WATER CHEMISTRY AQUATIC CHEMICAL EQUILIBRIA [OH––Alk] [Acy] In this section a few example will be given that demonstrate how elementary principles of physical chemistry can aid in the recognition of interrelated variables that establish the composition of natural waters Natural water systems usually consist of numerous mineral assemblages and often of a gas phase in addition to the aqueous phase; they nearly always include a portion of the biosphere Hence, natural aquatic habitats are characterized by a complexity seldom encountered in the laboratory In order to distill the pertinent variables out of a bewildering number of possible ones, it is advantageous to compare the real systems with their idealized counterparts Thermodynamic equilibrium concepts represent the most expedient means of identifying the variables relevant in determining the mineral relationships and in establishing chemical boundaries of aquatic environments Since minimum free energy describes the thermodynamically stable state of a system, a comparison with the actual free energy can characterize the direction and extent of processes that are approaching equilibrium Discrepancies between equilibrium calculations and the available data of real systems give valuable insight into those cases where chemical reactions are not understood sufficiently, where non-equilibrium conditions prevail, or where the analytical data are not sufficiently accurate or specific [CO2–Acy] [CO32––Alk] pH [H+–Acy] [Alk] x y z Addition of Acid Addition of Base FIGURE Alkalinity and acidity titration curve for the aqueous carbonate system The conservative quantities alkalinity and acidity refer to the acid neutralizing and base neutralizing capacities of a given aqueous system These parameters can be determined by titration to appropriate equivalence points with strong acid and strong base The equations given below define the various capacity factors rigorously Figure from Stumm, W and J Morgan, Aquatic Chemistry, Wiley-Interscience, New York, 1970, p 130 The following equations define for aqueous carbonate systems the three relevant capacity factors: Alkalinity (Alk), Acidity (Acy), and total dissolved carbonate species (CT):† Alkalinity and Acidity for Aqueous Carbonate Systems [ Alk ] ϭ ⎡HCO3− ⎤ ϩ ⎡CO32Ϫ ⎤ ϩ ⎡OHϪ ⎤ Ϫ ⎡Hϩ ⎤ ⎣ ⎦ ⎣ ⎦ ⎣ ⎦ ⎣ ⎦ Alkalinity and acidity are defined, respectively, as the equivalent sum of the bases that are titratable with strong acid and the equivalent sum of the acids that are titratable with strong base; they are therefore capacity factors which represent, respectively, the acid and base neutralizing capacities of an aqueous system Operationally, alkalinity and acidity are determined by acidimetric and alkalimetric titrations to appropriate pH end points These ends points (equivalence points) occur at the infection points of titration curves as shown in Figure for the carbonate system The atmosphere contains CO2 at a partial pressure of 2Ϫ ϫ 10Ϫ4 atmosphere, while CO2, H2CO3, HCOϪ and CO3 are important solutes in the hydrosphere Indeed, the carbonate system is responsible for much of the pH regulation in natural waters (1) [ Acy ] ϭ [H2 CO3 *]ϩ ⎡HCOϪ ⎤ ϩ ⎡Hϩ ⎤ Ϫ ⎡OHϪ ⎤ ⎦ ⎣ ⎣ ⎦ ⎣ ⎦ (2) C b ϭ [ H CO3 *]ϩ ⎡HCOϪ ⎤ ϩ ⎡CO3Ϫ ⎤ ⎦ ⎣ ⎣ ⎦ (3) where [H2CO3*] ϭ [CO2(aq)] ϩ [H2CO3] These equations are of analytical value because they represent rigorous conceptual definitions of the acid neutralizing and the base neutralizing capacities of carbonate systems The definitions of alkalinity and acidity algebraically † Brackets of the form [ ] refer to concentration, e.g., in moles per liter 1256 © 2006 by Taylor & Francis Group, LLC C023_002_r03.indd 1256 11/18/2005 1:32:06 PM WATER CHEMISTRY express the net proton deficiency and net proton excess of the systems with repect to specific proton reference levels (equivalance points) The definitions can be readily amplified to account for the presence of buffering components other than carbonates For example, in the presence of borate and ammonia the definition for alkalinity becomes [ Alk ] ϭ ⎡HCOϪ ⎤ ϩ ⎡CO32Ϫ ⎤ ϩ ⎡ B(OH)Ϫ ⎤ ⎦ ⎦ ⎣ ⎣ ⎦ ⎣ Ϫ ϩ ϩ[ NH ]ϩ ⎡OH ⎤ Ϫ ⎡H ⎦ ⎣ ⎦ ⎣ ⎤ Dissolved Carbonate Equilibria Two systems may be considered: (1) a system closed to the atmosphere and (2) one that is in equilibrium with the atmosphere Closed Systems In this case H2CO3* is considered a non2Ϫ volatile acid The species H2CO3*, HCO3, CO3 and are interrelated by the equilibria:† [Hϩ ][HCOϪ ]ր[H CO3 *] ϭ K1 (4) Although individual concentrations or activities, such as [H2CO3*] and pH, are dependent on pressure and temperature, [Alk], [Acy], and CT are conservative properties that are pressure and temperature independent (Alkalinity, acidity, and CT must be expressed in terms of concentration, e.g., as molarity, molality, equivalents per liter or parts per million as CaCO3) Note that 1meq/l 50 ppm as CaCO3 The use of these conservative parameters facilitates the calculation of the effects of the addition or removal of acids, bases, carbon dioxide, bicarbonates, and carbonates to aqueous systems As shown in Figure 2, each of these conservative quantities remains constant for particular changes in the chemical composition The case of the addition or removal of dissolved carbon dioxide is of special interest Respiratory activities of aquatic biota contribute carbon dioxide to the water whereas photosynthetic activities decrease the concentration of this weak acid An increase in carbon dioxide increases both the acidity of the system and CT, the total concentration of dissolved carbonic species, and it decreases the pH, but it does not affect the alkalinity Alternatively, acidity remains unaffected by the addition or removal of CaCO3(s) or Na2CO3(s) CT , on the other hand, remains unchanged in a closed system upon addition of strong acid or strong base For practical purposes, systems may be considered closed if they are shielded from the atmosphere and lithosphere or exposed to them only for short enough periods to preclude significant dissolution of CO2 or solid carbonates Dissolution of Carbon Dioxide Though much of the CO2 which dissolves in solution may ion2Ϫ ize to form HCOϪ CO3 , depending upon the pH, only a small fraction (0.3% at 25ЊC) is hydrated as H2CO3 Hence, the concentration of the unhydrated dissolved carbon dioxide, CO2(aq), is nearly identical to the analytically determinable concentration of H2CO3* ( ϭ [CO2(aq)] ϩ [(H2CO3]) The equilibrium of a constituent between a gas phase and a solution phase can be characterized by a mass law relationship Table gives the various expressions and their interrelations for the characterization of the CO2 dissolution equilibrium A water that is in equilibrium with the atmosphere (Pco2 ϭ 10Ϫ3.5 atm) contains at 25ЊC approximately 0.44 milligram per liter (10Ϫ5 M) of CO2; KH (Henry’s Law constant) at 25ЊC is 10Ϫ1.5 mole per liter-atm 1257 [Hϩ][CO3Ϫ ]ր[HCOϪ ] ϭ K where K1 and K2 represent the equilibrium constants (acidity constants) The ionization fractions, whose sum equals unity (see Eq (3)), can be defined as follows: a0 ϭ [H CO3 *]րCT (7) Ϫ a1 ϭ [HCO ]CT (8) (9) a2 ϭ [CO3Ϫ ]րCT From Eqs (3) to (9) the ionization fractions can be expressed in terms of [Hϩ] and the equilibrium constants: a0 ϭ (1ϩ K1 