Ionization equilibria of acids and bases under

Aqueous Systems at Elevated Temperatures and Pressures: Physical Chemistry in Water, Steam and Hydrothermal Solutions D.A. Palmer, R. Fernańdez-Prini and A.H. Harvey (editors) q 2004 Elsevier Ltd. All rights reserved

Chapter 13

Ionization equilibria of acids and bases under hydrothermal conditions Peter Tremaine,a,* Kai Zhang,a Pascale Beńe´zethb and Caibin Xiaoc a

Department of Chemistry, University of Guelph, Guelph, Ont., Canada N1G 2W1 Chemical Sciences Division, Oak Ridge National Laboratory, Building 4500S, P.O. Box 2008, Oak Ridge, TN 37831-6110, USA c GE Water Technologies, 4636 Somerton Road, P.O. Box 3002, Trevose, PA 19053-6783, USA b

13.1. Introduction 13.1.1. Acids and Bases Under Hydrothermal Conditions The properties of acids and bases control much of the aqueous chemistry of geochemical, industrial and biological systems. Ionization constants for simple acids and bases at 25 8C are tabulated in many sources, including all undergraduate chemistry textbooks. The behavior of acids and bases, including the ionization of water itself, under extremes of temperature and pressure is much less widely known. Our purpose in this chapter is to present a practical discussion and compilation of the effects of temperature, pressure, and in some cases, ionic strength on the ionization constants of simple acids and bases, from room temperature to hydrothermal conditions. The first measurements of the ionization constants of water and aqueous acids and bases were made by Noyes (1907), who used the change in conductance associated with ionization to measure equilibrium constants up to about 300 8C at steam saturation. Only modest research on hydrothermal effects was carried out until the 1950s, when interest in nuclear reactor coolant chemistry led national laboratories in several countries to develop experimental methodologies suitable for the corrosive conditions encountered at elevated temperatures. Complementary studies by geochemists investigating geothermal systems and ore body formation have led to the development of additional experimental techniques suitable for near critical and supercritical conditions

* Corresponding author. E-mail: [email protected]

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(see, e.g., Mesmer et al., 1997; Ulmer and Barnes, 1983). Academic research has been spurred by these applications and by a desire to use wide variations in temperature and pressure as a probe to understand ion– water and ion – ion interactions. The first two sections of this chapter consist of a short review of the underlying chemical thermodynamics, experimental methods and the substituent and hydration effects that determine the magnitude of the ionization constants of acids and bases at elevated temperatures and pressures. The remaining four sections describe the behavior of several classes of inorganic and organic acids and bases. The chapter includes practical tables for use by non-specialists, based on the equations and database for the dissociation of water developed at Oak Ridge National Laboratory (Mesmer et al., 1970; Busey and Mesmer, 1978; Palmer and Drummond, 1988). 13.1.2. Thermodynamic Relations 13.1.2.1. Equations for Pressure and Temperature Dependence of DGo and log10 K Here we are concerned with the Bronsted definition of acids and bases, as solutes capable of releasing hydrogen ions and hydroxide ions, respectively. HAðaqÞ O Hþ ðaqÞ þ A2 ðaqÞ

ð13:1Þ

and BðaqÞ þ H2 OðlÞ O BHþ ðaqÞ þ OH2 ðaqÞ

ð13:2Þ

2

The ionization product A (aq) is the conjugate base of HA(aq), because it behaves as a base in reacting with water to form HA(aq). A2 ðaqÞ þ H2 OðlÞ O HAðaqÞ þ OH2 ðaqÞ

ð13:3Þ

Similarly, BHþ(aq) is the conjugate acid of B(aq). The equilibrium quotient of the acid ionization reaction, reaction 13.1, is defined as Q1a ¼ mA2 mH2 =mHA

ð13:4Þ

where mA2 ; mHþ and mHA are molalities of the species A2(aq), Hþ(aq) and HA(aq), respectively. Molalities (mol·kg21) are generally used instead of concentration (mol·dm23) because molalities are not affected by the expansion or contraction of water with temperature and pressure. The equilibrium quotient Q1a is a function of temperature, pressure and ionic strength. The equilibrium constant of reaction 13.1 refers to infinitely dilute solutions in the hypothetical 1 mol·kg21 standard state, and thus it is not a function

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of ionic strength: K1a ¼ aA2 aHþ =aHA

ð13:5Þ

where aA2 ; aHA and aHþ are activities in molality units. The corresponding expressions may be written for the ionization of bases, which we define as Qb and Kb. The ratio between molalities and activities of solutes is defined as the activity coefficient, g ¼ a=m; so that log10 K1a ¼ log10 Q1a þ log10 ðgA2 gHþ =gHA Þ

ð13:6Þ

where gA2 ; gHþ and gHA are activity coefficients of A2(aq), Hþ(aq) and HA(aq), respectively. Since the last term in Eq. 13.6 vanishes as ionic strength approaches zero, log10 K1a is usually obtained from experimentally determined log10 Q1a values by extrapolation to infinite dilution. Values for log10 K can also be calculated from the Gibbs energy change of the reaction through the relationship: DGo ¼ 2RT ln K

ð13:7Þ

where T is the temperature in kelvin and R is the molar gas constant. The Gibbs energy change is not usually determined experimentally at elevated temperature but rather is calculated from experimental values of K measured by means of potentiometric titration or other techniques. The temperature dependence of log10 K is described by the following relationships. Starting with two basic thermodynamic equations, DGo ¼ DH o 2 TDSo and DSo ¼ 2ð›DGo =›TÞp ; we have ð

dðDGo =TÞ ¼ 2DH o =T 2 dT

ð13:8Þ

If DH o of a reaction is independent of temperature and pressure, then log10 KT;p ¼ log KTr ;pr þ DHTor ;pr ð1=Tr 2 1=TÞ=ð2:303RÞ

