COMPUTATION OF AQUEOUS METAL SOLUBILITIES USING SPREADSHEET PROGRAMS David A. Vaccari, Ph.D., P.E. Dept. of Civil, Environmental and Ocean Engineering Stevens Institute of Technology Hoboken, NJ 07030 June 1992 NOTE: This disk contains software which is given free for copying, provided that the file METALS.TXT is included with each copy, and that the author's name and references not be removed from these versions nor from any versions derived from them. No warranty is expressed or implied as to the accuracy of the software. It is up to each user to validate the results obtained with these programs. AQUEOUS METAL SOLUBILITY SPREADSHEETS This disk contains software for computing the aqueous solubilities of several metals, as well as other water quality parameters such as Langelier stability index, hardness, and carbonate system concentrations. They require LOTUS 123 software or equivalent to run. The disk should have the following files on it: METALS.TXT This file LEAD.WK1 Spreadsheet program for lead solubility COPPER.WK1 Copper solubility spreadsheet program IRON.WK1 Ferrous and ferric iron solubility program HARDNESS.WK1 Computes solubility of calcium and magnesium; and hardness and Langelier Stability index The calculation of lead solubility is described in some detail. Calculations for the other metals are similar, and so are more briefly described. Lead Solubility Oxidized lead is present in water in the +2 valence state. This is capable of forming precipitates of lead hydroxide, Pb(OH)2, lead carbonate, PbCO3 (cerrusite), or basic lead carbonate, Pb3(OH)2(CO3)2 (hydrocerrusite). The solubility of each of these phases must be computed separately. The solid which produces the lowest solubility under given conditions will be the only stable solid phase in that instance. The conditions which define the system are, fundamentally, the concentrations of the counterions in solution -- hydroxide and carbonate -- and the ionic strength, which affects the activity coefficients of the ions. These can be related to more directly measured parameters: pH, alkalinity, and total dissolved solids. When one of the lead salts dissolves, it releases Pb++ ions. That concentration can be computed using the solubility product constant, Ksp. The Ksp values for lead hydroxide, lead carbonate, and basic lead carbonate used in this study are 2.95e- 7, 9.38e-10, and 8.48e-11, respectively. All equilibrium constants for lead used in this study are from Schock and Gardels [1983]. The Pb++ ions also enter into equilibrium reactions with hydroxide and carbonate ions in solution to form a number of stable complex ions. Table 1 gives the complex ions used in the solubility calculations here. TABLE 1. Soluble lead complexes and formation constants [Schock & Gardels, 1983]. PbOH+ 5.89e6 Pb(OH)2 1.17e11 Pb(OH)3+ 7.94e13 Pb2OH+++ 4.27e7 Pb3(OH)4++ 1.26e32 Pb4(OH)4++++ 1.23e35 Pb6(OH)8++++ 2.04e68 PbCO3 1.26e7 Pb(CO3)2-- 2.14e10 The equilibrium for the reaction of each of these species with Pb++ can be expressed by an equilibrium constant called the formation constant (beta). The formation constants can be computed from the standard free energy of formation of each species. Solubilities of Copper, Iron, Calcium and Magnesium Similar relationships can be given for other metals, such as copper [Patterson] and iron, calcium and magnesium [Snoeyink and Jenkins]. Spreadsheet programs for computing their solubilities are also given. The calculations for copper also include complex ion formation with carbonate as a ligand. However, the references used did not propose any stable carbonate complexes for ferric iron. Therefore, while pH has a strong effect on solubility of all the metals, alkalinity would be expected to affect lead and copper, but not ferric iron. The IRON.WK1 spreadsheet computes the solubility for both ferrous (Fe(II)) and ferric (Fe(III)) iron separately. It does not compute the oxidation/reduction equilibrium between the two iron species. The HARDNESS.WK1 spreadsheet performs other calculations besides solubility of calcium and magnesium. When measured concentrations are entered for calcium and magnesium in cells B12 and B13, the program computes the total hardness (cell B14), the pH of saturation (pHs) (cell D16) and the Langelier Stability Index (cell D18). Also, this program is different from the other metals solubility spreadsheets in that several of the equilibrium constants are computed as functions of temperature, which is entered in cell B11. The temperature-dependent constants are the calcite solubility product (cell B22), and the pK1 and pK2 of the carbonate system (cells D38 and D39, respectively). The temperature dependency for the solubility product was obtained directly from Stumm & Morgan; the relation for pK1 and pK2 was obtained by regression of data in Tables 4.8 and 4.9 of Stumm & Morgan. Note that this results in the alpha values varying with temperature, which may result in alkalinity relationships which are slightly different than those obtained with the other programs. The possiblity of a dolomite solid phase is not considered in calculation of calcium or magnesium solubility. Use of LOTUS Programs to Compute Metal Solubilities The solubility calculations for