ր[Hϩ ]ϩ K1 K ր[Hϩ ]2 )Ϫ1 ϩ ϩ Ϫ1 a1 ϭ ([H ]րK1 ϩ1ϩ K ր[H ]) ϩ ϩ (10) (11) Ϫ1 a2 ϭ ([H ] րK1 K ϩ[H ]րK ϩ1] (12) Values for K1 and K2 are given in Tables 2A and 2B Because HCOϪ and CO2Ϫ may form complexes with other ions in 3 the systems (e.g., in sea water, MgCO3, NaCOϪ, CaCO,3 MgHCOϩ, it is operationally convenient to define a total concentration of the species to include an unknown number of these complexes For example, 2 [CO3Ϫ ] ϭ [CO3Ϫ ]ϩ[ MgCO3 ] T T ϩ[CaCO3 ]ϩ[ NaCOϪ ]ϩ⌳ (13) The distribution of carbonate species in sea water as a function of pH is given in Figure Systems Open to the Atmosphere A very elementary model showing some of the characteristics of the carbonate system in natural waters is provided by equilibrating pure water with a gas phase (e.g., the atmosphere) containing CO2 at a constant partial pressure Such a solution will remain in † To facilitate calculations the equilibria are written here in terms of concentration quotients The activity corrections can be considered incorporated into the equilibrium “constants” which therefore vary with the particular solution Such constants for given media of constant ionic strength, as well as the true thermodynamic constants, are listed in Tables 2A and 2B © 2006 by Taylor & Francis Group, LLC C023_002_r03.indd 1257 11/18/2005 1:32:07 PM WATER CHEMISTRY 5 9 8 Alkalinity (milliequivalents/liter) 9 9 11 11 11 10 10 10 10 0.5 10 0.4 10 0.1 11 11 11 1258 6.7 6.6 6.5 6.4 6.3 6.2 6.1 6.0 5.9 5.8 5.7 –0.5 5.6 5.5 5.3 5.1 5.4 5.2 5.0 4.5 4.0 3.9 3.8 3.7 3.6 3.5 3.4 CT(Total Carbonate carbon; millimoles/liter) CB CO2 CaCO3 Na2CO3 NaHCO3 CA Dilution 1 FIGURE Closed system capacity diagram: pH contours for alkalinity versus CT (total carbonate carbon) The point defining the solution composition moves as a vector in the diagram as a result of the addition (or removal) of CO2, NaHCO3, and CaCO3 (Na2CO3) or CB (strong base) and C (strong acid) (After K.S Deffeyes, Limnol., Oceanog., 10, 412, 1965.) Figure from Stumm, W and J Morgan, Aquatic Chemistry, WileyInterscience, New York, 1970, p 133 equilibrium with pco, despite any variation of pH by the addition of strong base or strong acid This simple model has its counterpart in nature when CO2 reacts with bases of rocks, for example with clays and silicates Figure shows the distribution of the solute species of such a model A partial pressure of CO2 equivalent to that in the atmosphere and equilibrium constants valid at 25ЊC have been assumed The equilibrium concentrations of the individual carbonate species can be expressed as a function of and [Hϩ]2 From Henry’s Law, [H CO3 *] ϭ K H pCO2 , (14) and Eqs (5) to (9), one obtains CT ϭ [HCOϪ ] ϭ K H pCO2 a0 K1 a1 K H pCO2 ϭ ϩ K H pCO2 a0 [H ] (15) (16) © 2006 by Taylor & Francis Group, LLC C023_002_r03.indd 1258 11/18/2005 1:32:07 PM WATER CHEMISTRY 1259 TABLE Solubility of gases Examplea: CO2(g) CO2(aq) Assumptions: Gas behaves ideally; [CO2(aq)] ϭ [H2CO3*] I Expressions for Solubility Equilibriumb (1) Distribution (mass law) constant, KD: KD ϭ [CO2(aq)]/[CO2(g)] (dimensionless) (2) (1) Henry’s law constant, KH: In (1), [CO2(g)] can be expressed by Dalton’s law of partial pressure: [CO2(g)] ϭ pCO2/RT (2) Combination of (1) and (2) gives [CO2 (aq)] ϭ (KD/RT)pCO2 ϭ KH pCO2, (3) where KH ϭ KD/RT (mole liter atm ) (3) –1 Bunsen absorption coefficient, aB: [CO2(aq)] ϭ (␣B/22.414)pCO2 (4) where 22.414 ϭ RT/p (liter mole–1) and aB ϭ KH ϫ 22.414 (atm–1) (5) Partial Pressure and Gas Composition pCO2 ϭ xCO2 (PT – w) (6) where XCO2 ϭ mole fraction or volume fraction in dry gas, PT ϭ total pressure and w ϭ water vapor pressure Values of Henry’s Law Constants at 25ЊC KH(mole liter–1 atm–1) Gas Carbon Dioxide CO2 33.8 ϫ 10–3 Methane CH4 1.34 ϫ 10–3 Nitrogen N2 – 0.642 ϫ 10–3 Oxygen O2 1.27 ϫ 10–3 a Same types of expressions apply to other gases The equilibrium constants defined by (1)–(4) are actually constants only if the equilibrium expressions are formulated in terms of activities and fugacities Table from Stumm, W and J Morgan, Aquatic Chemistry, Wiley-Interscience, New York, 1970, p 125 b and [CO3Ϫ ] ϭ a2 KK K H PCO2 ϭ 1ϩ K H pCO2 a0 [H ]2 (17) It follows from these equations that in a logarithmic concentration—pH diagram (Figure 4) the lines of H2CO3*, 2Ϫ HCO3 , CO3 have slopes of 0, ϩ1, and ϩ2, respectively If we equilibrate pure water with CO2, the system is defined by two independent variables, for example, temperature and Pco2, In other words, the equilibrium concentrations of all solute components can be calculated by means of Henry’s Law, the acidity constants and the proton condition or charge balance if, in addition to temperature, one variable, such as Pco2, [H2CO3*] or [Hϩ], is known or measured Use of the proton condition instead of the charge balance generally facilitates calculations because species irrelevant to the calculation need not be considered The proton condition merely expressed the equality between the proton excess and the proton deficiency of the various species with respect to a convenient proton reference level Figure furnishes a graphic illustration of its use Solubility Equilibria Minerals dissolve in or react with water Under different physico-chemical conditions minerals are precipitated and accumulate on the ocean floor and in the sediments of rivers and lakes Dissolution and precipitation reactions impart to the water and remove from it constituents which modify its chemical properties © 2006 by Taylor & Francis Group, LLC C023_002_r03.indd 1259 11/18/2005 1:32:07 PM 1260 WATER CHEMISTRY TABLE 2A Equilibrium constant for CO2 solubility Equilibrium: CO2(g) ϩ aq ϭ H2CO3 Henry’s law constant: K ϭ [H2CO3]/pCO2(M.atm–1) Temp., ЊC →0 Medium, M NaClO4 Seawater, 19% C1– –log K –logcK –log cK 1.11a — 1.19a 1.19a — 1.27a 10 1.27a — 1.34a 15 1.32a — 1.41a 20 1.41a — 25 1.47 a 1.51 1.53a 1.53 a — 1.58a 30 1.47a c c 35 — 1.59 — 40 1.64b — — 50 1.72b — — a Values based on data taken from Bohr and evaluated by K Buch, Meeresforschung, 1951 b A.J Ellis, Amer J Sci., 257, 217 (1959) c G Nilsson, T Rengemo, and L G Sillen, Acta Chem Sand., 12, 878 (1958) Ref.: Stumm, W and J Morgan, Aquatic Chemistry, Wiley-Interscience, New York, 1970, p 148 It is difficult to generalize about rates of precipitation and dissolution other than to recognize that they are usually slower than reactions between dissolved species Data concerning most geochemically important solid-solution reactions are lacking, so that kinetic factors cannot be assessed easily Frequently the solid phase initially formed is metastable with respect to a thermodynamically more stable solid phase Relevant examples of such metastability are the formation of aragonite under certain conditions instead of calcite, the more stable form of calcium carbonate, and the over-saturation of quartz in most natural waters This over-saturation persists due to the extremely slow establishment of equilibrium between silicic acid and quartz The solubilities of most inorganic salts increase with increasing temperature However, a number of compounds of interest in natural waters (e.g CaCO3, CaSO4) decrease in solubility with increasing temperature The dependence of solubility on pressure is very slight but must be considered for the extreme