ð13:9Þ

where r is the reference state ðTr ¼ 298:15 KÞ: The above equation does not provide a satisfactory estimation for log10 K at elevated temperatures, especially for reactions with an asymmetric charge distribution. More accurate estimations for log10 K require the addition of standard partial molar heat capacity and volume functions for the reaction. Adding DV ¼ ð›DG=›pÞT and DCp ¼ Tð›DS=›TÞp into the exact differential equation yields the expression: dDG ¼ ð›DG=›TÞp dT þ ð›DG=›pÞT dp

ð13:10Þ

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which can be integrated from the reference state ðTr ; pr Þ to state ðT; pÞ; yielding the expression: ð ð o o o o o DCp =T dT þ DSTr ;pr dT þ DV dp ð13:11Þ DGT;p ¼ DGTr ;pr þ path

path

The above line integral is independent of the path chosen. However, the path for the first part (heat capacity) must be the same as for the second (volume) part. For T , critical temperature, integration along the saturation curve yields log10 KT;p ¼ ðlog10 KTr ;pr þ DHTor ;pr ð1=Tr 2 1=TÞÞ=ð2:303RÞ ð ð ð þ ðDCpo =TÞ dT 2 ð1=TÞ DCpo dT 2 ðDV o =TÞ dp

ð13:12Þ

Appropriate expressions for DCpo and DV o can be used as a fitting expression in Eq. 13.12, to represent the temperature and pressure dependence of experimental values for log10 K. Alternatively, if DCpo and DV o are known as a function of temperature, Eq. 13.12 can be used to calculate log10 K vs. T and p (Pitzer, 1995; Mesmer et al., 1988). The effects of temperature and pressure on activity coefficients are discussed below. 13.1.3. Acid– Base Equilibria to 300 8C 13.1.3.1. Factors Controlling the Ionization of Acids and Bases at Elevated Temperatures and Pressures The principles governing the ionization of acids and bases at elevated temperatures and pressures have been discussed by Mesmer et al. (1988, 1991) and others (e.g., Fernańdez-Prini et al., 1992; Levelt Sengers, 1991), using interpretations based on hard-won experimental data for about 20 systems, described in subsequent sections. At ambient temperatures, liquid water consists of long-range hydrogen-bonded networks, roughly tetrahedral, that extend on a time-averaged basis to three or more nearest neighbors, with a considerable degree of thermal motion and inter-penetration (Svishchev and Kusalik, 1995). As the temperature is raised along the saturation pressure curve, long-range hydrogen bonding breaks down and water becomes more compressible until, at the critical temperature and pressure, the compressibility of water becomes infinite. The degree of ionization, i.e., the magnitude of the ionization constant in reaction 13.1 or 13.2, is governed by the thermodynamic relationship that defines Gibbs energy: DGo ¼ DH o 2 TDSo ¼ DU o þ pDV o 2 TDS o

ð13:13Þ

At ambient temperatures and pressures, the hydration of the species HA(aq), Hþ(aq) and A2(aq) reflects hydrogen bonding effects associated with both


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short-range and long-range interactions with water. Strong hydrogen bonding to the acid or conjugate base that minimizes energetic effects (DU o) may cause the entropic term (DS o) and volumetric term (DV o) to also be reduced. The difficulties in modeling hydration effects that have occupied researchers for more than 100 years result from the subtle balance between these three effects that exists at temperatures near 25 8C. Raising the temperature and pressure causes the equilibrium of ionization reactions 13.1 and 13.2 to shift in the direction that favors smaller volumes ( pDV o , 0) and greater entropies (TDS o . 0). The effect is illustrated schematically in Fig. 13.1, which depicts the ionization process as the insertion of uncharged and charged spheres into liquid water. At ambient temperatures, short-range and long-range interactions around the ionized and neutral acids and bases are species-specific so that DG o can shift in either a positive or negative direction with modest increases in temperature and pressure, depending on the number of hydrogen-bond acceptors and donors, the charge, and the size and shape of the species in question. At temperatures above about 200 8C, however, longrange solute– water interactions begin to dominate as a result of the decreased hydrogen bonding in water itself and the resulting increased compressibility of liquid water. Figure 13.2 shows that the standard partial molar volumes of morpholine and its chloride salt, morpholinium chloride up to 300 8C (Tremaine et al., 1997) deviate towards þ and 2 infinity at the critical point of water. The result is that we can draw the following general conclusions: † Increasing the temperature above about 250 8C along the steam saturation pressure curve towards the critical point causes the ionization constants of neutral acids and bases to decrease. † Increasing the pressure at temperatures above about 250 8C causes the ionization constant to increase.

Fig. 13.1. The solvation of ions and non-electrolytes in high-temperature water. Elevated temperatures favor ion-pairing and long-range interactions dominate as the compressibility of liquid water increases.

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Neutral Species

125

C4H8ONH

V˚2 /(cm3. mol –1)

100

75

50

Ionic Species C4H8ONH2+Cl–

25

0 0

50

100

150

200

250

300

350

t / ˚C Fig. 13.2. Standard partial molar volumes of neutral morpholine and its salt, morpholinium chloride, showing increasingly large positive and negative deviations as the temperature is raised along the steam saturation curve (Tremaine et al., 1997). The solid line is a fit to an extended version of the ‘density’ model discussed in the text.

† At temperatures below 100 8C, ionization behavior is species-specific. † Ionization constants in the range 100 , t , 250 8C display intermediate behavior. Here and elsewhere, the symbol t is used for temperature in 8C. Typical values of log10 K for ionization equilibria below 300 8C are plotted as a function of temperature in Fig. 13.3. Experimental ionization and association constants have been measured under supercritical conditions, primarily using the conductivity, heat capacity and density methods described in a later section and by Mesmer et al. (1991). The major factors controlling ionization above the critical point of water continue to be temperature and solvent density, for the reasons described above. 13.1.3.2. Isocoulombic Extrapolations Experimental measurements of log10 K and the other thermodynamic constants used in Eq. 13.12 at elevated temperatures and pressures are extremely difficult. As a result, the standard Gibbs energies of formation, standard enthalpies of formation and partial molar entropies for many species are known only at ambient


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Fig. 13.3. Temperature dependence of the association constants for the formation of weak acids and bases.

temperatures. Many of the effects of ionic strength, temperature and pressure can be minimized by writing ionization reactions so that they are symmetric with respect to ionic charge, i.e., the so-called ‘isocoulombic’ reactions (Lindsay, 1989, 1990). For example, the ionization of an acid may be written as HAðaqÞ þ OH2 ðaqÞ O H2 OðlÞ þ A2 ðaqÞ

ð13:14Þ

so that the charges of the reactants and products are the same. Similarly, the ionization equilibrium of a base is written as BðaqÞ þ Hþ ðaqÞ O BHþ ðaqÞ

ð13:15Þ

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The equilibrium quotients of neutralization reactions, such as reactions 13.14 and 13.15, are defined as mA2 ð13:16Þ Q1a;OH ¼ Q1a =Qw ¼ mHA mOH2 and Q1b;H ¼ Q1b =Qw ¼

mBHþ mB mHþ

ð13:17Þ

with the analogous equations for K1a;OH and K1b;H : For several aqueous systems, both K1a;OH (or K1b;H ) and functions for DV o or DCpo have been independently measured. As an example to illustrate the usefulness of Eq. 13.12, Tremaine et al. (1997) have used the experimental values of V o for morpholine and the morpholinium ion shown in Fig. 13.2, and values of Cpo obtained below 55 8C, to estimate DCpo for the morpholine ionization equilibrium at high temperatures using the semi-empirical Helgeson– Kirkham– Flowers (HKF) model. Combining these contributions with that from the first term in Eq. 13.12 yields log10 K ¼ 24:843 at 300 8C, which is in excellent agreement with the values 24.79 ^ 0.06 and 24.69 ^ 0.06 measured in KCl media by Mesmer and Hitch (1977), and in sodium trifluoromethanesulfonate (NaCF3SO3) by Ridley et al. (2000), respectively. As a consequence of the symmetry of isocoulombic reactions, plots of log10 Q1a,OH vs. 1/T are almost linear over a very wide range of temperatures, and the temperature dependence can be described quite accurately by assuming a constant mean value of DCpo between some condition of T and p, and a reference condition, Tr and pr: log10 K1a;OH;T;p ¼ log10 K1a;OH;Tr ;pr þ {DHTor ;pr ð1=Tr 2 1=TÞ þ DCpo ½ln ðT=Tr Þ þ Tr =T 2 1 2 ðDV o =TÞ½p 2 pr }=ð2:303RÞ ð13:18Þ Typical examples are plotted in Fig. 13.4 in their isocoulombic forms. Figure 13.5 shows the temperature dependence of DCpo for several of these reactions when written in the non-isocoulombic and isocoulombic forms. For isocoulombic equilibria at temperatures below 300 8C, the contribution of DV o to log10 K1a,OH,T is often less than the experimental uncertainty. Values of log10 Q1a for ionization reaction 13.1 can be calculated from the experimentally determined value for the isocoulombic ionization equilibrium (Eq. 13.14), by using the value for the ionization of water at ionic strength I, log10 Qw: log10 Q1a ¼ log10 Qw þ log10 K1a;OH ðIsocoulombicÞ

ð13:19Þ

It has been shown in a number of experimental studies (Mesmer et al., 1988, 1991; Lindsay, 1989, 1990) that for most reactions log10 Q1a,OH is almost independent of ionic strength for most isocoulombic equilibria at moderate


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Fig. 13.4. log10 K for several ionization reactions written in the isocoulombic form, log10 ðK1a =Kw Þ; as a function of temperature.

molalities of supporting electrolyte. As a result, the assumption that log10 Q1a;OH ¼ log10 K1a;OH would not result in any major error in the speciation calculations at elevated ionic strengths. The log10 Qw values have been determined as a function of ionic strength at temperatures from 0 to 300 8C in several supporting electrolytes. 13.1.4. Equations of State 13.1.4.1. The ‘Density’ Model Franck (1956, 1961) observed that the ionization constants K of many aqueous species at elevated temperatures and pressures act as linear functions of the density of water rw, when log10 K is plotted against log10 rw over a very wide range. Based on this observation, Marshall and Franck (1981) developed the ‘density’

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Fig. 13.5. The behavior of DCpo for the ionization reactions written in both the non-isocoulombic and isocoulombic forms, as a function of temperature.

model to represent the ionization constant Kw of water at temperatures up to 1273 K and at pressures up to 1000 MPa. Equations of this form have been used for representing K of general ionization reactions by Mesmer et al. (1988): b c d ð13:20Þ þ 2 þ 3 þ k log10 rw log10 K ¼ a þ T T T f g þ 2 ð13:21Þ k ¼ eþ T T where a, b, c, d, e, f and g are adjustable parameters (a number of these parameters may be set to zero for many reactions) and rw is the density of pure water (in g·cm23).


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Other thermodynamic quantities can be derived from the above equations. The Gibbs energy of ionization DG o is related to K by Eq. 13.7, so that b c d f g o þ 2 þ 3 þ eþ þ 2 log10 rw DG ¼ 22:303RT a þ T T T T T ð13:22Þ The enthalpy of ionization DH o can be obtained from the identity: › DGo DH o ¼2 2 ›T T p T

ð13:23Þ

to yield 2c 3d 2g DH o ¼ 22:303R b þ þ 2 þ fþ log10 rw 2 RT 2 kaw T T T

ð13:24Þ

where aw ¼ 2ð1=rw Þð›rw =›TÞp is the thermal expansion coefficient of water and k is the fitted function given in Eq. 13.21. Similarly, the entropy of ionization DS o, the standard partial molar heat capacity of ionization DrCop, and the standard partial molar volume of ionization DV o can be derived from DG o using standard thermodynamic identities (Mesmer et al., 1988) so that c 2d g ð13:25Þ DSo ¼ 2:303R a 2 2 2 3 þ e 2 2 log10 rw 2 RTkaw T T T 2c 6d 2g log r DCpo ¼ 2 2:303R 2 2 2 3 2 10 w T T T2 2g ›aw 2 RT 2 k 2 Raw 2eT 2 T ›T p

