigate somewhat in depth the thermodynamics of dissolution of silica, and Al and Fe oxyhydroxides.

42. SOLUBILITY OF GIBBSITE - I
We will use gibbsite to illustrate principles of the solubility of Al-bearing minerals; the solubility of such minerals is highly pH-dependent.
The solubility product for gibbsite is given by:
Al(OH)3(gibbsite)  Al3+ + 3OH-
We can also write this in the alternate form:
Al(OH)3(gibbsite) + 3H+  Al3+ + 3H2O(l)
Gibbsite is perhaps the simplest Al-bearing mineral that might result from the incongruent dissolution of aluminosilicate minerals. We will use gibbsite as a model to illustrate the pH-dependence of the solubility of similar Al-minerals. We will see that the solubility of Al-minerals is very dependent on the pH.
The solubility product for gibbsite is quite small, reflective of its low solubility. The solubility product is not in the most convenient form for calculations. It would be more convenient to have this equation in a form that includes H+ as a reactant instead of OH-. We can convert the reaction to the desired form by subtracting three times the water dissociation reaction.
Al(OH)3(gibbsite)  Al3+ + 3OH- KSP =
-3(H2O  H+ + OH-) K = 1/Kw3 = 1042
Al(OH)3(gibbsite) + 3H+  Al3+ + 3H2O Kgibbsite = KSP/Kw3 =
If we take the logarithm of both sides of the mass-action expression shown at the bottom of the above slide (assuming activity coefficients to be unity), we obtain
log MAl3+ = log Kgibbsite - 3pH
This implies that the concentration of Al3+ falls 3 orders of magnitude with every unit increase in pH!

43. SOLUBILITY OF GIBBSITE - II
Use of the latter equation shows that the concentration of Al3+ will be very low in the pH range of most natural waters.
For example, at pH = 7, we calculate the concentration of Al3+ to be 2.2910-12 mol L-1!
However, Al3+ forms a series of hydroxide complexes which increase its solubility somewhat:
Al3+ + H2O(l)  Al(OH)2+ + H+ K h,1
Al3+ + 2H2O(l)  Al(OH)2+ + 2H+ K h,2
Al3+ + 4H2O(l)  Al(OH)4- + 4H+ K h,4
The concentration of Al3+ will be very low at near-neutral pH. However, the concentration increases very steeply as pH decreases. At pH = 4, the concentration of Al3+ in equilibrium with gibbsite increases to 2.2910-3 mol L-1!
Although the concentration of Al3+ in equilibrium with gibbsite is quite low under near-neutral pH conditions, this does not mean that the total Al concentration will also be low. It is well known that Al3+ forms a series of hydroxide complexes, e.g., Al(OH)2+, Al(OH)2+ and Al(OH)4-. The concentrations of these complexes must be added together to obtain the total solubility of gibbsite. The reactions given in the slide are called hydrolysis reactions. The term hydrolysis comes from the Greek words hydro = water and lysis = breaking. The reactions shown result in the breaking of water into H+ and OH-. The equilibrium constants for these reactions are called hydrolysis constants (hence the subscript h).

44. SOLUBILITY OF GIBBSITE - III
The mass action expressions for these reactions may be written:
The total dissolved aluminum concentration is given by:
To calculate the solubility of gibbsite over the entire pH range of interest, we need, in addition to the solubility product of gibbsite, the mass-action expressions for each of the hydrolysis reactions. We also define the solubility of gibbsite to be equal to the sum of the concentrations of all the dissolved Al-species.

45. SOLUBILITY OF GIBBSITE - IV
We now assume that activity coefficients are unity, so that activity equals concentration.
Next, we rewrite the solubility product of gibbsite to obtain:
We see that the logarithm of the concentration of Al3+ in equilibrium with gibbsite is a straight line function of pH, with a slope of -3. In other words, the concentration of Al3+ decreases 3 log units for every unit increase in pH.
We now make the assumption that activity coefficients are equal to unity, and derive an equation for the log of the concentration of Al3+ as a function of pH. We already derived this equation in the notes to slide 3. This equation tells us that, a plot of the log of the concentration of Al3+ vs. pH will be a straight line with a slope of -3.

46. SOLUBILITY OF GIBBSITE - V
The concentration of Al(OH)2+ can be obtained from:
but the concentration of Al3+ has already been calculated so:
We see that the logarithm of the concentration of Al(OH)2+ in equilibrium with gibbsite is also a straight line function of pH, but with a slope of -2.
The concentration of Al(OH)2+ can be obtained by rearranging the mass-action expression for the first hydrolysis reaction. The resulting equation expresses the concentration of Al(OH)2+ as a function of the pH and the concentration of Al3+. However, as long as the solution is in equilibrium with gibbsite, the concentration of Al3+ is fixed by the equation given in slide 6. Making this substitution we find that the concentration of Al(OH)2+ in equilibrium with gibbsite is a straight line function of pH with a slope of -2. So the concentration of Al(OH)2+ decreases 2 log units for each unit increase in pH.

47. SOLUBILITY OF GIBBSITE - VI
Similarly for the other two species:
We perform similar manipulations for the other two species, in each case finding that their concentrations are functions of the concentration of Al3+. Once again, as long as the solution is in equilibrium with gibbsite, the concentration of Al3+ is given by the equation:
log MAl3+ = log Kgibbsite - 3pH = pH
From the resulting equations, we see that the concentration of Al(OH)2+ in equilibrium with gibbsite will decrease one order of magnitude for each unit increase in pH, and the concentration of Al(OH)4- in equilibrium with gibbsite will increase one log unit for each unit increase in pH.

48. SOLUBILITY OF GIBBSITE - VII
Now, substituting into the mass-balance expression:
we get
and taking the logarithm of both sides and substituting the K values at 25°C:
Now that we have derived expressions for the concentrations of each of the dissolved Al species in terms of hydrogen-ion activity, we can substitute each of these into the mass-balance expression, along with the appropriate values for the equilibrium constants. Finally, we take the logarithm of both sides of the equation and we obtain an expression with which we can plot the total solubility in log concentration vs. pH coordinates.

49. Log Activity Al Species
If we plot the functions derived in the preceding slides we obtain the graph shown in this slide. The light colored lines represent the concentrations of individual Al species. The heavy black line represents the total concentration of all Al species, i.e., the solubility of gibbsite. Solutions with compositions plotting above the heavy black line would be supersaturated, and those plotting below the line would be undersaturated. On the low-pH side of this diagram, Al3+ is the predominant species, and so the total solubility curve (in black) follows the line representing the concentration of Al3+. On the high-pH side, Al(OH)4- is the predominant species so the total solubility curve follows the blue line. The species Al(OH)2+ is predominant only over a very narrow pH range near the minimum in the solubility curve. The species Al(OH)2+ is never predominant, but it makes a significant contribution to total solubility over a very narrow range near pH = 5. The solubility curve shown here is typical of most oxides and hydroxides. It is U-shaped, with high solubilities at low pH where cationic species predominate, high solubilities at high pH where anionic species predominate, and a minimum in between. The minimum broadly corresponds to the range of pH commonly encountered in most natural waters. Thus, the Al concentration in most natural waters will be quite low. However, note that, as was pointed out earlier, the solubility on the low-pH side increases very steeply as the pH decreases, resulting in very high Al concentrations at pH < 4. This is one of the reasons why acidification of natural waters, through such processes as acid rain or acid-mine drainage, is of considerable environmental concern. Aluminum is quite toxic to fish and other organisms. As long as the pH is near neutral, Al concentrations remain low. But even slight degrees of acidification can lead to the dissolution of hazardous levels of Al.
Concentrations of dissolved Al species in equilibrium with gibbsite as a function of pH.

50. SOLUBILITY OF ZINCITE (ZnO) - I
The thermodynamic data for solubility problems can be presented in another way. At 25°C and 1 bar:
ZnO(s) + 2H+  Zn2+ + H2O(l) log Ks0 = 11.2
ZnO(s) + H+  ZnOH+ log Ks1 = 2.2
ZnO(s) + 2H2O(l)  Zn(OH)3- + H+ log Ks3 = -16.9
ZnO(s) + 3H2O(l)  Zn(OH) H+ log Ks4 = -29.7
The solubility of zincite is given by:
In the next few slides, a solubility diagram depicting the solubility of zincite as a function of pH will be constructed. We calculate this diagram solely to provide an additional example to help solidify the concepts already covered. There is really nothing new here. There is a minor twist in the way the thermodynamic data are presented, but there are no major differences in how the calculations are to be performed.

