Modeling Oxygen Solubility in Water and Electrolyte Solutions

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Ind. Eng. Chem. Res. 2000, 39, 805-812

805

Modeling Oxygen Solubility in Water and Electrolyte Solutions Desmond Tromans† Department of Metals and Materials Engineering and the Pulp and Paper Center, University of British Columbia, 6350 Stores Road, Vancouver, British Columbia, Canada V6T 1Z4

A model is presented for estimating oxygen solubility in water and solutions of inorganic electrolytes (I) as a function of oxygen pressure PO2 (atm), temperature T (K), and I. It is based on a thermodynamic analysis for water, where the molal concentration caq of oxygen follows an equation of the form caq ) PO2k and k is a T-dependent function (equilibrium constant) related to the chemical potential, entropy, and partial molar heat capacity of the gaseous oxygen (O2)g and dissolved oxygen (O2)aq species. In the presence of I, the oxygen solubility becomes (caq)I ) φcaq, where φ is a modifying factor < 1 that is dependent on I and its molal concentration CI. The decreasing molar heat capacity of (O2)aq with rising T, which affects k, is discussed. The decrease in φ with increasing CI is related in a general way to the decrease in partial molar volume of the water. Introduction Oxygen dissolved in the aqueous phase (O2)aq is an important oxidant in several industrial processes, ranging from hydrometallurgical pressure leaching and heap leaching of minerals to the bleaching of pulp (wood) fibers. Frequently, (O2)aq is a prime agent promoting metal corrosion. Under circumstances where such processes become limited by mass transport of oxidant, the (O2)aq concentration will exert a major affect on oxidation kinetics. Also, for system design purposes, it is necessary to estimate oxygen evolution during cooling of solutions from high-temperature oxygen pressure leaching conditions to ambient conditions. Thus, a quantitative and predictive knowledge of oxygen solubility is desirable, particularly because it is affected by such process variables as temperature T, partial pressure PO2 of oxygen in the gas phase (O2)g, and inorganic electrolyte solutes I. Measurements of oxygen solubility in water and aqueous solutions have been made for many decades (Battino1). Generally, the development of a unifying and predictive equation model combining the conjoint effects of T, PO2, and I on (O2)aq has proven to be elusive, partly because of the variety of concentration units used for dissolved species and considerable empiricism in reported relationships. Recent thermodynamic studies by the author2,3 have made some progress toward a unifying model. In these studies, a standard set of units, consistent with those generally recommended by IUPAC,4 were adopted and are used in the current study. Thus, pressures are expressed in units of atmospheres (atm), where 1 atm ) 101.325 kPa; the concentrations of (O2)aq and I species are in molal (m) units (i.e., mol/ kg of H2O); and temperature is in degrees Kelvin (K). This study is a continuation and extension of the earlier work (Tromans2,3). It is based on the development of a T- and PO2-dependent model equation describing (O2)aq solubility in pure water, which is presented first, followed by a modification to incorporate the presence of inorganic solutes I. Where possible, pub† Tel: (604) 822-2378. Fax: [email protected].

(604) 822-3619. E-mail:

lished (O2)aq solubility data are compared with the predictions of the model equations, using procedures described in the earlier work to convert original data from other concentration units to m. The objective is to provide a basic unifying model for estimating oxygen solubility in waters, brines, and industrial processing solutions under different combinations of T, PO2, and I. Oxygen in Pure Water The phase equilibrium between (O2)g and (O2)aq is given by

(O2)g ) (O2)aq, k ) [O2]aq/[O2]g ) [Rcaq]/[γPO2] (1) where k is the equilibrium constant, square brackets [ ] denote activity, R is the activity coefficient of (O2)aq, caq is the molal concentration of (O2)aq in pure water, and γ is the fugacity coefficient of (O2)g. The value of k at any T is related to the standard state molar chemical potentials µ°aq and µ°g of the (O2)aq and (O2)g species at T, respectively, and to the overall change in chemical free energy of the reaction ∆G° via eq 2, leading to eq 3, where R is the gas constant (8.3144 J