ð13:26Þ

DV o ¼ 2RTkbw

ð13:27Þ

Here bw ¼ ð1=rw Þð›rw =›pÞT is the compressibility of water. Equation 13.22 can be further simplified over a restricted region, and the simplified form has fewer parameters (Anderson et al., 1991). More complex versions have been adopted to describe DV o accurately at low temperatures (Clarke et al., 2000). Figure 13.6 shows the behavior of log10 K, DSo , DCpo and DV o for the ionization of ammonia over a wide range of temperature and pressure, according to the density model fit reported by Mesmer et al. (1988). The functions for DCpo and DV o clearly show the very large electrostriction effects that arise from the ability of ions to attract increasing numbers of water molecules as the compressibility of water increases under near critical conditions.

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Fig. 13.6.


453

Fig. 13.6. The behavior of (a) log10 K, (b) DS o and (c) DV o for the association of ammonia over a wide range of temperature and pressure, according to the density model fit reported by Mesmer et al. (1988).

13.1.4.2. The Revised Helgeson– Kirkham– Flowers Model Helgeson and co-workers (Helgeson et al., 1981; Tanger and Helgeson, 1988) have developed an equation of state, based on the Born equation for ionic hydration, which is widely used by geochemists (see Chapter 4 for more details). Briefly, the HKF model consists of expressions for standard partial heat capacity and volume functions in Eq. 13.12, and assumes that the standard molar Gibbs energy and enthalpy of formation of each species at 298.15 K and 0.1 MPa are known properties. In this model, the standard molar properties, Y o, of aqueous ions are considered o ; to have two contributions: an electrostatic term based on the Born equation DYBorn o and a non-electrostatic term Yn : o Y o ¼ Yno þ DYBorn

ð13:28Þ

The Born equation describes the Gibbs energy of ionic hydration, i.e., the transfer of an ion from the ideal gas state to liquid water, by representing the ion as

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a charged conducting sphere and water as a continuous dielectric medium without molecular structure. The Born equation takes the form: DGoBorn ¼ 2veff ð1=1r 2 1Þ

ð13:29Þ

with

veff ¼

NA ðzeÞ2 8p10 reff

ð13:30Þ

where 1r is the solvent dielectric constant; veff is a term that includes the ionic charge z, electron charge e, ionic radius reff, permittivity of free space 10 and Avogadro’s number NA. The HKF model employs an effective ionic radius, where reff is a linear function of crystallographic radius rx and charge z, reff ¼ rx þ 0:94lzl (with r in a˚ngstro¨ms) for cations and reff ¼ rx for anions. The revised HKF model (Tanger and Helgeson, 1988; Shock and Helgeson, 1988) also considered reff to be a function of T and p. The appropriate temperature and pressure derivatives of DGoBorn yield o o and DVBorn in terms of the same parameters. expressions for DCp;Born o The non-electrostatic term Yn includes three contributions: (i) the intrinsic gas phase property of the solute, (ii) the change arising from the difference in standard states between the gas phase and solution, and (iii) short-range hydration effects (Fernańdez-Prini et al., 1992). In the HKF treatment, Yno is used as an empirical fitting equation with the following form: 1 0 C B 1 1 1 C B o o ð13:31Þ V ¼ a1 þ a2 B 2 þ VBorn C þ a3 þ a4 A @ ›V T 2Q Cþp þp ›v2 Here Q is a solvent parameter equal to 228 K, which corresponds to the temperature at which supercooled liquid water may undergo anomalous behavior (Angell, 1983); C is a similar solvent parameter equal to 2600 bar; and a1, a2, a3 and a4 are temperature- and pressure-independent, but species-dependent, fitting parameters. o can be represented by a temperatureThe non-electrostatic contribution DCp;n o dependent function similar to that used for V o. The pressure dependence of DCp;n o can be derived from the V expression based on the thermodynamic identity ð›Cp =›pÞT ¼ 2Tð›2 V=›T 2 Þp to yield the following expression for the entire standard partial molar heat capacity: Cpo

¼ c1 þ c2

1 T 2Q

2

1 22T T 2Q

3 Cþp o a3 ðp 2 pr Þ þ a4 ln þ Cp;Born C þ pr ð13:32Þ


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Here c1 and c2 are temperature- and pressure-independent, but speciesdependent, parameters; Q is again a parameter with the value of 228 K; pr is the reference pressure (1 bar); and a3 and a4 are determined by the fits to V o from Eq. 13.31. Standard partial molar volumes and heat capacities of aqueous ions and electrolytes typically exhibit an inverted U-shape as a function of temperature (Fig. 13.2). This is consistent with the singularity at water’s critical temperature of 647 K where second-derivative thermodynamic parameters approach þ 1, and with the behavior in supercooled water where these properties also show a large increase (which may or may not be associated with a singularity near 228 K). The parameters in the revised HKF model have been selected so that the electrostatic contribution dominates at high temperatures where the Born model is most satisfactory, and the non-electrostatic contribution to V o and Cpo dominates at low temperatures. The revised HKF model has been used widely for the extrapolation of low-temperature standard partial molar properties of aqueous ions and electrolytes to elevated temperatures and pressures. The revised HKF model has also been used by Shock and Helgeson (1990) for the prediction of the standard partial molar properties of neutral aqueous organic species up to 1273 K and 500 MPa. It was fitted to the available experimental data for neutral aqueous organic species at elevated temperatures and pressures. The fitted parameters were then used to develop correlations with other low-temperature thermodynamic constants. In contrast to the negative o o and VBorn for aqueous ions and electrolytes, as required by theory, the fitted Cp;Born Born terms for neutral species can be either positive or negative. According to Eq. o o and VBorn correspond to negative values of veff, so 13.30, positive values of Cp;Born that z, the effective charge, is an imaginary number. Clearly, the expression for the electrostatic contribution has no physical meaning, and the validity of the revised HKF model for neutral species is questionable. The predictive capability stated in the paper is also limited by the rather sparse experimental data available at the time the correlations were derived. 13.1.4.3. Fluctuation Solution Theory Models O’Connell, Wood and their co-workers (Plyasunov et al., 2000a,b; Sedlbauer et al., 2000) have developed equations of state for aqueous electrolytes and nonelectrolytes based on the approach proposed by O’Connell et al. (1996). This approach makes use of the dimensionless Krichevskii parameter A12 ¼