pressures encountered at ocean depths For example, the solubility product of CaCO3 will increase by approximately 0.2 logarithmic units for a pressure of 200 atmospheres (ca 2000 meters) TABLE 2B First acidity constant: H2CO3 ϭ HCOϪ ϩ Hϩ K1 ϭ {Hϩ}{HCOϪ} {H CO3*} K1′ ϭ {Hϩ}[HCOϪT ] [H CO3* ] c K1 ϭ [Hϩ ][HCOϪT ] [H CO3* ] Medium Temp., °C →0 Seawater, 19% ClϪ Ϫlog K a Seawater M NaClO4 Ј Ϫlog K1 — ϪlogcK1 b 6.579 6.15 — — 6.517a 6.11b 6.01e — 10 6.464a 6.08b — — 14 — — 6.02f — 15 6.419a 6.05b — — 20 6.381a 6.02b — — 22 — 6.00c 5.89c — 25 6.352a 6.00b, 6.09d — 6.04g 30 6.327a 5.98b — — 35 a 6.309 5.97b — — 40 6.298a — — — 50 6.285a — — — a H S Harned and R Davies, Jr., J Amer Chem Soc., 65, 2030 (1943) After Lyman (1956), quoted in G Skirrow, Chemical Oceanography, Vol I, J P Riley and G Skirrow, Eds., Academic Press, New York, 1965, p 651 c A Distèche and S Distèche, J Electrochem Soc., 114, 330 (1967) d Ϫ Calculated as log (K1/fHCO3 ) as determined by A Berner, Geochim Cosmochim Acta, 29, 947 (1964) e D Dyrssen, and L G Sillén, Tellus, 19, 810 (1967) f D Dyrssen, Acta Chem Scand., 19, 1265 (1965) g M Frydman, G N Nilsson, T Rengemo, and L G Sillén, Acta Chem Scand., 12, 878 (1958) Ref.: Stumm, W and J Morgan, Aquatic Chemistry, Wiley-Interscience, New York, 1970, p 148 b © 2006 by Taylor & Francis Group, LLC C023_002_r03.indd 1260 11/18/2005 1:32:07 PM WATER CHEMISTRY 1261 TABLE 2B (continued) Solid acidity constant: HCOϪ ϭ Hϩ ϩ CO2Ϫ 3 K2 ϭ {Hϩ}{CO3Ϫ} Ϫ {HCO3 } K2 ϭ ′ {Hϩ}[CO3Ϫ ] T [HCO3T ] c K2 ϭ [Hϩ ][CO3Ϫ ] T Ϫ [HCO3 ] Medium Temp., °C →0 Seawater 0.75 M NaCl — Ϫlog K2 Ϫlog K2 Ј Ϫlog K2 Ј 10.625a 9.40b — — 10.557a 9.34b — — 10 10.490a 9.28b — — 15 a 10.430 9.23 b — — 20 10.377a 9.17b — — 22 — 9.12c 9.49c — 25 10.329a 9.10b — 9.57d 30 a 10.290 9.02 b — — 35 10.250a 8.95b — — 40 10.220a — — — 50 10.172a — — — M KclO4 Ϫlog cK2 a H S Harned and S R Scholes, J Amer Chem Soc., 63, 1706 (1941) After Lyman, quoted in G Skirrow, Chemical Oceanography, Vol I, J P Riley and G Skirrow, Eds., Academic Press, New York, p 651 c A Distèche and S Distèche, J Electrochem Soc., 114, 330 (1967) d M Frydman, G N Nilsson, T Rengemo, and L G Sillén, Acta Chem Scand., 12, 878 (1958) Ref.: Stumm, W and J Morgan, Aquatic Chemistry, Wiley-Interscience, New York, 1970, pp 149 and 150 b pH –1 H+ –2 log CONC (M) P2 P1 10 seawater 11 13 13 12 OH– C2– HB HC– –2 –3 –4 –4 –5 HC– HC– P2 P1 –6 –7 –1 B– H2C –3 HB B– C2– H2C –5 –6 –7 FIGURE Logarithmic concentration—pH equilibrium diagram for seawater as a closed system For seawater log BT ϭ Ϫ3.37, log CT ϭ Ϫ2.62 and the following pK values: 6.0 for H2CO3*, 9.4 for and pK ϭ 13.7 BT ϭ total borate boron and CT ϭ total carbonate carbon Arrows gives [Hϩ] for seawater (pH ϭ 8.0) and for two equivalence points (points of minimum buffer intensity): P1, corresponding to a proton reference level of HB ϩ HCϪ ϩ H2O, and P2, corresponding to a proton reference level of HB ϩ H2C ϩ H2O (From Dyrssen, D and L.G Sillén, Tellus, 19, 110, 1967) © 2006 by Taylor & Francis Group, LLC C023_002_r03.indd 1261 11/18/2005 1:32:08 PM 1262 WATER CHEMISTRY pKH2CO3 pK2 pK1 -1 log CONCENTRATION (MOLAR) -2 -3 CT -4 H+ -2 CO3 * H2CO3 OH– -5 -6 P – HCO3 -7 TRUE H2CO3 -8 a pH 10 11 FIGURE Logarithmic concentration—pH equilibrium diagram for the aqueous carbonate system open to the atmosphere Water is equilibrated with the atmosphere (pCO2 = 10Ϫ3.5 atm) and the pH is adjusted with strong base or strong acid Eqs (14), (15), (16), (17) with the constants (25ЊC) pKH ϭ 1.5, pK1 ϭ 6.3, pK2 ϭ 10.25, pK(hydration of CO2) ϭ Ϫ2.8 have been used The pure CO2 solu2Ϫ tion is characterized by the proton condition [Hϩ] ϭ [HCOϪ] ϩ 2[CO3 ]+[OHϪ] Ϫ see point P) and the equilibrium concentrations Ϫlog[Hϩ] ϭ Ϫlog[HCO3 ] ϭ 2Ϫ 5.65; Ϫlog[CO2aq] ϭ Ϫlog[H2CO3] ϭ 5.0; Ϫlog[H2CO3] Ϸ 7.8; Ϫlog[CO3 ] ϭ 8.5 Ref.: Stumm, W and J Morgan, Aquatic Chemistry, Wiley-Interscience, New York, 1970, p 127 Solubility of Oxides and Hydroxides If pure solid oxide or hydroxide is in equilibrium with free ions in solution, for example, Me(OH)2(s) ϭ Me2ϩ ϩ 2OHϪ MeO(s) ϩ H2O ϭ Me ϩ 2OH Ϫ 2ϩ (18) (19) the conventional (concentration) solubility product is given by * cKs ϭ [ Me 2ϩ ][OHϪ ]2 (mole3 literϪ3 ) , (20) where the subscript “0” refers to solution of the simple, uncomplexed forms of the metal ion Sometimes it is more appropriate to express the solubility in terms of reaction with protons, for example, Me(OH)2(s) ϩ 2Hϩ ϭ Me2ϩ ϩ 2H2O MeO(s) ϩ 2H ϭ Me ϩ 2ϩ ϩ H2O (21) (22) In the general case for a cation of charge z, the solubility equilibrium for Eqs (21) and (22) is characterized by * cK s ϭ cK [ Me zϩ ] [mole(1Ϫz ) liter ( zϪ1) ϭ sz0 , ϩ [H ] Kw (23) where Kw is the ion product of water This constant and also a number of solubility equilibrium constants relevant to natural waters are given in Table Equation (23) can be written in logarithmic form to express the equilibrium concentration of a cation Mezϩ as a function of pH: log[ Me zϩ ] ϭ log c* K s Ϫ pH (24) Equation (24) is plotted for a few oxides and hydroxides in Figure © 2006 by Taylor & Francis Group, LLC C023_002_r03.indd 1262 11/18/2005 1:32:08 PM WATER CHEMISTRY 1263 TABLE Equilibrium constants for oxides, hydroxides, carbonates, hydroxide carnonates, sulfates, silicates, and acids Symbol for equilibrium constants Reaction log K (25ЊC) I I OXIDES AND HYDROXIDES H2O(1) ϭ Hϩ ϩ OHϪ Ϫ14.00 Ϫ13.77 Kw 1M NaClO4 (am)Fe(OH)3(s) ϭ Fe3ϩ ϩ 3OHϪ Ks0 Ϫ38.7 3M NaClO4 (am)Fe(OH)3(s) ϭ FeOH2ϩ ϩ 2OHϪ Ks1 Ϫ27.5 3M NaClO4 (am)Fe(OH)3(s) ϭ Fe(OH)ϩ ϩ OHϪ Ks2 Ϫ16.6 3M NaClO4 (am)Fe(OH)3(s) ϩ OHϪ ϭ FE(OH)4 Ks4 Ϫ4.5 3M NaClO4 2(am)Fe(OH)3(s) ϭ Fe2(OH)4ϩ ϩ 4OHϪ Ks22 Ϫ51.9 3M NaClO4 (am)Fe(OOH)(s) ϩ 3Hϩ ϭ Fe3ϩ ϩ 2H2O * 3.55 3M NaClO4 a—FeOOH(s) ϩ 3Hϩ ϭ Fe3ϩ ϩ 2H2O * 1.6 3M NaClO4 a—Al(OH)3(gibbsite) ϩ 3Hϩ ϭ Al3ϩ ϩ 3H2 * 8.2 g—Al(OH)3(bayerite) ϩ 3H ϭ Al * 9.0 * Ks0 10.8 K4 32.5 ϩ 3ϩ ϩ 3H2O (am)Al(OH)3(s) ϩ 3Hϩ ϭ Al3ϩ ϩ 3H2O Al3ϩ ϩ 4OHϪ ϭ Al(OH)Ϫ CuO(s) ϩ 2Hϩ ϭ Cu2ϩ ϩ H2O Ks0 Ks0 Ks0 Ks0 * Ks0 7.65 Cu2ϩ ϩ OHϪ ϭ CuOHϩ K1 6.0 (18ЊC) 2Cu2ϩ ϩ 2OHϪ ϭ Cu2(OH)2ϩ K22 17.0 (18ЊC) Cu2ϩ ϩ 3OHϪ ϭ Cu(OH)Ϫ K3 15.2 Cu2ϩ ϩ 4OHϪ ϭ Cu(OH)2Ϫ K4 16.1 Ks0 11.18 Zn2ϩ ϩ OHϪ ϭ ZnOHϩ K1 5.04 Zn2ϩ ϩ 3OHϪ ϭ Zn(OH)Ϫ K3 13.9 Zn2ϩ ϩ 4OHϪ ϭ Zn(OH)2Ϫ K4 15.1 Ks0 13.61 Cd2ϩ ϩ OHϪϭ CdOHϩ K1 3.8 Mn(OH)2(s) ϭ Mn2ϩ ϩ 2OHϪ Ks0 Ϫ12.8 Mn(OH)2(s) ϩ OHϪ ϭ Mn(OH)Ϫ Ks3 Ϫ5.0 Fe(OH)2(active) ϭ Fe ZnO(s) ϩ 2Hϩ ϭ Zn2ϩ ϩ H2O * Cd(OH)2(s) ϩ 2H2ϩ ϭ Cd2ϩ ϩ 2H2O 1M LiClO4 Ks0 Ϫ14.0 Fe(OH)2(inactive) ϭ Fe2ϩ ϩ 2OHϪ Ks0 Ϫ14.5 (Ϫ15.1) Fe(OH)2(inactive) ϩ OHϪ ϭ Fe(OH)3 Ks3 Ϫ5.5 Mg(OH)2 ϭ Mg2ϩ ϩ 2OHϪ Ks0 Ϫ9.2 Mg(OH)2(brucite) ϭ Mg2ϩ ϩ 2OHϪ Ks0 Ϫ11.6 Mg2ϩ ϩ OHϪ ϭ MgOHϩ K1 2.6 Ca(OH)2(s) ϭ Ca2ϩ ϩ 2OHϪ Ks0 Ϫ5.43 Ca(OH)2(s) ϭ CaOHϩ ϩ OHϪ Ks1 Ϫ4.03 Sr(OH)2(s) ϭ Sr2ϩ ϩ 2OHϪ Ks0 Ϫ3.51 Sr(OH)2(s) ϭ SrOHϩ ϩ OHϪ Ks1 0.82 AgOH(s) ϭ Agϩ ϩ OHϪ Ks0 Ϫ7.5 Kp1 Ϫ7.82 2ϩ ϩ 2OH * Ϫ II CARBONATES AND HYDROXIDE CARBNONATES CO2(g) ϩ H2O ϭ Hϩ ϩ HCOϪ Ϫ7.5 Seawater 5ЊC, 200 atm seawater HCOϪ ϭ Hϩ ϩ CO2Ϫ 3 (K2) Ϫ10.33 Ϫ9.0 Seawater (Continued) © 2006 by Taylor & Francis Group, LLC C023_002_r03.indd 1263 11/18/2005 1:32:08 PM 1264 WATER CHEMISTRY TABLE (continued ) Symbol for equilibrium constants Reaction log K (25ЊC) Ϫ9.0 CaCO3(calcite) ϭ Ca2ϩ ϩ CO2Ϫ I 5ЊC, 200 atm seawater Ϫ8.35 Ϫ6.2 Ks0 Seawater CaCO3(aragonite) ϭ Ca2ϩ ϩ CO2Ϫ Ks0 Ϫ8.22 SrCO3(s) ϭ Sr2ϩCO2Ϫ Ks0 Ϫ9.03 Ϫ6.8 Seawater ZnCO3(s) ϩ 2Hϩ ϭ Zn2ϩ ϩ H2O ϩ CO2(g) Zn(OH)1.2(CO3)0.4(s) ϩ 2H ϭ Zn CO2(g) ϩ 2ϩ ϩ H2O ϩ * Kps0 7.95 * K0 9.8 Cu(OH)(CO3)0.5(s) ϩ 2Hϩ ϭ Cu2ϩ ϩ 3/2H2O ϩ 1/2CO2(g) * Kps0 7.08 Cu(OH)0.67(CO3)0.67(s) ϩ 2Hϩ ϭ Cu2ϩ ϩ 4/3H2O ϩ 2/3CO2(g) * 7.08 MgCO3(magnesite) ϭ Mg2ϩ ϩ CO2Ϫ Ks0 Ϫ4.9 MgCO3(nesquehonite) ϭ Mg2ϩ ϩ CO2Ϫ Ks0 Ϫ5.4 Mg4(CO3)3(OH)2.3H2O(hydromagnesite) ϭ 4Mg2ϩ ϩ 3CO2Ϫ 2OHϪ Ks0 29.5 CaMg(CO3)2(dolomite) ϭ Ca3ϩ ϩ Mg2ϩ ϩ 2CO2Ϫ Ks0 FeCO3(siderite) ϭ Fe2ϩ ϩ 2CO2Ϫ Ks0 CdCO3(s) ϩ 2Hϩ ϭ CD2ϩ ϩ H2O ϩ CO2(g) Kps0 6.44 MnCO3(s) ϭ Mn2ϩ2CO2Ϫ Ks0 Ϫ10.41 Kps Ϫ16.7 Ϫ10.4 (Ϫ10.24) 0 1M NaCl4 III SULFATES, SULFIDES, AND SILICATES CaSO4(s) ϭ Ca2ϩ ϩ SO2Ϫ Ks0 Ϫ4.6 H2S ϭ H ϩ HSϪ K1 Ϫ7.0 HSϪ ϭ Hϩ ϩ S2Ϫ K2 Ϫ12.96 MnS(green) ϭ Mn2ϩ ϩ S2Ϫ Ks0 Ϫ12.6 Ks0 Ϫ9.6 FeS(s) ϭ Fe2ϩ ϩ S2Ϫ Ks0 Ϫ17.3 SiO2(quartz) ϩ 2H2 ϭ H4SiO4 Ks0 Ϫ3.7 (am)SiO2(s) ϩ 2H2O ϭ H4SiO4 Ks0 Ϫ2.7 H4SiO4 ϭ Hϩ ϩ H3SiO4 Ks0 Ϫ9.46 NHϩ ϭ Nϩ ϩ NH3(aq) Ka Ϫ9.3 HOCl ϭ Hϩ ϩ OClϪ Ka Ϫ7.53 MnS(pink) ϭ Mn 2ϩ ϩS 2Ϫ IV ACIDS The constants given here are taken from quotations or selections in (a) L G Sillén and A E Martell, Stability Constants of Metal Ion Complexes, Special Publ., No 17, the Chemical Society, London, 1964: (b) W Feitknecht and P Schindler, Solubility Constants of Metal Oxides, Metal Hydroxides and Metal Hydroxide Salts in Aqueous Solutions, Butterworths, London, 1963; (c) P Schindler, “Heterogeneous Equilibria Involving Oxides, Hydroxides, Carbonates and Hydroxide Carbonates”, in Equilibrium Concepts in Natural Water Systems, Advance in Chemistry Series, No 67, American Chemical Society, Washington, DC, 1967, p 196; and (d) J N Butler, Ionic Equilibrium, A Mathematical Approach, Addison-Wesley Publishing, Reading, Mass., 1964 Unless otherwise specified a pressure of atm is assumed a Most of the symbols used for the equilibrium constants are those given in Stability Constants of Metal-Ion Complexes Table from Stumm, W and J Morgan, Aquatic Chemistry, Wiley-Interscience, New York, 1970, pp 168 and 169 © 2006 by Taylor & Francis Group, LLC C023_002_r03.indd 1264 11/18/2005 1:32:08 PM WATER CHEMISTRY 1265 CO2+ –log [Mez+] Cu2+ CuO(s) Fe3+ Al3+ Cu2+ Zn2+ Fe2+ 2+ Mg2+ Cd pH 10 Ag+ 12 FIGURE Solubility of oxides and hydroxides: free metal ion concentration in equilibrium with solid oxides ore hydroxides As shown explicitly by the equilibrium curve for copper, free metal ions are constrained to concentrations to the left of (below) the respective curves Precipitation of the solid hydroxides and oxides commences at the saturation concentrations represented by the curves The formation of hydroxo metal complexes must be considered for the evaluation of complete solubility of the oxides or hydroxides Ref.: Stumm, W and J Morgan, Aquatic Chemistry, Wiley-Interscience, New York, 1970, p 171 The relations in Figure not fully describe the solubility of the corresponding oxides and hydroxides, since in addition to free metal ions, the solution may contain hydrolyzed species (hydroxo complexes) of the form The solubility of the metal oxide or hydroxide is therefore expressed more rigorously as n z MeT ϭ [ Me zϩ ]ϩ ∑ [ Me(OH)nϪn ] (25) Plots of this equation as a function of pH are given in Figure for ferric hydroxide, zinc oxide, and cupric oxide Solubility of Carbonates The maximum soluble metal ion concentration is a function of pH and concentration of total dissolved carbonate species Calculation of the equilibrium solubility of the metal ion for a given carbonate for a water of a specific analytic composition discloses whether the water is over-saturated or undersaturated with respect to the solid metal carbonate In the case of calcite [Ca 2ϩ ] ϭ Ks0 K ϭ s0 [CO3Ϫ ] CT a2 (26) Since a2 is known as a function of pH, Eq (26) gives the equilibrium saturation value of Ca2ϩ as a function of CT and pH An analogous equation can be written for any metallic cation in equilibrium with its solid metallic carbonate These equations are amenable to simple graphical representation in a log concentration versus pH diagram as illustrated in Figure Control of Solubility Solubility calculations, such as those exemplified above, give thermodynamically meaningful conclusions, under the specified conditions (e.g., concentrations, pH, temperature and pressure), only if the solutes are in equilibrium with that solid phase for which the equilibrium relationship has been formulated For a given set of conditions the solubility is controlled by the solid giving the smallest concentration of solute For example, within the pH range of carbonate bearing natural waters, the stable solid phases regulating the solubility of Fe(II), Cu(II), and Zn(II) are, respectively, FeCO3 (siderite), CuO (tenorite) and Zn (OH) (CO3) (hydrozincite) Unfortunately, it has not yet been possible to determine precise solubility data for some solids important in the regulation of natural waters Among these are many clays and dolomite (CaMg(CO3)2), a mixed carbonate which constitutes a large fraction of the total quantity of carbonate rocks The conditions under which dolomite is formed in nature are not well understood and attempts to precipitate it in the laboratory from solutions under atmospheric conditions have been unsuccessful These difficulties in ascertaining equilibrium have resulted in a diversity of published 2Ϫ figures for its solubility product, ({Ca2ϩ}{Mg2ϩ}{Co3 }2}†, Ϫ16.5 Ϫ19.5 ranging from 10 to 10 (25ЊC) The Activity of the Solid Phase In a solid-solution equilibrium, the pure solid phase is defined as a reference state and its activity is, because of its constancy, † Note that this solubility product is expressed for activities, as represented by {} © 2006 by Taylor & Francis Group, LLC C023_002_r03.indd 1265 11/18/2005 1:32:09 PM WATER CHEMISTRY ZnO(s) ZnOH+ CuO(s) CuOH Mg+2 –2 Zn(OH)4 – ZnOH3 Cu Zn+2 11 pH Cu(OH)– +2 (Ks0) –2 Cu(OH)4 a – log CONC (M) –2 CO3 + 10 12 pH b * am-Fe(OH)3(s) –log CONC (M) – log CONC (M) 1266 CO+2 Ks0 CT SR+2 Fe+2 Zn+2 Fe+3 10 FeOH+2 – Fe(OH)4 10 + 12 Fe(OH)2 pH c FIGURE Solubility of amorphous Fe(OH)3, ZnO, and CuO The equilibrium solubility curves for the hydroxo metal complexes and for the free metal ion have been combined to yield the composite curve bordered by the cross hatching The constituent curves were constructed from the data in Table The possible occurrence of poly2ϩ nuclear complexes, for example Fe2(OH)2Ϫ, CU2(OH)2 , has been ignored Such complexes not change the solubility characteristics markedly for the solids considered Also ignored is complexing with other ligands such as NH3 Ref.: Stumm, W and J Morgan, Aquatic Chemistry, Wiley-Interscience, New York, 1970, p 173 set equal to unity This means that the activity of the solid phase is implicitly contained in the solubility equilibrium constant Therefore, experimental differences from precisely known equilibrium constants can be used to deduce information about the constitution of the solid phase There are various factors that affect the activity of the solid phase: (1) the lattice energy, (2) the degree of hydration, (3) solid solution formation, (4) the free energy of the surface and (5) the presence of constituents affecting the purity of the solid The solids occurring in nature are