1. Solublility

2. 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.

3. 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.

4. 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.

5. Being an acid, H4SiO40 can dissociate at elevated pH
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.

6. 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.

7. log MH3SiO4- = log (K1MH4SiO40) + pH and
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.

8. 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.
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.

9. This plot illustrates the principles discussed in the previous slide
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.

10. 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.

11. 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.

12. 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.
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.

13. This plot illustrates the principles discussed in the previous slide
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.

14. 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.

15. SOLUBILITY OF OXIDES AND HYDROXIDES
Governing reactions for divalent metals are:
Me(OH)2(s)  Me2+ + 2OH-
MeO(s) + H2O(l)  Me2+ + 2OH-
cKs0 = [Me2+][OH-]2
Sometimes it is more appropriate to write:
Me(OH)2(s) + 2H+  Me2+ + 2H2O(l)
MeO(s) + 2H+  Me2+ + H2O(l)

16. TRIVALENT METALS For a trivalent metal oxide, e.g., goethite
FeOOH(s) + 3H+  Fe3+ + 2H2O(l)
In general,
MeOz/2 + zH+  Mez+ + z/2H2O(l)
Me(OH)z + zH+  Mez+ + zH2O(l)
Log [Mez+] = log c*Ks0 - z pH

17. NEED TO INCLUDE HYDROXIDE COMPLEXES
Need also to consider the formation hydroxide complexes, i.e., hydrolysis.
For example:
Zn2+ + H2O(l)  ZnOH+ + H+
Al(OH)2+ + H2O(l)  Al(OH)2+ + H+
In general, the total solubility of a metal oxide or hydroxide in the absence of complexing ligands is:

18. 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.

19. 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.

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

21. Concentrations of dissolved Zn species in equilibrium with ZnO as a function of pH.
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.
A U-shaped curve results with solubilities high at low and high pH, and lower
in the middle. This is typical of all amphoteric oxides and hydroxides.

22. 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.