V2o ›ðpV=RTÞ ¼ lim n2 !0 kRT ›n2 T;V;n2

ð13:33Þ

which is a smooth, continuous and finite function, even at the critical point. Here n2 is the number of moles of solute. The equations are constructed so that they

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have the correct limiting behavior in dilute solutions of low-pressure steam, i.e., they converge to the second cross virial coefficient between the solute and water. Details are discussed in Chapter 4. 13.1.4.4. Propagation of Error Uncertainties associated with log10DCpo in Eq. 13.9 lead to an uncertainty in the estimated values for log10 KT,p: X s2log10 K ¼ ð› log10 K=›xÞ2 s2x ð13:34Þ where s2x is the variance of independent variable x and s2log10 K is the variance of the dependent variable log10 KT,p. For the special case of Eq. 13.12, where DCpo is temperature independent and DV o is small:

s2log10 K ¼ s2log10 K;298 þ ½ð1=298:15 2 1=TÞ=Rs2H þ ½{lnðT=298:15Þ þ 298:15=T 2 1}=Rs2Cp

ð13:35Þ

If the uncertainty in DH o at 25 8C is assumed to be 4 kJ·mol21, this leads to an uncertainty of 0.34 in log10 K at 300 8C. If the uncertainty in DCpo is 2 J·K21·mol21 and 10 J·K21·mol21 at 25 and 300 8C, respectively, and linear with respect to temperature in this temperature range, these uncertainties result in an error of 0.05 in log10 K at 300 8C. This analysis reveals that accurate DH o values for the heat capacity function at the reference temperature (usually 25 8C) are essential for the accurate estimation of log10 K using the equations given above. 13.1.5. Activity Coefficients Equilibrium quotients Q are usually measured in a solution in which ionic strength is dictated by the addition of supporting electrolytes such as NaCl, KCl or NaCF3SO3. Clearly, activity coefficient models are needed to extrapolate the Q values to infinite dilution for such equilibria. A detailed discussion of models that incorporate pressure and temperature effects has been given by Millero (1979) and Pitzer (1991). As an example, the following semi-empirical equation has been widely used to analyze high-temperature potentiometric titration data by the ORNL group: pffi pffi pffi log10 Q ¼ log10 K 2 ðDz2 Aw =2:303Þ{ I =ð1 þ 1:2 I Þ þ 1:667 lnð1 þ 1:2 I Þ} ð13:36Þ þ a1 I þ a2 I 2 þ a3 FðIÞ þ 0:0157fI P 2 Here I is the ionic strength (I ¼ ð1=2Þ mi zi ; where the summation P 2 extends to 2 ¼ z ðproductsÞ 2 all ions in solution of molality m and charge z), Dz P2 z ðreactantsÞ is related to the coulombic asymmetry of the equilibrium and Aw represents the Debye– Hu¨ckel limiting slope for the osmotic coefficient. The term


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f is the osmotic coefficient of the solution, which is only needed for equilibria in which water is involved. The values of f for NaCl reported by Archer (1992) as a function of temperature and ionic strength are used as an approximation. The Debye–Hu¨ckel limiting law term in the above equation was proposed by Pitzer (1991); the function F(I), takes the form: pffi pffi FðIÞ ¼ ½1 2 ð1 þ 2 I 2 2IÞ expð22 I Þ=ð4IÞ

ð13:37Þ

The quadratic term a2I 2 is not always needed. Because solute ions undergo specific interactions with the highly charged anions and cations in the supporting electrolyte, activity coefficients cannot be described solely by the ionic strength of the medium. However, it has been found that the nature of the supporting electrolyte (KCl, NaCl or NaCF3SO3) barely affects the value of log10 K. Practically, Eq. 13.36 with the coefficients reported by the ORNL group can be used in speciation calculations at ionic strengths up to 5 mol·kg21 (Baes and Mesmer, 1986). Concentrated aqueous media containing more than one pair of ions can be treated with the Pitzer ion interaction theory for activity coefficients. The Pitzer equation contains many terms that arise from the binary and ternary interactions of the ions. These parameters are usually determined by fitting the Pitzer equation to the experimental activity coefficient of a single electrolyte or a common-ion mixed electrolyte system and can be used to calculate activity coefficients for more complicated systems. Although the binary and ternary interaction parameters for many ions are reported at ambient conditions, these parameters for several important electrolyte systems such as sulfate and phosphate are still not available at elevated temperatures. Extensive databases for the Pitzer ion interaction model, as well as its application to modeling industrial and geochemical systems, have been presented in several reviews (see, e.g., Pitzer, 1991). † It is very important to use the same activity coefficient model as that used to treat the original extrapolation of log10 Q to infinite dilution, or errors will arise from loss of self-consistency. When no data are available, empirical and semi-empirical approaches can be used to estimate activity coefficients for concentrated, mixed electrolytes at elevated temperatures. For many engineering applications (e.g., bulk properties of steam condensate and boiler water), the aqueous media are rather dilute (I p 0.01 mol·kg21), so that the Debye– Hu¨ckel limiting law provides sufficiently accurate activity coefficients. The most practical method at low to moderate ionic strengths (I & 2.0 mol·kg21) is to avoid using any activity coefficient model if possible by writing each weak acid/base ionization equilibrium in an isocoulombic fashion and using Eq. 13.18. When the isocoulombic approximation is not feasible, an approach suggested by Lindsay (1989, 1990) can be useful in engineering calculations involving acid– base equilibria. Here, the activity coefficient of a single ion is estimated by using

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NaCl(aq) as a model system, through the expression: 2

z glzl ¼ g^ðNaClÞ

ð13:38Þ

where gjzj is the single-ion activity coefficient for an ion with charge z, and g^(NaCl) is the activity coefficient of NaCl(aq) at the same temperature and ionic strength. = Within this approximation, the activity coefficient quotient, log10 ðgHPO22 4 2 22 gH2 PO4 gOH2 Þ for H2 PO2 ðaqÞ þ OH ðaqÞ O HPO ðaqÞ; is estimated to be 4 4 2 log10 g^(NaCl). It has been shown that this approximation could provide a reasonable estimation for activity coefficients of electrolytes at ionic strengths up to about 1.0 mol·kg21 at temperatures in the range 200 , t , 300 8C (Lindsay, 1989, 1990).

