Solublility SILICA SOLUBILITY I In the absence of

Solublility

SILICA SOLUBILITY - I • In the absence of organic ligands or fluoride, quartz solubility is relatively low in natural waters. • Below p. H 9, the dissolution reaction is: Si. O 2(quartz) + 2 H 2 O(l) H 4 Si. O 40 for which the equilibrium constant at 25°C is: • At p. H < 9, quartz solubility is independent of p. H. • Quartz is frequently supersaturated in natural waters because quartz precipitation kinetics are slow.

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: Si. O 2(am) + 2 H 2 O(l) H 4 Si. O 40 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

SILICA SOLUBILITY - III At p. H > 9, H 4 Si. O 40 dissociates according to: H 4 Si. O 40 H 3 Si. O 4 - + H+ H 3 Si. O 4 - H 2 Si. O 42 - + H+ The total solubility of quartz (or amorphous silica) is:

Being an acid, H 4 Si. O 40 can dissociate at elevated p. H. The value of p. K 1 = 9. 9 suggests that it is a very weak acid, and that it will only undergo significant dissociation at p. H > 9. At p. H = 9. 9, H 4 Si. O 40 and H 3 Si. O 4 - are present in equal amounts, but at p. H > 9. 9, the latter predominates. The p. K 2 value of 11. 7 indicates that at p. H > 11. 7, H 2 Si. O 42 - becomes the predominant species. The total solubility of silica is the sum of all silica species in solution. Because the concentrations of H 3 Si. O 4 - and H 2 Si. O 42 - p. H-dependent, once these species become predominant over H 4 Si. O 40, silica solubility also becomes p. H-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 H 4 Si. O 40 remains constant, even though this species tends to dissociate to H 3 Si. O 4 - and H 2 Si. O 42 - as the p. H rises. As some of the H 4 Si. O 40 dissociates, more quartz or amorphous silica dissolves to replace the H 4 Si. O 40 lost to dissociation. Because H 4 Si. O 40 is constant, significant dissociation leads to increased total silica in solution, because eventually H 3 Si. O 4 - and H 2 Si. O 42 make important contributions to dissolved silica on top of the constant amount of H 4 Si. O 40 always present.

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 H 3 Si. O 4 - and H 2 Si. O 42 - 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 H 4 Si. O 40, 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 H 3 Si. O 4 - and H 2 Si. O 42 - 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 p. H, and rearrange the equations a bit, we obtain log MH 3 Si. O 4 - = log (K 1 MH 4 Si. O 40) + p. H and log MH 2 Si. O 42 - = log (K 1 K 2 MH 4 Si. O 40) + 2 p. H To summarize these results, the concentration of H 4 Si. O 40 is independent of p. H, the concentration of H 3 Si. O 4 - increases one log unit for each unit increase in p. H, and the concentration of H 2 Si. O 42 - increases two log units for each unit increase in p. H. If we plotted the logarithm of the concentrations of each of these species vs. p. H, we would get a horizontal line for H 4 Si. O 40, a line with slope +1 for H 3 Si. O 4 -, and a line with slope +2 for H 2 Si. O 42 -. 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.

Activities of dissolved silica species in equilibrium with quartz and amorphous silica at 25°C. Note that silica solubility is p. H-independent at p. H < 9, but increases dramatically with increasing p. H at p. H >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 H 4 Si. O 40 is represented by the horizontal line. The concentration of H 3 Si. O 4 - is represented by the straight line with slope +1, and that of H 2 Si. O 42 - by the straight line with slope +2. The points where the lines for the concentrations of two successive species cross occur at the p. K values for silicic acid. For example, the lines representing the species H 4 Si. O 40 and H 3 Si. O 4 - cross at p. H = p. K 1 = 9. 9, and the lines for the species H 3 Si. O 4 - and H 2 Si. O 42 - cross at p. H = p. K 2 = 11. 7. 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 p. H < 9. 9, H 4 Si. O 40 accounts for almost all the dissolved silica, so the curve representing the total solubility is nearly coincident with the line representing the concentration of H 4 Si. O 40. Similarly, at 9. 9 < p. H < 11. 7, the predominant species is H 3 Si. O 4 -, so the total solubility curve has a slope near +1, and at p. H > 11. 7, the total solubility curve follows the line representing the concentration of H 2 Si. O 42 -. Near each of the p. K 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 p. H range of most natural waters, silica solubility is independent of p. H. However, as p. H rises above 9, the solubility of silica can increase dramatically.