seldom pure substances For example, isomorphous replacement by a foreign constituent in the crystalline lattice is an important factor by which the activity of the solid phase may be decreased 10 pH 12 FIGURE Solubility of carbonates in solutions of constant total dissolved carbonate carbon The maximum soluble 2ϩ metal ion concentration ([Me2ϩ] ϭ ks0/[(CO3 ] ϭ Ks0/a2CT) Ϫ2.5 is shown as a function of pH for CT ϭ 10 M The acidity constants for H2CO3* are indicated on the horizontal axis Dashed portions of the curves indicated conditions under which MeCO3(s) is not thermodynamically stable due to the formation of the more stable solid hydroxide or oxide Ref.: Stumm, W and J Morgan, Aquatic Chemistry, WileyInterscience, New York, 1970, p 179 acceptors, reductants and oxidants are defined as electron donors and electron acceptors Since free electrons not exist in solution, every oxidation is accompanied by a reduction and vice versa An oxidant is thus a substance which causes oxidation to occur, while itself becoming reduced The oxidation states of the reactants and products change as a result of the electron transfer which mechanistically may occur as a transfer of a group that carries one or more electrons Since electrons are transferred in every redox reaction they can be treated conceptually like any other discrete reacting species, namely, as free electrons The following redox reaction is illustrative: O2 ϩ 4Hϩ ϩ 4e ϭ 2H2O Redox Equilibria and Electron Activity 4Fe2ϩ ϭ 4Fe3ϩ 4e There is a conceptual analogy between acid-base and oxidation-reduction reactions In a similar way that acids and bases have been interpreted as proton donors and proton O2 ϩ 4Fe reduction 2ϩ oxidation ϩ 4H ϭ 4Fe ϩ 3ϩ ϩ 2H2O redox reaction (27) © 2006 by Taylor & Francis Group, LLC C023_002_r03.indd 1266 11/18/2005 1:32:09 PM WATER CHEMISTRY This treatment of electrons is no different from that of many other species such as hydrogen ions and silver ions, which not actually exist in aqueous solution as free and unhydrated species but which are expressed as Hϩ and Agϩ in reactions For example, the Hϩ really takes the form of ϩ hydrated protons (H9O4 ) or hydrogen complexes (acids such as HCl) From the following general reduction reaction: aA ϩ bB ϩ ne ϭ cC ϩ dD the generalized expression for any redox couple is given by pε ϭ pε Ϫ pH ϭ Ϫlog{Hϩ}, (29) that measures the relative tendency of a solution to donate or transfer electrons In a highly reducing solution the tendency to donate electrons, that is, the hypothetical “electron pressure” or electron activity, is relatively large Just as the activity of hypothetical hydrogen ions is very low at high pH, the activity of hypothetical electron is very low at high p␧ Thus a high p␧d indicates a relatively high tendency for oxidation In equilibrium equations Hϩ and e are treated in an analogous way Thus oxidation or reduction equilibrium constants can be defined and treated similarly to acidity constants as shown by the following equations: For protolysis: HA ϭ Hϩ ϩ AϪ (30) {Hϩ}{AϪ}/{HA} ϭ KHA, or pH ϭ Ϫlog KHA ϩ log({AϪ}/{HA}) b n pB ϩ c n pC ϩ d np D (34) 1 ⌬G pε ϭϪ log K ox ϭ log K red ϭ n n n n2.3 RT Kox and Kred are the equilibrium constants for the oxidation and reduction reactions; n is the number of electrons transferred in the reaction ⌬G represents the free energy change for the reduction Thus it is seen that p␧ is a measure of the electron free energy level per mole of electrons Equation (34) permits the expression of the redox intensity by p␧ for any redox couple for which the equilibrium constant is known Numerical illustrations of the calculation of p␧ values (25ЊC) are given for the following equilibrium systems in which the ionic strength, I,‡ is assumed to approach O: a) An acid solution 10Ϫ5 M in Fe3ϩ and 10Ϫ3 M in Fe2ϩ b) A natural water at pH ϭ 7.5 in equilibrium with the atmosphere (Po2 ϭ 0.21 atm.) c) A natural water at pH ϭ containing 10Ϫ5 M Mn2ϩ in equilibrium with g ϪMnO2(s) “Stability Constant of Metal-Ion Complexes” gives the following equilibrium constants (Kred): a) Fe3ϩ ϩ e ϭ Fe2ϩ; (31) Kϭ (32) {e}{Fe3ϩ}/{Fe2ϩ} ϭ Kox, or p␧ ϭ Ϫlog Kox ϩ log({Fe3ϩ/Fe2ϩ}) Ϫ where pX ϭ Ϫlog[X] and For the oxidation of Fe2ϩ to Fe3ϩ: Fe2ϩ ϭ Fe3ϩ ϩ e pA (28) Sørenson (1909) established a convenient intensity parameter that measures the relative tendency of a solution to donate or transfer protons In an acid solution this tendency is high and in an alkaline solution it is low Similarly, Jørgensen (1945) has established an equally convenient redox intensity parameter, p␧ ϭ Ϫlog{e}, a n ⌬G ϭ n 2.3 RT Ј Redox Intensity By introducing the definition pH ϭ Ϫlog[Hϩ], which under idealized conditions is formulated as 1267 {Fe 2ϩ} ; log K ϭ 12.53 {Fe 3ϩ}{e} b) 1/2 O2 (g) ϩ 2Hϩ ϩ 2e; (33) H2O(1) As seen from Eq (33) p␧ increases with the ratio of the activities (or concentrations) of oxidized to reduced species.† ‡ † The sign convention adopted here is that recommended by IUPAC (International Union of Pure and Applied Chemistry) Ionic strength, I, is a measure of the interionic effect resulting primarily from electrical attraction and repulsions between the various ions; it is defined by the equation t = 1/2 ⌺iCiZ2i The summation is carried out for all types of ions, cations and anions, in the solution © 2006 by Taylor & Francis Group, LLC C023_002_r03.indd 1267 11/18/2005 1:32:09 PM 1268 WATER CHEMISTRY p⑀ log CONC (M or atm.) –12 –4 –8 – –4 and the redox equilibrium equation is 12 pε ϭ 1ր log K ϩ1ր log SO4–2 HS [SO2Ϫ ][Hϩ ] [HSϪ ] (36) pH=10 where log K (for the reduction reaction) is 1034 Hence, –8 –2 SO4 –12 p ϭ 4.25 Ϫ11.25pH ϩ1ր log[SO2Ϫ ]Ϫ1ր log[HSϪ ] PO2 pH2 or, for pH ϭ 10, – HS –16 10–92 10–76 10–60 10–44 10–28 10–12 10+4 Po 10+4 10–4 10–12 10–20 10–28 10–36 10–44 PH FIGURE Equilibrium distribution of sulfur compounds as a function of p␧ at pH ϭ 10 and 25ЊC Total concentration is 10Ϫ4 M The dotted curve shows that solid sulphur cannot exist thermodynamically at pH ϭ 10, since its activity never becomes unity Figure from Stumm, W and J Morgan, Aquatic Chemistry, Wiley-Interscience, New York, 1970, p 311 Kϭ ; log K ϭ 41.55 Po1 / {Hϩ}2 {e}2 ϭ Mn2 ϩ 2H2O(1); {Mn 2ϩ} ; log K ϭ 40.84 {Hϩ}4 {e}2 For the conditions stipulated the following p␧ values are obtained: {Fe 3ϩ} ϭ 10.53 {Fe 2ϩ} a) p ϭ 12.53 ϩ log b) p ϭ 20.78 ϩ1 / log( Po1 / {Hϩ}2 ) ϭ 13.11 c) {Hϩ}4 p ϭ 20.42 ϩ1ր log ϭ 6.92 {Mn 2ϩ} Equilibrium constants for some redox processes pertinent in aquatic conditions are listed in Table A quite comprehensive reference source for such constants is Stability Constants for Metal-Ion Complexes, L G Sillén and A E Martell, The Chemical Society, London (1964) and its Supplement (1971) Significantly, the first section of this reference deals with the electron as a ligand, similarly to its treatment above Another compilation, somewhat outdated though still very useful, is Oxidation Potentials, 2nd ed., W M Latimer, Prentice-Hall, (1952) This treatise lists redox potentials rather than equilibrium constants, but, as shown in the next section, the latter are readily obtained from the former The Determination of p␧ and Redox Potential Equilibrium Distribution in the Sulphur System Figure shows the p␧ dependence of a 10Ϫ4M SO2Ϫ ϪHSϪsystem at pH ϭ 10 and 25ЊC The reaction is SO2Ϫ ϩ 9Hϩ ϩ 8e ϭ HSϪ ϩ 4H O(1) HSϪ is the predominant S(ϪII) species at pH ϭ 10 Figure shows that the lines for [SO2Ϫ] and [HSϪ] intersect at p␧ ϭ Ϫ7 The asymptotes for [SO2Ϫ] have slopes of ϩ8 and 0, whereas those for [HSϪ] have slopes of and Ϫ8 Lines for the equilibrium partial pressure of O2 and H2 are also given in the diagram As the diagram shows, rather high relative electron activities are necessary to reduce SO2Ϫ At the pH value selected, the reduction takes place at p␧ values slightly less negative than for the reduction of water Thus in the presence of oxygen and at pH ϭ 10, only sulfate can exist; its reduction is possible only at p␧ values less than Ϫ6 Equilibrium Constants for Redox Reactions c) gϪMnO2(s) ϩ 4Hϩ ϩ 2e Kϭ p ϭϪ ϩ1ր log[SO2Ϫ ]Ϫ1ր log[ HSϪ ] (35) As with pH, p␧ can be measured with a potentiometer using an indicator electrode (e.g., a platinum or gold electrode) and a reference electrode The result is read as a potential difference in volts When a reversible hydrogen electrode, at which the electrode reaction is H2 ϭ 2Hϩ ϩ 2e, is used as the reference, the resulting potential difference is termed the redox potential, EH , where the suffix H refers to the hydrogen electrode as the reference Usually another reference electrode is used, e.g., a calomel electrode, but the addition of a constant factor (i.e., the potential difference between the calomel electrode and the hydrogen electrode) to the © 2006 by Taylor & Francis Group, LLC C023_002_r03.indd 1268 11/18/2005 1:32:09 PM WATER CHEMISTRY observed voltage gives EH p␧ is then readily computed by dividing EH by a constant factor according to Eq (27): pε EH , (2.3 RT ր F ) where F ϭ the Faraday constant (96,500 coulombs per equivalent), R ϭ the gas constant (8.314 volt-coulombs per degree—equivalent), and T ϭ the absolute temperature in degrees Kelvin At 25ЊC, (2.3 ␻T/F) ϭ 0.059 volt Both conceptually and computationally, it is more convenient to use the dimensionless p␧ rather than the more directly measured EH, as a measure of the redox intensity Every tenfold change in the activity ratio of Eq (34) causes a change in p␧ of one unit divided by the number of electrons transferred in the redox reaction The fact that one electron can reduce one proton is another reason for expressing the intensity parameter for oxidation in a form equivalent to that used for acidity Incidentally, pH is also not measured directly It is determined by measuring the potential (in volts) of an indicator electrode (e.g., a glass electrode) with respect to a reference electrode If the hydrogen electrode is used or referred to as the reference electrode, the resulting potential difference is called the acidity potential The pH is calculated by dividing the acidity potential by 2.3 RT/F The Peters-Nernst Equation Since much literature still describes the electron activity in volts rather than on a scale† similar to that for other reagents, the Peter-Nernst equation is still of utility It is easily expressed by substituting Eq (37) into Eq (34): EH ϭ EH ϩ 2.3 RT {oxidized} log {reduced} nF Ϫ⌬G ϭ , nF (38) where EH ϭ (2.3 RT րF )pε;ϭ Ϫ⌬G nF 1269 potentials (as listed in “Stability Constants of Metal-Ion Complexes” and other references) have been derived from equilibrium data, thermodynamic data, the chemical behavior of a redox couple with respect to known oxidizing and reducing agents, and from direct measurements of electrochemical cells Direct measurement of EH for natural water environments involves complex theoretical and practical problems in spite of the apparent simplicity of the electrochemical technique For example, the EH of aerobic (dissolved oxygen containing) waters, measured with a platinum or gold electrode, does not agree with that predicted by Eq (38) Even when reproducible results are obtained, they often not represent reversible Nernst potentials Among the considerations hindering the direct measurement of EH are the rates of electron exchange at certain electrodes and the occurrence of mixed potentials A mixed potential results when the rate of oxidation of one redox couple is compensated by the rate of reduction of a different couple during the measurement Although aqueous systems containing oxygen or similar oxidizing agents will usually give positive EH values and anaerobic systems will usually give negative ones, detailed quantitative interpretation with respect to concentrations of redox species is generally unwarranted Since natural waters are normally in a dynamic rather than an equilibrium condition, even the concept of a single oxidation–reduction potential characteristic of the aqueous system as a whole cannot be justified At best, measurement can give rise to an EH value applicable to a particular redox reaction or to redox species in partial chemical equilibrium and even then only if these redox agents are electrochemically reversible at the electrode surface at a rate that is rapid compared with the electron drain or supply by the measuring electrode system p␧–pH Diagrams A p␧–pH stability field diagram shows in a panoramic way which species predominate at equilibrium under any condition of p␧ (or EH) and pH The primary value of a p␧–pH diagram is its simultaneous representation of the consequences of the equilibrium constants of many reactions for any combination of p␧ and pH Figure shows stability fields for the various species pertinent to the chlorine system These diagrams are readily constructed from thermodynamic data such as those listed in Table (39) Measurement of EH It is essential to distinguish between the concept of a potential and the measurement of a potential Redox or electrode † With dilute solutions it is convenient to express concentrations on a minus log concentration scale, e.g., pNaϩ ϭ Ϫlog[Naϩ] Log Concentration—p␧ Diagrams The predominant redox species are depicted as a function of p␧ or redox potential in p␧-log concentration diagrams Upper or lower bounds of p␧ values for the occurrence of specific redox reactions are immediately evident from these double log-arithmetic diagrams Such diagrams, constructed from the data in Table with pH ϭ 7, are shown in Figure 10 for a few elements in the biochemical cycle © 2006 by Taylor & Francis Group, LLC C023_002_r03.indd 1269 11/18/2005 1:32:10 PM 1270 WATER CHEMISTRY +25 EH(v) HOCl Cl2(aq) 25 O2 +20 Cl– H2O +15 OCl– 20 p⑀ p⑀ +15 +10 +10 15 10 +0.5 +5 H2O H2 0 10 pH FIGURE Stability field diagram for the chlorine system: p␧ versus pH The curves labelled 1,2,3 and represent equilibria derived from Eqs (25) and (26) of Table and pKa for HOCl: This latter value is 7.53 at 25ЊC and is represented by the vertical line between HOCl and OClϪ stability fields In dilute solutions Cl2 (aq) exists only at low pH Cl2, OClϪ, and HOCl are all unstable or metastable in water since they are all slowly reduced by water as shown by the position of their stability fields, with respect to the H2O–O2 equilibrium curve Figure from Stumm, W and J Morgan, Aquatic Chemistry, Wiley-Interscience, New York, 1970, p 320 The boundary conditions for the stability of water (Figure 10(d)) are given at high p␧ values by the oxidation of water to oxygen: 1/2 H2O ϭ 1/4 O2 