13.2. Experimental Methods 13.2.1. Electrical Conductance The use of electric conductance measurements to determine the degree of association in aqueous solutions at high temperature was pioneered by Noyes (1907) and a detailed description of the conductance technique is given in Chapter 10. Throughout the 1950s and 1960s, Franck and Marshall carried out electrical conductance studies of a number of electrolytes, mostly in the temperature– pressure ranges of 400–800 8C and 1– 400 MPa, using a platinum-lined cell described by Franck (1956, 1961), Franck et al. (1962) and Quist and Marshall (1968a). The aqueous electrolytes studied include the alkali metal halides, K2SO4, KHSO4, HBr and NH3. A modified version of this apparatus was described by Ho et al. (1994). Much of our knowledge about ion association at temperatures above 200 8C was obtained from these investigations, which were made before other methods became available. Measuring the conductance of aqueous solutions under ambient conditions is straightforward, but specialized techniques are required to extend these techniques to high temperature and pressure conditions. Experimental challenges include the need to use corrosion-resistant metals (usually platinum and its alloys), accurate temperature and pressure control, and electrically insulated high-pressure seals for the electrodes. Experience has shown that a static apparatus, of the type used by Quist and Marshall, does not allow accurate measurements for very dilute solutions, especially under conditions close to the critical temperature of water. Accurate conductance values for dilute solutions (, 1025 mol·kg21) are essential if one wants to calculate ion association constants, which are independent of the activity coefficient model chosen. To overcome this problem, Wood and his co-workers at the University of Delaware and Ho and Palmer at Oak Ridge


459

National Laboratory have developed flow-through conductance apparatus for high-temperature applications (Zimmerman et al., 1995; Ho et al., 2000a). The flow-through cells allow rapid and accurate electric conductance measurements to be made on aqueous solutions with concentration as low as 4 £ 1028 mol·kg21, even in the vicinity of the critical point of water. Since then, a number of acids (HCl), bases (LiOH, KOH and NaOH) and salts (Na2SO4, alkali metal halides) have been studied (Zimmerman et al., 1995; Gruszkiewicz and Wood, 1997; Sharygin et al., 2001; Ho et al., 1994, 2000b, 2001; Ho and Palmer, 1995, 1996, 1997, 1998). Calculating ion association constants from conductivity data is tedious and difficult, because modern conductance equations for simple electrolyte solutions often contain several dozen terms (Fernańdez-Prini, 1969). Recently, Wood and co-workers have evaluated several data interpretation strategies for electrolyte mixtures that use various combinations of mixing rules, theoretical conductance equations and activity coefficient models (Sharygin et al., 2001). It was found that the latest conductance equation developed by Turq et al. (1995), together with the constant-ionic-strength mixing rule, was suitable for treating high-temperature conductance data for Na2SO4(aq) solutions containing six ionic species, to calculate ion association constants for species such as the Naþ·SO22 4 (aq) ion pair. This method should allow rapid and accurate determination of the equilibrium constant for any association reaction, which changes the concentration of ions in solution. Conductance techniques are treated in detail in Chapter 10.

13.2.2. The Hydrogen-Electrode Concentration Cell (HECC) The use of hydrogen electrodes in a concentration cell configuration was pioneered at Oak Ridge 30 years ago (Mesmer et al., 1970). The design and function of the HECC have been described in numerous publications (e.g., Mesmer et al., 1970; Kettler et al., 1991; Beńe´zeth et al., 1997) and have been used in a large number of studies of reactions such as acid– base ionization, metal ion hydrolysis and complexation, solubility measurements and adsorption studies. A detailed discussion of this cell is given in Chapter 11, but briefly, it consists of a 300 mL or 1 L capacity pressure vessel containing two concentric Teflon cups separated by a porous Teflon plug, which acts as a liquid junction completing the electric circuit. Teflon-insulated platinum wires coated with platinum black protrude into each cup and serve as electrodes. The solutions in each cup are stirred magnetically. The solution in the inner cup serves as the reference of known hydrogen ion molality (usually a strong acid or base), whereas the outer cup contains the test solution in which a titration can be performed. Both solutions are thoroughly purged with hydrogen at ambient temperature prior to placing the vessel in the aluminum block tube furnace or oil bath for equilibration at temperature.

460

P. Tremaine et al.

The initial configuration of the cell in a typical study of the ionization of a weak acid, HA, is as follows: Pt; H2 l mHA; mNaCl ; mNaA ll mNaCl ; mHCl lH2 ; Pt Test

ð13:39Þ

Reference

where NaCl represents a supporting, non-complexing electrolyte, which is ideally 50– 100 times more abundant than the other components so that gHþ,test < gHþ,ref and the liquid junction potential is minimized. Note that the working definition of pH is pHm ¼ 2log10 mHþ in stoichiometric molal concentration units. The convention used here is that Hþ is not complexed by the medium ions and ion pairing is treated implicitly by the activity coefficient model employed. Each platinum–hydrogen electrode responds to the half-cell reaction: H2 ðgÞ ! 2Hþ ðaqÞ þ 2e2