51. SOLUBILITY OF ZINCITE (ZnO) - II
We start with the mass-action expressions for each of the previous reactions:
Assuming that activity coefficients can be neglected we can now write the following expressions:
Note that in this case, because the reactions given in the previous slide all express the concentrations of the various species in equilibrium with the solid zincite, the mass-action expressions for ZnOH+, Zn(OH)3- and Zn(OH)42- do not contain a term in Zn2+ (contrast this situation with how the gibbsite problem was posed and solved). If we ignore activity coefficients, take the logarithm of both sides of each of these equations and rearrange them slightly, we get the same type of straight line equations as obtained previously for gibbsite.

52. SOLUBILITY OF ZINCITE (ZnO) - III
And the total concentration can be written:
We can also derive the expression for the total solubility as previously.

53. Log Activity Zn Species
This figure shows the results of the calculations for the solubility of zincite. We see the same general type of U-shaped curve with a minimum solubility. For Zn, the minimum occurs at a considerably higher pH than for Al, but the solubilities at the minima for zincite and gibbsite are roughly the same. Also, for Zn the solubility increases with decreasing pH on the left limb of the plot, but less drastically than was the case for Al (a slope of -2 for Zn vs. -3 for Al). The solubility of zincite over the range of pH commonly found for natural waters ( ) is considerably higher than the solubility of gibbsite over the same pH range. Thus, Zn concentrations can potentially be much higher than Al concentrations in many natural waters, all other things being equal.
The solubilities depicted in this slide, and slides 10 and 19, tell only part of the solubility story. The solubilities of the minerals could be much higher than shown here if additional ligands are available, and these ligands can form strong complexes with the metal ions. On the other hand, if it turns out that other phases are more stable, these other phases will, by definition, be less soluble. For example, in the case of Zn, smithsonite (ZnCO3), sphalerite (ZnS) or willemite (Zn2SiO4) could be more stable than zincite, depending on the composition of the natural water in question. The solubilities of these phases could be orders of magnitude less than that of zincite. However, the U-shape of the solubility curve with respect to pH is often preserved, even when phases other than oxides and hydroxides are more stable.
Concentrations of dissolved Zn species in equilibrium with ZnO as a function of pH.

54. SOLUBILITY OF Fe(OH)3 - I
For this problem we have the following thermodynamic data at 25°C:
Fe(OH)3(s) + 3H+  Fe3+ + 3H2O log Ks0 = 3.96
Fe3+ + H2O  FeOH2+ + H+ log Kh,1 = -3.05
Fe3+ + 2H2O  Fe(OH)2+ + 2H+ log Kh,2 = -6.31
Fe(OH)3(s) + H2O  Fe(OH)4- + H+ log Ks4 = -18.7
These reactions are a mix of two different types of reactions, but the same principles apply. The total solubility is given by:
As a final example, we construct a solubility diagram for ferrous hydroxide. Once again, the same principles apply. In this case, the thermodynamic data are given partly in the form in which the gibbsite data were given, and partly in the form in which the zincite data were given.

55. SOLUBILITY OF Fe(OH)3 - II
To get the concentration of Fe3+, we start with the mass-action expression:
And for FeOH+:

56. SOLUBILITY OF Fe(OH)3 - III
But we already solved for the concentration of Fe3+, so
Now for Fe(OH)2+:

57. SOLUBILITY OF Fe(OH)3 - IV
Finally, for Fe(OH)4-:
For the total solubility we have:

58. Log Activity Fe Species
Comparison of this solubility diagram with those for gibbsite and zincite brings home the very low solubility of ferric iron (Fe3+) in natural waters. According to this diagram, the solubility of Fe(OH)3(s) is less than 10-6 mol L-1 (~ 0.06 mg L-1) over a wide pH range (from pH < 4 to pH > 12). To get iron into solution, we must either reduce it to Fe2+ (something we will investigate more in future lectures) or complex it with very strong ligands. Organisms generally require iron to survive, and low solubilities of this metal present a challenge. Many organisms have met this challenge by producing strong Fe complexing agents called siderophores. These siderophores locally increase the solubility of Fe minerals and permit Fe to be mobilized into the organisms.
Concentrations of dissolved Fe species in equilibrium with Fe(OH)3 as a function of pH.