∆G° ) µ°aq - µ°g ) -RT ln k

(2)

k ) exp(-∆G°/RT) ) exp{(µ°g - µ°aq)/RT}

(3)

mol-1 K-1). The T dependence of k (and caq) is controlled by the effect of T on the exponential function in eq 3. The value of µo for a single species at T2 is related to that at a reference T1 by the standard function in eq 4,2 where

(µ°)T2 ) (µ°)T1 +

∫TT CP ∂T - T2∫TT 2

1

2

1

CP ∂T T S°T1(T2 - T1) (4)

CP is the partial molar heat capacity of the species at constant pressure and S°T1 is its standard entropy at T1. Hence, from known µ° and S° data at T1 the new chemical potentials of each species in its standard state

10.1021/ie990577t CCC: $19.00 © 2000 American Chemical Society Published on Web 02/12/2000

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Ind. Eng. Chem. Res., Vol. 39, No. 3, 2000

Table 1. Standard State Thermodynamic Data, 298 K species statea species µ° (kJ mol-1) So (J mol-1 K-1) (O2)g (O2)aq

g aq

(O2)g (O2)aq

+205.028 +109

0 +16.506

ref Hoare5 Tromans2

a g ) gaseous phase; aq ) aqueous phase. Standard state is unit fugacity for [O2]g and unit activity for [O2]aq using atm for (O2)g and m for (O2)aq.

(unit activity or unit fugacity) may be calculated at T2 to give the new equilibrium constant kT2 at T2,

(

kT2 ) exp

) (

(-∆G°)T2 RT2

) exp

)

(µ°g)T2 - (µ°aq)T2 RT2

(5)

The most common reference T is 298 K (25 °C). Standard µ° and S° values for the gaseous and dissolved oxygen species at 298 K are listed in Table 1, together with their sources.2,5 From reported behaviors of (O2)g, the author2 found that its molar heat capacity (CP)g could be represented by a linearly increasing function of T in the range 273650 K,

(CP)g ) 26.65 + (9 × 10-3)T (J mol-1 K-1) (6)

Figure 1. Comparison of predicted oxygen solubility in pure water with experimental data.

Also, an analysis of oxygen solubility data established that the partial molar heat capacity (CP)aq of (O2)aq was much larger than (CP)g and could be represented by a linearly decreasing function of T in the range 273-650 K,2

For PO2 to ∼60 atm and T to 616 K, R/γ may be closely approximated to unity2 so that eq 9 becomes

(CP)aq ) 230 - (8.3 × 10-2)T (J mol-1 K-1) (7)

where caq is in units of mol of O2/kg of H2O (m), PO2 is in atm, and k is given by eq 8. Thus, eq 10 is a unified oxygen solubility model for pure water. It is based on thermodynamics and allows computation of the solubility of (O2)aq for any combination of T and PO2 up to 616 K and 60 atm. These conditions encompass those likely to be encountered during industrial pressure oxidation (leaching) processes. Figure 1 confirms the general validity of eq 10 by showing that predicted caq/PO2 values (equivalent to k) compare well with published experimental solubility data,6-11 after converting all original solubilities to molal (m) concentrations. Most importantly, the experimental data were obtained over a wide range of T and PO2 combinations spanning the applicable range of eq 10 up to 616 K and 60 atm. For example, Hayduk’s6 conditions cover 1-10 atm PO2 and 323-458 K; the studies of Pray et al.7 span ∼7-21 atm PO2 and 436616 K; the work of Broden and Simonson8 includes the ranges 10-49 atm PO2 and 373-423 K; the studies of Stephan et al.9 span ∼19-62 atm PO2 and 373-561 K; the conditions of Benson et al.10 are near 1 atm PO2 from 273-333 K; and Cramer’s11 conditions range from 42 atm PO2 at 278 K to 50 atm PO2 at 573 K. Note that eq 10 predicts a minimum solubility (minimum k) of 7.79 × 10-4 m/atm at 368 K (95 °C), consistent with the experimental data.