ð13:40Þ

and the difference in potential between the electrodes is described by the Nernst equation: RT lnðmHþ ;t =mHþ ;r Þ 2 Elj ð13:41Þ DE ¼ 2 F where mHþ ;t and mHþ ;r refer to the stoichiometric molalities of hydrogen ions in the test and reference compartments, respectively. The stoichiometric molal activity coefficients of Hþ in the test and reference compartments are assumed to be equal at all points in the titration. The ideal gas and Faraday constants are designated by R and F, respectively; T denotes the temperature in kelvin; and Elj represents the liquid junction potential based on the full Henderson equation (Baes and Mesmer, 1986), which involves the limiting conductivities of the individual ions. From the measured mHþ together with a solution of known pH m (; 2 log10 mHþ in molal units) used in the reference cup, and mass and charge balance constraints, the molal dissociation constant (QHA) for the acid at the ionic strength of interest can be calculated, typically with an accuracy of about ^0.01 log10 units. By varying the total ionic strength from ca. 0.1 – 5 molal, the pK value and activity coefficient ratio for the dissociation reaction can be obtained by regressing the equation log10 QHA ¼ log10 KHA 2 log10 ðgHþ gA2 =gHA Þ using an appropriate activity coefficient model such as the Pitzer ion interaction treatment. 13.2.3. Other pH Sensing Electrodes and Reference Electrodes Over the few past decades, numerous efforts have been made to develop instruments suitable for pH measurements in aqueous fluids at elevated temperatures and pressures other than the HECC described above. These include: † yttria-stabilized zirconia (YSZ) membrane electrodes (150 – 500 8C) (MacDonald et al., 1988; Hettiarachchi et al., 1992; Ding and Seyfried, 1995, 1996; Lvov et al., 1999);


461

† metal – metal oxide electrodes (100– 300 8C) such as Pt– PtO2, Ir– IrO2, Zr– ZrO2, Rh– Rh2O3, W/WO3 (e.g., Kriksunov et al., 1994); † glass electrode (25 – 200 8C) (Diakonov et al., 1996). The principles, development, application and limitations of pH-sensing electrodes and reference electrodes are discussed in detail in Chapter 11.

13.2.4. Spectroscopic Methods Over the years, there have been a series of attempts to use UV – visible and Raman spectroscopy to measure equilibrium constants at elevated temperatures, usually at steam saturation. The availability of stable UV – visible spectrometers with fast data acquisition has allowed several workers to develop high-pressure flow systems with on-line injection, using sapphire or quartz windows. Suleimenov and Seward (1997) have used these to determine ionization and complexation constants of species where the spectra of the acid and conjugate base differ in the visible or near-UV. An alternative approach has been taken by Johnston’s group, who have developed several thermally stable colorimetric pH indicators for hydrothermal applications (Johnston et al., 1997; Xiang et al., 1996). Several researchers have used Raman spectroscopy to study the speciation of hydrothermal solutions (see, e.g., Rudolph et al., 1997). Because of the small diameter of the exciting laser beam, cell construction can make use of small sapphire tubes or diamond windows, thereby simplifying construction and extending the temperature range. Recent developments in hydrothermal diamond anvil cells (Bassett et al., 1993), the use of high-pressure flow injection systems and the availability of Raman microscopes promise to increase the versatility of this technique as a tool for obtaining ionization constant data under extreme conditions. 13.2.5. Flow Calorimetry Flow calorimetry is an important tool for determining the thermodynamic properties of aqueous solutes under hydrothermal conditions. Two kinds of flow calorimeters have been used to determine ionization constants. High-pressure heat-of-mixing calorimeters have been used at Brigham Young University to determine DrH o of ionization reactions as a function of temperature, up to about 325 8C. These yield Dr Cpo by differentiation. In favorable cases, the instruments can be operated as titration calorimeters to obtain equilibrium constants directly at elevated temperature and pressure (Oscarson et al., 1992). The second method uses heat capacity flow micro-calorimeters and vibrating tube densimeters to determine the standard partial molar heat capacities and

462

P. Tremaine et al.

volumes of the acid and conjugate base, Cpo and V o, from which Cpo and DrV o can be calculated for use in Eq. 13.12 (Sedlbauer et al., 2000; Clarke et al., 2000). The method is particularly attractive because it yields standard partial molar properties of individual species, so that equations of state can be derived.

13.3. Ionization of Water 13.3.1. log10 Kw as a Function of Temperature and Pressure A number of research groups have used EMF methods, conductivity, calorimetry and spectroscopy to determine values of log10 Qw, which corresponds to the selfionization reaction: H2 OðlÞ O Hþ ðaqÞ þ OH2 ðaqÞ

ð13:42Þ

at elevated temperatures, as a function of ionic strength. The critical review by Marshall and Franck (1981) contains most of the modern values, and a comprehensive, weighted fit of the infinite-dilution values, log10 Kw, to the density model (Eq. 13.21): log10 Kw ¼ 24:098 2 3245:2=ðT=KÞ þ 2:2362 £ 105 =ðT=KÞ2 2 3:984 £ 107 =ðT=KÞ3 þ ½13:957 2 1262:3=ðT=KÞ þ 8:5641 £ 105 =ðT=KÞ2 log10 rw

ð13:43Þ

The temperature- and pressure-dependence of log10 Kw yields values of DH o, DS o, DCpo and DV o up to 1000 8C and 1 GPa. IAPWS has adopted the Marshall– Franck formulation as its ‘best’ values for log10 Kw vs. T and p for densities .0.35 g·cm23. Mesmer, Baes and others at Oak Ridge National Laboratory have measured ionization constants for water, log10 Qw, vs. I in KCl, NaCl and NaCF3SO3 media from 0 to 300 8C, and the corresponding values of DH o, DS o, DCpo and DV o (Sweeton et al., 1974; Busey and Mesmer, 1978; Palmer and Drummond, 1988). These are not entirely consistent with the IAPWS selection of Marshall and Franck’s values for the ion product of water, but they are complete, internally consistent with each other, and have been used as the de facto standard by most other workers. Values of log10 Qw vs. I are listed in Table 13.1. Olofsson and Hepler (1975) reported a critical evaluation of the consistency of the available data with the calorimetric results, and found them to be in very good agreement. Values of log10 Kw from Sweeton et al. (1974) are compared with those of Marshall and Franck (1981) in Table 13.2.

