Thermodynamic Considerations for Possible Immobilization Strategies for Pb, Cd, As, and Hg

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SDMS DOCID# 1127640

Toxic Metals in the Environment: Thermodynamic Considerations for Possible Immobilization Strategies for Pb, Cd, As, and Hg

SPENCER K. PORTER National Council on the Aging, Washington, DC, USA KIRK G. SCHECKEL, CHRISTOPHER A. IMPELLITTERI, AND JAMES A. RYAN United States Environmental Protection Agency, Cincinnati, OH, USA

The contamination of soils by toxic metals is a widespread, serious problem that demands immediate action either by removal or immobilization, which is defined as a process which puts the metal into a chemical form, probably as a mineral, which will be inert and highly insoluble under conditions that will exist in the soil. If metals are to be immobilized, this might be achieved by the addition of sufficient amounts of the anion or anions which can form the inert mineral. A serious complication arises from the fact that all soils have several other cations that can and do react with the anions. This paper is a review of the equilibrium-state chemistry for the possible immobilizations of four metals: lead, cadmium, arsenic, and mercury. The anions which might precipitate these metals include: oxide, hydroxide, chloride, sulfate, sulfide, phosphates, molybdate, and carbonate. The metal ions which can interfere with these precipitation reactions are calcium, magnesium, iron, aluminum, and manganese. All of the probable combinations are re- viewed, and possible immobilization strategies are evaluated from the point of view of thermodynamic stability using free energies of formation scattered throughout the literature. The systems are examined from the point of view of the phase rule and stoichiometric consideration over the 2–12 pH range.

KEY WORDS: equilibrium, precipitation, soil, solubility, remediation, modeling

Address correspondence to Kirk G. Scheckel, United States Environmental Protection Agency, 5995 Center Hill Avenue, Cincinnati, OH 45224. E-mail: [email protected]

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I. INTRODUCTION

Many soils in the industrial world are contaminated with toxic metals for which the health hazards are well documented.1–7 Metals are also known to seriously disrupt the life cycles of flora and fauna and the health of entire ecosystems.8–12 Regulatory efforts over the past few decades have succeeded in cutting off some of the sources of this pollution, but the neglect of previous years as well as more recent pollution has given us a difficult problem without obvious solution at any price. One possibility is surely removal, but experience has shown that treatments, such as concentrated nitric acid or ethylenediamminetetraacetic acid (EDTA), which will remove such metals, do severe damage to the soil itself, often rendering it sterile and useless.3,13–15 As a consequence considerable research has been focused on techniques for immobilization, which is defined to be a treatment which will put the toxic metal into a salt or mineral which is highly insoluble and stable over wide ranges of pH and oxidizing conditions (pe).16–21 It is also desirable that the salt or mineral be inert in the face of possible future manipulations of the soil’s chemistry by organisms, agriculture, industry, etc. While there is a large collection of information available on the thermodynamics of possible crystalline phases and the aqueous solutions in equilibrium with them,22–25 especially Gibbs free energies of formation, much of the research done to date must be described as Edisonian—the experimental approach of trying everything, relentlessly, until a solution is found. The goal of this paper is an extensive review of the thermodynamics of minerals and crystals relevant to the possible immobilization and long-term stabilities of Pb, Cd, As, and Hg. This review cannot tell us what treatments will work; like all results from thermodynamics it will tell us only what is impossible or possible. We may determine which salts or minerals of a particular metal will meet the test of being highly insoluble by calculating the solubility as a function of pH and pe, and this will be done for several compounds of each toxic metal by modeling methods to be described in the next section. We will then discuss possible treatments which could make the desired compounds, and it will be necessary to consider the possible interactions of these treatments with other constituents of a soil. For example certain lead phosphate minerals may result in the immobilization of lead, but the phosphate treatments can themselves react with a number of common minerals and salts in soils, and they do. The modeling methods will be used, therefore, to understand systems which contain phosphate minerals of several metals. The number of metallic elements in a soil which might precipitate phosphate is large, and this number includes Ca, Mg, Fe, Mn, Al, Zn, Cu, as well as Pb, Hg(II), and Cd. Thermodynamics can answer the question of which of the several phosphates is the most stable, even if the question of which will form the most P1: GIM TJ1228-02 EST.cls September 1, 2004 19:29

Toxic Metals in the Environment 497

rapidly requires experiment. This paper will present thermodynamic results, and these have proved to be quite useful in the design of experiments and treatments. Some treatments, such as phosphate, are benign or even beneficent in moderate amounts, but others are not. Lead may be precipitated as wulfenite, PbMoO4, but molybdate is in itself harmful. A similar case is that of making arsenic into Ag3AsO4, which is known to be highly insoluble, but the addition of silver ion to a soil is not likely to benefit its fertility. Such facts will limit possible remediation schemes. Minerals in soils may undergo redox reactions over time, and these may be quite significant to our purposes even if they are slow. For example galena, PbS, is quite insoluble but subject to slow oxidation to anglesite, 22 PbSO4, which is orders of magnitude more soluble. Mercury is a particular troublesome case in this regard because it has three oxidation states, and all three can exist in soils. It will be necessary to consider, therefore, the possible redox reactions of each element and each treatment as well as the conditions of pH and pe under which each form might be stable. These reactions will further limit our choices or perhaps the long-term efficacy of our methods.

II. MODELING 1. Systems of One Mineral in Equilibrium with Water The object of each model made for this study is a description of a particular chemical system at equilibrium. We know of course that not all chemical systems will come to equilibrium, but we do know that no chemical system can move by itself away from its equilibrium state.22,25 We also wish to know how a particular system will change as the pH and pe vary. For example we would like to know how the solubility of hydroxypyromorphite, Pb5(PO4)3OH, will change with pH (pe is not an issue in this case). It is certainly true that if solid hydroxypyromorphite is stirred with pure water until equilibrium is obtained, there will be a definite pH determined by the relative amounts of the different ions, but in soil systems the small concentrations of lead and phosphate ions will not determine pH. There will be many other ions of higher concentrations which will. The problem of describing a heterogeneous chemical system like hydroxypyromorphite in equilibrium with an aqueous solution is straight- forward even if the algebra can become complex. First the system must be defined with precision and the number of components determined. In the model we allow the mineral to come to equilibrium with a solution containing a fixed amount of NaCl, because chloro-complexes are likely to be significant, and an activity of CO2 which would be in equilibrium with the atmosphere. The system has, therefore, three phases and six components (PbO, P2O5,CO2,H2O, Na2O, and HCl). This gives five degrees of freedom, P1: GIM TJ1228-02 EST.cls September 1, 2004 19:29

498 S. K. Porter et al.

and two of these will be satisfied by using standard temperature and pressure. Thus three tests on the stoichiometry of the solution will be required, and these will be tests on the total amounts of sodium and chlorine and on the ratio of phosphorus to lead which must be three to five at equilibrium. Finally the charge of the model system must be determined. If the system is in a beaker, the definite pH described in the previous paragraph will be obtained. This pH is labeled the natural pH here. If the Pb5(PO4)3OH is in the environment, the aqueous phase and what that contains will determine the pH. For this reason the models done for this paper are calculated over a range of pH. If redox chemistry is possible, calculations are done over a range of pe as well. Areview of the thermochemical tables shows that there are forty- one solute species in the hydroxypyromorphite system, beside H+ and OH−, whose activities must be determined by equilibrium-constant equations found from Gibbs free energies of formation. All of this gives a few too many simultaneous equations to be solved conveniently, so the techniques developed by the authors (described below) were used. A spreadsheet of several columns was calculated (Table 1), and each column has a fixed pH. Each of the forty-four solute species, other than the hydrogen and hydroxide ions, was given a row, and the first three rows (21–23 in the example) were those that needed to be determined by trial and error in order to meet the three tests on the stoichiometry (rows 70–72). The three trial-and-error quantities must be one chlorine species, one sodium species, and one of either lead or phosphate. In this work these choices were always neutral species including the one from the anion of the mineral, and in this case these were 0 0 0 pHCl , pNaOH , and pH3PO4.Tobesure these choices were arbitrary, but always beginning with neutral species made the process consistent and the formulas for calculating the other species easy to debug. A sample is given in the next paragraph. The equilibrium-constant equations were always done in logarithmic form, and all activities are given as pa’s. (Since the spreadsheet program [LOTUS 1-2-3, Release 4] does not allow superscripts, it should be noted that pX[n] = pXn in the first column.) The activity of dissolved CO2 (row 24) was taken to be constant on the assumption of an atmosphere with the gas at 270 ppm. The activities of the species on rows 25 through 42 were calculated from the activities on rows 20 through 24 and equilibrium-constant equations derived from free energies of formation. Examples of the equations used:

pCl[−] = pHCl[0] − pH − 2.999 − = − + . pH2PO4[ ] pH3PO4[0] pH 2 148 pNa[+] = pNaOH[0] + pH − 13.994 − = + − + . , pNaCO3[ ] pNaOH[0] pCO2[0] pH 1 261 and so forth. P1: GIM TJ1228-02 EST.cls September 1, 2004 19:29 7.248 5.550 3.001 5.865 4.995 5.002 9.902 5.50 page) 16.811 20.031 24.732 14.099 10.729 11.494 11.500 aqueous next atmosphere on The 7.308 5.110 3.001 6.365 4.995 5.002 7.962 5.00 PYRMORPH 15.933 18.653 22.854 14.659 11.729 11.994 11.000 the 5 = 0.50. F with of (Continued ﬁlename: 7.371 4.673 3.001 6.865 4.995 5.002 7.025 4.50 15.058 17.278 20.979 15.222 12.729 12.494 10.500 intervals at equilibrium 7.436 4.238 3.003 7.365 4.995 5.002 6.090 4.00 14.189 15.909 19.110 15.787 13.729 12.994 10.002 3 in = gas sol’n 12.00 P Phases to Pb5(PO4)3OH 7.508 3.810 3.007 7.865 4.995 5.002 5.162 9.506 3.50 13.331 14.551 17.252 16.359 14.729 13.494 dioxide 0.00 carbon 7.596 3.398 3.018 8.365 4.995 5.002 4.250 9.017 range 3.00 12.508 13.228 15.429 16.947 15.729 13.994 pH text. the dissolved 7.728 3.030 3.050 8.865 4.995 5.002 3.382 8.549 2.50 11.772 11.992 13.693 17.579 16.729 14.494 s the i over in 6 = There HCl 7.939 2.741 3.150 9.365 4.995 5.002 2.593 8.149 CO2 PbO 2.00 H2O P2O5 Na2O C 11.194 10.914 12.115 18.290 17.729 14.994 system Components 3.00. described OH) is = 3 ) 4 8.237 2.539 3.408 9.865 4.995 5.002 1.891 7.907 1.50 10.750 10.010 10.711 19.088 18.729 15.494 (PO pCl(t) 5 = (Pb inc. spreadsheet 9.217 9.418 8.590 2.392 3.867 4.995 5.002 1.244 0.50 7.866 1.00 10.497 19.941 19.729 10.365 15.994 pH this pNa(t) of that 8.470 8.171 8.967 2.269 4.445 4.995 5.002 0.621 7.944 0.50 10.250 20.818 20.729 10.865 16.494 such making The 7.744 6.945 9.354 2.156 5.066 4.995 5.002 9.772 9.595 0.008 3.000 3.000 5.002 8.065 0.00 hydroxypyromorphite pKsp0 pKsp0 10.024 21.705 21.729 11.365 18.570 23.305 28.436 22.361 12.865 18.069 17.289 22.069 16.116 14.533 16.994 17.289 activity the an 5.002. of etc. = 0 2 with solution pCO ] ] − NaCl ] ] − ] ] ] − − carbonates. − spreadsheet − − giving ] A aqueous − n 1. contains pH2P2O7[2 pH3P2O7[ pH4P2O7[0] pPO4[3 pHPO4[2 pH2PO4[ pCl[ pCO3[2 pHCO3[ pH2CO3[0] pCO2[0] Pb(H2PO4)2 PbCl2 Pb2CO3Cl2 Pb3(CO3)2(OH)2 PbOPbCO3 Pb3(PO4)2 Pb5(PO4)3OH Pb5(PO4)3Cl PbHPO4 Pb4O(PO4)2 Pb(OH)2 PbCO3 Possible pH3PO4[0] pNa(t) pCl(t) pNaOH[0] pCO2[0] Hydroxypyromorphite Pb5(PO4)3OH pH pHCl[0] ppm) ABLE 9 8 7 6 5 4 1 2i 3 phase (270 T 34 33 32 31 30 29 28 27 26 25 24 12 13 14 15 16 17 18 19 11 10 23 22 20 21

499 P1: GIM TJ1228-02 EST.cls September 1, 2004 19:29 9.421 6.603 9.246 9.346 7.394 5.346 9.055 8.448 6.016 3.000 12.519 17.196 40.674 18.896 10.198 15.826 30.772 19.688 17.486 11.295 22.684 16.788 11.948 16.309 12.257 21.922 18.010 6.985 6.166 8.370 8.970 7.458 4.910 9.116 8.948 6.016 3.000 12.083 16.881 40.480 19.581 10.322 15.511 32.154 19.942 18.177 10.922 24.248 17.852 12.512 17.309 13.257 22.044 17.632 8.548 5.729 7.495 8.595 7.520 4.472 9.179 9.448 6.017 3.000 11.647 16.569 40.293 20.269 10.447 15.199 33.528 20.192 18.894 10.547 25.810 18.914 13.074 18.309 14.257 22.169 17.257 8.112 5.291 6.621 8.221 7.581 4.033 9.244 9.948 6.018 3.000 11.212 16.260 40.115 20.960 10.573 14.890 34.893 20.435 19.546 10.199 27.371 19.975 13.635 19.309 15.257 22.300 16.888 7.677 4.853 5.750 7.850 9.783 7.638 3.590 9.315 6.022 3.000 10.781 15.960 39.957 21.660 10.702 14.590 36.236 20.664 20.218 28.928 21.032 14.192 10.448 20.309 16.257 22.442 16.530 7.246 4.411 4.885 7.485 9.377 7.685 3.137 9.404 6.033 3.000 10.361 15.684 39.859 22.384 10.837 14.314 37.517 20.851 20.859 30.475 22.079 14.739 10.948 21.309 17.257 22.619 16.207 9.980 6.833 3.964 4.038 7.138 8.919 7.706 2.658 9.535 6.066 3.000 15.469 39.907 23.169 10.990 14.099 38.643 20.935 21.421 31.996 23.100 15.260 11.448 22.309 18.257 22.883 15.971 9.752 6.505 3.537 3.222 6.882 8.366 7.679 2.131 9.746 6.165 3.000 15.364 40.224 24.064 11.174 13.994 39.484 20.829 21.842 33.469 24.073 15.733 11.948 23.309 19.257 23.305 15.893 9.947 6.442 3.216 2.441 6.541 7.708 7.600 1.552 6.423 3.000 15.382 40.838 25.082 11.393 14.012 40.010 20.513 22.105 34.890 24.994 16.154 10.044 12.448 24.308 20.257 23.901 15.969 6.749 3.064 1.683 6.283 6.984 7.488 0.940 6.882 3.000 10.713 15.476 41.639 26.176 11.635 14.106 40.339 20.066 22.269 36.278 25.882 16.542 10.397 12.948 25.308 21.257 24.608 16.196 7.279 3.016 0.933 6.033 6.232 7.362 0.314 7.460 3.000 11.822 15.603 42.519 27.303 11.885 14.233 40.583 19.562 22.391 37.652 26.756 16.916 10.774 13.448 26.308 22.257 25.361 16.449 0.318 7.887 3.004 0.188 5.788 5.467 7.230 8.081 3.000 13.050 15.745 43.435 28.445 12.140 14.375 40.789 19.033 22.495 39.020 27.624 17.284 11.161 13.948 27.308 23.257 26.135 16.723 − ) ] ] ] ] ] ] − − ] ] + + + ] − ] ] ] − ] + − − ] − ] + ] − ] ] − − Continued − ] + ( − ] + ] + + 1. pPbCl3[ pPbCl2[0] pPbCl[ pPb(HPO4)2[2 pPb(P2O7)2[6 pPb(PO4)2[4 pPbPO4[ pPbP2O7[2 pPbH2PO4[ pPbHPO4[0] pPb6(OH)8[4 pPb4(OH)4[4 pPb3(OH)4[2 pPb2OH[3 pPb(OH)4[2 pPb(OH)3[ pPbOH[ pPb[2 pPb(OH)2[0] pNaHPO4[ pNaHCO3[0] pNa2CO3[0] pNaCO3[ pNaCl[0] pNa[ pP2O7[4 pHP2O7[3 ABLE 61 60 59 58 57 56 55 54 53 52 51 50 49 48 47 46 45 44 43 42 41 40 39 38 37 36 T 35

500 P1: GIM TJ1228-02 EST.cls September 1, 2004 19:29 page) 5.50 2.480 0.187 0.000 4.677 2.418 3.588 6.511 6.446 2.280 0.283 2.353 2.417 5.075 2.999 2.995 5.319 5.541 3.000 3.000 4.669 8.826 7.0E-16 16.309 15.820 − − 3.9E-16 7.7E-16 − next on 5.00 2.580 0.249 0.000 5.241 2.981 3.651 6.075 5.131 1.904 0.377 2.917 2.981 4.557 2.997 2.885 4.885 5.107 3.000 3.000 4.688 9.390 7.0E-16 17.873 15.384 − − 9.8E-16 8.2E-16 − (Continued 4.50 2.680 0.312 0.000 5.803 3.544 3.714 5.638 3.819 1.529 0.470 3.479 3.543 4.089 2.992 2.959 4.448 4.670 3.000 3.000 4.695 9.952 7.5E-16 19.435 14.949 − − 2.2E-16 9.6E-16 − 4.00 2.780 0.374 0.000 6.364 4.104 3.776 5.202 2.510 1.155 0.564 4.040 4.104 3.623 2.978 2.889 4.008 4.230 3.000 3.000 4.697 5.8E-16 20.996 10.513 14.515 − − 5.4E-16 9.4E-16 − 3.50 2.879 0.436 0.000 6.921 4.662 3.838 4.767 1.210 0.784 0.657 4.597 4.661 3.152 2.943 2.734 3.564 3.786 3.000 3.000 4.697 5.5E-16 22.553 11.070 14.088 − − 6.1E-16 9.0E-16 − 3.00 2.977 0.497 0.066 0.000 7.468 5.209 3.896 4.336 0.419 0.748 5.144 5.208 2.667 2.866 2.455 3.107 3.329 3.000 3.000 4.697 7.7E-16 24.100 11.617 13.680 − − − 4.4E-16 8.0E-16 − 2.50 3.070 0.555 1.281 0.000 7.989 5.729 3.949 3.923 0.072 0.835 5.665 5.729 2.159 2.739 2.058 2.620 2.842 3.000 3.000 4.697 8.5E-16 25.621 12.138 13.332 − − − 4.9E-16 9.1E-16 − 2.00 3.150 0.607 2.386 0.244 0.000 8.462 6.203 4.022 3.595 0.914 6.138 6.202 1.617 2.598 1.574 2.082 2.304 3.000 3.000 4.697 5.3E-16 27.094 12.611 13.202 − − − − 6.7E-16 6.7E-16 − 1.50 3.199 0.654 3.368 0.525 0.000 8.883 6.624 4.201 3.532 0.984 6.559 6.623 1.048 2.484 1.032 1.491 1.713 3.000 3.000 4.697 8.2E-16 28.515 13.032 13.656 − − − − 7.8E-16 8.5E-16 − 1.00 3.207 0.697 4.274 0.783 0.000 9.271 7.012 4.549 3.839 1.049 6.947 7.011 0.459 2.378 0.453 0.865 1.087 3.000 3.000 4.697 9.5E-16 29.903 13.420 14.881 − − − − 9.0E-16 9.5E-16 − 0.50 3.191 0.739 5.147 1.033 0.148 0.147 0.000 9.645 7.386 5.001 4.369 1.111 7.321 7.385 2.266 0.220 0.442 3.000 3.000 4.697 7.4E-16 31.277 13.794 16.568 − − − − − − 4.2E-16 5.8E-16 − 0.00 3.167 0.779 6.005 1.278 0.764 0.764 0.436 0.214 0.000 7.754 5.489 4.977 1.172 7.689 7.753 2.156 3.000 3.000 4.697 8.3E-16 10.013 32.645 14.162 18.417 − − − − − − − − 9.6E-18 6.7E-16 − ] − )) ] − precipitates: − pP(t)-pPb(t)-log(5/3) pCl(t)-pCl(*) pNa(t)-pNa(*) 3: 1: ) PbCO3 2: · + est Pb5(PO4)3Cl Pb5(PO4)3OH Pb3(PO4)2 PbO Pb3(CO3)2(OH)2 Pb2CO3Cl2 PbCl2 Pb(H2PO4)2 PbHPO4 Pb4O(PO4)2 Pb(OH)2 Possible pH pQsp0-pKsp0 PbCO3 p(abs(Q(t)) p(abs(Q( pQ( T TEST TEST pPb(t) pP(t) pNa(t) pC(t) pCl(t) pPb(CO3)2[2 pPbCO3[0] pPbCl4[2 90 89 88 87 86 85 84 83 82 81 80 76 77 78 79 75 74 73 71 72 70 69 68 67 66 65 64 63 62

501 P1: GIM TJ1228-02 EST.cls September 1, 2004 19:29 ] ] ] ] ] + + + ] ] ] ] ] − ] ] + − − − ] ] ] − ] + ] − − ] ] ] ] − − − − − + − ] − − ] ] + + − pPbPO4[ pPbP2O7[2 pPbH2PO4[ pPbHPO4[0] pPb6(OH)8[4 pPb4(OH)4[4 pPb3(OH)4[2 pPb2OH[3 pPb(OH)4[2 pPb(OH)3[ pPbOH[ pPb[2 pPb(OH)2[0] pNaHPO4[ pNaHCO3[0] pNa2CO3[0] pNaCO3[ pNaCl[0] pNa[ pP2O7[4 pHP2O7[3 pH2P2O7[2 pH3P2O7[ pH4P2O7[0] pPO4[3 pHPO4[2 pH2PO4[ pCl[ pCO3[2 pHCO3[ pH2CO3[0] pCO2[0] pH3PO4[0] pNaOH[0] pH pHCl[0] 2.271 0.635 6.068 6.128 6.732 8.392 5.726 5.693 3.002 9.760 6.745 7.775 0.525 0.174 4.976 3.000 4.995 5.002 8.739 12.00 11.123 18.118 11.716 35.438 31.465 19.819 23.684 10.338 14.790 10.798 10.363 15.664 25.384 36.585 14.828 17.999 − − 1.271 0.135 6.534 7.179 7.283 9.889 8.443 5.643 5.196 9.803 3.005 8.763 5.748 9.605 1.940 1.089 5.391 3.000 4.995 5.002 8.242 11.50 12.004 17.582 11.682 33.744 29.669 18.972 22.286 13.641 11.693 16.494 25.714 36.415 14.743 17.499 − − 0.271 7.023 8.195 7.799 9.405 8.459 5.629 4.708 8.829 3.017 7.775 4.760 3.413 2.062 5.864 3.000 0.365 4.995 5.002 7.754 11.00 12.966 17.071 11.671 31.841 27.734 18.020 20.618 12.857 11.551 13.139 17.440 26.160 36.361 14.716 16.999 − 7.520 9.201 8.305 8.911 8.465 5.700 4.287 7.986 3.096 6.854 3.839 4.904 3.053 6.355 3.000 0.729 0.865 4.995 5.002 7.333 10.50 13.954 16.569 11.668 29.871 25.754 17.036 19.328 11.863 13.534 14.622 18.423 26.643 36.344 14.707 16.499 8.017 8.809 8.415 8.469 6.075 4.170 7.753 3.479 6.238 3.222 6.397 4.046 6.848 3.000 1.729 1.365 4.995 5.002 7.216 10.00 14.944 16.065 11.665 27.899 23.773 16.050 17.837 10.205 10.867 15.518 16.106 19.407 27.127 36.328 14.700 15.999 8.492 9.347 7.953 9.905 8.507 6.828 4.486 8.385 4.295 6.054 3.038 7.834 4.983 7.285 3.000 2.729 1.865 4.995 5.002 7.532 9.50 15.856 15.540 11.640 26.125 21.923 15.162 16.413 11.243 17.393 17.481 20.282 27.502 36.203 14.637 15.499 8.869 7.636 9.088 8.690 7.492 4.956 9.323 5.265 6.023 3.008 9.028 5.677 7.479 3.000 3.729 2.365 4.995 5.002 8.002 9.00 16.428 14.917 11.517 25.226 20.657 14.713 15.280 12.426 10.030 18.781 18.369 20.670 27.390 35.591 14.331 14.999 9.148 7.469 8.421 9.023 7.933 5.450 6.259 6.018 3.002 9.974 6.123 7.425 3.000 4.729 2.865 4.995 5.002 8.496 8.50 16.652 14.196 11.296 25.220 19.986 14.710 14.444 13.759 10.863 10.312 19.674 18.762 20.563 26.783 34.484 13.777 14.499 9.403 7.336 7.788 9.390 8.318 5.949 7.258 6.016 3.001 6.510 7.312 3.000 5.729 3.365 4.995 5.002 8.995 8.00 16.794 13.451 11.051 25.427 19.458 14.813 13.680 15.126 11.730 11.310 20.447 19.035 20.336 26.056 33.257 10.861 13.164 13.999 9.642 7.227 7.179 9.781 8.667 6.449 8.258 6.016 3.001 6.860 7.162 3.000 6.729 3.865 4.995 5.002 9.495 7.50 16.883 12.690 10.790 25.769 19.019 14.984 12.961 16.517 12.621 12.309 21.146 19.234 20.035 25.255 31.956 11.711 12.514 13.499 9.826 7.202 6.654 8.875 6.948 9.257 6.016 3.000 7.067 6.869 3.000 7.729 4.365 4.995 5.002 9.994 7.00 16.774 11.874 10.474 26.621 18.921 15.411 12.411 17.992 13.596 10.256 13.309 21.562 19.150 19.451 24.171 30.372 12.418 11.721 12.999 ) 9.955 7.259 6.211 8.947 7.448 6.016 3.000 7.140 6.442 3.000 8.729 4.865 4.995 5.002 6.50 16.475 11.003 10.103 27.960 19.147 16.080 12.024 19.549 14.653 10.813 14.309 10.257 21.707 18.795 18.596 22.816 28.517 12.991 10.794 10.494 12.499 Continued ( 1. 9.723 7.328 5.780 8.998 7.948 6.016 3.000 7.191 5.993 3.000 9.729 5.365 4.995 5.002 9.845 6.00 10.075 16.147 10.123 29.376 19.424 16.788 11.663 21.118 15.722 11.382 15.309 11.257 21.809 18.397 17.698 21.418 26.619 13.542 10.994 11.999 ABLE T 55 54 53 52 51 50 49 48 47 46 45 44 43 42 41 40 39 38 37 36 35 34 33 32 31 30 29 28 27 26 25 24 23 22 20 21