lead, copper, iron, and hardness (calcium and magnesium) have been incorporated into several LOTUS programs which are included. The first program is LEAD.WK1. Use of the program is described here, and assumes basic familiarity with the use of the LOTUS spreadsheet program. The programs COPPER.WK1 and IRON.WK1 are also included for computation of the solubilities of copper and iron, respectively. The operation of these programs is similar to LEAD.WK1. The program for iron computes the solubilities of both ferrous (II) and ferric (III) iron. The file HARDNESS.WK1 is a LOTUS 123 program to compute the solubility of calcium and magnesium, and the Langelier Stability Index (LSI). The operation of this program is similar to LEAD.WK1, except as follows: Temperature values can be input and will influence the calcite solubility product [Stumm & Morgan]. Measured values for calcium and magnesium can be input; these are used to compute total hardness as calcium carbonate, and the measured calcium concentration is used to compute the pH of saturation and the LSI. After LOTUS 123 is run, LEAD.WK1 is loaded using the /File- Retrieve command. Only three inputs are required. They are the pH in cell B9 (see Table 2), the alkalinity in milligrams per liter as calcium carbonate in cell B10, and the total dissolved solids in cell B11. The lead solubility under those conditions is automatically computed, with the result appearing in cell B13, in units of micrograms per liter. Also displayed are the activities of hydrogen, hydroxyl, carbonate, and bicarbonate ions, the concentration (moles per liter) of undissociated H2CO3 (including free CO2), the total inorganic carbon concentration, CT (moles per liter), and the acidity, as mg calcium carbonate per liter. The values for species enclosed by parentheses are the activities, whereas the species enclosed by square brackets are given in molar concentrations. The program is useful for examining the relationships among these variables, as well as for solubility computations. Rows 23 to 45 contain intermediate values used in the computation, including the Ksp values, formation constants, and concentrations of each complex ion assuming each of the possible solid phases. The lead solubility displayed is the lowest solubility produced by any of the three solids: fresh lead hydroxide, lead carbonate, or basic lead carbonate. The solubility of aged lead hydroxide is computed, but not used in the calculation. It is interesting that to compute lead solubility from only three independent variables, over 50 intermediate values are required. Also included are the activity coefficients (gammas), the alpha values (which give the fraction of total inorganic carbon (CT) composed of each of the forms of carbonate in solution), and the ionic strength. This last value is estimated from the total dissolved solids input at the top of the spreadsheet, but the user can enter it directly if the /Worksheet-Global-Protection- Disable command is first used. A TDS value of 400 mg/L corresponds to an ionic strength of 0.010. The ionic strength is then used via the Davies equation to compute the activity coefficients of the ions [Snoeyink & Jenkins]. It can be seen by experimentation that TDS has a significant effect on lead solubility. REFERENCES Patterson, J., "Effect of Carbonate Ion on Precipitation Treatment of Cadmium, Copper, Lead, and Zinc", 30th Purdue Ind. Waste Conf. May 1975. Schock, M.R. "Response of Lead Solubility to Dissolved Carbonate in Drinking Water", JAWWA, 72, 12, 695 (Dec 1980). Schock, M.R. and M.C. Gardels, "Plumbosolvency reduction by high pH and low carbonate -- solubility relationships", JAWWA (February 1983). "Aquatic Chemistry", W. Stumm and J. J. Morgan, Wiley (1981). Snoeyink, V.L., and D. Jenkins, "Water Chemistry", John Wiley & Sons (1980). TABLE 2. Spreadsheet program for computing lead solubility. CALCULATION OF LEAD SOLUBILITY (based on Schock, JAWWA, 75(2), 1987) David A. Vaccari, Ph.D., P.E. Dept. of Civil, Environmental, and Coastal Engg. Stevens Institute of Technology Hoboken, NJ 07030 June 1991 ---------------------------------------------------------------------------- pH (units) 8.5 Alk (mg CaCO3/L) 150.0 TDS (mg/L) 500 Pb (ug/L): 104.87 Acidity (mgCaCO3/L) 295.1 (H+) 3.16E-09 (OH-) 3.16E-06 (CO3=) 2.73E-05 (HCO3-) 2.60E-03 [H2CO3*] 2.06E-05 [CT] 2.97E-03 SPECIES Fresh Aged Carbonate Basic Beta [Pb++] 1.85E-04 2.23E-09 4.48E-09 2.06E-09 [PbOH+] 2.45E-03 2.95E-08 5.93E-08 2.72E-08 5.89E+06 [Pb(OH)2] 1.36E-04 1.64E-09 3.29E-09 1.51E-09 1.17E+11 [Pb(OH)3-] 3.31E-07 3.98E-12 8.00E-12 3.67E-12 7.94E+13 [Pb2OH+++] 5.18E-06 7.49E-16 3.03E-15 6.39E-16 4.27E+07 [Pb3(OH)4++] 3.22E-02 5.59E-17 4.55E-16 4.41E-17 1.26E+32 [Pb4(OH)4++++] 1.45E-02 3.02E-22 4.94E-21 2.20E-22 1.23E+35 [Pb6(OH)8++++] 3.31E+01 1.00E-28 6.63E-27 6.23E-29 2.04E+68 [PbCO3] 3.98E-02 4.79E-07 9.63E-07 4.42E-07 1.26E+07 [Pb(CO3)2--] 2.95E-03 3.55E-08 7.14E-08 3.28E-08 2.14E+10 log[Pb total] 2.30 -6.26 -5.96 -6.30 Pb (mg/l) *********** 0.113 0.228 0.105 I min calc'd 265.07738 0.00151 0.00151 0.00151 (Pb++) 1.17E-04 1.41E-09 2.84E-09 1.31E-09 Gamma 0 1.014 Alpha 0 0.0069 Gamma 1 0.893 Alpha 1 0.9786 Gamma 2 0.635 Alpha 2 0.0145 Gamma 3 0.359 1 Gamma 4 0.162 I 0.01250 Davies -0.049