If the heat capacities in eqs 6 and 7 do not change significantly with change in pressure at constant T (i.e., (∂CP/∂P)T ) 0), they may be inserted into eq 5 to yield T-dependent k values that are independent of PO2. In fact, (∂CP/∂P)T ) 0 for an ideal gas and (O2)g may be considered to exhibit ideal behavior up to 616 K and ∼60 atm, because the calculated fugacity coefficient γ remains close to unity.2 In the case of the aqueous phase (O2)aq, it is assumed that its behavior may be approximated to that of an ideal incompressible liquid (at least under the aforementioned temperature and pressure conditions). Thus, there is insignificant change in the molar volume of (O2)aq as the pressure is changed at constant T (insignificant work done by the system), leading to the condition (∂CP/∂P)T ) 0 for (O2)aq. In the final analysis, justification of these assumptions is determined by the level of agreement between oxygen solubility predictions based on the resulting k and reported experimental values. From eqs 4-7, together with the data in Table 1 and using a reference temperature T1 of 298 K, it is a straightforward exercise to show that the T-dependent value of k at any arbitrary value of T (equivalent to T2) is given by eq 8

k ) exp{[0.046T2 + 203.35T ln(T/298) - (299.378 + 0.092T)(T - 298) - 20.591 × 103]/8.3144T} (8) Furthermore, rearrangement of eq 1 leads to

caq(R/γ) ) PO2k

(9)

caq ) PO2k

or

caq/PO2 ) k

(10)

T Dependence of (CP)aq The value of (CP)aq and its specific T dependence controls the shape of the solubility curve and the position of the solubility minimum in Figure 1. Moreover, the higher value of (CP)aq, relative to (CP)g, is indicative of interactions between (O2)aq and the sur-

Ind. Eng. Chem. Res., Vol. 39, No. 3, 2000 807

D ) A exp(-∆HD/RT) (cm2 s-1)

(14)

where A is 1.383 × 107kB/λ (i.e., 1.363 × 10-2 cm2 s-1) and ∆HD is the T-dependent activation energy for selfdiffusion of water (i.e., ∆HD ) 14227 + 4.661 × 1019T-6.8132 (J mol-1 K-1). Evidently, ∆HD decreases with T (e.g., from 15.453 kJ mol-1 K-1 at 273 K to 14.417 kJ mol-1 K-1 at 373 K). The energy of the hydrogen bond in water is estimated to be near ∼17 kJ mol-1 (Pauling14), similar in magnitude to ∆HD. Thus, the decrease in ∆HD with rising T indicates a decrease in hydrogen bonding between H2O molecules and is consistent with the decrease in (CP)aq with rising T. Effect of Inorganic Solutes I on the Partial Molar Volume of Water

Figure 2. Comparison of eq 11 with viscosity data for water.

rounding water molecules, including changes in molecular rotations and bond vibrations between the neighboring water molecules. Consequently, the decrease in (CP)aq with rising T in eq 7 is likely to be related to a decrease in the hydrogen-bonding interactions between water molecules. If this interpretation is correct, other factors related to interactions and movement between water molecules, such as the activation energy for the self-diffusion of water, should decrease with increasing T. This may be confirmed by examining the relationship between T, viscosity η, and the self-diffusion coefficient D in pure water. Viscosity data listed by Weast12 in the range 273373 K are shown as data points in Figure 2. These were analyzed by the author and found to fit eq 11 (shown as a continuous line in Figure 2),

η ) 7.232 ×

(

10-8T exp

)

14277 + 4.661 × 1019T-6.8132 RT

(P) (11)

For convenience, the data are reported in cP units in Figure 2, where 1 cP ) 0.01 P, and the P units are g s-1 cm-1 (equivalent to 10-1 Pa s). The relationship between D and η for water has been derived by Glasstone et al.13

D)

( )

k BT (cm2 s-1) λη

(12)

where kB is the Boltzmann constant with a value of 1.38 × 10-16 erg K-1 molecule-1 (equivalent to 1.38 × 10-23 J K-1 molecule-1), λ is approximately 1.4 × 10-7 cm (1.4 nm) per molecule of water, and η is in P units. Combining eq 11 with eq 12 produces