502 P1: GIM TJ1228-02 EST.cls September 1, 2004 19:29 ] ] ] ] − − − − )) ] pKsp0 ] − − pP(t)-pPb(t)- pNa(t)-pNa(*) pCl(t)-pCl(*) ] − − + 3: 2: 1: ) + log(5/3) Pb5[PO4]3Cl Pb5(PO4)3OH Pb3(PO4)2 PbO.PbCO3 Pb3(CO3)2(OH)2 Pb2CO3Cl2 PbCl2 Pb(H2PO4)2 PbHPO4 Pb4O(PO4)2 Pb(OH)2 PbCO3 pH pQsp0 p(abs(Q(t)) p(abs(Q( pQ( TEST TEST TEST pPb(t) pP(t) pNa(t) pCl(t) pC(t) pPb(CO3)2[2 pPbCO3[0] pPbCl4[2 pPbCl3[ pPbCl2[0] pPbCl[ pPb(HPO4)2[2 pPb(P2O7)2[6 pPb(PO4)2[4 1.180 1.138 0.310 1.203 1.139 2.584 2.584 0.262 0.040 2.289 0.247 0.000 0.209 1.121 4.650 6.745 3.000 3.000 5.270 1.193 6.531 8.0E-16 8.4E-16 12.00 15.954 14.743 25.262 21.961 18.864 16.046 12.493 21.822 − − − − − − − − − − − 6.2E-16 − − 1.280 1.087 0.301 1.152 1.088 1.593 1.593 1.308 0.000 0.203 1.172 6.082 4.616 5.748 0.802 1.024 3.000 3.000 0.804 5.321 3.074 5.7E-16 7.4E-16 11.50 15.005 14.624 24.313 21.012 17.915 15.097 13.374 24.534 − − − − − − − − 8.7E-16 − − 1.380 1.071 0.299 1.136 1.072 0.625 0.625 0.367 0.000 0.201 1.188 5.598 4.605 4.760 1.620 2.042 3.000 3.000 1.820 5.337 5.036 9.5E-16 8.9E-16 11.00 14.021 14.586 23.329 20.028 16.931 14.113 14.336 27.442 − − − − − − − − 8.6E-16 − − 1.480 1.066 0.298 1.130 1.066 0.000 0.200 1.194 5.104 4.602 0.287 0.267 3.839 2.624 3.046 3.000 3.000 0.486 2.826 5.343 7.024 4.7E-16 9.8E-16 10.50 13.027 14.574 22.335 19.034 15.937 13.119 15.324 30.413 − − − − − 8.8E-16 − − 1.580 1.061 0.297 1.126 1.062 0.000 0.200 1.198 4.608 4.599 1.087 1.084 3.222 3.817 4.039 3.000 3.000 1.204 3.830 5.347 9.014 8.2E-16 5.2E-16 10.00 12.032 14.564 21.340 18.039 14.942 12.123 16.314 33.387 − − − − − 8.6E-16 − − 1.680 1.024 0.291 1.080 1.024 0.000 0.196 1.236 4.146 4.574 1.755 1.733 3.038 4.752 4.974 3.000 3.000 1.806 4.868 5.385 9.50 3.2E-16 6.5E-16 11.070 14.476 20.378 17.077 13.980 11.161 17.226 36.174 10.926 − − − − − 6.8E-16 − − 1.780 0.840 0.260 0.905 0.841 0.000 0.175 1.419 3.830 4.451 2.325 2.243 3.008 5.442 5.663 3.000 3.000 2.343 6.051 5.568 9.00 6.9E-16 10.253 14.048 19.562 16.261 13.163 10.345 17.798 38.134 12.498 − − − − − 9.9E-16 6.4E-16 − 1.880 0.508 0.205 0.572 0.508 0.000 0.138 1.752 3.662 9.585 4.230 2.850 2.619 3.002 5.873 6.095 3.000 3.000 2.851 7.384 5.901 9.677 8.50 3.8E-16 5.8E-16 13.272 18.894 15.593 12.495 18.022 39.251 13.722 − − − − − 7.5E-16 − − 1.980 0.140 0.143 0.205 0.141 0.000 0.098 2.119 3.530 8.953 3.985 3.358 2.843 3.001 6.218 6.440 3.000 3.000 3.342 8.751 6.268 9.045 8.00 2.3E-16 9.9E-16 12.414 18.262 14.961 11.863 18.164 40.166 14.864 − − − − − 5.1E-16 − − 2.080 0.078 0.000 0.054 2.510 0.250 3.420 8.344 3.724 0.186 0.250 3.861 2.944 3.000 6.457 6.679 3.000 3.000 3.803 6.659 8.435 7.50 6.7E-16 8.9E-16 11.503 10.142 17.652 14.351 11.254 18.253 40.954 15.953 − − 7.8E-16 − − 2.180 0.000 0.001 2.985 0.726 3.396 7.619 3.408 0.001 0.661 0.725 4.366 2.982 3.000 6.431 6.653 3.000 3.000 4.198 7.134 7.911 7.00 6.1E-16 10.394 11.617 17.128 13.826 10.729 18.144 41.260 16.844 − 2.8E-16 9.2E-16 − 2.280 0.060 0.000 3.542 1.282 3.452 7.376 9.095 3.037 0.094 1.218 1.282 4.901 2.994 3.000 6.139 6.361 3.000 3.000 4.471 7.691 7.467 6.50 7.0E-16 13.174 16.684 13.383 10.286 17.845 41.107 17.545 − − 2.5E-16 5.8E-16 − 2.380 0.124 0.000 4.111 1.852 3.522 6.945 7.767 2.657 0.189 1.787 1.851 6.029 2.998 2.998 5.744 5.966 3.000 3.000 4.613 8.260 9.855 7.037 6.00 5.2E-16 14.743 16.254 12.952 17.517 40.881 18.217 − − 4.2E-16 5.2E-16 − 90 89 88 87 86 85 84 83 82 81 80 77 78 79 76 75 74 73 72 71 70 69 68 67 66 65 64 63 62 61 60 59 58 57 56

503 P1: GIM TJ1228-02 EST.cls September 1, 2004 19:29

504 S. K. Porter et al.

In this work these equations were always written in terms of the neutral species, and this made the form of each equation easy to check because the sign and magnitude of the pH term equaled the ion’s charge. Row 43 has pPb(OH)2[0], and this activity was found as follows: A quan- 0 tity named pKsp was calculated for the mineral, and this is the negative log- arithm of the equilibrium constant for the reaction shown by equation [1].

/ + / = 0 + / 0 9 5H2O 1 5Pb5(PO4)3OH Pb(OH)2 3 5H3PO4 [1]

The conventions used are (1) the mineral is on the left-hand side, (2) the number of moles of the metal is one, and (3) the species on the right-hand side 0 are uncharged. Free energies of formation were then used to ﬁnd pKsp, and it is 17.289 for hydroxypyromorphite. It is shown on row 3 of the spreadsheet, 0 and the pKsp’s for other possible precipitates from the system’s components are shown on rows 8 through 19. These conventions allowed the calculation 0 of pPb(OH)2 on row 43from 0 = 0 − / 0 pPb(OH)2 pKsp 3 5p H3PO4

The activities of the other lead species were then calculated in terms of 0 0 0 0 pH, pHCl ,pH3PO4, pCO2, and pPb(OH)2 and put on rows 44 through 64. The total activities of each of the ﬁve elements in solution, C, Cl, Na, P, and Pb were found by summing the activities of each of the species containing them, and these are given on rows 65 through 69 as pX(t)’s. These totals were then used to make the tests on stoichiometry which determined the values for the variables on rows 21 through 23. A macro, written in the language supplied with Lotus 1-2-3, was used to make, by trial and error, each of the three agreements to be better than 1 × 10−15. These are shown on rows 70 through 72. (Experience has shown that the agreement must be this close to get with consistency smooth curves on the ﬁgures.) Thirty of the species in solution are charged, and ten of these are cations. The negative log of the sum of the cation charges in moles/liter is given on line 73. The negative log of the absolute value of the anion charges is shown on line 74, and the negative log of the absolute value of the total charge is on line 75. Figure 1 is a graph of rows 73 and 74, and it shows the lines crossing at pH 6. This pH is what would occur if the system were made exactly as described, and this is the natural pH. In a soil environment or in an analytical testing procedure the pH will usually be determined for the system rather than by it, and the charges of the system described by the spreadsheet will be unbalanced even as no actual system ever could be. Rows 79 through 90 are devoted to calculations to see if other minerals 0 or salts of the system’s components might precipitate. Further, pQsp has the 0 same form as pKsp but uses the actual activities instead of the ones needed for equilibrium. Thus, row 79, for cerrusite, is row 43 plus row 24 minus the P1: GIM TJ1228-02 EST.cls September 1, 2004 19:29

Toxic Metals in the Environment 505

FIGURE 1. The hydroxypyromorphite (Pb5(PO4)3OH) system: total cation charges as pQ(+) and total anion charges as p(abs(Q(−))). The natural pH of this system is shown by the crossing of these lines.

0 pKsp for cerrusite, which is 14.533 (row 8). Positive results for the difference show that the mineral cannot form, while negative results would show that it might. As can be seen, a number of other minerals may precipitate here, and the most prominent is chloropyromorphite, Pb5(PO4)3Cl. The finished spreadsheet was then used to make graphs of the mineral’s solubility as a function of pH. The principal solute species of lead and phosphorus for such a system are shown in Figures 2 and 3. These graphs have a number of interesting features. The solubility of the mineral reaches a minimum at a pH of about 7.5, about 1.5 above the natural pH, and increases sharply on either side of that. The principal lead species is the dipositive ion at low pH, but the complexes of chloride and phosphate are seen to be close behind in activity. At high pH the carbonate complexes accentuate the tendency of the mineral to be somewhat amphoteric. Surely a system with high phosphate or chloride concentration, as in a treatment or soil high in these elements, might result in a strong increase in soil-lead solubility leading to precipitation in more stable Pb forms. The chloride concentration in this model was arbitrarily fixed at one millimole per kilogram of water. Some of the systems that will be discussed in this paper have the possibility of redox chemistry with sulfur, arsenic, and mercury. The environment that each system finds itself in will determine the redox chemistry of these three elements, and it will be necessary to represent in a quantitative way the conditions just as is done with the pH. One way to do this is to increase the number of components in the system by P1: GIM TJ1228-02 EST.cls September 1, 2004 19:29

506 S. K. Porter et al.

FIGURE 2. The hydroxypyromorphite (Pb5(PO4)3OH) system: the activities as functions of pH of the important solute species which contain lead.

noting that water is made of H2 and O2. This increases the degrees of freedom as well and does allow for changes in redox conditions. A simpler method which allows the methods of calculation described above to be used is to make the electron a reactant with an activity given by pe, i.e., the negative log of the virtual activity of the free electron in solution.

FIGURE 3. The hydroxypyromorphite (Pb5(PO4)3OH) system: the activities as functions of pH of the important solute species which contain phosphate. P1: GIM TJ1228-02 EST.cls September 1, 2004 19:29

Toxic Metals in the Environment 507

In what follows, when one of these three elements is part of the system, the spreadsheets and graphs are calculated across the pH range at some constant value of (pH + pe) and with H2Oasone component rather than two or calculations are made across an area in pH-pe space. Using constant values of (pH + pe) gives some interesting results. We ﬁnd, for example, that PbS and PbSO4 can co-exist at equilibrium at a constant value of (pH + pe), which we can calculate as 5.055. Incidentally, virtually all of the sulfur in solution over these two minerals at equilibrium is sulfate rather sulﬁde. If (pH + pe) > 5.055, then only lead sulfate will be stable, while PbS will remain unoxidized below 5.055. 0 0 pKsp for each mineral containing sulfur is calculated using pH2S ,regardless of the actual oxidation state in the mineral. So for the two lead minerals:

{ , } 0 = 0 + 0 = . PbS galena pKsp pPb(OH)2 pH2S 25 329 { , } 0 = 0 + 0 − + =− . PbSO4 anglesite pKsp pPb(OH)2 pH2S 8(pH pe) 15 111

+ = 0 Subtracting the second equation from the ﬁrst gives (pe pH) 5.055. pKsp values for minerals of iron are calculated using Fe(III), while arsenic minerals use As(V). Calculations for Hg will use Hg0, that is the atom as a solute.

2. Systems with Several Minerals The methods described above are easy to extend to systems with several minerals, and two examples will be given in this section. If the system has two minerals rather than one without an increase in the number of components, the number of degrees of freedom falls to four, and only two tests on the stoichiometry are needed. For example we may consider the system hydroxypyromorphite-cerrusite in contact with the same solution of NaCl and dissolved carbon dioxide. Now F = 4, and we need test only pCl(t) and 0 pNa(t). There are two minerals and, therefore, two pKsp equations:

{ } 0 = 0 + / 0 hydroxypyromorphite Pb5(PO4)3OH :pKsp pPb(OH)2 3 5pH3PO4 = 17.289 { } 0 = 0 + 0 cerrusite PbCO3 :pKsp pPb(OH)2 pCO2 = 14.533

0 0 = Since pCO2 is ﬁxed by the atmosphere at 5.002, pPb(OH)2 9.531, and 0 = pH3PO4 12.930. These quantities are constant over the entire pH range, and we may ﬁnd the activities of all 46 solute species as before. Figure 4 shows the total element concentrations with the changes in lead concentrations from the hydroxypyromorphite-only system, shown as pPb(*). P1: GIM TJ1228-02 EST.cls September 1, 2004 19:29

508 S. K. Porter et al.

FIGURE 4. Hydroxypyromorphite (Pb5(PO4)3OH) with cerrusite (PbCO3): elemental activities with pPb(t) compared to lead in the Pb5(PO4)3OH-only system, Figure 2.

Since pyromorphite will never be the only source of phosphate in a soil system, it is useful to examine its interaction with lead carbonate in a slightly different way. Consider the chemical equilibrium [2] below which also shows the chemistry under discussion.

/ + 0 + / = + / 0 4 5H2O pCO2 1 5Pb5(PO4)3OH PbCO3 3 5H3PO4 [2]

The equilibrium constant of this reaction may be found from the difference 0 between the pKsp’s as in = . − . = . pKeq 17 289 14 533 2 756

At equilibrium

. = / 0 − 0 2 756 3 5pH3PO4 pCO2

0 0 If pCO2 is ﬁxed at 5.002 from the atmosphere, then pH3PO4 is 12.930 as 0 before, but if pH3PO4 is not 12.930, as is usually the case; the equilibrium will shift one way or the other. Thus we see that if the total phosphate concentration is below the pP(t) line of Figure 4, the carbonate will be changed to hydroxypyromorphite. Since this line represents a very small concentration of phosphate at all pH’s below 9, we see that the conversion of cerrusite to hydroxypyromorphite may be easily done by adding phosphate unless something else is precipitating it. P1: GIM TJ1228-02 EST.cls September 1, 2004 19:29

Toxic Metals in the Environment 509

A different sort of problem arises if we have two minerals rather than one and there is one more component. An example of this sort of problem is anglesite (PbSO4), hydroxypyromorphite, a solution, and the atmosphere. The new component is SO3 (used in this example instead of H2Sbyassum- ing oxidizing conditions), and there are now seven of them. There are ﬁve degrees of freedom, and there will be three tests on the stoichiometry. There 0 are two pKsp equations:

{ }, 0 = 0 + 0 = . anglesite PbSO4 pKsp pPb(OH)2 pH2SO4 25 540 { }, 0 = 0 + / 0 = . pyromorphite Pb5(PO4)3OH pKsp pPb(OH)2 3 5pH3PO4 17 289 The three quantities in these equations cannot be constant, because two equations are not sufﬁcient to determine three variables. There will be a test on the stoichiometry, and it will be given by the following equation, provided that the only sources of these elements are the two minerals.

Pb(t) = 5/3 P(t) + S(t)

The result is Figure 5 which implies that pyromorphite is less soluble than anglesite at pH’s over 4 and more soluble below 4. The spreadsheet and this graph were constructed on the assumption that the only sources of phosphate and sulfate in the solution were the minerals themselves, but this situation is unlikely in a soil environment. If the two minerals are in equilibrium with a solution and each other, the shift of lead from one to

FIGURE 5. Hydroxypyromorphite (Pb5(PO4)3OH) with anglesite (PbSO4): elemental activities vs. pH. P1: GIM TJ1228-02 EST.cls September 1, 2004 19:29

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FIGURE 6. Hydroxypyromorphite (Pb5(PO4)3OH) with anglesite (PbSO4): the negative log of the phosphate-to-sulfate ratio vs. pH in the system of Figure 5.

the other is always possible, and Figure 6 shows what the P:S ratio must be to make either reaction happen. If the P:S ratio is actually above the curve, hydroxypyromorphite will spontaneously change to anglesite, while if the ratio is below the curve, the opposite reaction may occur. And as can be seen, the pH dependence is quite strong. At pH’s close to neutral, the conversion of anglesite to pyromorphite is easy in most cases, but there are plenty of polluted sites, such as those close to old mining and smelting operations, where the concentration of sulfate is very high. These sites may be quite acidic as well, and this will make conversion to the phosphate difﬁcult. The lesson from these observations would seem to be that we must know the chemistry of the soil system quite well, far beyond knowing how much lead is present and in what form. A further illustration of the complexity of the chemistry of these systems may be seen in Figure 7, which shows the principal lead-containing species as a function of pH. There are sixteen such species in the system, and thirteen are present in sufﬁcient quantities to appear on the graph. Five of these are complex ions of phosphate and chloride, and higher concentrations than we have here of either of these anions might increase the solubility substantially– even when very insoluble lead minerals are present. The two carbonate complexes are quite important at high pH and strengthen the tendency of lead minerals to be amphoteric. P1: GIM TJ1228-02 EST.cls September 1, 2004 19:29

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FIGURE 7. Hydroxypyromorphite (Pb5(PO4)3OH) with anglesite (PbSO4): activities of the important solute species of lead vs. pH.

III. STRATEGIES FOR LEAD IMMOBILIZATION 1. Slightly Soluble Lead Minerals If lead immobilization is going to work, the metal will have to be put into a form which is highly insoluble over a large pH range including that found in the stomach after ingestion.21,26,27 To see what forms might qualify, we calculated the solubility of several lead minerals as a function of pH by the methods described above. In each case the solution in contact had carbon dioxide from the atmosphere, assumed to be 270 ppm, and a concentration of sodium chloride equal to one millimole per liter. The results are given in Figure 8. Surely the best candidates are galena (PbS), chloropyromorphite (Pb5(PO4)3Cl), and wulfenite (PbMoO4). Galena is a common form for the element in nature, and it is quite insoluble. Unfortunately, it is subject to oxidation in the air, and it slowly goes to anglesite (PbSO4), which is several orders of magnitude more soluble. Wulfenite is a desirable form, but making it requires the addition of molybdates to soils, and such a treatment could cause more problems than it might solve. Chloropyromorphite leads to no such difﬁculty, as phosphate is a constituent of all living cells and a well known and useful fertilizer. Possible problems were set aside, and the modeling techniques described above were used to discover how easily these minerals might be converted, one to another. The ﬁrst model done was to study to the conversion of hydroxypyromorphite to chloropyromorphite. The calculations on P1: GIM TJ1228-02 EST.cls September 1, 2004 19:29

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FIGURE 8. The solubilities as pPb(t) of several lead minerals as functions of pH.

row 83 of Table 1 show that the chemical potential for the conversion is negative under the conditions of the model, and another was built to find the minimum concentration of chloride necessary for the conversion. This model assumed the presence of both pyromorphites and had four phases and six components. There were four degrees of freedom, and, therefore, two tests on stoichiometry: The ratio of lead to phosphate must be five to three, and the total concentration of sodium must be determined. Here we fix it at the same level as the total chloride, and in this system pHCl0 was 0 fixed by the two pKsp equations: { }, 0 = . = 0 + / 0 + / 0 Pb5(PO4)3Cl pKsp 22 069 pPb(OH)2 3 5pH3PO4 1 5pHCl { }, 0 = . = 0 + / 0 Pb5(PO4)3OH pKsp 17 289 pPb(OH)2 3 5pH3PO4 so pHCl0 = 23.900.

0 0 The trial-and-error variables were, therefore, pH3PO4 and pNaOH . The results, as total element activities as functions of pH, are shown in Figure 9. This graph shows that the amount of chloride needed to sustain the equilibrium is quite small at all pH’s, and we should, therefore, expect that chloropyromorphite will be the mineral which will form, if chloride is present at all. Next four separate models were made of pairs of minerals with one half of each pair being chloropyromorphite. The other minerals were cerrusite (PbCO3), anglesite (PbSO4), galena (PbS), and wulfenite (PbMoO4). These models gave the ratios of phosphate to the other anions at equilibrium such as was done with the hydroxypyromorphite-anglesite equilibrium in Figure 6. P1: GIM TJ1228-02 EST.cls September 1, 2004 19:29

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FIGURE 9. Hydroxypyromorphite (Pb5(PO4)3OH) with chloropyromorphite (Pb5(PO4)3Cl): elemental activities as functions of pH. All the phosphate in solution is from the minerals, and pNa(t) is forced to be equal to pCl(t).

The results are given as Figures 10 through 13, and these show that converting cerrusite and anglesite to chloropyromorphite will be relatively easy at most pH’s. The chloropyromorphite-wulfenite system could go either way, but either form is probably an excellent result for immobilization. The conversion

FIGURE 10. Chloropyromorphite (Pb5(PO4)3Cl) with cerrusite (PbCO3): elemental activities vs. pH. P1: GIM TJ1228-02 EST.cls September 1, 2004 19:29

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FIGURE 11. Chloropyromorphite (Pb5(PO4)3Cl) with anglesite (PbSO4) [oxidizing conditions]: elemental activities as functions of pH.

of galena to chloropyromorphite is another matter, and the phosphate-sulﬁde ratio in the solution is going to have to be quite large. Figure 14 shows calculations of p{P(t)/X(t)} for each of the four equilibria discussed in the previous paragraph, where X is carbonate, sulfate, sulﬁde, or molybdate. The larger this number the easier it is to make

FIGURE 12. Chloropyromorphite (Pb5(PO4)3Cl) with galena (PbS) [reducing conditions]: elemental activities as functions of pH. P1: GIM TJ1228-02 EST.cls September 1, 2004 19:29

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FIGURE 13. Chloropyromorphite (Pb5(PO4)3Cl) with wulfenite (PbMoO4): elemental activities vs. pH.

chloropyromorphite. So the ratio of phosphate to carbonate can be quite small, and cerrusite will still become chloropyromorphite. But with galena the phosphate-to-sulﬁde ratio will have to be very large, on the order of 104 at least. Of course PbS is by itself quite insoluble, and the concentration of

FIGURE 14. The negative logs of the ratios of phosphate to carbonate, sulfate, sulﬁde, and molybdate as functions of pH in the systems of Figures 10 through 13. P1: GIM TJ1228-02 EST.cls September 1, 2004 19:29

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sulﬁde over it in solution is not large, as shown in Figure 8. Whether any feasible phosphate treatment will give sufﬁcient phosphate in solution to react with galena remains to be seen. Other soil constituents, such as metal oxides and carbonates, are known to rapidly precipitate soluble phosphate and would probably limit the conversion of galena to pyromorphite.