ϩ Hϩ ϩ e (40) and at low p␧ values by the reduction of water to hydrogen H2O ϩ e ϭ 1/2 H2 ϩ OHϪ (41) Water in equilibrium with the atmosphere (P o2 ϭ 0.21 atm.) at pH ϭ 7.0 (25ЊC) has a p␧ ϭ 13.6 (EH ϭ 0.8 volt.) Figure 10(a) gives the relationships among several oxidation states of nitrogen as a function of p␧ For most of the aqueous range of p␧, N2 gas is the most stable species However, at large negative p␧ values ammonia becomes predominant and for p␧ greater than ϩ12 nitrate dominates pH ϭ The fact that the nitrogen gas of the atmosphere has not been converted largely into nitrate under the prevailing aerobic conditions at the land and water surfaces indicates a lack of efficient biological mediation FIGURE 10 Equilibrium concentrations of biochemically important redox components as a function of p␧ at a pH of 7.0 These equilibrium diagrams have been constructed from equilibrium constants listed in Table and for the following concentrations representative of natural water systems: pH ϭ 7.0; CT (total carbonate carbon) ϭ 10Ϫ3 M; [H2(aq)] 2Ϫ ϭ [H2S(aq)] ϩ [HSϪ] ϩ [SO4 ] ϭ 10Ϫ5M; 3Ϫ 2Ϫ 4ϩ [NO ] ϩ [NO ] ϩ NO ] ϭ 10Ϫ3M; pN22 ϭ 0.78 atm and thus [N2(aq)] ϭ 0.5 ϫ 10Ϫ3M Figure from Stumm, W and J Morgan, Aquatic Chemistry, Wiley-Interscience, New York, 1970, p 331 © 2006 by Taylor & Francis Group, LLC C023_002_r03.indd 1270 11/18/2005 1:32:10 PM WATER CHEMISTRY 1271 TABLE Equilibrium constants of redox processes pertinent in aquatic conditions (25ЊC) pε°(ϭ Ϫlog K) Reaction pε°(W)a (1) 1/4 O2(g) ϩ Hϩ (W) ϩ e ϭ 1/2 H2O ϩ20.75 ϩ13.75 (2) 1/5 NOϪ ϩ 6/5Hϩ (W) ϩ e ϭ 1/10 N2(g) ϩ 3/5 H2O ϩ21.05 ϩ12.65 (3) 1/2 MnO2 (S) ϩ 1/2HCOϪ ϩ 3/2 Hϩ (W) ϩ e ϭ 1/2MnCO3(s) ϩ 3/8 H2O ϩ20.46 ϩ9.96 ϩ8.46 (3a) 1/2 MnO2(s) ϩ 2Hϩ (W) ϩ e ϭ 1/2 Mn2ϩ ϩ H2O ϩ20.42 ϩ6.42 (4) 1/2 NOϪ ϩ Hϩ (W) ϩ e ϭ 1/2 NOϪ ϩ 1/2 H2O ϩ14.15 ϩ7.15 (5) 1/8 NO2 ϩ 5/4 Hϩ (W) ϩ e ϭ 1/8 NHϩ ϩ 3/8 H2O ϩ14.90 ϩ6.15 (6) 1/6 NOϪ ϩ 4/3 Hϩ (W) ϩ e ϭ 1/6 NHϩ ϩ 1/3 H2O ϩ15.14 ϩ5.82 (7) 1/2 CH3OH ϩ Hϩ (W) ϩ e ϭ 1/2 CH4(g) ϩ 1/2 H2O ϩ9.88 ϩ2.88 (8) 1/4 CH2O ϩ Hϩ (W) ϩ e ϭ 1/4 CH4(g) ϩ 1/4 H2O ϩ6.94 Ϫ0.06 (9) FeOOH(s)ϩ HCOϪ ϩ 2Hϩ (W) ϩ e ϭ FeCO3(s) ϩ 2H2O ϩ15.33 ϩ1.33 Ϫ1.67b 3ϩ ϩ e ϭ Fe ϩ12.53 2ϩ ϩ 12.53 (9a) Fe (10) 1/2 CH2O ϩ Hϩ (W) ϩ ϭ 1/2 CH3OH ϩ3.99 Ϫ3.01 (11) 1/6 SO2Ϫ ϩ 4/3 Hϩ (W) ϩ e ϭ 1/6 S(s) ϩ 2/3 H2O ϩ6.03 Ϫ3.30 (12) 1/8 SO2Ϫ ϩ 5/4Hϩ (W) ϩ ϭ 1/8 H2S(g) ϩ 1/2 H2O ϩ5.75 Ϫ3.50 (13) 1/8 SO2Ϫ ϩ 9/8 Hϩ (W) ϩ e ϭ 1/8 HSϪ ϩ 1/2 H2O ϩ4.13 Ϫ3.75 (14) 1/2 S(s) ϩ Hϩ (W) ϩ e ϭ 1/2 H2S(g) ϩ2.89 Ϫ4.11 (15) 1/8 CO2(g) ϩ Hϩ (W) ϩ e ϭ 1/8 CH4(g) ϩ 1/4 H2O ϩ2.87 Ϫ4.13 (16) 1/6 N2(g) ϩ 4/3 H (W) ϩ e ϭ 1/3 NH ϩ4.68 Ϫ4.68 (17) 1/2 (NADPϩ) 1/2 Hϩ (W) ϩ e ϭ1/2 (NADPH) Ϫ2.0 Ϫ5.5c (18) Hϩ (W) ϩ e ϭ 1/2 H2(g) 0.0 Ϫ7.00 (19) Oxidized ferredoxin ϩ e ϭ reduced ferredoxin Ϫ7.1 Ϫ7.1d (20) 1/4 CO2(g) ϩ H (W) ϩ e ϭ 1/24 (glucose) ϩ 1/4 H2O Ϫ0.20 Ϫ7.20e (21) 1/2 HCOOϪ ϩ 3/2Hϩ (W) ϩ e ϭ 1/2 CH2O ϩ 1/2 H2O ϩ2.82 Ϫ7.68 (22) 1/4 CO2(g) ϩ Hϩ (W) ϩ e ϭ 1/4 CH2O ϩ 1/4 HO2 Ϫ1.20 Ϫ8.20 (22a) 1/4 HCOϪ ϩ 5/4 Hϩ (W) ϩ e ϭ 1/4 CH2O ϩ 1/2 H2O ϩ0.76 Ϫ7.99 Ϫ8.74b (23) 1/2 CO2(g) ϩ 1/2 Hϩ (W) ϩ e ϭ 1/2 HCOOϪ Ϫ4.83 (24) 1/2 C12(aq) ϩ e ϭ C1Ϫ ϩ23.6 ϩ23.6 (25) HOCl ϩ Hϩ (W) ϩ e ϭ 1/2 C12 (aq) ϩ H2O ϩ26.9 ϩ19.9 ϩ ϩ ϩ Ϫ8.73 (W) signifies that the pH ϭ Ϫ These data correspond to (HCO3 ) ϭ 10Ϫ3M rather than unity and so are not exactly pε(W); they represent typical aquatic data conditions more nearly than pε(W) values c M Calvin and J.A Bassham, The Photosynthesis of Carbon Compounds, Benjamin, New York, 1962 d D I Arnon, Science, 149, 1460 (1965) e A L Lehninger, Bioenergetics, Benjamin, New York, 1965: Table from Stumm, W and J Morgan, Aquatic Chemistry, Wiley-Interscience, New York, 1970, p 318 a b © 2006 by Taylor & Francis Group, LLC C023_002_r03.indd 1271 11/18/2005 1:32:10 PM 1272 WATER CHEMISTRY Because of these peculiarities in equilibria with N2, Figure 10(b) has been constructed for the metastable equilibria between NOϪ, and NOϪ by assuming the transition between bound nitrogen and N2 to be hindered This diagram shows that the shifts in relative predominance of the three species, NHϩ, NOϪ and NHϪ occur within a rather narrow p␧ range That each of these species has a dominant zone within this range would seem to be a contributing factor to the highly mobile characteristics of the fixed species of the nitrogen cycle Note that the relevant species of N (ϪIII) at pH ϭ is NHϩ rather than NH3 since the ammonia system pKa ϭ 9.3 2Ϫ The reduction of SO4 to H2S or HSϪ provides a good example of the application of equilibrium concepts to aquatic relationships Figure 10(d) shows that significant reduction 2Ϫ of SO4 to H2S at pH ϭ requires p␧ Ͻ Ϫ3 The biological enzymes that mediate this reduction must therefore operate at or below this p␧ Because the system is dynamic rather than static only an upper bound can be set in this way, for the excess driving force in terms of p␧ at the mediation site cannot be determined by equilibrium computations Since, however, many biologically mediated reactions seem to operate with relatively high efficiency in utilizing free energy, it Electron Transfer Capacity “Titration Curve” (REDOX INTENSITY VS REDOX CAPACITANCE) 15 900 O2 – NO3 H2O N2 10 600 MnO2 p⑀ Mn(I) EH (mv) – NO3 a 25° + NH4 300 0 FeOOH CH2O 2– CO2 SO4 Fe(II) CH3OH HS– CH4 –5 –300 REDUCTION BY ORGANICS OXIDATION BY OXYGEN H2O H2 10 15 meq / liter FIGURE 11 Electron transfer capacity “Titration Curve.” In a system with excess organic material, the redox intensity falls as the electron acceptors are successively reduced This diagram was constructed from the redox intensities and initial concentrations (expressed as electron equivalents) listed in Table The reactions indicated on the curve proceed sequentially during the stagnation period in the deeper waters of a polluted lake, vertically downward or temporally in sediments, sequentially after starting an anaerobic digester and chronologically in ground water contaminated with organic nutrients © 2006 by Taylor & Francis Group, LLC C023_002_r03.indd 1272 11/18/2005 1:32:11 PM WATER CHEMISTRY appears likely that the operating p p␧ value does not differ greatly from the equilibrium value The diagram also indicates the possibility of formation of elemental sulfur within a narrow p␧ range at neutral and low pH The major feature of the carbon system, shown in Figure 10(e), is simply the interconvertibility of C(IV) to C (ϪIV): i.e., the reduction of carbon dioxide bicarbonates and carbonates to methane and the reverse oxidation reactions Formation of solid carbon is thermodynamically possible close to p␧ ϭ Ϫ4 but its inclusion does not change other relationships Other carbon compounds exist under equilibrium conditions only at very small concentrations (Ͻ10Ϫ9 M) The existence of myriad synthetic and biochemical organic compounds at ambient p␧ levels is due to their exceedingly slow rates of equilibration to CO2 or CH3 or, in the case of the complicated organic structures in living systems, to the constant input of energy Microbial Mediation and Free Energy of Redox Reactions To survive and hence reproduce, microorganisms must not only capture a significant fraction of the thermodynamically available energy but must also acquire this energy at a rate compatible with the maintenance of life Thus the salient