D ) 1.383 × kB -14277 - 4.661 × 1019T-6.8132 (cm2 s-1) 107 exp λ RT (13)

(

)

which has the form of an Arrhenius rate equation

Complex interactions and disturbances occur between the polar water molecules and the ionic components of inorganic electrolytes I, such as salts (e.g., see Robinson and Stokes,15 Samoilov,16 Loche and Donohue,17 and Conway and Ayranci18). For convenience, such behavior is often considered in terms of near-field (primary hydration) and far-field (secondary hydration) effects. Near- and far-field distinctions are used primarily for separating and analyzing the dominant effects of nearest water interactions on the kinetic properties of ions, such as diffusion and viscosity behavior. For nonkinetic properties, such as solution density and heats of hydration, all ion-water interactions (near and distant) contribute to the behavior (Samoilov16). Without specifying the detailed (and unresolved) mechanisms by which the presence of an ionized solute interacts with water and influences the solubility of a neutral species such as (O2)aq, it seems likely that oxygen solubility will exhibit behavior that relates in a general manner to changes in the nonkinetic properties of the solution. Interactions between ions and water should influence the overall average spacing between H2O molecules so that the partial molar volume of the water component changes from that of pure water, VH2O, to an apparent value Vapp,

Vapp )

{(

)

}

MH2O 1000 + CIMI - CIVI ds 1000

(15)

where CI is the molal concentration of solute I, MI is the molecular weight of I, VI is the molar volume of the anhydrous crystalline I (assumed to remain unaffected by solvation), MH2O is the molecular weight of water (18 g), and ds is the density of the solution. Values of VI for 22 solutes were obtained from published crystallographic and density information at ∼298 K (Powder Diffraction File19). These are listed in Table 2, together with their corresponding MI. In situations where several sets of diffraction data were reported for I, the NBS set was chosen. Subsequently, Vapp was calculated from eq 15, using ds data from the International Critical Tables.20 In all cases, Vapp decreased with increasing CI. Results illustrating this behavior are shown for seven representative I in Figures 3 and 4, where they are presented in terms of the ratio Vapp/VH2O and VH2O is given by

VH2O ) MH2O/dH2O

(16)

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Ind. Eng. Chem. Res., Vol. 39, No. 3, 2000

Table 2. Molar Volume (VI) and Molecular Weight (MI) of Anhydrous Solutes (I) solute I

VI (mL)

MI (g)

solute I

VI (mL)

MI (g)

NaNO3 Na2SO3 Na2CO3 NaOH KOH NaBr KBr NaCl KCl Na2SO4 K2SO4

37.6 47.93 41.74 18.93 29.22 32.16 43.21 27.02 37.52 53.33 65.48

85 126.06 106.01 40 56.11 102.9 119 58.44 74.56 142.04 174.25

Ca(NO3)2 MgSO4 ZnSO4 CoSO4 NiSO4 CuSO4 MgCl2 CaCl2 BaCl2 AlCl3 Al2(SO4)3

66.09 40.7 41.57 40.18 38.58 40.87 40.81 50.5 52.87 53.64 119.5

164.09 120.37 161.44 155 154.76 159.56 95.22 111 208.24 133.34 342.14

Figure 4. Effect of solute concentration and T on the apparent partial molar volume water.

φ ) f(CI), where φ f 1 as CI f 0 and φ f 0 as CI . 1 (Tromans3). A suitable function requiring positive values for the coefficient κ and exponents y and h is given by eq 18, leading to eq 19 after combining with eq 17.