2. The Fates of Phosphate Additions to Soils This section will discuss possible phosphate treatments and their likely fates when added to soils. There are several elements in soils present in large amounts as oxides and carbonates which have the capacity to precipitate phosphate and lower its activity in ground water. This chemistry must be understood before we can determine whether any phosphate treatment could ever change lead in contaminated soils to chloropyromorphite. The elements which must be considered are aluminum, iron, calcium, magnesium, and manganese. Soil compositions vary widely, but if we use the average compositions from Lindsay’s table {p7},22 we can get a rough idea of how much phosphate might react with each. The numbers which follow are in micromoles of the element per gram of soil with the content in parts per million following: P (20 µmol/g, 600 ppm); Al (2600, 70,000); Fe (700, 40,000); Ca (350, 14,000); Mg (200, 5000); and Mn (11, 600). With the exception of manganese all the amounts of the metallic elements are much larger than the amount of phosphate in an “average” soil. All five of these elements form multiple insoluble phosphates, and we must consider them all if we are going to understand how the activity of phosphate in the water is controlled by them. Fortunately, thermodynamic data are available for these salts and 0 minerals, and it was possible to calculate pKsp’s for them. The Appendix contains these numbers as well as values for all the minerals used in this paper hereafter. All of these compounds can and do occur in soils, and there are as well cations of the five elements either free in the water or adsorbed on clays or in combination with a variety of organic molecules. These facts make for systems of staggering complexity, but modeling is possible simply because the phosphate minerals will be in the thermodynamic sense the most stable forms of phosphate. Ultimately, as the systems go to equilibrium, the phosphate will be found in the least soluble phosphate minerals, and we can make useful models by discovering which these are. We will consider the five most common metallic elements in order of their abundances beginning with aluminum. The chemistry of this element in soils is complex, and it is found in many minerals, not just the hydroxide or oxide.22 (There is no stable Al carbonate.) Aluminum is most commonly found in alumino-silicate minerals such as pyrophyllite and albite.28 Alumina or gibbsite is usually found only in weathered soils as silica tends to dissolve more rapidly over time than alumina.29,30 In spite of the complexity, we can P1: GIM TJ1228-02 EST.cls September 1, 2004 19:29

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do a rather simple analysis to understand the effect on phosphate. Of the two 0 phosphates of aluminum, variscite is the less soluble. Its pKsp equation is

{ , · } 0 = 0 + 0 = . variscite AlPO4 2H2O pKsp pAl(OH)3 pH3PO4 19 250

0 If pAl(OH)3 is determined by the alumino-silicate minerals, and it would 0 seem that it is, we can ﬁnd the value of pH3PO4 and determine the solubility of phosphate as a function of pH. If we have gibbsite, then

0 = 0 = . , pAl(OH)3 pKsp 6 956 and 0 = . pH3PO4 12 294

If we have an alumino-silicate mineral such as dickite, we will also have silica and the following equations:

{ , } 0 = 0 = . silica SiO2 pKsp pH4SiO4 3 096 { , } 0 = . = 0 + 0 dickite Al2Si2O5(OH)4 pKsp 15 474 pAl(OH)3 pH4SiO4 0 = . . giving pAl(OH)3 12 378

0 (There are in fact several forms of silica, and each has its own pKsp. Here we have used an active form, which Lindsay22 labels silica, “soil,” and such a substance will suppress the level of aluminum. Thus we get the range discussed immediately hereafter.) If we have sillimanite with silica, the same sort of 0 = calculation gives pH3PO4 9.673, and these two numbers give a range for this activity for all the alumino-silicate minerals which we have found in the literature. Figures 15 and 16 show the total element concentrations for the systems of variscite, silica, and either dickite or sillimanite. It is reasonable to suppose that the pP(t) line for any similar system would be between the two lines shown. Comparing either of these to Figure 12 shows that the phosphate activity should be sufﬁcient to convert galena to chloropyromorphite above pH six. But we have not yet considered the other abundant metallic elements, and they may impact the activity of phosphate in solution. The second most abundant element on our list is iron (700 µmol/g soil). The most likely and stable combination is iron(III) oxide and strengite, FePO4·2H2O, but the situation is complicated by the fact that iron forms several oxides from Fe(III), several more from Fe(II), and a number with mixed oxidation states. Furthermore, iron(II) forms two phosphates, and the more stable of these is vivianite, Fe3(PO4)2·8H2O. Using the same technique as was used to ﬁnd the equilibrium between galena and anglesite (p 5), (pe + pH) was set at 8.763 so that strengite and vivianite might co-exist. Of the several iron oxides and hydroxides, the one described as “crystalline”24 0 0 with a pKsp of 8.083 was used because this was the smallest pKsp of the P1: GIM TJ1228-02 EST.cls September 1, 2004 19:29

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FIGURE 15. Variscite (AlPO4·2H2O), silica (SiO2), and dickite (Al2Si2O5(OH)4): elemental activities vs. pH.

several calculated from the data in the literature, leading to the lowest activity of phosphate in the solution. (See the Appendix.) If we assume sodium chloride in solution at one mmol/kg and carbon dioxide from the atmosphere as before, we have a system of four phases with six components and four degrees of freedom. Figure 17 shows the results, and the amount of phosphate in solution is similar to that of Figure 16, that

FIGURE 16. Variscite (AlPO4·2H2O), silica (SiO2), and sillimanite (Al2SiO5): elemental activities vs. pH. P1: GIM TJ1228-02 EST.cls September 1, 2004 19:29

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FIGURE 17. Iron(III) hydroxide “crystalline” (Fe(OH)3), strengite (FePO4·2H2O), and vivianite (Fe3(PO4)2·8H2O): elemental activities and the activities of Fe(II) and Fe(III) as functions of pH when (pH + pe) = 8.763, so that the two phosphates will be in equilibrium.

is to say sufﬁcient to convert galena to chloropyromorphite. The situation described by this model is what might be obtained by adding freshly made iron(III) hydroxide to a soil. Over time and with weathering the more stable oxides are likely to form, and these will give lower levels of iron in the water along with higher levels of phosphate. Consequently, we may say that the combination of iron(III) oxide and iron phosphate will give a level of dissolved phosphate sufﬁcient to the transformation of galena to chloropyromorphite, at least as long as the conditions are not highly reducing. Another model was made with iron(III) hydroxide and vivianite at (pe + pH) equal to four (results not shown). Compared to Figure 17, it was seen that the iron activity increased by two or three orders, with much more Fe(II), and that the phosphate activity decreased by two or three orders. This combination would probably not change galena. It should also be noted that changing iron(III) hydroxide to iron(II) oxide or carbonate takes severely reducing conditions. “Crystalline” Fe(OH)3 will co-exist with Fe(OH)3 (siderite) at (pe + pH) = 3.638, and it will take conditions much more reducing than this 0 = for hematite, Fe2O3 (pKsp 11.820) to co-exist with siderite. The third most abundant element is calcium (350 µmol/g soil), and the situation is complicated by the existence of an oxide, a hydroxide, a carbonate, and at least eight minerals of the system CaO-P2O5-H2O-CO2. The solubilities of six of these as functions of pH are shown in Figure 18. Over much of the range the least soluble, and therefore the most likely to be stable is hydroxyapatite, Ca10(PO4)6(OH)2. P1: GIM TJ1228-02 EST.cls September 1, 2004 19:29

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FIGURE 18. The solubilities vs. pH of six minerals and crystals of the system CaO-P2O5-H2O- CO2.

In a thought experiment calcite, CaCO3, was added to the system shown as Figure 17. The results are shown in Figure 19, and the most important result is that the activities of calcium and phosphorus are both high. The natural pH of this system is close to 7.5, and the system might exist as shown. Other calculations show, however, that the chemical potentials for the formations of the minerals of the system CaO-P2O5-H2O (Figure 18) are almost all negative.

FIGURE 19. The system of Figure 17 plus calcite (CaCO3): elemental activities vs. pH. P1: GIM TJ1228-02 EST.cls September 1, 2004 19:29

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FIGURE 20. Iron(III) hydroxide “crystalline” (Fe(OH)3), apatite (Ca10(PO4)6(OH)2), and calcite (CaCO3): elemental activities vs. pH. (pH + pe) = 8.763 as in Figure 17, but the phosphates of iron will not form.

These results tell us that the strengite will likely disappear and that a calcium phosphate will form by a metathesis reaction like [3].

CaCO3 + FePO4·2H2O + H2O = Fe(OH)3 + 1/10Ca10(PO4)6(OH)2 + 0 + / 0 CO2 3 5H3PO4 [3]

In a second thought experiment we have all the variscite being changed to iron(III) oxide and apatite, which occurs as Equation [3] goes to the right- hand side. We also assume that since calcium is much more abundant in soils than phosphate, some calcite will remain. This system is shown in Figure 20, and the most important result here is that the excess calcium suppresses the level of phosphate to the point where the conversion of galena to chloropyromorphite is either not possible or marginal (compare the pP(t) curves of Figures 20 and 12). Figure 20 also shows that the calcium concentration becomes very large below pH 6 indicating that calcite does in fact dissolve, and that this model does not hold at low pH. Figure 21 shows the same components under more reducing conditions with (pH + pe) = 4.417. This is the boundary between apatite and vivianite, with the latter being the single stable phosphate below 4.417. The level of dissolved phosphate is still quite low here and controlled by apatite. If (pH + pe) < 4.417, phosphate is controlled by iron (vivianite) and is even lower. P1: GIM TJ1228-02 EST.cls September 1, 2004 19:29

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FIGURE 21. The system of Figure 20 at (pH + pe) = 4.417, the condition under which vivianite (Fe3(PO4)2·8H2O) will be in equilibrium with apatite (Ca10(PO4)6(OH)2).

If we assume a total calcium content in the soil of 350 µmol/g soil, a soil-to-water ratio of 10:1, and 10% of the calcium in solution; we have Figure 22. The pP(t) curve here is higher than the one in Figure 20 at pH’s above 6.5. The upshot is that having calcium in excess of phosphate, as it almost always is in a soil, results in a dramatic depression of the amount of

FIGURE 22. Iron(III) hydroxide “crystalline” (Fe(OH)3), apatite (Ca10(PO4)6(OH)2), and dissolved calcium with the molality at 0.342. (pH + pe) = 8.763 as in Figures 17 and 20. P1: GIM TJ1228-02 EST.cls September 1, 2004 19:29

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FIGURE 23. Silica (SiO2), bobberite (Mg3(PO4)2·8H2O), apatite (Ca10(PO4)6(OH)2), and calcite (CaCO3): elemental activities vs. pH. This system is not thermodynamically stable as described in the text.

dissolved phosphate available to change lead minerals such as galena. Either the amount will be so low that no reaction will occur at all, or when it is high enough to allow reaction, the reaction itself will deplete the phosphate to the point that the change will stop. Furthermore, the chemical potentials for the formations of iron-phosphate minerals are positive, indicating that phosphate must bind with calcium rather than iron. The magnesium content of the “average” soil is a bit less than that of calcium at 200 µmol/g soil. This element forms a number of phosphate minerals as well as the hydroxide (brucite), two carbonates, and dolomite, 0 MgCa(CO3)2.Values for pKsp for each of these were calculated, and models 0 were made. The least soluble of the phosphates, as shown by the sizes of pKsp is boberrite, Mg3(PO4)2·8H2O, and Figure 23 shows the results when this mineral is added to the calcite-apatite system. Silica was also put into the model because magnesium is known to form a number of silicate minerals. The silica which Lindsay22 labels “soil” is also used here. It is the most active and most likely to model a real soil environment. The line for pP(t) reaches a maximum of 5.4, sufﬁciently low to convert galena to chloropyromorphite, but calculations of chemical potentials show that a number of other minerals may form. These other minerals include several magnesium silicates, two carbonates, and dolomite. Surely this system will not be thermodynamically stable. Two other models were run by substituting carbonates for the boberrite. Magnestite, MgCO3, gave a pP(t) curve with a maximum of 7.34 at pH 6.5, and only dolomite’s formation had a negative chemical potential. Figure 24 shows the results when dolomite, MgCa(CO3)2,issubstituted for magnestite, P1: GIM TJ1228-02 EST.cls September 1, 2004 19:29

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FIGURE 24. The system of Figure 23 with dolomite (MgCa(CO3)2)inplace of bobberite. This system is stable, but the phosphate level is controlled by the apatite-calcite combination.

and here pP(t) peaks at 8.36 at pH 7.0. This curve is very similar to that seen in Figure 20, and in fact the level of phosphate is being controlled by the apatite-calcite combination in both cases. The upshot of this analysis is that phosphate in soils will not be controlled by aluminum, iron, or magnesium as long as calcium is present in its usual abundance. This leaves only manganese to consider, and this element may be important in spite of the fact that its typical abundance is only about half that of phosphate. Figure 25 shows the system apatite-calcite-Mn3(PO4)2. The phosphate curve has not shifted at all, that is the addition of this compound of manganese has no effect on the phosphate level. On the other hand, three other compounds of manganese, Mn(OH)2, MnCO3, and MnHPO4 all have negative chemical potentials for their precipitation reactions. Figure 26 shows what happens when MnHPO4 is substituted for Mn3(PO4)2 in the system of Figure 25. The phosphate and calcium curves are the same, but the curves for carbonate and manganese are shifted upward. MnHPO4 is less soluble than Mn3(PO4)2, and the chemical potentials show that no other compound of this element could precipitate. It would seem from this that the presence of manganese has no effect on the phosphate, but this is not quite so. Consider reaction [4].

1/5H2O + CaCO3 + MnHPO4 = MnCO3 + 1/10 Ca10(PO4)6(OH)2 + / 0 2 5H3PO4 [4] 0 = . + . − . − . = . pKeq 19 679 26 253 16 007 23 809 6 116 , 0 = . . at equilibrium pH3PO4 15 290 P1: GIM TJ1228-02 EST.cls September 1, 2004 19:29

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FIGURE 25. Manganese phosphate (Mn3(PO4)2), apatite (Ca10(PO4)6(OH)2), and calcite (CaCO3): elemental activities vs. pH.

This result represents a very low activity of phosphate, very similar to that seen in Figure 26. As a consequence very low concentrations of soluble phosphate will be sufﬁcient to shift phosphate from apatite to MnHPO4, and any added phosphate will surely do so. This salt is, therefore, the ultimate phosphate sink in these systems.

FIGURE 26. Manganese hydrogen phosphate (MnHPO4), apatite (Ca10(PO4)6(OH)2), and calcite (CaCO3): elemental activities as functions of pH. P1: GIM TJ1228-02 EST.cls September 1, 2004 19:29

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TABLE 2. Equilibria Between Various Metal Oxides and Carbonates with Phosphates, Ordered by the 0 Equilibrium Values of pH3PO4

0 Reactant Product pH3PO4

Al2Si2O5(OH)4 AlPO4·2H2O + SiO2 6.87 Fe(OH)3 FePO4·2H2O 7.40 Al(OH)3 AlPO4·2H2O 8.69 MnCO3 Mn3(PO4)2 9.45 MgCO3 Mg3(PO4)2·8H2O 12.20 CaCO3 Ca10(PO4)6(OH)2 15.22 MnCO3 MnHPO4 15.25

Furthermore, the equilibrated system of [4] is short one degree of freedom, which is to say that one crystalline phase must disappear. Four models were constructed with one each of the four solid phases missing, and the stable system, as shown by the chemical potentials for precipitating the missing phase, was that shown by Figure 26. Therefore, MnCO3, rhodochrosite, will disappear when this system becomes thermodynamically stable. Table 2 summarizes the equilibria of the phosphates of the common metallic elements in soils with their oxides and carbonates. Each line shows the result from either a carbonate or a hydroxide (depending on which is 0 more stable when exposed to the atmosphere) in terms of pH3PO4 as in this reaction:

+ / + 0 = + / 0 H2O 1 3M3(PO4)2 CO2 MCO3 2 3H3PO4 [5]

0 = Here pCO2 5.002 in equilibrium with the atmosphere. The table is ordered so that the most stable phosphates are at the bottom while the most stable oxides and carbonates are at the top. When dissolved phosphate is added to soil, its concentration at first will probably be sufficient to react with all the reactants in the first column of the table. As the system moves toward chemical equilibrium, at whatever rate, the phosphate will move down the table. This analysis describes, therefore, the environment in which the immobilization of lead, or any other element, by phosphate must occur based on thermodynamic principles.

3. Immobilized Lead in the Soil Environment Without the interference of the elements discussed above, the conversion of lead minerals and salts to chloropyromorphite would be easy as the ratios shown in Figure 14 would not be a problem. For example pS(t) over galena might be about 9.0 (Figure 8), and a pP(t) of 1 or 2 would be sufﬁcient for the conversion. Section 4 will be a discussion of some of the many possible P1: GIM TJ1228-02 EST.cls September 1, 2004 19:29

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treatment strategies, and an examination of whether or not the chloropyromorphite will be likely to endure in the soil environment for long periods. Thus we have worked backwards by first assuming that we have succeeded in changing the lead in soil to this mineral. This was done by thermodynamic analyses of systems containing chloropyromorphite, cerussite, and one of three pairs of minerals. The first was calcite-apatite, the second MnCO3− MnHPO4, and the third Ca(OH)2-apatite. The carbonates of calcium and manganese were studied because they are the most active reactants in Table 2 (for a natural system), and calcium hydroxide was studied because it might be added to a soil in a liming treatment. The first of these systems (calcite, etc.) has six phases and seven components: PbO, CaO, P2O5,CO2, HCl, H2O, and Na2O. Thus there are three degrees of freedom, and only one test needs to be made on the stoichiometry and that is on sodium, which here is forced to be equal to the total chloride. To understand this system, consider the equation below with Figure 27.

1/5H2O + CaCO3 + 1/5Pb5(PO4)3Cl = 1/10 Ca10(PO4)6(OH)2 0 + PbCO3 + 1/5 HCl [6]

The only solute in this equation is the HCl. So long as the actual total chloride is greater than that needed to maintain the equilibrium, that is the pCl(t) line in the Figure, the reaction will not go to the right, and chloropyromorphite will be stable. In Figure 27 we see that this line represents a very small concentration of chloride, especially at moderate pH, and pyromorphite will

FIGURE 27. Chloropyromorphite (Pb5(PO4)3Cl), cerrusite (PbCO3), apatite (Ca10(PO4)6- (OH)2), and calcite (CaCO3): elemental activities vs. pH. P1: GIM TJ1228-02 EST.cls September 1, 2004 19:29

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be very unlikely to change. In fact modest amounts of chloride in solution will drive this system left, a desirable result for immobilization. The second system comes from this equation:

0 MnHPO4 + PbCO3 + 1/5 HCl = MnCO3 + 1/5Pb5(PO4)3Cl + / 0 + 2 5H3PO4 H2O [7]

0 The equilibrium constant for this equation may be found from the pKsp’s of the minerals as 0 = . + . − . − . = . pKeq 26 253 14 533 16 007 22 070 2 709 And 0 = / 0 + . pH3PO4 1 2 pHCl 6 773 This system is pictured in Figure 28. In a soil environment this system is unlikely to be at equilibrium, and it will shift one way or the other depending on the concentrations of phosphate and chloride relative to their lines on the ﬁgure. Nonetheless, we may say that during any phosphate treatment of a soil the total phosphate activity in the water will almost certainly be below the phosphate line. Even when the phosphate activity is controlled by calcite as in Figure 27, the phosphate activity is sufﬁcient to move phosphate from chloropyromorphite to MnHPO4. This reaction would also give lead carbonate, an undesirable result. The only way out of this dilemma would

FIGURE 28. Chloropyromorphite (Pb5(PO4)3Cl) cerrusite (PbCO3), manganese hydrogen phosphate (MnHPO4), and rhodochrosite (MnCO3): elemental activities vs. pH. P1: GIM TJ1228-02 EST.cls September 1, 2004 19:29

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seem to be adding sufﬁcient phosphate to the system to insure that all the manganese is changed to MnHPO4. Thus the equilibrium system of Figure 28 and Equation [7] would be destroyed, and chloropyromorphite could remain. Finally we consider the stability of Pb5(PO4)3Cl in the presence of lime, Ca(OH)2. This is shown by Equation [8].

0 + + / = / CO2 Ca(OH)2 1 5Pb5(PO4)3Cl 1 10 Ca10(PO4)6(OH)2 0 + PbCO3 + 1/5 HCl [8] 0 = . + . − . − . =− . pKeq 5 190 22 069 23 809 14 533 11 083

0 = 0 =− If pCO2 5.002, then pHCl 30.5. Such an activity of chloride is of course absurd, and this system will have to go to the right-hand side. Chloropyromorphite cannot be fully stable if it is mixed with hydrated quick lime (Ca(OH)2). We would have to insure that a soil containing Pb5(PO4)3Cl would never be treated with hydrated quick lime.

4. Possible Phosphate Treatments The number of ways that phosphate might be added to a soil is quite large, and a few possibilities that seem to be or that have proved to be promising will be discussed. The simplest and most straight-forward technique is simply to add soluble phosphate.21,31,32 This could be phosphoric acid in some concentration, or it might be a salt of a cation such as sodium or ammonium ion. There are obvious cautions with regard to the pH of the addition, al- though the natural buffering tendency of any soil will mitigate the effects to some extent. Adding large amounts of sodium could be the cause of later problems, but this could be avoided by using ammonium salts, perhaps as a buffered mixture of NH4H2PO4 and (NH4)2HPO4. Surely the dissolved phosphate would react with all the reactants in Table 2 as well as some forms of lead. The ratios plotted in Figure 14 would have to be exceeded when the particular lead mineral came in contact with the solution. Such a situation is difﬁcult to model, very complex, and close to chaotic. It does seem very likely that any application of dissolved phosphate to a soil contaminated with lead will change some of it to chloropyromorphite. This is to say that treatment will probably provide an improvement in the sense that less lead would be taken up by biological systems. Whether such a treatment could ever provide a permanent reduction to acceptable levels in lead’s availability to organisms is still an open question. In spite of the complexity we can gain an understanding of what is possible by remembering that calcium is almost always more abundant than phosphate in soils and that the stable phosphate sinks in a soil are apatite and MnHPO4. The latter will form in an unwanted side reaction, from our P1: GIM TJ1228-02 EST.cls September 1, 2004 19:29

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point of view, but the former might even be part of a treatment. Surely added soluble phosphate will make apatite in most soils, and other minerals of its components might also form. According to thermodynamic calculations, the only way to avoid making only apatite and manganese hydrogen phosphate is to add more than enough phosphate to change all the calcium in the soil to apatite. To do this we would have to increase the amount of phosphorus in a soil up to 400 µmol/g, which is many times the normal 20 µmol/g. Whether this high P application would be either desirable or acceptable is beyond the scope of this discussion, but suspicion is advised. On a mass basis 400 µmol/g of phosphorus is approximately 12 parts per thousand phosphorus or close to four percent as phosphoric acid. If we do a bench-scale experiment with one kilogram of dry soil, we would need 100 mL of 4.0 M H3PO4 to achieve the change. Furthermore, a soil containing large amounts of apatite could cause unacceptable changes in soil structure.

