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Solublility

Solublility. 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: SiO 2 (quartz) + 2H 2 O(l)  H 4 SiO 4 0 for which the equilibrium constant at 25°C is:

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Solublility

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  1. Solublility

  2. 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.

  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

  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:

  5. 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:

  7. 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.

  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 = 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 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)  H4SiO40Kqtz H4SiO40  H3SiO4- + H+ K1 SiO2(quartz) + 2H2O(l)  H3SiO4- + H+K

  11. SILICA SOLUBILITY - VI Taking the log of both sides and rearranging we get: Finally adding the three reactions: SiO2(quartz) + 2H2O(l)  H4SiO40Kqtz H4SiO40  H3SiO4- + H+ K1 H3SiO4-  H2SiO42- + H+ K2 SiO2(quartz) + 2H2O(l)  H2SiO42- + 2H+K

  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.

  13. 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 = 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 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)42- + 2H+ log Ks4 = -29.7 The solubility of zincite is given by:

  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:

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

  21. Concentrations of dissolved Zn species in equilibrium with ZnO as a function of pH. 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 (5.5-8.5) 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.

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