Figure 3. Effect of solute concentration on the apparent partial molar volume of water.

where the T-dependent density values of pure water, dH2O, were obtained from Weast.12 Effect of Inorganic Solutes I on Oxygen Solubility On the basis that the Vapp/VH2O ratio decreases with increasing CI, it would appear likely that the solubility of (O2)aq should also decrease with increasing CI. For example, simple logic suggests that if the addition of a specific I lowers the ratio, the water component has less “volume” in which to accommodate the (O2)aq species and oxygen is “squeezed” from solution. This may be restated another way by proposing that only a fraction φ of the water component is available for dissolving the oxygen, the other (1 - φ) fraction being unavailable because of ion-water interactions with I. This leads to a conceptually simple relationship between the molal oxygen solubility (caq)I in the presence of I and the oxygen solubility caq in pure water,

(caq)I ) φcaq ) φPO2k

(17)

where caq and k are obtained from eqs 10 and 8, respectively. For modeling purposes, it is sufficient to treat the dependence of φ on CI in terms of an empirical function,

φ ) {1 + κ(C1)y}-h

(18)

(caq)I ) PO2k{1 + κ(C1)y}-h

(19)

Experimental φ fractions at 298 K and 1 atm PO2 may be obtained from the ratio (caq)I/caq, using available solubility data (after converting all data to molal concentrations). These may then be fitted to eq 18 to determine the corresponding κ, y, and h for each I. Experimental values for seven different I (corresponding to those in Figures 3 and 4) are shown in Figures 5 and 6, respectively. The original data sources (Figures 521-23 and 621,22,24-27) are listed in each figure. Where possible, systematic errors between different data sets were minimized by normalizing the measured (caq)I with respect to the measured caq in each data set. If the measured caq differed by >(10% from that in eq 10 (i.e., 12.878 × 10-4 m), the whole data set was discarded. If no caq was reported, the value from eq 10 was used. The solid lines in Figures 5 and 6 represent bestfitting curves, according to eq 18. The corresponding κ, y, and h values are listed in Table 3. It is evident that eq 18 is a satisfactory relationship at 298 K and may be used with great utility in eq 19 to compute (estimate) the value of (caq)I at any arbitrary CI, provided the necessary κ, y, and h are known. In this regard, sets of κ, y, and h values for 15 other I, obtained previously in the same manner (Tromans3), are included in Table 3. No specific conclusions should be drawn from the absolute values of κ, y, and h, because they are empirical modeling parameters required to satisfy the boundary conditions of eq 18. They are not based on detailed (and unresolved) mechanisms by which an ionized solute interacts with water to influence the solubility of a neutral species, such as (O2)aq. Consequently, no value

Ind. Eng. Chem. Res., Vol. 39, No. 3, 2000 809 Table 3. Values of Coefficients and Exponents in Equation 17 solute I

κ

y

h

ref

NaNO3 Ca(NO3)2 Na2SO3 Na2CO3 NaCl NaOH CuSO4 CoSO4 NiSO4 KOH KBr NaBr KCl Na2SO4 K2SO4 MgSO4 ZnSO4 MgCl2 CaCl2 BaCl2 AlCl3 Al2(SO4)3

0.314 0.021 0.332 0.34 0.076 0.102 2.232 2.232 2.232 0.102 0.035 0.035 0.407 0.63 0.55 0.12 0.233 0.18 0.18 0.18 0.381 0.641

1.084 0.947 1.03 1.1 1.01 1.0 1.116 1.116 1.116 1.0 0.926 0.926 1.116 0.912 0.912 1.108 1.01 0.985 0.985 0.985 0.804 0.955

0.883 21.04 2.67 3.13 4.224 4.309 0.223 0.223 0.223 4.309 7.095 7.095 0.842 1.44 1.44 5.456 2.656 2.711 2.711 2.711 1.684 3.034

this study

Tromans3

Figure 5. Effect of solute concentration on the φ fraction.

Figure 6. Effect of solute concentration on the φ fraction.