5. Minerals of the Components CaO, P2O5,H2O, and CO2 To begin we will study the system calcite-apatite which is a stable part of a number of the systems considered earlier. This is shown in Figure 29, which includes the phosphate curve from apatite alone from Figure 18. The most interesting feature here is the extremely low level to which phosphate is suppressed by the presence of calcite at all pH’s below 9.5. A recipe for a successful treatment will be one which increases this level of phosphate in spite of abundant calcium. The discussion which follows will discuss possible

FIGURE 29. Apatite (Ca10(PO4)6(OH)2) with calcite (CaCO3): elemental activities vs. pH. The pP(*) curve from Figure 18, apatite alone, is included for sake of comparison. P1: GIM TJ1228-02 EST.cls September 1, 2004 19:29

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ways that this might be done, and we will take the calcite-apatite system to be the base system. 0 0 = The pKsp equations show that pCa(OH)2 14.677 so long as the ground and/or pore water is exposed to the atmosphere and the carbon dioxide in it 0 = and that pH3PO4 15.220. These activities are constant over the pH range. The pCa(t) curve goes below zero at pH 6.7, and this simply means that calcite dissolves. When it does, the calcium activity will rise to whatever level is allowed by its abundance, and the phosphate activity will be suppressed below that shown by the pP(t) curve in Figure 29. Surely we must add soluble phosphate to this system and do it in such a way that it will not all precipitate as apatite. Apatite itself is, nonetheless, a possible treatment,33–38 and when it is added to a soil, the level of phosphate in solution will reach that described in the previous paragraph. It is certainly possible that the parts of the very heterogeneous soil mixture will have solutions in which the phosphate level will be closer to that from apatite alone, especially soon after it is added. Since this is so, we would expect that a treatment of apatite alone would change some of the PbCO3, Pb(OH)2, PbCl2, and PbSO4 to Pb5(PO4)3Cl, and such reactions would surely be beneficial. Such a treatment would of course cause these changes to lead minerals in soils which did not contain apatite in the first place, and soils that had not been fertilized in some time (if ever) might very well fit this description. It is also true that the level of phosphate in the apatite-calcite system is great enough to change MnCO3 to MnHPO4 (see Equation [4]). Theoretical thought experiments with modeling programs give some interesting results with pairs of minerals from the CaO-P2O5-H2O system. One of these is apatite-monetite (CaHPO4), and the total element concentrations are shown as a function of pH in Figure 30. This figure also shows the pP(t) curve from the apatite-calcite system, and there clearly has been a dramatic 0 change. To understand this system a bit more we note that the two pKsp equa- 0 0 tions have two unknowns, and pCa(OH)2 is constant at 21.312 while pH3PO4 is fixed at 4.162. This compares to 15.220 for this quantity in the apatite-calcite system. Figure 31 shows the many important phosphate species. Such a system certainly appears to describe a possible treatment as the level of phosphate is certainly high enough to effect the desired changes. Unfortunately, if we were to put this system into a soil, the amount of calcium in the soil environment would surely be several times the amount of phosphate. While a small amount of calcite would dissolve in the apatite- monetite system, a large amount of calcite, or dissolved calcium, will have another effect altogether as shown by

+ / 0 = / + CaHPO4 2 3 Ca(OH)2 1 6Ca10(PO4)6(OH)2 H2O [9] 0 = . − ∗ . / =− . pKeq 25 474 5 23 809 3 14 208 P1: GIM TJ1228-02 EST.cls September 1, 2004 19:29

532 S. K. Porter et al.

FIGURE 30. Apatite (Ca10(PO4)6(OH)2) with monetite (CaHPO4): elemental activities vs. pH. The pP(*) curve from Figure 29, apatite with calcite, is included.

0 = At equilibrium, pCa(OH)2 21.31, which is a negligible amount of calcium when compared to that supplied by calcite. The reaction [9] surely goes to the right, and we are back to the apatite-calcite system once again. The only escape is to add so much monetite that all the calcite reacts. Only if we get the total amount of phosphate in soil high enough to make the phosphate- calcium ratio greater than three-ﬁfths, will we succeed. If the soil to be treated

FIGURE 31. The activities vs. pH of the several phosphate species in the system of Figure 30. P1: GIM TJ1228-02 EST.cls September 1, 2004 19:29

Toxic Metals in the Environment 533

has 350 µmol/g of calcium and 20 of phosphorus, we would need to add 475 µmol/g of CaHPO4 to make the P:Ca ratio equal to three-ﬁfths. This is 65 g of monetite per kilogram of dry soil, and we would have to wait for the solid monetite to react with the solid calcite.

6. “Super Phosphate,” Ca(H2PO4)2·H2O The salt calcium dihydrogen phosphate, which has a P:Ca ratio of two, can be shown to be quite soluble in water by thermodynamic analysis, but the route it takes on the way to dissolving is an interesting and possibly useful 26,32,37 one. This salt dissolves incongruently forming CaHPO4·2H2O and then CaHPO4 as it dissolves. Furthermore, the process takes days, and the system with two solids and the solution persists for quite a long time. The following equations are valid during that time:

{ · }, 0 = . = 0 + 0 Ca(H2PO4)2 H2O pKsp 24 846 pCa(OH)2 2pH3PO4 { }, 0 = . = 0 + 0 CaHPO4 pKsp 25 474 pCa(OH)2 pH3PO4

0 = 0 =− These equations give pCa(OH)2 26.102, and pH3PO4 0.628. In this system calcium is severely depressed while phosphate’s level in solution is extraordinarily high. It is the phosphate fertilizer without peer, and thus its popular name. Figure 32 gives the activities of the principal solute species as

FIGURE 32. The principal solute species above the metastable combination of Ca(H2PO4)2·H2O and CaHPO4 as the former, known as super phosphate, dissolves incongruently. The range is 0.00 < pH < 2.40, and the natural pH of the system is approximately 1.6. P1: GIM TJ1228-02 EST.cls September 1, 2004 19:29

534 S. K. Porter et al.

functions of pH up to 2.4. The natural pH of this system is a little above 1.6, and the acidic conditions could be quite useful in the making of chloropyromorphite. Even metallic lead will dissolve under these conditions and change to Pb5(PO4)3Cl. Surely the soil itself will buffer the action of this acid, but we could expect an acidic pH in any case. Applications of super phosphate are often followed by lime to restore a neutral pH. As noted above calcium hydroxide must not be used. Calcium carbonate could be or perhaps some combination of ammonium and potassium phosphates. Of course when super phosphate is put into a soil, much of its phosphate will go to apatite. This result suits plants very well indeed, but it does not serve the purposes being explored in this paper. It may be true that we will as before have to raise the over-all P:Ca ratio to above three-ﬁfths. To treat the soil described in section 2, we would need 136 mmol of Ca(H2PO4)2·H2O per kilogram of soil, that is 34 g. Most of this would react eventually according to

3 Ca(H2PO4)2·H2O + 7 CaCO3 = Ca10(PO4)6(OH)2 + 7CO2 + 8H2O [10]

We would need super phosphate beyond this amount to react with the lead in the system and with the manganese as well. It should be noted that the situation described by Figure 32 is not likely to ever be realized throughout the ground and pore water in a soil system. If we have 100 mL of water mixed with one kilogram of dry soil, the solution would have to be 6.91 M in phosphoric acid. Such would require 174 g of super phosphate solid. Since soil systems are quite heterogeneous, there will be pockets of phosphoric acid solution of high concentration, and we certainly do not need to have the concentration as high as 6.91 M to effect the desired changes. The amount that would be effective is probably between 34 and 174 g, and experiment is needed. Thorough mixing or tilling will certainly be important as well. Super phosphate certainly could be an effective agent in changing other lead minerals to chloropyromorphite. A model was made with super phosphate and galena under various conditions as shown by (pH + pe), and the chemical potential for changing PbS to chloropyromorphite was calculated. The results are shown in Figure 33, and they show that super phosphate may effect the desired change without the oxidation of galena to lead sulfate. What 0 − 0 < is required is that (pQsp pKsp) 0. Even so it is surely easier to convert lead sulfate to pyromorphite than it is galena, so the oxidation of galena to PbSO4 (anglesite) was considered. Figure 34 shows the results. Under this condition (pH + pe) = 5.055, the two minerals may co-exist at all pH’s, and it is interesting to note that virtually all the sulfur in solution is in the form of sulfate. We also note in passing that under these mildly oxidizing conditions that gypsum, CaSO4·2H2O, may form as well. Simple metathesis reactions between calcium phosphates and P1: GIM TJ1228-02 EST.cls September 1, 2004 19:29

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FIGURE 33. Chemical potentials vs. pH at different (pH + pe) for the formation of chloropyromorphite (Pb5(PO4)3Cl) from galena (PbS) in the solution formed by super phosphate, Figure 32.

lead sulfates or sulﬁdes to give gypsum and chloropyromorphite ought to be both possible and beneﬁcial. A model like that used to make Figure 33 was made by substituting wulfenite, PbMoO4, for galena, and it is shown in Figure 35. The chemical

FIGURE 34. Galena (PbS) with anglesite (PbSO4)atequilibrium when (pH + pe) = 5.055: elemental activities as functions of pH and the activities of the important solute species. P1: GIM TJ1228-02 EST.cls September 1, 2004 19:29

536 S. K. Porter et al.

FIGURE 35. Wulfenite (PbMoO4)inthe presence of super phosphate (Ca(H2PO4)2·H2O and CaHPO4) elemental activities as functions of pH up to 2.4.

potential for the formation of chloropyromorphite is shown in Figure 36, and we see that this mineral may form at pH > 1.3. In principle at least super phosphate will convert any form of lead to Pb5(PO4)3Cl, but it will probably be necessary always to add sufﬁcient treatment to make the phosphate-to- calcium ratio greater than three-ﬁfths.

FIGURE 36. The chemical potential for the formation of chloropyromorphite (Pb5(PO4)3Cl) in the system of Figure 35 as a function of pH. P1: GIM TJ1228-02 EST.cls September 1, 2004 19:29

Toxic Metals in the Environment 537

There could be a distinct advantage to super phosphate as compared to soluble phosphate. The fact that it is a solid would mean that once mixed with a soil it would remain in place. By contrast a liquid application to a ﬁeld might simply preferentially ﬂow in the path of least resistance. Furthermore, soluble phosphate will simply react with the several soil constituents that are more basic than itself, but the solution in equilibrium with the two minerals from super phosphate will stay acidic for as long as it is in contact with those minerals. Since super phosphate dissolves very slowly, this could be quite a long time.

7. Conclusions Concerning Phosphate Treatments of Lead Of the several lead phosphate minerals and salts only chloropyromorphite is stable in soil environments and then only if the soil is never treated with quick lime, Ca(OH)2.Inorder to make all other forms of lead into chloropyromorphite, it is necessary to change all of the calcium in the soil, whether it is solid calcite, some other mineral, or in solution, to hydroxyapatite, Ca10(PO4)6(OH)2. Since the typical abundance of calcium is ten or twenty times that of phosphate, very large amounts of phosphate must be added to bring the phosphate-calcium ratio up to three-ﬁfths. This may be done in principle with soluble phosphate or with solid calcium phosphate minerals whose phosphate-calcium ratio is above three-ﬁfths. The possibilities include monetite, CaHPO4, and super phosphate, Ca(H2PO4)2·H2O. An added complication is the high stability and very low solubility of manganese hydrogen phosphate, and enough phosphate must be added during treatment to convert all of the manganese in the soil to this salt. The treated soil may have a very low level of lead available to biological systems, but it will also have very high levels of both calcium and phosphate. Furthermore, virtually all of the calcium will be precipitated as apatite. Whether such is desirable and acceptable is beyond the scope of this paper, but since it is well known that apatite and other minerals of its components are found in bones and teeth, the friability of any soil so treated may very well disappear.

8. Wulfenite, PbMoO4,asaPossible Remediation Wulfenite is one of the three least soluble minerals of lead as shown in Figure 8, and this section will examine ﬁrst whether it would remain unre- acted if left in a soil and second what actions might be required to form it from other compounds of lead. We will ﬁrst consider the acid-base chemistry of lead molybdate without the possibility of reducing Mo(VI) to Mo(IV). The solubility curve of Figure 8 shows that acids will react with wulfenite only if they are quite strong, and we P1: GIM TJ1228-02 EST.cls September 1, 2004 19:29

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would expect that it would dissolve only in strong mineral acids. Bases could be a different story, and paralleling the earlier discussion of pyromorphites, we will examine the possible reactions of wulfenite with calcite and lime. Either of these bases might change wulfenite to powellite, CaMoO4, and we 0 0 can calculate the pKeq of each reaction from the pKsp’s for the minerals.

PbMoO4 + CaCO3 = CaMoO4 + PbCO3 [11] 0 = . + . − . − . = . pKeq 25 549 19 679 27 688 14 533 3 007

PbMoO4 + Ca(OH)2 = CaMoO4 + Pb(OH)2 [12] 0 = . + . − . − . =− . pKeq 25 549 5 190 27 688 9 595 6 544 Wulfenite will not be changed by calcite, but calcium hydroxide will easily change it to lead hydroxide. These results parallel those found in the study of chloropyromorphite done earlier. If dissolved molybdate is added to a soil, there are several metal, Me2+, salts and minerals that may form by reactions of the type shown by equation [13].

H2MoO4 + MeCO3 = MeMoO4 + CO2 + H2O [13]

Table 3 is constructed with the same logic as Table 2, which was concerned with the formation of phosphates. The third column gives the activity of 0 H2MoO4 when the reactants and products are at equilibrium. This table is ordered with the most stable products at the bottom of the second column and the most stable reactants at the top of the ﬁrst column, and we see that wulfenite, PbMoO4,isindeed in the most advantageous position. Nonetheless, an added solution of molybdate will make several of the products in the table at least for a time. Since calcium is quite abundant,

TABLE 3. Equilibria Between Various Metal Oxides and Carbonates with Molybdates, Ordered by Equi- 0 librium Values of pH2MoO4

0 Reactant Product pH2MoO4

MgCa(CO3)2 CaCO3, MgMoO4 4.648 CuO CuMoO4 5.898 MgCO3 MgMoO4 6.629 ZnO ZnMoO4 7.408 MnCO3 MnMoO4 7.531 MgCa(CO3)2 MgMoO4, CaMoO4 8.820 FeCO3 FeMoO4 10.925 MgCa(CO3)2 MgCO3, CaMoO4 11.010 CaCO3 CaMoO4 12.991 Ag2CO3 Ag2MoO4 13.922 Pb(OH)2 PbMoO4 15.953 P1: GIM TJ1228-02 EST.cls September 1, 2004 19:29

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we will consider what happens when some of the added molybdate makes powellite, CaMoO4. As shown by equation [11] (reversed) and its equilibrium constant, powellite will react with cerrusite to form wulfenite. Table 3 shows that the same product will be produced by Pb(OH)2. This is surely a desirable result, but it does not tell us whether galena might be changed to wulfenite. The issue is complicated by the fact that while molybdate will make CaMoO4,itwill not change all the calcium in the system to this mineral. The mole ratio of calcium to molybdenum will be a large number in any conceivable scenario, and the excess calcium will severely reduce the activity of molybdate in solution. To study the possible reactions, a system with five minerals (seven phases) and nine components was modeled. The components were PbO, MoO3, CaO, H2S, P2O5,CO2,Na2O, HCl, and H2O. The five minerals on the first try were calcite, apatite, powellite, galena, and wulfenite. It is assumed that the calcite or other more active forms of calcium will control the activities of both phosphate and molybdate because the calcium will be much more abundant than either phosphorus or molybdenum. The two lead minerals were put into the systems to see how easily one might be converted to the other. Along with the several possible precipitation reactions it was necessary to consider the redox chemistry of both molybdenum and sulfur. The Mo(VI) in molybdate may very well be reduced to Mo(IV), and both MoS2 and MoO2 are possible. Sulfur has several oxidation states, and as was shown in the discussion with Figure 34 the formation of sulfate from sulfide can be done under mildly oxidizing conditions. The consideration of such redox chemistry actually increases the number of components and the degrees of freedom by one, and models were made at a variety of constant (pH + pe)’s. In this system there are three values of (pH + pe) at which two minerals of the components are in equilibrium. If (pH + pe) = 4.489, then molybdenite (MoS2) and gypsum (CaSO4·2H2O) are in equilibrium. At (pH + pe) = 4.381 there is equilibrium between powellite (CaMoO4) and MoO2. Finally and most importantly there is equilibrium between wulfenite (PbMoO4) and galena (PbS) at (pH + pe) = 4.122. This is also of course the region of the (pH + pe) scale where we see the change from S(-II) to S(VI). Galena and anglesite (PbSO4)are in equilibrium at 5.055, and the hydrogen sulfate ion is in equilibrium with the hydrogen sulfide ion with equal activities at 3.963. The upshot of all this is that molybdate will make wulfenite from galena if at least some of the sulfur in the system has been oxidized to sulfate, but under reducing conditions galena will not be changed. The relative positions of the curves on Figure 8 also indicate this. Several models were made of the system, and two are included. Fig- ure 37, done under reducing conditions has PbS, MoS2, MoO2, CaCO3, and Ca10(PO4)6(OH)2. Figure 38, done under somewhat more oxidizing conditions has PbMoO4, CaSO4·2H2O, CaMoO4, CaCO3, and Ca10(PO4)6(OH)2. P1: GIM TJ1228-02 EST.cls September 1, 2004 19:29

540 S. K. Porter et al.

FIGURE 37. Galena (PbS), molybdenite (MoS2), molybdenum(IV) oxide (MoO2), calcite (CaCO3), and apatite (Ca10(PO4)6(OH)2): elemental activities as functions of pH at (pH + pe) = 3.50.

The curve for pPb(t) has shifted very little, and both models show a very low level of dissolved lead at neutral pH’s. In one sense the wulfenite is superior, in that it could never be oxidized to a more soluble form as galena can be and is. On the other hand it is possible that the Mo(VI) in wulfenite could be

FIGURE 38. Wulfenite (PbMoO4), gypsum (CaSO4·2H2O), powellite (CaMoO4), calcite (CaCO3), and apatite (Ca10(PO4)6(OH)2): elemental activities as functions of pH at (pH + pe) = 5.00. P1: GIM TJ1228-02 EST.cls September 1, 2004 19:29

Toxic Metals in the Environment 541

reduced to Mo(IV), and PbMoO4 would be destroyed. Apart from all of this any soil treatment that uses molybdenum in any form would not be acceptable. The reasons for this are beyond the scope of this paper, but there are quite compelling. We may conclude that existing wulfenite can probably be left alone but that we should never attempt a treatment that would make it.

9. Galena, PbS, as a Possible Remediation Since galena is very difficult to change to more thermodynamically stable minerals, we can elect to leave it alone while changing other more soluble lead minerals such as PbCO3. PbS will oxidize in the air to PbSO4, but the process is usually very slow, and PbS itself has a very low solubility. How- ever, it is important to remember that a mixture of these two solids, of any proportions, will have the lead solubility of the more soluble sulfate. We could even consider trying to make the more soluble minerals of lead into galena in order to reduce the level in solution. To make galena it would be necessary to add H2Sorsome other sulfide to the soil. At low concentrations this would make the soil smell like the seashore at low tide; at higher concentrations the gas would be highly poisonous. It might be possible to use a solid compound like thioacetamide which releases hydrogen sulfide as it dissolves in water, but we would always have to worry about the effect of this gas on biological systems. Furthermore, the sulfide would make several compounds in addition to PbS. A number of dipositive metal cations (Me2+)insoil make insoluble sulfides as Me2+S (i.e., FeS, ZnS, MnS, and SnS). To be sure, the addition of hydrogen sulfide would make most or all the lead, except for the metal, into galena, but it is doubtful that the side reactions or the effect of high sulfide concentrations would be acceptable.

10. Changing Some Lead (but not all) to Pb5(PO4)3Cl If we elect to try to change the more soluble forms of lead, the carbonate, the sulfate, the chloride, etc., into chloropyromorphite without touching the galena, the important question becomes: Can we effect these changes with a phosphate-to-calcium ratio of less than three-ﬁfths? This would be highly desirable by making the treatment easier, and the result could certainly be an acceptable remediation. We could treat with phosphoric acid or with any of the minerals of the CaO-P2O5-H2O system, including apatite itself, and we might be able to use modest amounts. Apatite is highly basic, so it could pay to use a more acidic mineral, perhaps even super phosphate. As was discussed in section 2, any MnO, Mn(OH)2,orMnCO3 that is present will likely react with any added phosphate to make MnHPO4 before chloropyromorphite can form. The resulting system is shown by Figure 26, P1: GIM TJ1228-02 EST.cls September 1, 2004 19:29

542 S. K. Porter et al.

FIGURE 39. Chloropyromorphite (Pb5(PO4)3Cl), manganese hydrogen phosphate (MnHPO4), lead hydroxide (Pb(OH)2), apatite (Ca10(PO4)6(OH)2), and calcite (CaCO3): elemental activities vs. pH.

the level of phosphate is the key, and we may now ask whether this level of phosphate will be sufﬁcient to change the relatively more soluble minerals and salts of lead to chloropyromorphite. The system shown in Figure 39 provides the probable answer. It has lead hydroxide (slightly more stable than the carbonate), chloropyromorphite, apatite, calcite, manganese hydrogen phosphate, a solution with sodium chloride, and carbon dioxide in the solution and the atmosphere. It has seven phases, eight components, and three degrees of freedom. Since two of these are temperature and pressure, only one test on the stoichiometry is necessary. This was done by requiring that pCl(t) equal pNa(t). Since the hydroxide of lead exists in this system, we need to ask whether its remediation is possible. This can be done by considering the equilibrium of equation [14].

6/5H2O + CaCO3 + 1/5Pb5(PO4)3Cl = Pb(OH)2 + 1/10 Ca10(PO4)6(OH)2 + / 0 + 0 1 5 HCl CO2 [14] = . + . − . − . = . pKeq 19 679 22 069 9 595 23 809 8 344 0 = . , 0 = . . If pCO2 5 002 then pHCl 16 710 The system as described is quite stable, and lead hydroxide is not reacting. The level of chloride as shown by the pCl(t) curve of Figure 39 (which shows this equilibrium system plus MnHPO4) is, however, quite low, and it P1: GIM TJ1228-02 EST.cls September 1, 2004 19:29

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is not unreasonable to imagine that the naturally occurring chloride in any real soil system will be orders of magnitude higher. This chloride will drive the chemical reaction above to the left until either lead hydroxide or apatite is gone. Thus the addition of apatite or other calcium phosphate minerals will change lead hydroxide and other lead minerals, which are more soluble than the hydroxide, to chloropyromorphite without raising the phosphate- to-calcium ratio to three-ﬁfths. Hydroxypyromorphite, if it is present, will be changed at the same time as shown by Figure 9, and so will any other lead phosphate. We conclude, therefore, that if a soil system is treated by any calcium phosphate so that there is sufﬁcient phosphate to change all the manganese present to manganese hydrogen phosphate and to change all the lead to chloropyromorphite, assuming thorough mixing, that the only forms of lead which would remain would be galena, chloropyromorphite, wulfenite, and the element itself.

11. Conclusions Concerning Lead Remediation The three least soluble minerals of lead are galena, chloropyromorphite, and wulfenite, and any of the three would be an acceptable result for rendering lead inert to biolgical systems, i.e., immobilization, except that galena slowly oxidizes to the much more soluble anglesite. Furthermore, if a pair of lead minerals is in contact with a solution, the solubility of lead will be determined by one with the higher solubility, regardless of their relative amounts. It is possible in principle to change any form of lead, including galena, to chloropyromorphite by bringing the phosphate-to-calcium ratio up from what is typically found in soils, one to ten, to three to five or higher. Such can be done with phosphoric acid or an acidic calcium phosphate. Super phosphate is especially efficient as it produces a solution of phosphoric acid which is 6.9 M and with a pH of 1.6. This solution will dissolve and react with lead metal as well. The drawback to this idea is that the amounts of phosphate which must be added to and left in the soil are quite large. A much less drastic treatment can be done by adding sufficient phosphate to react all the manganese carbonate and hydroxide and all the more soluble lead salts and minerals, the carbonate, the hydroxide, the chloride, and the sulfate. This will leave only the three least soluble minerals and the metal, and such could be an acceptable result, or at least an improvement.

IV. CADMIUM IN SOILS

Cadmium is similar to lead in that it is almost always found as a divalent cation, and the two metals form a number of minerals with similar formulas.39 Figure 40 shows the solubilities of several cadmium salts as functions of pH. P1: GIM TJ1228-02 EST.cls September 1, 2004 19:29

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FIGURE 40. Solubilities as pCd(t) vs. pH for several minerals and salts of cadmium.