capability is that of power production per unit biomass and therefore kinetics (or the rate of movement toward equilibrium) should be considered as well as thermodynamics To provide for such energy production microorganisms have developed highly efficient and specific biological compounds (enzymes) which catalyze energy yielding reactions and cell constituent producing processes Organisms not oxidize organic substrates or reduce 2Ϫ O2 or SO4 ; they only mediate those reactions which are thermodynamically possible, or more specifically, the electron transfer occurring in these reactions The p␧ range in which certain oxidation or reduction reactions are possible may be estimated by calculating the equilibrium concentrations of the relevant species as a function of p␧ Since, 2Ϫ for example, SO4 can be reduced only below a given p␧ or redox potential, an equilibrium model can characterize the p␧ ranges in which reduction of sulfate is possible and is not possible Such models are graphically presented in Figure 11, where all the reactions are amenable to microbial mediation These diagrams manifest the use of p␧ as a parameter that characterizes the ecological milieu in a restrictive fashion The data in Table permit the calculation of combinations of the listed half reactions to give complete redox reactions Those that are thermodynamically possible are always accompanied by a decrease in free energy The free energy change of the complete redox reaction, ⌺⌬G, is easily calculated from the p␧ values through rearrangement of Eq (34): ∑ ⌬G ϭϪ 2.3 RT ϫ [(npε)for reduction ∑ (npε) (42) for oxidation ] 1273 If Ϫ⌬G is negative, the reaction can occur Combinations that lead to energetically possible reactions are given in Table All of these reactions are mediated by microorganisms REFERENCES American Chemical Society: Equilibrium concepts in natural water systems, Advances in Chem Series, 67, Washington (1967) Berner, R.A., The Benthic Boundary Layer from the viewpoint of a geochemist, in The Benthic Boundary Layer, I N McCave, Ed., Plenum, New York, 1976, pp 33–55 Berner, R.A., Early Diagenesis; A Theoretical Approach, Princeton University Press, Princeton, 1980 Brewer, P.G., Minor elements in seawater, in Chemical Oceanography, J.P Riley and G Broecker, W.S., Chemical Oceanography, Harcourt Brace Jovanovich, New York, 1974 Broecker, W.S., A kinetic model for the chemical composition of seawater, Quatern Res., 1, 188–207 (1971) Butler, J.N., Ionic Equilibrium a Mathematical Approach, AddisonWesley, Reading, Mass (1964) Conway, B.E., Annual Review of Physical Chemistry, 17, Annual Reviews Inc., Palo Alto Calif (1966) Dorsey, N.E., Properties of Ordinary Water-Substance, ACS monograph No 81, Reinhold Publishing Corp., New York (1940) 10 Drever, J.I., The Geochemistry of Natural Waters, Prentice Hall, Englewood Cliffs, 1981 11 Eisenberg, D and W Kauzmann, The Structure and Properties of Water, Oxford University Press, England, 1969 12 Fletcher, N.H., The Chemical Physics of Ice, Cambridge University Press, England, 1970 13 Frank, H.S Science, 169, 635 1970 14 Freze, R.A and J.A Cherry, Groundwater, Prentice Hall, Englewood Cliffs, NJ, 1979 15 Garrels, R.M and F.T Mackenzie, Origin of the chemical composition of some spring and lakes, in Equilibrium Concepts in Natural Water Systems, Advances in Chemistry Series, No 67, American Chemical Society, Washington, DC, 1967, pp 222–242 16 Garrels, R.M and C.L Christ, Solutions, Minerals and Equilibria, Harper and Row, New York, 1965 17 Hem, J.D., Study and Interpretation of the Chemical Characteristics of Natural Water, US Geological Survey Water Supply Paper, No 1473, Washington, DC, 1970 18 Hoigne, J and H Bader, Combination of ozone/UV and Ozone/ hydrogen peroxide; Formation of Secondary Oxidants, in Proc 8th World Conference on Ozone, Zurich, 1987 19 Hoigne, J., The Chemistry of Ozone in Water, in Process Technologies for Water Treatment, Plenum, New York, 1988 20 Holland, H.D., The Chemistry of the Atmosphere and Oceans, WileyInterscience, New York, 1978 21 Horne, R.A., Marine Chemistry, The Structure of Water and the Chemistry of the Hydrosphere, Wiley-Interscience, New York, 1969 22 Horne, R.A., Water and Aqueous Solutions, Structure, Thermodynamics, and Transport Processes, Wiley-Interscience, New York, 1972 23 Horne, R.A., Surv Progr Chem., (1968) 24 Hush, N.S., Reactions at Electrodes, Wiley-Interscience New York (1971) 25 Kamb, Structure of the ices, in Horne, R.A., Water and Aqueous Solutions, Wiley-Interscience, New York (1972) 26 Kavanau, J.L., Water and Solute-Water Interactions, Holden-Day, San Francisco, 1964 27 Keyes, F.G., J Chem Phys 17, 923, 1949 28 King, T., Water: Miracle of Nature, The Macmillan Company, New York, 1953 29 Klein, H.P., Ozone in Water Treatment Processes, in Process Technologies for Water Treatment, Plenum, New York, 1988 30 Krindel, P and I Eliezer, Coord Chem Rev., 6, 217, 1971 31 Lerman, A., Geochemical Processes: Water and Sediment Environments, Wiley-Interscience, New York, 1979 © 2006 by Taylor & Francis Group, LLC C023_002_r03.indd 1273 11/18/2005 1:32:11 PM 1274 WATER CHEMISTRY 32 Martin, J.M and M Meybeck, Elemental mass-balance of material carried by major world rivers, Marine Chem., 7, 173, 1979 33 Narten, A.H and H.A Levy, Science, 165, 447, 1969 34 Pimental, G.C and A.L McClellan, The Hydrogen Bond, W.H Freeman and Co., San Francisco, 1960 35 Punzi, V and B.M Nebens, The Chemistry of Seawater Chlorination Advances in Environmental Science and Engineering, Vol 5, Gordon and Breach, New York, 1986 36 Riley, J.P and G Shirrow (eds.), Chemical Oceanography, Volumes, Academic Press, London, 1965 37 Riley, J.P and R Chester, Introduction to Marine Chemistry, Academic Press, London, 1971 38 Sayles, F.L., The Composition and Diagenesis of Interstitial Solutions— Fluxes across the Seawater-Sediment Interface, Geochim Cosmochim Acta, 43, 527–545, 1979 39 Skinner, B.J., Earth Resources, Prentice-Hall, Inc., Englewood Cliffs, New Jersey, 1969 40 Stumm, W and J J Morgan, Aquatic Chemistry: An Introduction Emphasizing Chemical Equilibria to the Chemistry of Natural Waters, Wiley-Interscience, New York, 2nd ed., 1981 41 “Water II” Topic of Journal Colloid Interface Science, 36, No 4, 1971 42 White, G.C., Handbook of Chlorination, Van Nostrant Reinhold, New York, 1989 WERNER STUMM (DECEASED) Swiss Federal Institute of Technology, Zürich MARTIN FORSBERG STEVEN GHERINI Harvard University WASTES OF INDUSTRY: see INDUSTRIAL WASTE MANAGEMENT WATER—DESALTING: see DESALINATION © 2006 by Taylor & Francis Group, LLC C023_002_r03.indd 1274 11/18/2005 1:32:11 PM ... of Water and the Chemistry of the Hydrosphere, Wiley-Interscience, New York, 1969 22 Horne, R.A., Water and Aqueous Solutions, Structure, Thermodynamics, and Transport Processes, Wiley-Interscience,... Electrodes, Wiley-Interscience New York (1971) 25 Kamb, Structure of the ices, in Horne, R.A., Water and Aqueous Solutions, Wiley-Interscience, New York (1972) 26 Kavanau, J.L., Water and Solute -Water Interactions,... 11/18/2005 1:32:08 PM 1262 WATER CHEMISTRY pKH2CO3 pK2 pK1 -1 log CONCENTRATION (MOLAR) -2 -3 CT -4 H+ -2 CO3 * H2CO3 OH– -5 -6 P – HCO3 -7 TRUE H2CO3 -8 a pH 10 11 FIGURE Logarithmic concentration—pH