SILICA SOLUBILITY - V An alternate way to understand quartz solubility is to start with: Si. O 2(quartz) + 2 H 2 O(l) H 4 Si. O 40 Now adding the two reactions: Si. O 2(quartz) + 2 H 2 O(l) H 4 Si. O 40 Kqtz H 4 Si. O 40 H 3 Si. O 4 - + H+ K 1 Si. O 2(quartz) + 2 H 2 O(l) H 3 Si. O 4 - + H+ K

SILICA SOLUBILITY - VI Taking the log of both sides and rearranging we get: Finally adding the three reactions: Si. O 2(quartz) + 2 H 2 O(l) H 4 Si. O 40 Kqtz H 4 Si. O 40 H 3 Si. O 4 - + H+ K 1 H 3 Si. O 4 - H 2 Si. O 42 - + H+ K 2 Si. O 2(quartz) + 2 H 2 O(l) H 2 Si. O 42 - + 2 H+ K

Activities of dissolved silica species in equilibrium with quartz and amorphous silica at 25°C. Note that silica solubility is p. H-independent at p. H < 9, but increases dramatically with increasing p. H at p. H >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 H 4 Si. O 40 is represented by the horizontal line. The concentration of H 3 Si. O 4 - is represented by the straight line with slope +1, and that of H 2 Si. O 42 by the straight line with slope +2. The points where the lines for the concentrations of two successive species cross occur at the p. K values for silicic acid. For example, the lines representing the species H 4 Si. O 40 and H 3 Si. O 4 - cross at p. H = p. K 1 = 9. 9, and the lines for the species H 3 Si. O 4 - and H 2 Si. O 42 - cross at p. H = p. K 2 = 11. 7. 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 p. H < 9. 9, H 4 Si. O 40 accounts for almost all the dissolved silica, so the curve representing the total solubility is nearly coincident with the line representing the concentration of H 4 Si. O 40. Similarly, at 9. 9 < p. H < 11. 7, the predominant species is H 3 Si. O 4 -, so the total solubility curve has a slope near +1, and at p. H > 11. 7, the total solubility curve follows the line representing the concentration of H 2 Si. O 42 -. Near each of the p. K 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 p. H range of most natural waters, silica solubility is independent of p. H. However, as p. H rises above 9, the solubility of silica can increase dramatically.

SILICA SOLUBILITY - VII • • SUMMARY Silica solubility is relatively low and independent of p. H at p. H < 9 where H 4 Si. O 40 is the dominant species. Silica solubility increases with increasing p. H above 9, where H 3 Si. O 4 - and H 2 Si. O 42 - 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.

SOLUBILITY OF OXIDES AND HYDROXIDES Governing reactions for divalent metals are: Me(OH)2(s) Me 2+ + 2 OHMe. O(s) + H 2 O(l) Me 2+ + 2 OHc. K = [Me 2+][OH-]2 s 0 Sometimes it is more appropriate to write: Me(OH)2(s) + 2 H+ Me 2+ + 2 H 2 O(l) Me. O(s) + 2 H+ Me 2+ + H 2 O(l)

TRIVALENT METALS For a trivalent metal oxide, e. g. , goethite Fe. OOH(s) + 3 H+ Fe 3+ + 2 H 2 O(l) In general, Me. Oz/2 + z. H+ Mez+ + z/2 H 2 O(l) Me(OH)z + z. H+ Mez+ + z. H 2 O(l) Log [Mez+] = log c*Ks 0 - z p. H

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

SOLUBILITY OF ZINCITE (Zn. O) - I The thermodynamic data for solubility problems can be presented in another way. At 25°C and 1 bar: Zn. O(s) + 2 H+ Zn 2+ + H 2 O(l) log Ks 0 =11. 2 Zn. O(s) + H+ Zn. OH+ log Ks 1 = 2. 2 Zn. O(s) + 2 H 2 O(l) Zn(OH)3 - + H+ log Ks 3 = -16. 9 Zn. O(s) + 3 H 2 O(l) Zn(OH)42 - + 2 H+ log Ks 4 = -29. 7 The solubility of zincite is given by:

SOLUBILITY OF ZINCITE (Zn. O) - 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:

SOLUBILITY OF ZINCITE (Zn. O) - III And the total concentration can be written:

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

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 p. H 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 p. H 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 p. H commonly found for natural waters (5. 5 -8. 5) is considerably higher than the solubility of gibbsite over the same p. H 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 (Zn. CO 3), sphalerite (Zn. S) or willemite (Zn 2 Si. O 4) 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 p. H is often preserved, even when phases other than oxides and hydroxides are more stable.