We may say in general that, except for the sulfide, the compounds of cadmium are more soluble than those of lead. Cadmium sulfate is quite soluble at all pH’s, and cadmium phosphate is more soluble across the range than any of the several lead phosphates. The silicate, carbonate, and hydroxide are all insoluble at neutral pH, but their solubilities increase sharply in acid. The only two possibilities for immobilization are, therefore, CdS and Cd3(PO4)2, and we shall examine how stable each of these might be in a soil environment and whether making them in those environments is feasible. Except for the fact that cadmium sulfide could and does oxidize to cadmium sulfate, it is surely the mineral of choice for our purposes. It is quite insoluble at all pH’s above one, and it could probably be ingested without harm. Unfortunately, CdS is quite easily oxidized, and it is in equilibrium with the sulfate at (pe + pH) = 5.751. The question then becomes whether the oxidation process in a soil system will be slow enough to make remediation feasible. This is certainly possible, but our predictive thermodynamic calculations can not tell us one way or the other. If the oxidation is slow enough, and such depends on the condition of the CdS itself as well as the environment, the mineral might simply be left alone. However, trying to change other forms of cadmium into the sulfide would probably not be desirable for the same reasons that making lead into PbS would not be. We may examine the possibility of making cadmium into its phosphate by the same methods that were used above to test the feasibility of making chloropyromorphite out of lead. A glance at Figure 40 tells us that this may be difficult because it shows that at pH’s above 7 or 8 Cd3(PO4)2 is not even the P1: GIM TJ1228-02 EST.cls September 1, 2004 19:29

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second least soluble compound of cadmium. Nonetheless, we ﬁrst examine the following:

+ 0 + / = + / 0 H2O pCO2 1 3Cd3(PO4)2 CdCO3 2 3H3PO4 0 = . − . = . pKeq 18 531 15 568 2 963 0 = . , 0 = . . if pCO2 5 002 pH3PO4 11 948

Reference to Table 2 shows that a cadmium row would be above that of Mn, Ca, and Mg, which is to say that there would have to be sufﬁcient phosphate to change all the carbonates and oxides of these three elements before the change from cadmium carbonate to cadmium phosphate would work. As was discussed in Section 7 of Part III for Pb, this would require high amounts of phosphate. In the case of lead we came to the conclusion that it might not be necessary to add massive amounts of phosphates if we would be satisﬁed with changing only the carbonate, sulfate, and hydroxide. By analogy with the discussion of Section 10 of Part III for Pb, we look at the system represented by the following equilibrium:

+ / = / + + / 0 CaCO3 1 3Cd3(PO4)2 1 10 Ca10(PO4)6(OH)2 CdCO3 1 15 H3PO4 0 = . + . − . − . =− . pKeq 19 679 18 531 23 809 15 568 1 167 0 =− . at equilibrium pH3PO4 17 505

This is impossible, and this system will have to go the right-hand side until either the calcite or the cadmium phosphate disappears. Very large amounts of phosphate would be required. If this were achieved, we would have the system of Figure 41 which shows the four minerals, less calcite, in the equation above. Of course the cadmium goes into solution at moderately acidic pH’s, and the cadmium curve is essentially the cadmium carbonate curve of Figure 40. This system also has the active form of silica found in soils in order to see if cadmium silicate might form, but the chemical potential of that reaction is positive. The system also has ammonium chloride with an activity of 10−5 molal, and both the chloro- and ammine-complexes have important activities. Finally we have Figure 42, which comes from the same system, showing the important cadmium species when the activity of NH4Cl is 0.10 M. Surely the ammine-complexes and the chloro-complexes of cadmium increase the element’s solubility. The conclusion that one must come to is that the chemical immobilization of cadmium in soils is probably not feasible, at least with the common anions that are likely to be acceptable treatments to soils. P1: GIM TJ1228-02 EST.cls September 1, 2004 19:29

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FIGURE 41. Cadmium phosphate (Cd3(PO4)2), cadmium carbonate (CdCO3), apatite (Ca10(PO4)6(OH)2), and silica (SiO2): elemental activities as functions of pH. Also present are sodium chloride, pNa(t) = 3.0 and ammonium chloride, pN(t) = 5.0.

V. ARSENIC

Arsenic is a widespread pollutant which can and has caused cancer and death in thousands.40–46 It can be found in wells, most famously and tragically in Bangladesh in recent years,41,47–49 mine wastes,50–54 pesticides,55,56 and

FIGURE 42. The same system as Figure 41 with pN(t) = 1.0: Activities of the important species of cadmium as functions of pH. P1: GIM TJ1228-02 EST.cls September 1, 2004 19:29

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wood treatment compounds.57 Its disposal or immobilization presents one of the most urgent problems of modern society, and it has been extensively studied. A recent review58 discussed the chemistry of the technology in use at the present time. Most of the techniques presently employed use some form of iron with the hope of making insoluble iron arsenates or having arsenate sorbed onto the surface of an iron oxide or hydroxide. This section will discuss the former as well as other possible forms of arsenic which are only slightly soluble, but the surface phenomenon of sorption is beyond the scope of the present work.

1. The Chemistry of Arsenic Unlike the other three elements discussed in this paper, arsenic is not truly a metal. It is in the middle of Group 15 of the periodic table, and the elements above it are non-metals which form acidic oxides, while the elements below it are metals. Arsenic itself lies somewhere in between, and its chemical behavior is mixed.59 Its oxides and sulfides are acidic like those of phosphorus, but it is much easier to reduce As(V) to As(III) than it is to reduce P(V) to P(III). The latter reaction requires severe conditions which are most unlikely to occur in the systems under discussion here, while conditions for the former are quite common. The range of insoluble compounds of arsenic is quite impressive. We may be able to use arsenic cations with either oxide or sulfide to immobilize arsenic, and we may be able to use other metals in combination with the oxyanions of either As(III) or As(V). There are many more possible precipitates with arsenic than with any of the other metals discussed in this paper. The text which follows will speak to several of the reasonable possibilities. The situation is complicated by the fact that oxidation-reduction chemistry (redox) is very important to the understanding of what is stable under what conditions. At least three of the elements which are present in possible immobilizing precipitates undergo fairly easy redox reactions: arsenic itself, iron, which can be found as Fe(II), Fe(III), and the metal, and sulfur, which is found in solution as S(-II) [sulfide], S(VI) [sulfate], and a menagerie of ions and molecules with intermediate oxidation states. The approach taken here uses pe, the negative log of the virtual activity of free electrons. As has been done by many other authors, the sum (pH + pe) was used. If (pH + pe) is zero, the conditions are strongly reducing, and water will be in equilibrium with hydrogen gas. At the other extreme used, (pH + pe) is equal to twenty, nearly oxidizing enough to oxidize water to oxygen. The conditions in soil systems are almost always much more moderate than either of these extremes, but to cover all the possible situations, calculations of solubilities have been done over these ranges of pH and of pe: 0 < (pH + pe) <20, and 2 < pH <12. The method of calculation was like P1: GIM TJ1228-02 EST.cls September 1, 2004 19:29

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that used earlier to make spreadsheets and graphs, but here each spreadsheet was made assuming a constant value of (pH + pe). Several spreadsheets were then made on each system at intervals of 0.2 for (pH + pe) with a like interval for pH, and the results were arrays of numbers, pE(t)’s, that were used to make contour maps of solubilities over the entire area. The systems discussed below are deﬁned ﬁrst by their components. Analysts have long calculated which solid phases and solute species are stable under what conditions of pH and pe. That was done here as well, and combined with the contours of solubility to give a complete picture of the equilibrium states over the range of conditions. The boundaries of stability for each solid phase were calculated by using chemical potentials for precipitation, as before, and all the diagrams show systems that are stable with one exception, that of the iron oxides. The situation with iron is especially interesting and important because iron oxides have been used as arsenic treatments. This element forms several oxides, some from Fe(III), some from Fe(II), and some mixed. There is also a carbonate known as siderite, FeCO3. (There is no carbonate of Fe(III).) The solubilities of all these phases vary widely, and to cover the possibilities two different kinds of iron systems were used, and thus the exception to stability. Using free energies from Bard,24 the most stable iron oxides under different conditions were found to form one kind of system. This worked out as follows:

Fe2O3·H2O: stable if (pH + pe) >2.397

Fe3O4: stable if 2.397 > (pH + pe) > 0.722

FeO1.062: stable if 0.722 > (pH + pe)

0 These numbers were calculated using the pKsp numbers tabulated in Appendix A. Figure 43 is a map of pFe(t) contours over the pH-pe space. An amount of iron was assumed sufﬁcient to make a solution of 1.0 M when all is in solution as it is at low pH’s and low pe’s. This map shows the situation with stable iron oxides, and it will be applied below. Figure 44 parallels this using reactive compounds of iron. Under oxi- 24 dizing conditions the hydroxide described by Bard as Fe(OH)3(c) is used, and siderite, FeCO3,isused under reducing conditions. The two are in equilibrium at (pH + pe) = 3.638. While this system is not stable thermodynamically, it could approximate the situation soon after an iron treatment of arsenic-bearing waste, and it might persist for a long time. This system will also be applied to a number of models in what follows. The minimum solubilities of iron as shown by the heights of the peaks in the middle of Figures 43 and 44 differ by about four orders of magnitude, and such a change will surely have an affect on the solubility of arsenic in minerals of iron. P1: GIM TJ1228-02 EST.cls September 1, 2004 19:29

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FIGURE 43. Contour map of pFe(t) in pe-pH space over stable oxides of iron.

2. The System Orpiment, As2S3 The first system of arsenic to be considered will be the simplest, with no components from metallic elements other than arsenic itself. The components of the system seen in Figure 45 are As2O5,H2S, HCl, Na2O, CO2,H2, and O2.Inthe region where a precipitate exists, at low pH and low pe, there are three phases and six degrees of freedom. Two are satisfied by using standard temperature and pressure, and two by stoichiometric tests on Na and Cl. One is satisfied by the ratio of As to S over As2S3 or by a test on the amount of S over As4O6. The last degree of freedom is done by calculating at constant values of (pH + pe). Orpiment itself is thermodynamically stable only up to approximately (pH + pe) = 6 and then only at low pH’s. Just above this area is a region where As4O6 can precipitate if the amount of arsenic in the system is quite large. In this diagram it is 0.82 M. Above about 10 in (pH + pe) even this amount of As4O6 completely dissolves. Under even more strongly oxidizing conditions the stable compound is As4O10, and this is even more soluble, forming a solution of arsenic acid. P1: GIM TJ1228-02 EST.cls September 1, 2004 19:29

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FIGURE 44. Contour map of pFe(t) in pe-pH space over reactive iron oxide, Fe(OH)3(c), and siderite, FeCO3.

Since the conditions in the area where orpiment is stable are difficult to realize, we can say that this system will give soluble arsenic, sooner or later. It is probably true, however, that orpiment is like most metal sulfides in the environment, metastable but long lived nonetheless. Other sulfides of arsenic are possible. One of these does appear, and that is realgar, As4S4, which is stable in a small region at about pH 6 and pe =−6. Such strongly reducing conditions are unlikely in the environment. The other is As2S5. Numerous chemistry books speak of this “compound”, but its structure seems to be a mystery, and thermodynamic data were not found. If it exists, it would likely show up at low pH and intermediate pe’s. It would surely be quite acidic, and it is hard to imagine that it could exist above pH three or so. Furthermore, one has to wonder about the coexistence in one molecule of As(V) and S(−II). The reduction potentials would seem to say that such is impossible. Even so, many chemists seem to believe that the compound exists. We take the existence to be an open question but believe that even if it does, it would contribute little to the stability of arsenic in the environment. P1: GIM TJ1228-02 EST.cls September 1, 2004 19:29

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FIGURE 45. Contour map of pAs(t) in pe-pH space over orpiment, As2S3, and oxides of arsenic. Except for the area at low pH and low pe, the arsenic is in solution, and no contours appear.

3. Orpiment plus Reactive Iron Oxides The next system shown is a combination of what we find in Figure 45 with what we have in Figure 44. Arsenates, arsenites, and arsenides of iron become possible, and four of them do appear as stable precipitates. Under strongly oxidizing conditions and at low pH we find scorodite, FeAsO4·2H2O. At low pH and low pe we find orpiment and arsenolite as before, and the iron has no effect. At neutral pH’s and moderate pe we find iron(II) arsenate, and under strongly reducing conditions both arsenopyrite, FeAsS, and loellingite, FeAs2 are stable. Figure 46a shows contours of pAs(t), and Figure 46b shows the regions of stability for each precipitate of arsenic. The hole in the contour map between scorodite and orpiment is arsenolite, here going into solution entirely since we have assumed only enough arsenic to make pAs(t) = 1.00. In places on this diagram the solubility of arsenic is low, but rarely does it fall below the recommended level for drinking water of 10 ppb, which comes P1: GIM TJ1228-02 EST.cls September 1, 2004 19:29

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(a)

(b)

FIGURE 46. (a.) Contour map in pe-pH space of pAs(t) for orpiment, As2S3, with reactive iron oxides as in Figure 44. (b.) Phase diagram for the same system showing the stable crystalline phases of arsenic. P1: GIM TJ1228-02 EST.cls September 1, 2004 19:29

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out to pAs(t) > 6.87. The area with loellingite, which is stable under severely reducing conditions, does so. Such conditions are possible only in the vicinity of a cathode with an applied reducing potential sufﬁcient to reduce water to hydrogen. The center of the diagram, the area where soil systems are almost always found, does have iron(II) arsenate, but the minimum solubility is such that pAs(t) is close to 6. Furthermore, this minimum solubility covers quite a small area, and the gradients in the diagram are strong. This means that small changes in a system’s conditions will dramatically change the solubility of arsenic. These strong gradients are a common theme throughout this analysis as will be seen. Since this model was made using reactive iron oxide, it can be assumed that the solubility of arsenic in a model using the stable iron oxides would be a few orders of magnitude higher.

4. Adding Calcium to form Arsenates A number of calcium arsenates have been reported,60–62 and a model was made using orpiment, the stable iron oxides as in Figure 43 and either calcium carbonate as in Figure 18 or dissolved calcium at low pH. The pAs(t) contours are shown in Figure 47a, while Figure 47b is a phase diagram for the system. The difference between the stable and reactive iron oxides shows up here in that the solubility of arsenic over scorodite (low pH, high pe) is much higher if the stable oxides are in the model, and iron(II) arsenate does not appear at all. The presence of calcium does make an impact under highly oxidizing conditions and moderate pH: Both calcium hydrogen arsenate and calcium arsenate form. pAs(t) is never above 4 at all in these areas, and for the most part it is 1 to 3. Across the middle of this diagram there is a band covering the entire pH range in which the stable mineral of arsenic is As4O6, a compound which is highly soluble in water. If this model were done with reactive iron oxides, the area for Fe3(AsO4)2 would reappear as in Figure 46.

5. Oxides of Manganese The last metallic element examined for this study is manganese. Two models were made, and both had the same components: As2O5,H2S, MnO, Fe2O3, CaO, HCl, Na2O, CO2,H2, and O2. One system had the reactive iron oxides and the other the stable. It is assumed here that the stable oxides and carbonates of manganese coexist with the solution or are dissolved in it. It is also assumed that sufﬁcient Mn is in the system to make pMn(t) = 0.50 when it is fully dissolved. Three minerals are stable as follows:

pyrolusite, MnO2: (pH + pe) > 16.618 manganite, MnOOH: 16.618 > (pH + pe) > 13.614

rhodochrosite, MnCO3:13.614 > (pH + pe) P1: GIM TJ1228-02 EST.cls September 1, 2004 19:29

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(a)

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FIGURE 48. Contours of pMn(t) over pe-pH space to show the solubility of manganese over the stable oxides and carbonates of the element.

There is a large area of acidic pH’s where manganese is soluble, and even at 7 or 8 the amount of manganese in solution is fairly substantial, especially at intermediate pe’s. The solubility of manganese as pMn(t) is shown in Figure 48. The area of soluble manganese is large as noted, and there is also a large area contered around pH 10 and pe zero, where pMn(t) is on a 0 plateau with a value of 4.4. In this region the neutral solute species MnSO4 is prevalent, accounting for virtually all the manganese in solution. This result is just one instance of several in which soluble complexes of the metallic elements are quite important.

←−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−

FIGURE 47. (a.) Contour map in pe-pH space of pAs(t) for orpiment, As2S3, with stable iron oxides as in Figure 43 and either calcium carbonate as in Figure 18 or dissolved calcium at low pH. (b.) Phase diagram of the same system. P1: GIM TJ1228-02 EST.cls September 1, 2004 19:29

556 S. K. Porter et al.

The formation of manganese arsenates ought to be a possibility. The amount of thermodynamic data on such salts is not large at all, but one reference was found to Mn3(AsO4)2·8H2O, and this information proved to be quite useful. In these models nine different minerals or salts of arsenic including this one proved to be stable in different parts of the pe-pH space. Figure 49a is a contour map of pAs(t) for the system with the stable iron oxides (Figure 43), and Figure 49b is a phase diagram in pe-pH space. Figure 50a is a contour map of pAs(t) with the reactive iron oxides (Figure 44), and 50b is the phase diagram. In Figure 49b we see areas of possible precipitation for eight salts of arsenic, viz.: FeAsO4·2H2O (scorodite), CaHAsO4, Ca3(AsO4)2,Mn3(AsO4)2·8H2O, As4O6 (arsenolite), As2S3 (orpiment), FeAsS (arsenopyrite), and FeAs2 (loellingite). The list for 50b is the same except that CaHAsO4 does not appear, and there is an area of Fe3(AsO4)2. The contour maps bear some resemblance to a map of Switzerland with a number of hills and valleys and several sharp gradients. The most promising area for possible remediation is as always near the center of the graph where the pH’s are close to neutral, and the redox conditions are what one would expect in the environment. On both maps there is an area with Mn3(AsO4)2·8H2O which could be quite useful. If pAs(t) = 7, then we have less than ten parts per billion. Unfortunately, the area with this condition is not large, and the solubility of arsenic increases strongly in all directions. Under strongly oxidizing conditions (up) the nature of the manganese- oxygen phase changes, and manganese becomes less soluble (Figure 48). The result is that Mn3(AsO4)2·8H2Oisnolonger the stable phase of arsenic, and one or both of the calcium arsenates precipitate. Here solubilities are much higher than those of Mn3(AsO4)2·8H2O. If the pH is reduced as well (up and left), the stable mineral becomes FeAsO4·2H2O (scorodite). With the reactive iron oxides, the pH must be below 5, and with the stable iron oxides the pH must be below 3.5. Scorodite is truly stable only in quite acidic conditions that are strongly oxidizing, certainly extreme for most environmental systems. Below scorodite and to the left of Mn3(AsO4)2·8H2Oisawedge-shaped area where the stable mineral is arsenolite, and this oxide of arsenic(III) is highly soluble. Below this and stable at the extreme conditions of low pH and low pe is orpiment. This sulfide, like many other metal sulfides, probably persists for long periods in conditions where it is truly not stable, but the thermodynamic stability is confined to extreme conditions. To the right of orpiment and below Mn3(AsO4)2·8H2Oare found two minerals which are under the right conditions extremely insoluble. The first is arsenopyrite, which occurs in a small area, and loellingite, which occurs over a large area along the lower limit of (pH + pe). The numbers on the contours get into the teens, very impressive indeed, but the conditions required are so strongly reducing that water will go to hydrogen. At high pH’s, except for the very bottom of the map, arsenic goes into solution. Under strongly oxidizing conditions the arsenates become more P1: GIM TJ1228-02 EST.cls September 1, 2004 19:29

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(a)

(b) FIGURE 49. (a.) Contour map in pe-pH space of pAs(t) in the system with the stable iron oxides (Figure 43) plus manganese and calcium. (b.) Phase diagram for the same system showing eight minerals and salts of arsenic. P1: GIM TJ1228-02 EST.cls September 1, 2004 19:29

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soluble as the solubilities of their metallic elements fall with increasing pH. Under reducing conditions the solubility of arsenic increases with increasing pH because orpiment is a Lewis acid. This means that one or more complex 3n−2m ions of the type AsnSm will form. Thermodynamic information on the ion with n = 3 and m = 6 was found, and its stability accounts for the ﬁnger of high arsenic solubility between Mn3(AsO4)2·8H2O and FeAs2 in Figure 49a. Finally there is an important area of stability for iron(II) arsenate on the diagram for reactive iron oxides (50b), and it is just below the area for Mn3(AsO4)2·8H2O. The Fe3(AsO4)2 area covers most of the area of high arsenic solubility discussed in the previous paragraph. This yields pAs(t) peaks at about 5 in this area, and the conditions under which this compound is stable are certainly more common than those for scorodite. It might even form the basis of a useful remediation strategy.

6. Sulfur and Phosphorus in the Manganese System Contour maps and phase diagrams were also made for the minerals of sulfur and phosphorus in each of these systems. Figure 51a gives the contours for phosphorus in the system with the reactive iron oxides, and 51b shows the stable phases. Figure 52 does the same for sulfur. The phosphorus diagram shows four phases: FePO4·2H2O (strengite), MnHPO4,Ca10(PO4)6(OH)2 (hydroxyapatite), and Fe3(PO4)2·2H2O (vivianite). The manganese salt occupies the center of the diagram and has a low solubility as was noted above in the section on lead. Strengite appears only at low pH and high pe, and its area disappears when the stable iron oxides are in the system. Vivianite appears only at high pH and low pe, and its area also disappears when the stable iron oxide is used. Apatite is stable under highly oxidizing conditions, when the solubility of manganese itself is quite low, and with moderate to high pH. The boundaries of the phases are shown in Figure 51b. The sulfur diagram shows six solid phases: CaSO4·2H2O (gypsum), As2S3 (orpiment), FeS2 (pyrite), FeAsS (arsenopyrite), Fe2S3, and FeS1.053 (iron- pyrrhotite). Two of these phases also occur on the arsenic diagram. The stable mineral when (pH + pe) > 6isgypsum. The others appear under more reducing conditions as shown in Figure 52b. Most of the gradients on these contour maps are much less severe than those on the arsenic maps, and keeping either sulfur or phosphorus in a crystalline state is much simpler than keeping arsenic out off solution.

←−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−

FIGURE 50. (a.) Contour map in pe-pH space of pAs(t) in the system with reactive iron oxides (Figure 44) plus manganese and calcium. (b.) Phase diagram for the same system showing eight minerals and salts of arsenic. P1: GIM TJ1228-02 EST.cls September 1, 2004 19:29

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(a)

(b) FIGURE 51. (a.) Contour map in pe-pH space of pP(t) in the system with reactive iron oxides (Figure 44) and oxides and carbonates of manganese (Figure 48). (b.) Phases diagram of this system showing the areas of stability for four phosphate minerals. P1: GIM TJ1228-02 EST.cls September 1, 2004 19:29

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(a)

(b)

FIGURE 52. (a.) Contour map in pe-pH space of pS(t) in the system with reactive iron oxides (Figure 44) and oxides and carbonates of manganese (Figure 48). (b.) Phases diagram of this system showing the areas of stability for four phosphate minerals. P1: GIM TJ1228-02 EST.cls September 1, 2004 19:29

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7. Conclusions Regarding the Immobilization of Arsenic It is possible to use precipitation reactions to make arsenic highly insoluble, especially by the formation of Mn3(AsO4)2·8H2O. This can be done under moderate conditions, and the region of lowest solubility is centered around pH = 6.2 and pe = 6.0. pAs(t) becomes as high as 7.0. Under more reducing conditions, but not severely so, it also possible to make Fe3(AsO4)2, and its solubility is also low with pAs(t) as high as 6.0. These two solids are without doubt the best choices. The conditions under which the other arsenic minerals are stable are simply too severe as shown on Figures 49b and 50b. Furthermore, their solubilities are with one exception not as low as those over Mn3(AsO4)2·8H2OorFe3(AsO4)2. That exception is FeAs2, and its formation would require a strong reducing potential. Many of the gradients in the contour map are steep, and this means that changing conditions can signiﬁcantly change the equilibrium solubility of arsenic. For example if pe is ﬁxed at 5.0, and the pH increases from 6.2 to 7.2, the solubility of arsenic increases by a factor of 29. Any scheme for immobilizing arsenic and leaving it in the environment must take this into account.

8. Possibilities for Further Work Twoprojects can be suggested. The first is calculating the contours with a finer resolution. The maps done here are done at intervals of 0.2 in both pe and pH. Maps with intervals of 0.1 would give smoother curves, and there are places in our maps that are difficult to follow. The second concerns the thermodynamic data. Every effort has been made to be as complete and accurate as possible in searching the literature, but no thermodynamic measurements were made. The models cannot be better than the data used. Two classes are of special concern. The first is the manganese arsenates. As noted earlier, there seems to be a paucity of data, and knowing if the free energy of formation used for the octa-hydrate is accurate is important. Knowing if this is the only arsenate of the element is also important, and the authors do not. MnHPO4 is an important solid. Does MnHAsO4 exist? If it does, how insoluble is it? 3n−2m The second class is the thioarsenate ions of the form AsnSm and their conjugate acids. Thermodynamic information was found on three only: 0 − + 3− HAsS2, AsS2 (but not AsS ), and As3S6 . These ions seem to have a pro- found effect on the solubility of orpiment at neutral and high pH’s, and more complete and accurate information would be quite useful.

VI. MERCURY

The ﬁnal element to be modeled will be mercury. The possible precipitates include sulﬁdes, chlorides, sulfates, phosphates, oxides, and carbonates. There P1: GIM TJ1228-02 EST.cls September 1, 2004 19:29

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is also the metal itself, and this may be insoluble enough for purposes of immobilization.

1. Modeling Systems with Mercury The modeling techniques used for mercury were very similar to those used for arsenic. Calculations were made over wide ranges of pH’s and pe’s, and both contour maps and phase diagrams were made. Two model systems were run, and the first was exactly like the system with stable oxides of iron discussed in the arsenic section, but with mercury substituted for arsenic. Sulfur solubility is controlled by iron sulfides under reducing conditions and gypsum under oxidizing conditions. Phosphate is controlled by either hydroxyapatite or manganese hydrogen phosphate. The carbon dioxide activity is controlled by the atmosphere. The second was like the first except that an activity of iodine was added to make pI(t) = 3.00. This element is usually soluble, commonly present in the environment at least in small concentrations, and it can be precipitated as either HgI2 or Hg2I2. 0 The technique of using pKsp was adapted for possible precipitates of 0 mercury. No information on Hg(OH)2 was found, but the neutral mercury atom itself, Hg0, seems to be an important solute species. Furthermore, the thermodynamics of its formation have been studied with some care.63 Con- 0 sequently, pKsp’s were calculated using the free energy of formation of this species. Two examples follow:

, 0 = 0 = . Hg(liq.) pKsp pHg 6 517 , 0 = 0 + 0 − + = . HgS pKsp pHg pH2S 2(pH pe) 9 764

The others are tabulated in the Appendix. There is a signiﬁcant area in the pH-pe space over which the liquid metal is the stable condensed phase, and the stable species in solution is the neutral atom with pHg(t) = 6.517.