Figure 7. Effect of solute-induced fractional decrease in the molar volume ratio of water on φ.

other than the requirement to be positive is preassigned to any one parameter. It is the shape and relative position of each φ curve that is important in regard to its functional utility. Some curves may have similar shapes but different parameters. The use of three parameters, κ, y, and h, simply allows the φ curve to be fitted more closely to the available experimental data. Using eq 19 and the data in Table 3 to find the changes in φ with CI and using eqs 15 and 16 to find the Vapp/VH2O ratio at the same CI, it is now possible to plot the effect of the fractional decrease in the molar volume ratio of water, Vapp/VH2O, on the φ fraction for all I listed in Tables 2 and 3. The results are presented in Figures 7-9 at 298 K. Figures 7 and 8 show that 14 I solutes exhibit similar behavior. As the fraction 1 - Vapp/VH2O increases, the φ fraction decreases and all behaviors are close to that of

the KOH curve. Such effects suggest a common relationship between the decreasing molar volume of the water component and decreasing oxygen solubility. The remaining seven solutes in Figure 9 also show a decreasing φ with increasing 1 - Vapp/VH2O, consistent with the trend in Figures 7 and 8. However, the solute effects are separated into two groups of behavior, with one group lying above the KOH curve and one below. The upper curve contains 2:2 salts of divalent transition metal ions (Cu2+, Co2+, and Ni2+), all of which contain an unsaturated 3d-electron shell in the ionic state. The lower curve contains 1:1 salts (excluding the hydroxides) of the univalent group I metals (Na+ and K+). Thus, while changes in Vapp/VH2O are sufficient to indicate trends in oxygen solubility behavior for many inorganic solutes, the specific ionic (electronic) nature of the solute may influence the detailed behavior.

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Ind. Eng. Chem. Res., Vol. 39, No. 3, 2000

Figure 8. Effect of solute-induced fractional decrease in the molar volume ratio of water on φ.

Figure 10. Predicted and measured effects of T and three solutes on oxygen solubility.

in Figure 9. For example, NaOH belongs to the KOH group (Figure 7), CuSO4 lies above the KOH group, and NaCl lies below the KOH group (Figure 9). To test the relative T independence of φ for CuSO4, NaCl, and NaOH, eq 19 was rearranged to give

(caq)I/PO2 ) kφ ) k{1 + κ(CI)y}-h

(20)

The predicted (caq)I/PO2 ratio is plotted against T in Figure 10 for three solutions containing 1.5254 m CuSO4 (φ ) 0.713), 1.5011 m NaOH (φ ) 0.541), and 5.59 m NaCl (φ ) 0.216), using eq 8 for k and eq 18 and Table 3 to calculate φ. These are compared with experimental (caq)I/PO2 ratios obtained for the same solutions from the work of Von Bruhn et al.24 and Cramer.11 Within the limitations and difficulties of measuring oxygen solubility at the higher T (and higher PO2), there is reasonable agreement between predicted and experimental (caq)I/ PO2 ratios. Thus, eq 20 appears to be a generally useful relationship for predicting (estimating) oxygen solubility for engineering purposes under different combinations of T, PO2, and CI. Multiple I Figure 9. Effect of solute-induced fractional decrease in the molar volume ratio of water on φ.

Conjoint Effects of T and I on Oxygen Solubility The φ function of eq 17 becomes an effective modeling parameter if it may be assumed to be independent of T, at least as far as first approximation treatments are concerned. In this event, values of κ, y, and h obtained under the conditions of 298 K and 1 atm PO2 in Table 3 may be used in eq 19 to cover different T. There is a general lack of data against which to test this assumption widely. However, some indirect information indicating the possible T-independent nature of φ is found in Figure 4. This figure shows that the Vapp/VH2O ratio curves for CuSO4, NaCl, and NaOH are relatively independent of T, an important observation because these solutes belong to the three groupings of φ behavior

A multiple I situation is probably more common for industrial oxygenated solutions and also one for which there is a dearth of experimental information against which to test oxygen solubility models. However, it seems likely that in the presence of z different solutes I1, I2, ..., Iz, with φ factors φ1, φ2, ..., φz, arranged so that φ1 q > 0, that has been shown to have a likely value near 0.8 (Tromans3). After substituting φeff for φ in eq 20, the solubility model for multiple I becomes z