2. The Mercury System without Iodine The results for this system are shown in the several parts of Figure 53. Figure 53a is a contour map showing pHg(t) over the ranges of pH and pe, and Figure 53b shows which condensed phases are stable under which conditions. At no point does mercury become highly soluble, and pHg(t) >3.20 everywhere. There are two regions where the gradients are steep, but in the large region near the center the map is close to level. The phase diagram has five areas but only four condensed phases with the element itself appearing twice. The stable sulfide is mercury(I) sulfide rather than HgS (cinnabar), and both Hg2Cl2 (calomel) and HgCO3 show up under oxidizing conditions. As noted in the previous paragraph there is an area at neutral pH and moderately P1: GIM TJ1228-02 EST.cls September 1, 2004 19:29

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reducing conditions where the stable mercury species in solution is the neutral Hg atom. Mercury has three common oxidation states, and Figures 53c, 53d, and 53e are contour maps for the total activities for each of these states over the pH-pe range. Figure 53c shows the activity of Hg0 only as this is the single species of the zero oxidation state. Comparing Figures 53c to 53a shows that this species is dominant under reducing conditions. Figure 53d shows the activity of Hg(I), and this state is always negligible in solution in spite of the fact that two precipitates of it are stable. Hg(II) is important under oxidizing conditions, and there are several species of this state including a number of complex ions. The ion Hg2+ or its conjugate base is never the most important Hg(II) species in solution. The most common species of Hg(II) are both 0 0 neutral: HgCl2 and HgClOH . Figure 53f shows the boundary between the dominance of Hg0 and Hg(II) in this system. The position of this boundary is in an area where the conditions are at least moderately oxidizing with (pH + pe) in the neighborhood of ten.

3. Mercury Vapor The thermodynamics for the formation of mercury vapor was also studied by Glew and Hames,63 and the conclusions they came to need to be considered. In particular the S0 of vaporization is extraordinarily large, and according to these authors shows the largest known positive deviation from the value expected by Trouton’s Rule for a liquid that does not contain ions. At 298 K, S0 = 210.9 J/K, and this quantity rises with falling temperature. (The S0 from the “rule” is usually quoted as 88 J/K.) The free energy of formation for the vapor is also known, and it is possible to write

= 0 − . pHg(gas) pHg 0 937

The reference state for gas activities is 100 kPa, and if pHg0 = 6.517, then pHg = 0.263 Pa. Perhaps by itself this is not a large pressure, but certainly any system with such an aqueous phase exposed to the atmosphere will lose a lot of mercury over time. Oxidizing the mercury, difﬁcult as this may be, to lower the activity of pHg0 could be very useful. −−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−→

FIGURE 53. A model with mercury rather than arsenic added to the stable iron oxides, the oxides and carbonate of manganese, and the carbonate of calcium. (a.) The total solubility of mercury as pHg(t) as a function of pH and pe. (b.) The stable phases of mercury over the same range of pH and pe. (There are no areas where this element goes into solution completely.) (c.) The solubility of the neutral mercury atom as pHg0 as a function of pH and pe. (d.) The solubility of Hg(I) over the same space as pHg(I). (e.) The solubility of Hg(II) as pHg(II). (f.) A diagram showing the areas in pH-pe space in which Hg0 and Hg(II) are dominant. (Hg(I) never is in spite of the fact that both Hg2S and Hg2Cl2 have areas of stability.) P1: GIM TJ1228-02 EST.cls September 1, 2004 19:29

Toxic Metals in the Environment 565

(a)

(b) P1: GIM TJ1228-02 EST.cls September 1, 2004 19:29

566 S. K. Porter et al.

(c)

(d) FIGURE 53. (Continued). P1: GIM TJ1228-02 EST.cls September 1, 2004 19:29

Toxic Metals in the Environment 567

(e)

(f) FIGURE 53. (Continued). P1: GIM TJ1228-02 EST.cls September 1, 2004 19:29

568 S. K. Porter et al.

4. The Mercury System with Iodine Added Iodine is a common element, usually found in the environment in solution. The most abundant elements in pore water do not precipitate it, but very heavy elements such as mercury will. The several parts of Figure 54 show what happens when pI(t) is fixed at 3.00, and the parts of the figure parallel Figure 53. Figure 54a is the contour map, and the solubility of mercury is lowered by the addition of iodine over much of the pH and pe ranges. Figure 54b is the phase diagram, and the iodides of both Hg(I) and Hg(II) do form under conditions that are not strongly reducing. Figures 54c is a map of pHg0, and the activities of it and, therefore, the vapor pressure are lowered over much but not all of the area by the addition of iodine. Iodine will not, however, eliminate the problem discussed in the previous section. Figure 54d is a map of pHg(I), and its activity is still quite insignificant. In the upper left portion of the diagram, the activity of this state does increase by several orders of magnitude, but it is still quite small. Figure 54e and 54f parallel those in Figure 53. Under oxidizing conditions the activity of mercury falls significantly with the addition of iodine, and the boundary between the dominance of Hg(II) and the dominance of Hg(0) is lowered to more strongly reducing conditions. The abundances of species of Hg(II) in solution under oxidizing con- 2-n ditions are dominated by a series of complexes of the form HgIn . These complexes make mercury more soluble than it would be otherwise at the same time iodide is precipitating the element.

5. The Solubility Product Constant

The solubility product, Ksp and its negative log pKsp are often used to calculate solubilities of slightly-soluble salts and minerals such as Hg2S. The free energies of formation used in this work can be used to calculate these numbers, so it is of interest to compare the results to what we have found. The pKsp for Hg2S describes the reaction

= 2+ + 2− Hg2S Hg2 S = 2+ + 2− and pKsp pHg2 pS

Free energies of formation give us pKsp = 54.77, and it is often thought that 2+ 2− the solubility of this salt can be found by assuming that pHg2 = pS = pKsp/2 = 27.38. If this were true, the activity of mercury in a solution over −−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−→

FIGURE 54. The same model and the same diagrams except that iodine is added and ﬁxed so that pI(t) = 3.00. This includes the several species and oxidation states of iodine listed in Appendix A. P1: GIM TJ1228-02 EST.cls September 1, 2004 19:29

Toxic Metals in the Environment 569

(a)

(b) P1: GIM TJ1228-02 EST.cls September 1, 2004 19:29

570 S. K. Porter et al.

(c)

(d) FIGURE 54. (Continued). P1: GIM TJ1228-02 EST.cls September 1, 2004 19:29

Toxic Metals in the Environment 571

(e)

(f) FIGURE 54. (Continued). P1: GIM TJ1228-02 EST.cls September 1, 2004 19:29

572 S. K. Porter et al.

mercury(I) sulﬁde would be very low indeed. (It also assumed that the only mercury species in solution is the mercury(I) ion.) These things are not true, and they would not be worth mentioning except for the fact that millions of college students have learned that they are. The pKsp equation itself is, by the way, true, but it is also irrelevant. If we look at the model in section 4 for Hg and the results at pH = 7.2 and pe =−3.0, we ﬁnd the following: Hg2S is the stable mineral phase containing mercury; pHg(t) = 9.241, meaning that the calculation using pKsp is off by 18 orders of magnitude; and pS(t) = 2+ = 2− = 3.467 (almost all sulfate), pHg2 38.359, and pS 16.413. (The last two numbers do add to give the pKsp.)

6. Conclusions Concerning the Possible Immobilization of Hg It is beyond the scope of this work to wonder what levels of mercury are safe, but the authors are suspicious of anything above zero. The results of this section can be used to predict what might be possible or not possible if some immobilization strategy or another is tried. It would seem to be true that immobilization is much harder than it appears, and that it is probably not a good technique for risk reduction under any circumstances. If the system with Hg in it is exposed to the atmosphere under any but the most severe oxidizing conditions, the metal will get into the atmosphere sooner or later. Such is surely the case with any strategy using sulfide, the formation of which requires highly reducing conditions. Even a strategy using HgI2 runs into the difficulty that the iodide ion itself is a fairly active reducing agent. When (pH + pe) is 18.345, iodide is in equilibrium with iodate. This is a strong condition but certainly not beyond the realm of the possible. The metal itself should not be left in an environment open to the air or worse, the water at the bottom of a lake or river. Closed containers probably need to be the rule as the old name quicksilver fits even better than most imagine.

VII. CONCLUSIONS REGARDING IMMOBILIZATION

This paper has used equilibrium calculations to test the stabilities and probable efﬁcacies of reasonable immobilization strategies for lead, cadmium, arsenic, and mercury. The need for such strategies is urgent as the damage to the environment has already been done. On the basis of the thermodynamic calculations made, it would seem that virtually all such treatments are doomed to failure. Making chloropyromorphite the only Pb form in soil may require huge amounts of phosphate, amounts large enough to potentially turn the soil into a very hard and intractable substance. No compound of cadmium is both thermodynamically stable and insoluble enough to work. P1: GIM TJ1228-02 EST.cls September 1, 2004 19:29

Toxic Metals in the Environment 573

Arsenic could be made into manganese arsenate and be left alone so long as stable conditions of pH and pe could be guaranteed for very long periods of time. Mercury is perhaps the most difﬁcult case of the four metals examined, slowly but quite surely living up to its ancient name. The objection could be raised that systems in the environment do not come to equilibrium and that, therefore, such calculations are useless. It certainly is true that systems of interest are not at equilibrium, but the fact is that interesting chemical systems are never at equilibrium. The point is that they always go that way unless they are driven in the opposite direction by stronger potentials. Systems left in any ecosystem will move toward the systems described by these models if they change at all. Some immobilization strategies, such as leaving liquid mercury or cinnabar exposed to air, are simply slow but deadly. In parting, the endeavor of this work shows that thermodynamic calculations, as presented here, can tell us what is theoretically possible or impossible.

ACKNOWLEDGMENTS

The US EPA has not subjected this manuscript to internal policy review, thus it does not necessarily reﬂect Agency policy. Mention of trade names of commercial products does not constitute endorsement or recommendation for use. The use of existing literature-derived data not generated by US EPA was not subjected to US EPA quality assurance procedures, therefore no attempt to was made to verify the quality of the data. The authors wish to thank P. Burke for his careful review of the manuscript.

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APPENDIX OF THERMOCHEMICAL DATA AND EQUILIBRIUM CONSTANT EQUATIONS

This appendix is divided into three parts. Part I is a table of free energies of formation for the neutral species, one for each element, that are used in the 0 equilibrium-constant equations, including those for pKsp. These species are ordered according to position on the periodic table, going from left to right, group 1 to group 18. The other two parts of this appendix are ordered the same way. Part II of the appendix is information on condensed phases, organized as follows: 0 FORMULA, mineral name, Gf in kJ/mol as the formula is written, reference, 0 pKsp: numeric value, formula using the conventions described on page four

Part III of the appendix gives the information for the solute species not listed in part one. The data are given as follows: 0 chemical formula, Gf in kJ/mol as the formula is written, reference, algebraic formula for the negative log of the activity as the formula is written P1: GIM TJ1228-02 EST.cls September 1, 2004 19:29

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Part I. Reference Species 0 Formula ∆Gf in kJ/mol Reference

e− (the electron) 0 standard state H+ (the proton) 0 standard state 24 H2O −237.178 Bard NaOH0 −419.17 Bard KOH0 −436.89 Lindsay22 0 − Mg(OH)2 769.1 Bard Ca(OH)2 −869.06 Lindsay 0 − H2MoO4 883.16 Lindsay 0 − 12 Mn(OH)2 610.45 Weast 0 − Fe(OH)3 659.4 Bard 0 − Cd(OH)2 442.6 Bard Hg0 +37.2 Bard, Glew63 0 − Al(OH)3 1094.6 Lindsay 0 − CO2 386.225 Bard 0 − H4SiO4 1308.17 Lindsay 0 − Pb(OH)2 397.73 Lindsay 0 − NH3 26.6 Lindsay 0 − H3PO4 1149.68 Lindsay 0 − 58 64 H3AsO4 766.1 Welham, Hem 0 H2S −27.87 Lindsay, Bard 0 HCl −114.14 Bard and est. pKa =−3.0 Part II. Minerals and Other Condensed Phases KEY: 0 FORMULA mineral name Gf in kJ/mol as the formula is written refer- 0 ence pKsp: numeric value formula using the conventions described on page four SODIUM NaAlSiO4 nepheline −1996.77 Lindsay 0 + 0 + 0 21.644 pNaOH pAl(OH)3 pH4SiO4 NaAlSi3O8 Na glass −366.52 Lindsay 0 + 0 + 0 22.016 pNaOH pAl(OH)3 3pH4SiO4 NaAlSi3O8 high albite −3707.65 Lindsay 0 + 0 + 0 29.222 pNaOH pAl(OH)3 3pH4SiO4 NaAlSi3O8 low albite −3712.92 Lindsay 0 + 0 + 0 30.145 pNaOH pAl(OH)3 3pH4SiO4 NaAlSi2O6 jadeite −2854.20 Lindsay 0 + 0 + 0 25.781 pNaOH pAl(OH)3 2pH4SiO4 P1: GIM TJ1228-02 EST.cls September 1, 2004 19:29

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NaAlSi2O6·H2O analcime −3091.7 Bard 0 + 0 + 0 25.838 pNaOH pAl(OH)3 2pH4SiO4 NaAl3Si3O10(OH)2 paragonite −5559.82 Lindsay 0 + 0 + 0 53.281 pNaOH 3pAl(OH)3 3pH4SiO4 NaAl7Si11O30(OH)6 beidellite −16,081.75 Lindsay 0 + 0 + 0 127.162 pNaOH 7pAl(OH)3 11pH4SiO4 NaAlSi3O8 anabite −3706.5 Bard 0 + 0 + 0 29.020 pNaOH pAl(OH)3 3pH4SiO4 65 Na3As −187.44 Itagaki − 0 + 0 + + 10.071 pNaOH pH3AsO4/3 8(pH pe)/3 NaAs −89.12 Itagaki 0 + 0 + + 15.925 pNaOH pH3AsO4 6(pH pe) NaAs2 −103.76 Itagaki 0 + 0 + + 50.485 pNaOH 2pH3AsO4 11(pH pe)

MAGNESIUM MgO periclase −569.2 Lindsay, Bard 0 6.243 pMg(OH)2 Mg(OH)2 brucite −834.3 Lindsay 0 11.142 pMg(OH)2 MgOHCl −732.2 Weast 0 + 0 14.951 pMg(OH)2 pHCl MgCO3 magnestite −1026.6 Lindsay 0 + 0 18.719 pMg(OH)2 pCO2 MgCO3·3H2O nesquehodite −1722.2 Lindsay 0 + 0 15.926 pMg(OH)2 pCO2 MgCa(CO3)2 dolomite −2168.4 Lindsay 0 + 0 + 0 40.379 pMg(OH)2 pCa(OH)2 2pCO2 MgHPO4·3H2O newberryite −2297.2 Lindsay 0 + 0 24.456 pMg(OH)2 pH3PO4 Mg3(PO4)2 −3503.3 Lindsay 0 + 0 18.382 pMg(OH)2 2pH3PO4/3 Mg3(PO4)2·8H2O boberrite −5460.1 Lindsay 0 + 0 21.850 pMg(OH)2 2pH3PO4/3 Mg3(PO4)2·22H3O −8769.7 Lindsay 0 + 0 21.216 pMg(OH)2 2pH3PO4/3 P1: GIM TJ1228-02 EST.cls September 1, 2004 19:29

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MgCO3·5H2O lansfordite −2195.85 Lindsay 0 + 0 15.797 pMg(OH)2 pCO2 MgSiO3 clinoenstatite −1461.9 Lindsay 0 + 0 16.567 pMg(OH)2 pH4SiO4 Mg2SiO4 forsterite −2055.6 Lindsay 0 + 0 13.547 pMg(OH)2 pH4SiO4/2 Mg2SiO6(OH)4 sepolite −4271.7 Lindsay 0 + 0 20.038 pMg(OH)2 3pH4SiO4/2 Mg3Si2O5(OH)4 chrystolite −4034.2 Lindsay 0 + 0 17.027 pMg(OH)2 2pH4SiO4/3 Mg3Si4O10(OH)2 talc −5525.2 Lindsay 0 + 0 20.564 pMg(OH)2 4pH4SiO4/3 Mg3Si4O10(OH)2·2H2O vermiculite −5953.2 Lindsay 0 + 0 17.855 pMg(OH)2 4pH4SiO4/3 Mg6Si4O10(OH)8 serpentine −8091.2 Lindsay 0 + 0 17.693 pMg(OH)2 2pH4SiO4/3

CALCIUM CaS oldhamite −469.5 USGS66 0 + 0 8.214 pCa(OH)2 pH2S CaSO4·2H2O gypsum −1799.83 Lindsay − 0 + 0 − + 8.033 pCa(OH)2 pH2S 8(pH pe) CaSO4 −1320.3 Lindsay − 0 + 0 − + 8.265 pCa(OH)2 pH2S 8(pH pe) Ca10(PO4)6(OH)2 hydroxyapatite −12,678.5 Lindsay 0 + 0 23.809 pCa(OH)2 3pH3PO4/5 Ca3(PO4)2 α −3860.6 Lindsay, Naumov67 0 + 0 22.022 pCa(OH)2 2pH3PO4/3 Ca3(PO4)2 whitelockite −3880.1 Lindsay 0 + 0 23.163 pCa(OH)2 2pH3PO4/3 Ca8H2(PO4)6·5H2O octa-calcium phos. −12,311.9 Lindsay 0 + 0 23.439 pCa(OH)2 3pH3PO4/4 CaHPO42H2O brushite −2162.7 Lindsay 0 + 0 25.215 pCa(OH)2 pH3PO4 CaHPO4 monetite −1690.17 Lindsay 0 + 0 25.540 pCa(OH)2 pH3PO4 Ca2P2O7 β −3105.91 Lindsay 0 + 0 22.277 pCa(OH)2 pH3PO4 P1: GIM TJ1228-02 EST.cls September 1, 2004 19:29

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Ca(H2PO4)2 “super phosphate” −3073.1 Lindsay 0 + 0 24.846 pCa(OH)2 2pH3PO4 CaCO3 calcite −1130.4 Lindsay 0 + 0 19.679 pCa(OH)2 pCO2 CaCO3·6H2O ikaite −2541.9 Lindsay 0 + 0 17.806 pCa(OH)2 pCO2 CaO lime −603.58 Lindsay − 0 4.957 pCa(OH)2 Ca(OH)2 portlandite −898.68 Lindsay 0 5.190 pCa(OH)2 CaO·Fe2O3 −1412.81 Bard 0 + 0 30.586 pCa(OH)2 pFe(OH)3 2CaO·Fe2O3 −2001.8 Bard 0 + 0 11.615 pCa(OH)2 pFe(OH)3/2 CaSiO3 wollastanite −1549.71 Bard, Lindsay 0 + 0 14.719 pCa(OH)2 pH4SiO4 CaSiO3 pseudo-wollastanite −1497.04 Weast 0 + 0 13.766 pCa(OH)2 pH4SiO4 Ca2SiO4 β-laruite −2192.8 Bard 0 + 0 8.183 pCa(OH)2 pH4SiO4/2 Ca2SiO4 γ -olivine −2201.2 Bard 0 + 0 9.085 pCa(OH)2 pH4SiO4/2 CaMoO4 powellite −1435.9 Lindsay 0 + 0 27.688 pCa(OH)2 pH2MoO4 Ca3(AsO4)2 −3063.1 Bard 0 + 0 20.252 pCa(OH)2 2pH3AsO4/3 Ca3(AsO4)2·4H2O −4018.73 Naumov 0 + 0 20.656 pCa(OH)2 2pH3AsO4/3 Ca(H2AsO4)2 −2053.93 Itagaki, Naumov 0 + 0 22.257 pCa(OH)2 2pH3AsO4 CaHAsO4 −1287.42 Itagaki, Naumov 0 + 0 22.184 pCa(OH)2 pH3AsO4 Ca(AsO2)2 −1292.02 Itagaki, Naumov 0 + 0 + + 54.985 pCa(OH)2 2pH3AsO4 4(pH pe) CaAsO2OH −1112.94 Itagaki, Naumov 0 + 0 + + 33.169 pCA(OH)2 pH3AsO4 2(pH pe) Ca5H2(AsO4)4 −5636.7 Itagaki, Naumov 0 + 0 20.983 pCa(OH)2 4pH3AsO4/5 Ca2AsO4OH −1987.82 Itagaki, Naumov 0 + 0 17.094 pCa(OH)2 pH3AsO4/2 P1: GIM TJ1228-02 EST.cls September 1, 2004 19:29

582 S. K. Porter et al.

MOLYBDENUM Mo metal 0 standard state 0 + + 11.485 pH2MoO4 6(pH pe) MoO2 −533.08 Lindsay 0 + + 21.773 pH2MoO4 2(pH pe) H2MoO4 −912.45 Lindsay 0 5.131 pH2MoO4 MoO3 molybdite −668.0 Lindsay 0 3.861 pH2MoO4 MoS2 molybdenite −266.48 Lindsay 0 + 0 + + 48.391 pH2MoO4 2pH2S 2(pH pe)

MANGANESE Mn metal 0 standard state − 0 + + 17.736 pMn(OH)2 2(pH pe) MnS “green” −211.38 Lindsay 0 + 0 14.414 pMn(OH)2 pH2S MnS alabandite −218.07 Lindsay 0 + 0 15.586 pMn(OH)2 pH2S MnS2 hauerite −232.34 Lindsay 0 + 0 − + 13.203 pMn(OH)2 pH2S 2(pH pe) MnSO4 −955.54 Lindsay − 0 + 0 − + 21.422 pMn(OH)2 pH2S 8(pH pe) MnSO4H2O −1209.64 Lindsay − 0 + 0 − + 18.458 pMn(OH)2 pH2S 8(pH pe) Mn2(SO4)3 −2469.15 Lindsay − 0 + 0 − + 58.083 pMn(OH)2 3pH2S /2 13(pH pe) Mn3(PO4)2 −2899.3 Lindsay 0 + 0 17.302 pMn(OH)2 2pH3PO4/3 MnHPO4 −1400.8 Lindsay 0 + 0 26.253 pMn(OH)2 pH3PO4 MnCl2 scacchite −440.50 Bard 0 + 0 19.444 pMn(OH)2 pHCl MnCl2H2O −696.1 Bard 0 + 0 22.672 pMn(OH)2 pHCl MnCO3 rhodochrosite −816.01 Lindsay 0 + 0 16.007 pMn(OH)2 pCO2 MnO manganosite −362.80 Lindsay 0 4.272 pMn(OH)2 P1: GIM TJ1228-02 EST.cls September 1, 2004 19:29

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Mn(OH)2 pyrochorite −618.23 Lindsay 0 7.470 pMn(OH)2 MnO2 pyrolusite −465.85 Lindsay − 0 − + 19.227 pMn(OH)2 2(pH pe) MnO1.8 birnessite −455.60 Lindsay − 0 − + 12.712 pMn(OH)2 8(pH pe)/5 MnO1.9 nsutite −459.28 Lindsay − 0 − + 16.222 pMn(OH)2 9(pH pe)/5 Mn2O3 bixbyite −879.02 Lindsay − 0 − + 3.065 pMn(OH)2 (pH pe) Mn3O4 hausmannite −1280.76 Lindsay 0 − + 1.655 pMn(OH)2 2(pH pe)/3 MnOOH manganite −560.70 Lindsay − 0 − + 2.609 pMn(OH)2 (pH pe) MnAs kaneite −57.32 Itagaki, Naumov 0 + 0 + + 24.301 pMn(OH)2 pH3AsO4 7(pH pe) Mn3(AsO4)2 −2145.14 Itagaki, Naumov 0 + 0 18.060 pMn(OH)2 2pH3AsO4/3 Mn3(AsO4)2·8H2O −4055.13 Naumov 0 + 0 18.793 pMn(OH)2 2pH3AsO4/3

IRON Fe metal 0 standard state 0 + + 9.134 pFe(OH)3 3(pH pe) FeO −251.454 Welham 0 + + 11.635 pFe(OH)3 (pH pe) Fe(OH)2 −486.6 Bard 0 + + 11.279 pFe(OH)3 (pH pe) Fe3O4 magnetite −1015.359 Bard 0 + + 13.026 pFe(OH)3 (pH pe)/3 FeO1.062 wustite −276.336 Bard 0 + + 13.418 pFe(OH)3 0.876(pH pe) Fe3(OH)8 −1921.4 Lindsay 0 + + 10.533 pFe(OH)3 (pH pe)/3 FeOOH goethite −490 Welham 0 12.190 pFe(OH)3 Fe2O3·H2O −984.03 Bard 0 12.277 pFe(OH)3 P1: GIM TJ1228-02 EST.cls September 1, 2004 19:29

584 S. K. Porter et al.

Fe2O3 maghemite −726.97 Lindsay 0 10.486 pFe(OH)3 Fe2O3 hematite −742.2 Bard 0 11.820 pFe(OH)3 FeOOH lepidocrocite −483.25 Lindsay 0 10.587 pFe(OH)3 Fe(OH)3 (c) −705.535 Bard 0 8.083 pFe(OH)3 Fe(OH)3 “soil” −712.95 Lindsay 0 9.382 pFe(OH)3 FeCO3 siderite −677.60 Lindsay 0 + 0 + + 16.723 pFe(OH)3 pCO2 (pH pe) FeCl2 lawrencite −302.38 Lindsay 0 + 0 + + 22.82 pFe(OH)3 2pHCl (pH pe) FeCl3 molysite −334.97 Lindsay 0 + 0 7.667 pFe(OH)3 3pHCl FeOCl −359.234 Bard 0 + 0 10.521 pFe(OH)3 pHCl FeS2 pyrite −162.26 Lindsay 0 + 0 − + 28.594 pFe(OH)3 2pH2S (pH pe) FeS2 markasite −158.28 Lindsay 0 + 0 − + 27.084 pFe(OH)3 2pH2S (pH pe) Fe7S8 S-rich pyrrhotite −748.5 Bard 0 + 0 + + 22.279 pFe(OH)3 8pH2S /7 5(pH pe)/7 FeS1.053 Fe-rich pyrrhotite −105.61 Lindsay 0 + 0 + + 22.487 pFe(OH)3 1.053pH2S 0.894(pH pe) FeS troilite −97.91 Lindsay 0 + 0 + + 21.397 pFe(OH)3 pH2S (pH pe) Fe2S3 −278.40 Lindsay 0 + 0 26.187 pFe(OH)3 3pH2S /2 FeSO4 −820.61 Lindsay − 0 + 0 − + 18.199 pFe(OH)3 pH2S 7(pH pe) FeSO4·7H2O tauriscite −2510.3 Lindsay − 0 + 0 − + 13.046 pFe(OH)3 pH2S 7(pH pe) KFe3(SO4)2(OH)6 jarosite −3316.5 Lindsay − 0 + 0 + 0 − + 18.069 pKOH 3pFe(OH)3 2pH2S 16(pH pe) FePO4 −1184.9 Lindsay, Naumov 0 + 0 15.298 pFe(OH)3 pH3PO4 P1: GIM TJ1228-02 EST.cls September 1, 2004 19:29

Toxic Metals in the Environment 585

FePO4·2H2O strengite −1667.7 Lindsay 0 + 0 16.784 pFe(OH)3 pH3PO4 Fe3(PO4)2·8H2O vivianite −4428.18 Lindsay 0 + 0 + + 22.647 pFe(OH)3 2pH3PO4/3 (pH pe) Fe2P2O7 −2195.93 Lindsay 0 + 0 + + 20.850 pFe(OH)3 pH3PO4 (pH pe) FeAs −28.0 Barton 0 + 0 + + 46.032 pFe(OH)3 pH3AsO4 8(pH pe) Fe2As −20.9 Barton 0 + 0 + + 26.961 pFe(OH)3 pH3AsO4/2 11(pH pe)/2 FeAs2 loellingite −52.3 USGS 0 + 0 + + 82.282 pFe(OH)3 2pH3AsO4 13(pH pe) FeAsS arsenopyrite −109.6 Barton 0 + 0 + 0 + + 55.438 pFe(OH)3 pH3AsO4 pH2S 6(pH pe) Fe3(AsO4)2 −1765.3 Itagaki 0 + 0 + + 23.832 pFe(OH)3 2pH3AsO4/3 (pH pe) FeAsO4 −774.58 Barton 0 + 0 11.539 pFe(OH)3 pH3AsO4 FeAsO4·2H2O scorodite −1280.0 Bard 0 + 0 16.062 pFe(OH)3 pH3AsO4 CADMIUM Cd metal 0 standard state 0 + + 5.564 pCd(OH)2 2(pH pe) CdO monteponite −228.66 Bard 0 4.070 pCd(OH)2 Cd(OH)2 β −474.34 Bard, Lindsay 0 5.561 pCd(OH)2 CdCO3otavite −674.29 Lindsay, Bard 0 + 0 14.484 pCd(OH)2 pCO2 CdCl2 −343.93 Bard 0 + 0 25.825 pCd(OH)2 2pHCl Cd3(PO4)2 −2502.70 Lindsay 0 + 0 17.438 pCd(OH)2 2pH3PO4/3 CdSiO3 −1105.33 Lindsay 0 + 0 11.579 pCd(OH)2 pH4SiO4 CdS greenokite −146.57 Lindsay 0 + 0 26.358 pCd(OH)2 pH2S CdSO4 −822.66 Bard, Lindsay − 0 + 0 − + 21.403 pCd(OH)2 pH2S 8(pH pe) P1: GIM TJ1228-02 EST.cls September 1, 2004 19:29

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CdSO4·H2O −1068.68 Bard, Lindsay − 0 + 0 − + 19.854 pCd(OH)2 pH2S 8(pH pe) CdSO4·8/3H2O −1465.141 Bard − 0 + 0 − + 19.650 pCd(OH)2 pH2S 8(pH pe) CdSO4·2Cd(OH)2 −1797.57 Lindsay − 0 + 0 − + 1.895 pCd(OH)2 pH2S /3 8(pH pe)/3 2CdSO4·Cd(OH)2 −2158.65 Lindsay − 0 + 0 − + 10.138 pCd(OH)2 2pH2S /3 16(pH pe)/3

MERCURY Hg liquid metal 0 standard state 6.517 pHg0 HgO red, orthorhombic −58.555 Bard −24.777 pHg0 − 2(pH + pe)

Hg(OH)2 −294.85 Lindsay −24.932 pHg0 − 2(pH + pe)

Hg2(OH)2 −290.75 Lindsay −9.567 pHg0 − (pH + pe)

HgCO3 −492.122 Lindsay − 0 + 0 − + 16.483 pHg pCO2 2(pH pe) Hg2CO3 −468.2 Bard − 0 + 0 − + 7.078 pHg pCO2/2 (pH pe) HgCl2 −180.3 Bard −1.889 pHg0 + 2pHCl0 − 2(pH + pe)

Hg2Cl2 calomel −210.374 Bard 4.949 pHg0 + pHCl0 − (pH + pe)

Hg2HPO4 −966.57 Bard − 0 + 0 − + 9.523 pHg pH3PO4/2 (pH pe) HgS cinnabar −46.4 Bard, Lindsay 0 0 9.764 pHg + pH2S − 2(pH + pe)

HgSO4 −594 Bard 0 0 −60.509 pHg + pH2S − 10(pH + pe)

Hg2SO4 −626.34 Bard, Lindsay 0 0 −24.163 pHg + pH2S /2 − 5(pH + pe)

Hg2S −73.18 Lindsay 0 0 10.486 pHg + pH2S /2 − (pH + pe)

HgI2 “red” −101.7 Bard 25.435 pHg0 + 2pHI0 − 2(pH + pe)

Hg2I2 −111.002 Bard P1: GIM TJ1228-02 EST.cls September 1, 2004 19:29

Toxic Metals in the Environment 587

16.791 pHg0 + pHI0 − (pH + pe)

Hg(IO3)2 −167.2 Bard −212.955 pHg0 + 2pHI0 − 13(pH + pe)

Hg2(IO3)2 −179.9 Bard −101.832 pHg0 + pHI0 − 7(pH + pe)

ALUMINUM

Al(OH)3 gibbsite −1156.58 Lindsay 0 10.564 pAl(OH)3 Al(OH)3 “amorphous” −1147.30 Lindsay 0 9.233 pAl(OH)3 Al(OH)3 bayerite −1153.86 Lindsay 0 10.382 pAl(OH)3 Al(OH)3 nordstrandite −1156.04 Lindsay 0 10.764 pAl(OH)3 Al(OH)3·H2O −1376.42 Bard 0 7.821 pAl(OH)3 Al(OH)3·3H2O −1850.4 Bard 0 14.763 pAl(OH)3 AlOOH α, diaspore −920.06 Lindsay 0 11.051 pAl(OH)3 AlOOH γ , boehmite −918.85 Lindsay 0 9.684 pAl(OH)3 Al2O3 corundum −158.26 Lindsay 0 9.162 pAl(OH)3 Al2O3 γ −1562.22 Lindsay 0 9.407 pAl(OH)3 AlPO4 berlinite −1625.48 Lindsay 0 + 0 16.247 pAl(OH)3 pH3PO4 AlPO4·2H2O variscite −2116.98 Lindsay 0 + 0 19.250 pAl(OH)3 pH3PO4 Al2SiO2O5(OH)4 kaolinite −3804.22 Lindsay 0 + 0 16.168 pAl(OH)3 pH4SiO4 Al2SiO5 andalusite −2444.50 Lindsay 0 + 0 11.652 pAl(OH)3 pH4SiO4/2 Al2SiO5 kyanite −2440.86 Lindsay 0 + 0 11.333 pAl(OH)3 pH4SiO4/2 Al2SiO5 sillimanite −2438.48 Lindsay 0 + 0 11.125 pAl(OH)3 pH4SiO4/2 P1: GIM TJ1228-02 EST.cls September 1, 2004 19:29

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Al2Si2O5(OH)4 dickite −3796.3 Bard 0 + 0 15.474 pAl(OH)3 pH4SiO4 Al2Si2O5(OH)4 halloysite −3785.6 Lindsay 0 + 0 14.533 pAl(OH)3 pH4SiO4 Al2Si4O10(OH)2 pyrophillite −5276.74 Lindsay 0 + 0 19.853 pAl(OH)3 2pH4SiO4

SILICON

SiO2 “soil” −851.49 Lindsay 0 3.096 pH4SiO4 SiO2 quartz −856.67 Lindsay 0 4.005 pH4SiO4

LEAD Pb metal 0 standard state 0 + + 13.424 pPb(OH)2 2(pH pe) PbO “yellow” −188.28 Lindsay 0 4.858 pPb(OH)2 PbO “red” −189.28 Lindsay 0 5.034 pPb(OH)2 PbO “white” −183.72 Bard 0 4.059 pPb(OH)2 Pb(OH)2 “aged” −452.5 Lindsay 0 9.595 pPb(OH)2 (68) Pb(OH)2 “fresh” −420.91 Smith 0 4.542 pPb(OH)2 PbO2 −215.52 Bard − 0 − + 31.923 pPb(OH)2 2(pH pe) Pb3O4 −601.659 Bard − 0 − + 6.843 pPb(OH)2 2(pH pe)/3 Pb2O3 −411.78 Bard − 0 − + 12.833 pPb(OH)2 (pH pe) PbO1.57 −211.21 Bard − 0 − + 14.810 pPb(OH)2 1.14(pH pe) PbCO3 cerrusite −629.73 Lindsay 0 + 0 14.533 pPb(OH)2 pCO2 Pb2CO3Cl2 phosgenite −953.70 Lindsay − 0 + 0 + 0 39.968 pPb(OH)2 pCO2/2 pHCl P1: GIM TJ1228-02 EST.cls September 1, 2004 19:29

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Pb3(CO3)2(OH)2 −1711.6 Lindsay 0 + 0 12.865 pPb(OH)2 2pCO2/3 PbO·PbCO3 −818.9 Lindsay 0 + 0 9.772 pPb(OH)2 pCO2/2 Pb(OH)2·(PbCO3)2 Smith 0 + 0 12.178 pPb(OH)2 2pCO2/3 2PbO·PbCO3 −1012 Smith 0 + 0 8.416 pPb(OH)2 pCO2/3 (25) PbCl2 −314.0 Wall 0 + 0 28.436 pPb(OH)2 2pHCl PbS galena −95.86 Lindsay 0 + 0 25.329 pPb(OH)2 2pH2S PbS2O3 −560.6 Smith − 0 + 0 − + 22.784 pPb(OH)2 2pH2S 8(pH pe) PbS3O6 −894.5 Smith − 0 + 0 − + 93.827 pPb(OH)2 3pH2S 16(pH pe) PbSO4 anglesite −813.70 Lindsay, Smith − 0 + 0 − + 15.111 pPb(OH)2 pH2S 8(pH pe) PbSO4·PbO −1032.2 Lindsay − 0 + 0 − + 2.408 pPb(OH)2 pH2S /2 4(pH pe) PbSO4·2PbO −1230.1 Lindsay 0 + 0 − + 0.527 pPb(OH)2 pH2S /3 8(pH pe)/3 PbSO4·3PbO −1427.6 Lindsay 0 + 0 − + 2.013 pPb(OH)2 pH2S /4 2(pH pe) PbHPO4 −1186.4 Lindsay 0 + 0 19.853 pPb(OH)2 pH3PO4 Pb(H2PO4)2 −2355.8 Lindsay 0 + 0 23.306 pPb(OH)2 2pH3PO4 Pb3(PO4)2 −2378.9 Lindsay 0 + 0 18.069 pPb(OH)2 2pH3PO4/3 Pb5(PO4)3OH hydroxypyromorphite −3796.5 Lindsay 0 + 0 17.289 pPb(OH)2 3pH3PO4/5 Pb5(PO4)3Cl chloropyromorphite −3809.91 Lindsay 0 + 0 + 0 22.069 pPb(OH)2 3pH3PO4/5 pHCl /5 Pb4O(PO4)2 −2598.0 Lindsay 0 + 0 16.117 pPb(OH)2 pH3PO4/2 PbMoO4 wulfenite −952.36 Lindsay 0 + 0 25.548 pPb(OH)2 pH2MoO4 P1: GIM TJ1228-02 EST.cls September 1, 2004 19:29

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ARSENIC As2O5 −781.4 Bard − 0 3.440 pH3AsO4 As4O6 arsenolite −1153.0 Bard 0 + + 20.164 pH3AsO4 2(pH pe) (69) As4S4 realgar −142.26 Barton 0 + 0 + + 33.334 pH3AsO4 pH2S 3(pH pe) As2S3 orpiment −90.4 USGS 0 + 0 + + 38.417 pH3AsO4 2pH2S /3 2(pH pe)

III. Solute Species 0 chemical formula Gf in kJ/mol as the formula is written reference algebraic formula for the negative log of the activity as the formula is written

SODIUM Na+ −261.87 Bard pNa+ = pNaOH0 + pH −13.994 NaCl0 −393.04 Bard pNaCl0 = pNaOH0 + pHCl0 − 16.978 − − NaCO3 797.05 Lindsay − = 0 + 0 − + pNaCO3 pNaOH pCO2 pH 1.261 0 − Na2CO3 1051.77 Lindsay 0 = 0 + 0 − pNa2CO3 2pNaOH pCO2 11.682 0 − NaHCO3 850.19 Lindsay 0 = 0 + 0 − pNaHCO3 pNaOH pCO2 8.048 − NaHPO4 Smith − = 0 + 0 − − pNaHPO4 pNaOH pH3PO4 pH 5.841 − − NaSO4 1010.39 Lindsay − = 0 + 0 − + − + pNa2SO4 pNaOH pH2S 8(pH pe) pH 25.767 0 − Na2SO4 1265.7 Bard 0 = 0 + 0 − + + pNa2SO4 pNaOH pH2S 8(pH pe) 13.116

MAGNESIUM Mg2+ −456.10 Lindsay 2+ = 0 + − pMg pMg(OH)2 2pH 27.981 MgOH+ −627.93 Lindsay + = 0 + − pMgOH pMg(OH)2 pH 16.534 0 − MgCO3 1002.53 Lindsay 0 = 0 + 0 − pMgCO3 pMg(OH)2 pCO2 14.496 P1: GIM TJ1228-02 EST.cls September 1, 2004 19:29

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+ − MgHCO3 1049.10 Lindsay + = 0 + 0 + − pMgHCO3 pMg(OH)2 pCO2 pH 22.655 MgCl+ −587.18 Weast + = 0 + 0 + − pMgCl pMg(OH)2 pHCl pH 29.94 0 − MgCl2 718.43 Lindsay 0 = 0 + 0 − pMgCl2 pMg(OH)2 2pHCl 33.948 0 − MgHPO4 1569.04 Lindsay 0 = 0 + 0 − pMgHPO4 pMg(OH)2 pH3PO4 21.546 2− − MgP2O7 2413.8 Bard 2− = 0 + 0 − − pMgP2O7 pMg(OH)2 2pH3PO4 2pH 9.964 0 − MgSO4 1211.81 Naumov 0 = 0 + 0 − + + pMgSO4 pMg(OH)2 pH2S 8(pH pe) 12.689 CALCIUM Ca2+ −554.46 Lindsay 2+ = 0 + − pCa pCa(OH)2 2pH 27.989 CaOH+ −719.19 Lindsay + = 0 + − pCaOH pCa(OH)2 pH 15.295 − − CaPO4 1617.16 Lindsay − = 0 + 0 − pCaPO4 pCa(OH)2 pH3PO4 pH 12.750 0 − CaHPO4 1666.45 Lindsay 0 = 0 + 0 − pCaHPO4 pCa(OH)2 pH3PO4 21.384 + − CaH2PO4 1699.88 Lindsay + = 0 + 0 + − pCaH2PO4 pCa(OH)2 pH3PO4 pH 27.241 2− − CaP2O7 2506.38 Lindsay 2− = 0 + 0 − − pCaP2O7 pCa(OH)2 2pH3PO4 2pH 8.671 − − CaHP2O7 2541.82 Lindsay − = 0 + 0 − − pCaHP2O7 pCa(OH)2 2pH3PO4 pH 14.880 3− − CaOHP2O7 2675.63 Lindsay 3− = 0 + 0 − + pCaOHP2O7 pCa(OH)2 2pH3PO4 3pH 3.252 0 − CaCO3 1100.39 Lindsay 0 = 0 + 0 − pCaCO3 pCa(OH)2 pCO2 14.416 + − CaHCO3 1147.80 Lindsay + = 0 + 0 + − pCaHCO3 pCa(OH)2 pHCl pH 22.721 CaCl+ −680.03 Lindsay + = 0 + 0 + − pCaCl pCa(OH)2 pHCl pH 29.990 0 − CaCl2 816.97 Lindsay 0 = 0 + 0 − pCaCl2 pCa(OH)2 2pHCl 33.984 0 − CaSO4 1312.19 Lindsay 0 = 0 + 0 − + + pCaSO4 pCa(OH)2 pH2S 8(pH pe) 12.648 P1: GIM TJ1228-02 EST.cls September 1, 2004 19:29

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MOLYBDENUM 2+ − MoO2 411.16 Lindsay 2+ = 0 + − pMoO2 pH2MoO4 2pH 0.413 + MoO2OH −645.76 Lindsay + = 0 + + pMoO2OH pH2MoO4 pH 0.039 − − HMoO4 860.31 Lindsay − = 0 − + pHMoO4 pH2MoO4 pH 4.002 2− − MoO4 836.13 Lindsay 2− = 0 − + pMoO4 pH2MoO4 2pH 8.239 6− − Mo7O24 5251 Bard 6− = 0 − − pMo7O24 7pH2MoO4 6pH 3.524 MANGANESE Mn2+ −230.58 Lindsay, Bard 2+ = 0 + − pMn pMn(OH)2 2pH 22.661 MnOH+ −407.31 Lindsay + = 0 + − pMnOH pMn(OH)2 pH 12.071 − − Mn(OH)3 748.10 Lindsay − = 0 − + pMn(OH)3 pMn(OH)2 pH 11.330 2− − Mn(OH)4 903.70 Lindsay 2− = 0 − + pMn(OH)4 pMn(OH)2 2pH 25.621 3+ Mn2OH −637.85 Lindsay 3+ = 0 + − pMn2OH 2pMn(OH)2 3pH 34.725 + − Mn2(OH)3 1036.34 Lindsay + = 0 + − pMn2(OH)3 2pMn(OH)2 pH 21.432 − − HMnO2 507 Bard − = 0 − + pHMnO2 pMn(OH)2 pH 12.017 Mn3+ −84.77 Lindsay, Bard 3+ = 0 − + + + pMn pMn(OH)2 (pH pe) 3pH 2.885 MnOH2+ −324.22 Lindsay 2+ = 0 − + + + pMnOH pMn(OH)2 (pH pe) 2pH 2.487 Mn4+ +60.79 Lindsay 4+ = 0 − + + + pMn pMn(OH)2 2(pH pe) 4pH 28.387 3− − MnO4 527 Bard 3− = 0 − + − + pMnO4 pMn(OH)2 3(pH pe) 3pH 91.618 2− − MnO4 504.09 Lindsay, Bard 2− = 0 − + − + pMnO4 pMn(OH)2 4(pH pe) 2pH 95.632 P1: GIM TJ1228-02 EST.cls September 1, 2004 19:29

Toxic Metals in the Environment 593

− − MnO4 477.2 Bard − = 0 − + − + pMnO4 pMn(OH)2 5(pH pe) pH 100.344 MnCl+ −493.34 Lindsay + = 0 + 0 + − pMnCl pMn(OH)2 pHCl pH 26.824 0 − MnCl2 754.46 Lindsay 0 = 0 + 0 − pMnCl2 pMn(OH)2 2pHCl 29.258 0 − MnCO3 754.46 Lindsay 0 = 0 + 0 − pMnCO3 pMn(OH)2 pCO2 5.225 + − MnHCO3 827.76 Lindsay + = 0 + 0 + − pMnHCO3 pMn(OH)2 pCO2 pH 18.067 0 − MnSO4 988.01 Lindsay 0 = 0 + 0 − + + pMnSO4 pMn(OH)2 pH2S 8(pH pe) 15.735

IRON(III) Fe3+ −4.6 Bard 3+ = 0 + − pFe pFe(OH)3 3pH 9.940 FeOH2+ −229.41 Bard + = 0 + − pFeOH2 pFe(OH)3 2pH 7.668 + − Fe(OH)2 438.1 Bard + = 0 + − pFe(OH)2 pFe(OH)3 pH 2.677 − − Fe(OH)4 842.2 Bard − = 0 − + pFe(OH)4 pFe(OH)3 pH 9.632 4+ − Fe2(OH)2 491.45 Lindsay 4+ = 0 + − pFe2(OH)2 2pFe(OH)3 4pH 23.286 5+ − Fe3(OH)4 963.28 Lindsay 5+ = 0 + − pFe3(OH)4 3pFe(OH)3 5pH 32.988 FeCl2+ −143.9 Bard 2+ = 0 + 0 + − pFeCl pFe(OH)3 pHCl 2pH 14.242 + − FeCl2 291.5 Lindsay + = 0 + 0 + − pFeCl2 pFe(OH)3 2pHCl pH 17.932 0 − FeCl3 415.0 Lindsay 0 = 0 + 0 − pFeCl3 pFe(OH)3 3pHCl 19.222 + − FeHPO4 1175.4 Lindsay + = 0 + 0 + − pFeHPO4 pFe(OH)3 pH3PO4 pH 15.020 2+ − FeH2PO4 1244.0 Lindsay 2+ = 0 + 0 + − pFeH2PO4 pFe(OH)3 pH3PO4 2pH 16.742 + − FeSO4 772.8 Bard + = 0 ++ 0 − + + + pFeSO4 pFe(OH)3 pH2S 8(pH pe) pH 26.568 P1: GIM TJ1228-02 EST.cls September 1, 2004 19:29

594 S. K. Porter et al.

− − Fe(SO4)2 1524.6 Bard − = 0 ++ 0 − + − + pFe(SO4)2 pFe(OH)3 2pH2S 16(pH pe) pH 65.949 2+ − FeH2AsO4 793.7 Welham 2+ = 0 + 0 + − pFeH2AsO4 pFe(OH)3 pH3AsO4 2pH 13.864 + − FeHAsO4 788.2 Welham + = 0 + 0 + − pFeHAsO4 pFe(OH)3 pH3AsO4 pH 12.900 0 − FeAsO4 773.6 Welham 0 = 0 + 0 − pFeAsO4 pFe(OH)3 pH3AsO4 10.343 IRON(II) Fe2+ −78.87 Bard 2+ = 0 + + + − pFe pFe(OH)3 (pH pe) 2pH 22.951 FeOH+ −277.4 Bard + = 0 + + + − pFeOH pFe(OH)3 (pH pe) pH 16.180 0 − Fe(OH)2 441.0 Bard 0 = 0 + + − pFe(OH)2 pFe(OH)3 (pH pe) 3.290 − − Fe(OH)3 615.0 Bard − = 0 + + − + pFe(OH)3 pFe(OH)3 (pH pe) pH 7.779 2− − Fe(OH)4 769.9 Bard 2− = 0 + + − + pFe(OH)4 pFe(OH)3 (pH pe) 2pH 22.193 2+ − Fe2(OH)2 467.27 Bard 2+ = 0 + + + − pFe2(OH)2 pFe(OH)3 2(pH pe) 2pH 17.026 − − HFeO2 377.8 Bard − = 0 + + − + pHFeO2 pFe(OH)3 (pH pe) pH 7.783 2− − FeO2 455.2 Bard 2− = 0 + + − − pFeO2 pFe(OH)3 (pH pe) 2pH 5.778 FeCl+ −361.08 Weast + = 0 + 0 + + + − pFeCl pFe(OH)3 pHCl (pH pe) pH 25.949 0 − FeCl2 341.37 Bard 0 = 0 + 0 + + − pFeCl2 pFe(OH)3 2pHCl (pH pe) 28.947 0 − FeHPO4 1208.09 Lindsay 0 = 0 + 0 + + − pFeHPO4 pFe(OH)3 pH3PO4 (pH pe) 19.367 0 − FeSO4 823.49 Bard 0 = 0 0 − + + pFeSO4 pFe(OH)3 +pH2S 7(pH pe) 17.687 FeSH+ −120 Weast + = 0 + 0 + + + − pFeSH pFe(OH)3 pH2S (pH pe) pH 25.213 0 − Fe(SH)2 119.24 Naumov 0 = 0 + 0 + + − pFe(SH)2 pFe(OH)3 2pH2S (pH pe) 20.259 − − Fe(SH)3 118.83 Naumov − = 0 + 0 + + − − pFe(SH)3 pFe(OH)3 3pH2S (pH pe) pH 15.304 P1: GIM TJ1228-02 EST.cls September 1, 2004 19:29