(caq)I/PO2 ) kφeff ) kφ1(

φi)q ∏ 2

(22)

where k is given by eq 8 and the individual φ factors, φ1, φ2, ..., φz, are obtained from eq 18 and Table 3. Conclusions A thermodynamics-based model equation has been developed for the quantitative prediction of the molal concentration of oxygen in pure water as a function of T and PO2 that is in excellent agreement with published solubility data. This has been modified for inorganic solutes by multiplying the equation by an empirical, T-independent factor (φ fraction) that is < 1 and is dependent upon the type of solute I and its concentration CI. The modified equation is capable of providing quantitative estimates of oxygen solubility in aqueous inorganic solutions under different combinations of T, PO2, and CI. The decrease in φ with increasing CI appears to be related to the apparent decrease in the molar volume of the water component. Acknowledgment The author thanks the Natural Sciences and Engineering Research Council of Canada for financial support of the work. Nomenclature caq ) concentration of (O2)aq in pure water (mol/kg of H2O) (caq)I ) concentration of (O2)aq in solution of I (mol/kg of H2O) ds ) density of solution dH2O ) density of pure water CI ) concentration of I (mol/kg of H2O) CP ) molar heat capacity at constant pressure (CP)aq ) CP for (O2)aq (CP)g ) CP for (O2)g D ) diffusion coefficient of H2O ∆G° ) standard change in chemical free energy h ) empirical exponent ∆HD ) self-diffusion activation energy of H2O I ) inorganic solute k ) equilibrium constant kB ) Boltzmann constant m ) molal (mol/kg of H2O) MI ) molecular weight of I MH2O ) molecular weight of water (O2)aq ) molecular oxygen in the aqueous phase (O2)g ) molecular oxygen in the gas phase PO2 ) partial pressure of (O2)g (atm) q ) empirical exponent, 1 > q > 0 R ) gas constant S° ) standard entropy of species T ) temperature (K) VI ) molar volume of anhydrous I Vapp ) apparent molar volume of water in solution VH2O ) molar volume of pure water y ) empirical exponent z ) number of different I R ) activity coefficient φ ) fraction < 1 dependent upon I

φi ) value of φ for the ith I φeff ) effective value of φ in the presence of multiple I γ ) fugacity coefficient η ) viscosity κ ) empirical coefficient λ ) linear dimension related to diffusion of a H2O molecule µ° ) standard chemical potential of species µ°aq ) standard chemical potential of (O2)aq µ°g ) standard chemical potential of (O2)g