Toxic Metals in the Environment 595

CADMIUM Cd2+ −77.86 Lindsay 2+ = 0 + − pCd pCd(OH)2 2pH 19.205 CdOH+ −257.4 Lindsay + = 0 + − pCdOH pCd(OH)2 pH 9.106 − − Cd(OH)3 601.0 Lindsay − = 0 − + pCd(OH)3 pCd(OH)2 pH 13.803 2− − Cd(OH)4 756.68 Lindsay 2− = 0 − + pCd(OH)4 pCd(OH)2 2pH 28.080 3− − Cd(OH)5 910.31 Lindsay 3− = 0 − + pCd(OH)5 pCd(OH)2 3pH 42.716 4− − Cd(OH)6 1062.57 Lindsay 4− = 0 − + pCd(OH)6 pCd(OH)2 4pH 57.594 3+ Cd2OH −356.39 Lindsay 3+ = 0 + − pCd2OH 2pCd(OH)2 3pH 32.013 4+ − Cd4(OH)4 1100.81 Lindsay 4+ = 0 + − pCd4(OH)4 4pCd(OH)2 4pH 48.901 0 − CdCO3 629.19 Lindsay 0 = 0 + 0 − pCdCO3 pCd(OH)2 pCO2 6.582 + − CdHCO3 676.72 Lindsay + = 0 + 0 + − pCdHCO3 pCd(OH)2 pCO2 pH 14.909 2+ − CdNH3 118.91 Lindsay 2+ = 0 + 0 + − pCdNH3 pCd(OH)2 pNH3 2pH 22.844 2+ − Cd(NH3)2 156.86 Lindsay 2+ = 0 + 0 + − pCd(NH3)2 pCd(OH)2 2pNH3 2pH 24.852 2+ − Cd(NH3)3 191.00 Lindsay 2+ = 0 + 0 + − pCd(NH3)3 pCd(OH)2 3pNH3 2pH 26.194 2+ − Cd(NH3)4 222.25 Lindsay 2+ = 0 + 0 + − pCd(NH3)4 pCd(OH)2 4pNH3 2pH 27.029 + − CdNO3 191.08 Lindsay + = 0 + 0 − + + + pCdNO3 pCd(OH)2 pNH3 8(pH pe) pH 89.169 0 − Cd(NO3)2 300.79 Lindsay 0 = 0 + 0 − + + pCd(NO3)2 pCd(OH)2 2pNH3 16(pH pe) 199.247 0 − CdHPO4 1192.4 Lindsay 0 = 0 + 0 − pCdHPO4 pCd(OH)2 pH3PO4 14.147 2− − CdP2O7 2040.6 Lindsay 2− = 0 + 0 − − pCdP2O7 pCd(OH)2 2pH3PO4 2pH 2.880 P1: GIM TJ1228-02 EST.cls September 1, 2004 19:29

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0 − CdSO4 836.38 Lindsay 0 = 0 + 0 − + + pCdSO4 pCd(OH)2 pH2S 8(pH pe) 17.911 CdCl+ −220.41 Lindsay + = 0 + 0 + − pCdCl pCd(OH)2 pHCl pH 25.270 0 − CdCl2 355.22 Lindsay 0 = 0 + 0 − pCdCl2 pCd(OH)2 2pHCl 28.891 − − CdCl3 485.34 Lindsay − = 0 + 0 − − pCdCl3 pCd(OH)2 3pHCl pH 31.691 2− − CdCl4 617.14 Lindsay 2− = 0 + 0 − − pCdCl4 pCd(OH)2 4pHCl 2pH 34.785 MERCURY Hg2+ +164.703 Bard, Lindsay pHg2+ = pHg0 − 2pe + 22.338 2+ + Hg2 153.607 Bard, Lindsay 2+ = 0 − + pHg2 2pHg 2pe 13.877 HgOH+ −52.01 Bard pHgOH+ = pHg0 − 2(pH + pe) + pH + 25.923 − − HHgO2 190.0 Bard − = 0 − + − + pHHgO2 pHg 2(pH pe) pH 43.301 − − Hg(OH)3 426.43 Lindsay − = − pHg(OH)3 pHHgO2 0 − Hg(OH)2 274.5 Bard 0 = 0 − + + pHg(OH)2 pHg 2(pH pe) 65.616 HgCl+ −5.0 Bard pHgCl+ = pHg0 + pHCl0 − 2(pH + pe) + pH + 12.604 0 − HgCl2 172.8 Bard 0 = 0 + 0 − + + pHgCl2 pHg 2pHCl 2(pH pe) 3.203 − − HgCl3 308.8 Bard − = 0 + 0 − + − − pHgCl3 pHg 3pHCl 2(pH pe) pH 0.627 2− − HgCl4 446.4 Bard 2− = 0 + 0 − + − − pHgCl4 pHg 4pHCl 2(pH pe) 2pH 4.737 HgClOH0 −222.17 Lindsay pHgClOH0 = pHg0 + pHCl0 − 2(pH + pe) + 16.109 HgI+ +40.2 Bard pHgI+ = pHg0 + pHI0 − 2(pH + pe) + pH − 0.025 0 − HgI2 74.9 Bard P1: GIM TJ1228-02 EST.cls September 1, 2004 19:29

Toxic Metals in the Environment 597

0 = 0 + 0 − + − pHgI2 pHg 2pHI 2(pH pe) 20.740 − − HgI3 148.1 Bard − = 0 + 0 − + − − pHgI3 pHg 3pHI 2(pH pe) pH 34.114 2− − HgI4 211.3 Bard 2− = 0 + 0 − + − − pHgI4 pHg 4pHI 2(pH pe) 2pH 45.737 HgIOH0 −173.22 Lindsay pHgIOH0 = pHg0 + pHI0 − 2(pH + pe) + 4.138 2− − Hg2P2O7 1820 Bard 2− = 0 + 0 − + − + pHg2P2O7 2pHg 2pH3PO4 2(pH pe) 2pH 29.395 3− Hg2OH(P2O7) −2012 Bard 3− = 0 + 0 − + − + pHg2OH(P2O7) 2pHg 2pH3PO4 2(pH pe) 3pH 37.310 4− − Hg2(OH)2P2O7 2197 Bard 4− = 0 + 0 − + − + pHg2(OH)2P2O7 2pHg 2pH3PO4 2(pH pe) 4pH 46.451 6− − Hg2(P2O7)2 3694 Bard 6− = 0 + 0 − + − + pHg2(P2O7)2 2pHg 4pH3PO4 2(pH pe) 6pH 62.293 0 − Hg(SH)2 26.53 Lindsay 0 = 0 + 0 − + − pHg(SH)2 pHg 2pH2S 2(pH pe) 1.399 2− + HgS2 45.27 Lindsay 2− = 0 + 0 − + − + pHgS2 pHg 2pH2S 2(pH pe) 2pH 11.179 0 − HgSO4 587.9 Bard 0 = 0 + 0 − + + pHgSO4 pHg pH2S 10(pH pe) 61.579 ALUMINUM Al3+ −458 Bard 3+ = 0 + − pAl pAl(OH)3 3pH 17.858 AlOH2+ −694.1 Bard 2+ = 0 + − pAlOH pAl(OH)3 2pH 12.939 AlO+ −654.2 Bard + = 0 + − pAlO pAl(OH)3 pH 5.949 + − Al(OH)2 699.44 Lindsay + = 0 + − pAl(OH)2 pAl(OH)3 pH 9.597 − − AlO2 823.4 Bard − = 0 − + pAlO2 pAl(OH)3 pH 5.961 − − Al(OH)4 1297.8 Bard − = 0 − + pAl(OH)4 pAl(OH)3 pH 5.953 2− − Al(OH)5 1481.39 Lindsay 2− = 0 − + pAl(OH)5 pAl(OH)3 2pH 15.341 4+ − Al2(OH)2 1412.27 Lindsay 4+ = 0 + − pAl2(OH)2 2pAl(OH)3 4pH 30.095 P1: GIM TJ1228-02 EST.cls September 1, 2004 19:29

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+ − AlSO4 1253.69 Lindsay + = 0 + 0 − + + + PAlSO4 pAl(OH)3 pH2S 8(pH pe) pH 18.570 − − Al(SO4)2 1990.83 Lindsay − = 0 + 0 − + − + pAl(SO4)2 pAl(OH)3 2pH2S 16(pH pe) pH 60.526 0 − Al2(SO4)3 3204.62 Lindsay 0 = 0 + 0 − + − pAl2(SO4)3 2pAl(OH)3 3pH2S 24(pH pe) 86.082

CARBON 0 − H2CO3 623.42 Bard 0 = 0 − pH2CO3 pCO2 0.007 − − HCO3 587.06 Bard − = 0 − + pHCO3 pCO2 pH 6.363 2− − CO3 527.90 Bard 2− = 0 − + pCO3 pCO2 2pH 16.727

SILICON − − H3SiO4 1223.4 Bard − = 0 − + pH3SiO4 pH4SiO4 pH 9.215 2− − H2SiO4 1152.7 Bard 2− = 0 − + pH2SiO4 pH4SiO4 2pH 21.602 3− − HSiO4 1120.7 Lindsay 3− = 0 − + pHSiO4 pH4SiO4 3pH 32.838 4− − SiO4 1046.0 Lindsay 4− = 0 − + pSiO4 pH4SiO4 4pH 45.938 − − HSiO3 955.46 Bard − = 0 − + pHSiO3 pH4SiO4 pH 20.241 2− − SiO3 887 Bard 2− = 0 − + pSiO3 pH4SiO4 2pH 32.234 2− − Si2O3(OH)4 2211.2 Bard 2− = 0 − + pSi2O3(OH)4 2pH4SiO4 2pH 18.154 2− − Si4O6(OH)6 4079.8 Bard 2− = 0 − + pSi4O6(OH)6 4pH4SiO4 2pH 13.225 4− − Si4O8(OH)4 3969.8 Bard 4− = 0 − + pSi4O8(OH)4 4pH4SiO4 4pH 32.497

LEAD Pb2+ −24.69 Lindsay 2+ = 0 + − pPb pPb(OH)2 2pH 17.749 P1: GIM TJ1228-02 EST.cls September 1, 2004 19:29

Toxic Metals in the Environment 599

PbOH+ −217.94 Lindsay + = 0 + − pPbOH pPb(OH)2 pH 10.005 − − Pb(OH)3 575.89 Lindsay − = 0 − + pPb(OH)3 pPb(OH)2 pH 10.341 2− − Pb(OH)4 748.02 Lindsay 2− = 0 − + pPb(OH)4 pPb(OH)2 2pH 21.737 3+ Pb2OH −250.04 Lindsay 3+ = 0 + − pPb2OH 2pPb(OH)2 3pH 29.361 2+ − Pb3(OH)4 886.42 Lindsay 2+ = 0 + − pPb3(OH)4 3pPb(OH)2 2pH 29.361 4+ − Pb4(OH)4 928.22 Lindsay 4+ = 0 + − pPb4(OH)4 4pPb(OH)2 4pH 50.108 4+ − Pb6(OH)8 1796.82 Lindsay 4+ = 0 + − pPb6(OH)8 6pPb(OH)2 4pH 62.921 0 − PbHPO4 1138.72 Lindsay 0 = 0 + 0 − pPbHPO4 pPb(OH)2 pH3PO4 11.504 + − PbH2PO4 1170.68 Lindsay + = 0 + 0 + − pPbH2PO4 pPb(OH)2 pH3PO4 pH 17.104 2− − PbP2O7 2002.25 Lindsay 2− = 0 + 0 − − pPbP2O7 pPb(OH)2 2pH3PO4 2pH 2.925 − PbPO4 Smith − = 0 + 0 − − pPbPO4 pPb(OH)2 pH3PO4 pH 5.152 4− Pb(PO4)2 Smith 4− = 0 + 0 − + pPb(PO4)2 pPb(OH)2 2pH3PO4 4pH 11.145 6− Pb(P2O7)2 Smith 6− = 0 + 0 − + pPb(P2O7)2 pPb(OH)2 4pH3PO4 6pH 26.119 2− Pb(HPO4)2 Smith 2− = 0 + 0 − − pPb(HPO4)2 pPb(OH)2 2pH3PO4 2pH 1.555 PbCl+ −165.06 Lindsay + = 0 + 0 + − pPbCl pPb(OH)2 pHCl pH 22.345 0 − PbCl2 297.36 Lindsay 0 = 0 + 0 − pPbCl2 pPb(OH)2 2pHCl 25.527 − − PbCl3 428.07 Lindsay − = 0 + 0 − − pPbCl3 pPb(OH)2 3pHCl pH 28.429 2− − PbCl4 557.60 Lindsay 2− = 0 + 0 − − pPbCl4 pPb(OH)2 4pHCl 2pH 31.127 0 − PbCO3 626.34 Weast 0 = 0 + 0 − pPbCO3 pPb(OH)2 pCO2 8.124 P1: GIM TJ1228-02 EST.cls September 1, 2004 19:29

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2− Pb(CO3)2 Smith 2− = 0 + 0 − + pPb(CO3)2 pPb(OH)2 2pCO2 2pH 5.357 0 − PbSO4 784.17 Lindsay 0 = 0 + 0 − + + pPbSO4 pPb(OH)2 pH2S 8(pH pe) 20.286 2− − Pb(SO4)2 1533.56 Lindsay 2− = 0 + 0 − + − + pPb(SO4)2 pPb(OH)2 2pH2S 16(pH pe) 2pH 60.088 2− − PbO3 272.7 Bard 2− = 0 − + − + pPbO3 pPb(OH)2 2(pH pe) 2pH 63.458 4− − PbO4 282.1 Bard 4− = 0 − + − + pPbO4 pPb(OH)2 2(pH pe) 4pH 103.363 NITROGEN + − NH4 79.45 Lindsay + = 0 + − pNH4 pNH3 pH 9.280 0 NH4OH −263.8 Lindsay, Bard 0 = 0 − pNH4OH pNH3 0.032 0 + N2H4 127.9 Lindsay 0 = 0 − + + pN2H4 2pNH3 2(pH pe) 31.689 + + N2H5 82.4 Lindsay, Bard + = 0 − + + + pN2H5 2pNH3 2(pH pe) pH 23.721 2+ + N2H6 94.14 Lindsay 2+ = 0 − + + + pN2H6 2pNH3 2(pH pe) 2pH 25.773 0 NH2OH −23.43 Lindsay 0 = 0 − + + pNH2OH pNH3 2(pH pe) 42.088 + − NH2OH2 56.65 Bard + = 0 − + + + pNH2OH2 pNH3 2(pH pe) pH 36.268 − + N3 348.3 Lindsay − = 0 − + − + pN3 3pNH3 8(pH pe) pH 74.944 0 N2O +101.0 Lindsay 0 = 0 − + + pN2O pNH3 8(pH pe) 68.535 0 + H2N2O2 36 Bard 0 = 0 − + + pH2N2O2 2pNH3 8(pH pe) 98.692 − HN2O2 Weast − = 0 − + − + pHN2O2 2pNH3 8(pH pe) pH 107.277 2− + N2O2 139 Bard 2− = 0 − + − + pN2O2 2pNH3 8(pH pe) 2pH 116.692 − + NH2O2 76.1 Bard − = 0 − + − + pNH2O2 pNH3 4(pH pe) pH 101.078 P1: GIM TJ1228-02 EST.cls September 1, 2004 19:29

Toxic Metals in the Environment 601

NO0 +102.1 Lindsay 0 = 0 − + + pNO pNH3 5(pH pe) 64.086 0 − HNO2 55.7 Lindsay 0 = 0 − + + pHNO2 pNH3 6(pH pe) 77.981 − − NO2 37.7 Lindsay − = 0 − + − + pNO2 pNH3 6(pH pe) pH 81.133 − − NO3 111.46 Lindsay − = 0 − + − + pNO3 pNH3 8(pH pe) pH 109.770

PHOSPHORUS − − H2PO4 1137.4 Lindsay − = 0 − + pH2PO4 pH3PO4 pH 2.148 2− − HPO4 1096.3 Lindsay 2− = 0 − + pHPO4 pH3PO4 2pH 9.346 3− − PO4 1025.8 Lindsay 3− = 0 − + pPO4 pH3PO4 3pH 21.697 0 − H4P2O7 2022.6 Lindsay 0 = 0 + pH4P2O7 2pH3PO4 6.929 − − H3P2O7 2018.1 Lindsay − = 0 − + pH3P2O7 2pH3PO4 pH 7.728 2− − H2P2O7 2005.1 Lindsay 2− = 0 − + pH2P2O7 2pH3PO4 2pH 10.008 3− − HP2O7 1966.8 Lindsay 3− = 0 − + pHP2O7 2pH3PO4 3pH 16.707 4− − P2O7 1913.1 Lindsay 4− = 0 − + pP2O7 2pH3PO4 4pH 26.119 0 − H3PO3 846.8 Lindsay 0 = 0 + + + pH3PO3 pH3PO4 2(pH pe) 11.518 − − H2PO3 838.2 Lindsay − = 0 + + − + pH2PO3 pH3PO4 2(pH pe) pH 13.021 2− − HPO3 799.4 Lindsay 2− = 0 + + − + pHPO3 pH3PO4 2(pH pe) 2pH 19.809 0 + PH3 9.0 Lindsay 0 = 0 + + + pPH3 pH3PO4 8(pH pe) 36.785

ARSENIC − − H2AsO4 753.3 Welham − = 0 − + pH2AsO4 pH3AsO4 pH 2.243 P1: GIM TJ1228-02 EST.cls September 1, 2004 19:29

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2− − HAsO4 714.7 Welham 2− = 0 − + pHAsO4 pH3AsO4 2pH 9.005 3− − AsO4 648.5 Welham 3− = 0 − + pAsO4 pH3AsO4 3pH 20.603 0 − HAsO2 402.7 Welham 0 = 0 + + − pHAsO2 pH3AsO4 2(pH pe) 19.439 − − AsO2 350.0 Welham − = 0 + + − − pAsO2 pH3AsO4 2(pH pe) pH 10.206 0 − H3AsO3 639.9 Welham 0 = 0 + + − pH3AsO3 pH3AsO4 2(pH pe) 19.443 − − H2AsO3 587.2 Welham − = 0 + + − − pH2AsO3 pH3AsO4 2(pH pe) pH 10.210 2− − HAsO3 524.3 Welham 2− = 0 + + − + pHAsO3 pH3AsO4 2(pH pe) 2pH 0.810 AsO+ −163.8 Welham + = 0 + + + − pAsO pH3AsO4 2(pH pe) pH 19.137 AsS+ −70.3 Welham + = 0 + 0 + + + − pAsS pH3AsO4 pH2S 2(pH pe) pH 19.0 0 − HAsS2 48.58 Welham 0 = 0 + 0 + + − pHAsS2 pH3AsO4 pH2S 2(pH pe) 30.724 − − AsS2 27.4 Welham − = 0 + 0 + + − − pAsS2 pH3AsO4 pH2S 2(pH pe) pH 27.014 3− − As3S6 252.38 Itagaki 3− = 0 + 0 + + − − pAs3S6 3pH3AsO4 6pH2S 6(pH pe) 3pH 110.861 SULFUR HS− +12.05 Bard − 0 pHS = pH2S − pH + 6.994 S2− +86.31 Bard 2− 0 pS = pH2S − 2pH + 20.004 2− + S2 79.5 Bard 2− = 0 − + − + pS2 2pH2S 2(pH pe) 2pH 23.693 2− + S3 73.6 Bard 2− = 0 − + − + pS3 3pH2S 4(pH pe) 2pH 27.543 2− + S4 69.0 Bard 2− = 0 − + − + pS4 4pH2S 6(pH pe) 2pH 31.619 2− + S5 65.7 Bard 2− = 0 − + − + pS5 pH2S 8(pH pe) 2pH 35.924 0 − H2S2O3 529.1 Lindsay 0 = 0 − + + pH2S2O3 2pH2S 8(pH pe) 41.749 P1: GIM TJ1228-02 EST.cls September 1, 2004 19:29

Toxic Metals in the Environment 603

− − HS2O3 525.6 Lindsay − = 0 − + − + pHS2O3 2pH2S 8(pH pe) pH 42.350 2− − S2O3 518.8 Lindsay 2− = 0 − + − + pS2O3 2pH2S 8(pH pe) 2pH 43.532 2− − S5O6 956.0 Bard 2− = 0 − + − + pS5O6 5pH2S 20(pH pe) 2pH 105.908 2− − S4O6 1022.2 Bard 2− = 0 − + − + pS4O6 4pH2S 18(pH pe) 2pH 86.577 0 − H2S2O4 616.7 Bard 0 = 0 − + + pH2S2O4 2pH2S 10(pH pe) 67.944 − − HS2O4 614.6 Bard, Lindsay − = 0 − + − + pHS2O4 2pH2S 10(pH pe) pH 68.310 2− − S2O4 600.4 Bard, Lindsay 2− = 0 − + − + pS2O4 2pH2S 10(pH pe) 2pH 70.803 2− − S3O6 958 Bard 2− = 0 − + − + pS3O6 3pH2S 16(pH pe) 2pH 96.125 0 − SO2 300.708 Bard 0 = 0 − + + pSO2 pH2S 6(pH pe) 35.233 0 − H2SO3 537.90 Bard 0 = 0 − + + pH2SO3 pH2S 6(pH pe) 35.304 − − HSO3 527.81 Bard − = 0 − + − + pHSO3 pH2S 6(pH pe) pH 37.092 2− SO3 −486.6 Bard 2− 0 pSO3 = pH2S − 6(pH + pe) − 2pH + 44.298 2− − S2O5 791 Bard 2− = 0 − + − + pS2O5 2pH2S 12(pH pe) 2pH 79.003 2− − S2O6 966 Bard 2− = 0 − + − + pS2O6 2pH2S 14(pH pe) 2pH 89.768 2− − S2O8 1110.4 Bard 2− = 0 − + − + pS2O8 2pH2S 18(pH pe) 2pH 146.849 − − HSO4 756.01 Bard − = 0 − + − + pHSO4 pH2S 8(pH pe) pH 38.695 2− − SO4 744.63 Bard 2− = 0 − + − + pSO4 pH2S 8(pH pe) 2pH 40.674

CHLORINE Cl− −131.26 Lindsay pCl− = pHCl0 − pH − 3.00 P1: GIM TJ1228-02 EST.cls September 1, 2004 19:29

604 S. K. Porter et al.

IODINE 0 + I2 16.43 Bard 0 = 0 − + + pI2 2pHI 2(pH pe) 1.778 I− −51.67 Bard pI− = pHI0 − pH − 9.602 − − I3 51.50 Bard − = 0 − + − − pI3 3pHI 2(pH pe) pH 10.673 HIO0 −98.67 Bard pHIO0 = pHI0 − 2(pH + pe) + 23.716 IO− −37.96 Bard pIO− = pHI0 − 2(pH + pe) − pH + 34.352 + I ·H2O −89.99 Bard + 0 pI ·H2O = pHI − 2(pH + pe) + pH + 25.237 ICl0 −14.85 Bard pICl0 = pHI0 − 2(pH + pe) + 16.845 − − pICl2 158.70 Bard − = 0 − + − + pICl2 pHI 2(pH pe) pH 11.640 0 − HIO3 139.94 Bard 0 = 0 − + + pHIO3 pHI 6(pH pe) 99.696 − − IO3 134.94 Bard − = 0 − + − + pIO3 pHI 6(pH pe) pH 100.467 − − IO4 53.14 Bard − = 0 − + − + pIO4 pHI 8(pH pe) pH 156.350 0 − H5IO6 537.14 Bard 0 = 0 − + + pH5IO6 pHI 8(pH pe) 154.661 − − H4IO6 518.35 Bard − = 0 − + − + pH4IO6 pHI 8(pH pe) pH 157.953 2− − H3IO6 480.11 Bard 2− = 0 − + − + pH3IO6 pHI 8(pH pe) 2pH 164.652 3− − H2IO6 410.47 Bard 3− = 0 − + − + pH2IO6 pHI 8(pH pe) 3pH 176.853