Literature Cited (1) Battino, R., Ed. Oxygen and Ozone; IUPAC Solubility Data Series 7; Pergamon: Elmsford, NY, 1981. (2) Tromans, D. Temperature and pressure dependent solubility of oxygen in water: a thermodynamic analysis. Hydrometallurgy 1998, 48, 327-342. (3) Tromans, D. Oxygen solubility modeling in inorganic solutions: concentration, temperature and pressure effects. Hydrometallurgy 1998, 50, 279-296. (4) Mills, I., Cvitasˇ, T., Homann, K., Kallay, N., Kuchitsu, K., eds. Quantities, Units and Symbols in Physical Chemistry; International Union of Pure and Applied Chemistry, Blackwell Science: Oxford, U.K., 1993. (5) Hoare, J. P. In Standard Potentials in Aqueous Solutions; Bard, A. J., Parsons, R., Jordan, J., Eds.; IUPAC, Marcel Dekker: New York, 1985; pp 49-66. (6) Hayduk, W. Final Report Concerning the Solubility of Oxygen in Sulfuric Acid-Zinc Pressure Leaching Solutions; DDS Contract UP 23440-8-9073/01-SS; Department Chemical Engineering, University of Ottawa: Ottawa, Ontario, Canada, 1991. (7) Pray, H. A.; Schweickwert, C. E.; Minnich, B. H. Solubility of hydrogen, oxygen, nitrogen, and helium in water at elevated temperatures. Ind. Eng. Chem. 1952, 44, 1146-1151. (8) Broden, A.; Simonson, R. Solubility of oxygen: Part I Solubility of oxygen in water at temperatures e 150 °C and pressures e 5 Mpa. Sven. Papperstidn. 1978, 81, 541-544. (9) Stephan, E. L.; Hatfield, N. S.; Peoples, R. S.; Pray, H. A. Report BMI 1067; Battelle Memorial Institute: Columbus, OH, 1956. (10) Benson, B. B.; Krause, D., Jr.; Peterson, M. A. The solubility and isotopic fractionation of gases in dilute aqueous solution. I. Oxygen. J. Solution Chem. 1979, 8 (9), 655-690. (11) Cramer, S. D. The solubility of oxygen in brines from 0 °C to 300 °C. Ind. Eng. Chem., Process Des. Dev. 1980, 19, 300-305. (12) Weast, R. C., Ed. CRC Handbook of Chemistry and Physics, 58th ed.; CRC Press Inc.: West Palm Beach, FL, 1978; pp D-180, F-11, F-51, F-210. (13) Glasstone, S.; Laidler, K. J.; Eyring, H. The Theory of Rate Processes; McGraw-Hill: New York, 1941; pp 516-521. (14) Pauling, L. The Nature of the Chemical Bond; Cornell University Press: Ithaca, NY, 1948; pp 303-304. (15) Robinson, R. A.; Stokes, R. H. Electrolyte Solutions; Butterworths: London. U.K., 1959; pp 1-23. (16) Samoilov, O. Ya. Structure of Aqueous Electrolyte Solutions and the Hydration of Ions, translated from Russian by D. J. G. Ives; Consultants Bureau: New York, 1965; pp 74-185. (17) Loche, J. R.; Donohue, M. D. Recent advances in modeling thermodynamic properties of aqueous strong electrolyte systems. AIChE J. 1997, 43 (1), 180-195. (18) Conway, B. E.; Ayranci, E. Effective Radii and Hydration Volumes for Evaluation of Solution Properties and Ionic Adsorption. J. Solution Chem. 1999, 28 (3), 163-192. (19) Powder Diffraction File; PCPDFWIN; JCPDS-International Center for Diffraction Data: Swarthmore, PA, 1995. (20) Washburn, E. W., Ed. International Critical Tables of Numerical Data, Physics, Chemistry and Technology; National Research Council; McGraw-Hill Inc.: New York, 1928; Vol. III, pp 54-95. (21) Khomutov, N. E.; Konnik, E. I. Solubility of oxygen in aqueous electrolyte solutions. Zh. Fiz. Khim. (in Russian) 1974, 48 (3), 620-625. (22) Yasunishi, A. Solubility of oxygen in aqueous electrolyte solutions. Kagaku Kogaku Ronbunshu, 1978, 4 (2), 185-189.

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(23) Gestrich, W.; Pontow, B. Oxygen solubility in aqueous sulfite solutions having concentrations up to 1.2 mol/L. Chem.Ing.-Tech. 1977, 49 (7), 564-565. (24) Von Bruhn, G.; Gerlach, J.; Pawlek, F. Untersuchungen u¨ber die Lo¨slichkeiten von Salzen und Gasen in Wasser und wa¨βrigen Lo¨sungen bei Temperaturen oberhalb 100 °C (Investigation on the Solubilities of Salts and Gases in Water and Aqueous Solutions at Temperatures above 100 °C). Z. Anorg. Allg. Chem. 1965, 337, 68-79. (25) Geffcken, G. Beitrage zur Kenntnis der Lo¨slichkeitsbeeinflussung (Contributions to the Knowledge of Factors Which Affect Solubilities). Z. Phys. Chem. 1904, 49, 257-302.

(26) Eucken, A.; Hertzberg, G. Z. Aussalzeffekt und Ionenhydratation (Salt Effects and Ion Hydration). Z. Phys. Chem. 1950, 195, 1-23. (27) MacArthur, C. G. Solubility of O2 in salt solutions and the hydrates of these salts. J. Phys. Chem. 1916, 20, 495-502.

Received for review August 2, 1999 Revised manuscript received December 2, 1999 Accepted December 6, 1999 IE990577T