t (8C)

log10 Qw

DG o (J·mol21)

DH o (J·mol21)

DS o (J·K21·mol21)

DCop (J·K21·mol21)

DV o (cm3·mol21)

I¼0 0 25 50 75 100 125 150 175 200 225 250 275 300

2 14.941 ^ 0.009 2 13.993 ^ 0.009 2 13.272 ^ 0.006 2 12.709 ^ 0.006 2 12.264 ^ 0.009 2 11.914 ^ 0.009 2 11.642 ^ 0.012 2 11.441 ^ 0.012 2 11.302 ^ 0.012 2 11.222 ^ 0.012 2 11.196 ^ 0.015 2 11.224 ^ 0.027 2 11.301 ^ 0.045

78 132 ^ 38 79 873 ^ 38 82 107 ^ 50 84 705 ^ 50 87 609 ^ 50 90 810 ^ 75 94 312 ^ 88 98 157 ^ 100 102 374 ^ 100 107 018 ^ 113 112 135 ^ 151 117 784 ^ 289 124 005 ^ 490

62 568 ^ 264 55 815 ^ 100 50 672 ^ 138 46 288 ^ 238 42 028 ^ 351 37 418 ^ 372 32 075 ^ 402 25 677 ^ 418 17 933 ^ 795 8527 ^ 1506 22975 ^ 2510 2 17 456 ^ 3891 2 37 259 ^ 5648

256.99 ^ 0.88 280.67 ^ 0.38 297.28 ^ 0.50 2110.33 ^ 0.75 2122.17 ^ 1.00 2134.10 ^ 1.00 2147.07 ^ 1.00 2161.71 ^ 1.00 2178.45 ^ 1.63 2197.69 ^ 3.01 2220.04 ^ 5.02 2246.73 ^ 7.53 2281.37 ^ 10.88

2 316.7 ^ 17.6 2 231.4 ^ 6.3 2 185.8 ^ 5.0 2 169.0 ^ 5.0 2 174.5 ^ 5.0 2 196.6 ^ 5.0 2 232.6 ^ 12.6 2 280.7 ^ 15.1 2 340.6 ^ 30.1 2 414.6 ^ 38.9 2 511.3 ^ 45.2 2 661.5 ^ 59.0 2 963.6 ^ 92.9

2 24.13 ^ 2.2 2 23.00 ^ 1.9 2 22.80 ^ 1.7 2 23.69 ^ 1.6 2 25.78 ^ 1.6 2 29.18 ^ 1.6 2 33.97 ^ 1.7 2 40.27 ^ 1.8 2 48.47 ^ 2.3 2 59.59 ^ 3.3 2 76.36 ^ 5.1 2 105.90 ^ 9.2 2 166.07 ^ 18.3

I ¼ 0:1 mol·kg21 0 2 14.740 ^ 0.005 25 2 13.781 ^ 0.006 50 2 13.047 ^ 0.006 75 2 12.468 ^ 0.006 100 2 12.004 ^ 0.006 125 2 11.631 ^ 0.009 225 2 10.804 ^ 0.012 250 2 10.723 ^ 0.015 275 2 10.676 ^ 0.024 300 2 10.653 ^ 0.042

77 078 ^ 25 78 659 ^ 25 80 714 ^ 25 83 098 ^ 38 85 755 ^ 50 88 659 ^ 63 103 039 ^ 117 107 399 ^ 151 112 039 ^ 126 116 888 ^ 452

63 162 ^ 264 56 618 ^ 100 51 819 ^ 138 47 903 ^ 226 44 229 ^ 351 40 338 ^ 414 17 979 ^ 1381 10 719 ^ 2343 3050 ^ 3598 25720 ^ 5188

250.96 ^ 0.88 273.93 ^ 0.38 289.41 ^ 0.50 2101.09 ^ 0.75 2111.29 ^ 1.00 2121.38 ^ 1.13 2170.75 ^ 2.76 2184.81 ^ 3.39 2198.82 ^ 7.03 2213.93 ^ 9.79

2 310.9 ^ 17.6 2 220.1 ^ 6.3 2 169.5 ^ 5.0 2 148.1 ^ 5.0 2 148.5 ^ 3.8 2 164.8 ^ 5.0 2 281.2 ^ 37.7 2 298.3 ^ 41.4 2 318.8 ^ 54.0 2 404.2 ^ 81.6

2 23.20 ^ 1.8 2 22.00 ^ 1.5 2 21.68 ^ 1.4 2 22.38 ^ 1.3 2 24.20 ^ 1.2 2 27.19 ^ 1.2 2 53.33 ^ 2.6 2 67.42 ^ 4.1 2 92.03 ^ 7.0 2 141.72 ^ 18.8 463

(continued )


Table 13.1. Thermodynamic quantities for the dissociation of water at saturation pressure in KCl media from Sweeton et al. (1974)

464

Table 13.1. continued t (8C)

log10 Qw

DG o (J·mol21)

DH o (J·mol21)



DV o (cm3·mol21)

76 78 80 82 85 87 90 93 97 100 104 108 111

785 ^ 38 295 ^ 38 257 ^ 38 525 ^ 50 031 ^ 63 747 ^ 88 671 ^ 113 809 ^ 138 173 ^ 151 734 ^ 176 445 ^ 201 194 ^ 301 776 ^ 490

63 57 52 49 46 42 39 35 30 26 23 23 25

580 ^ 289 212 ^ 188 697 ^ 213 175 ^ 276 020 ^ 377 794 ^ 439 225 ^ 439 233 ^ 439 983 ^ 711 932 ^ 1339 928 ^ 2301 163 ^ 3682 882 ^ 5732

2 48.37 ^ 1.00 2 70.71 ^ 0.63 2 85.27 ^ 0.75 2 95.81 ^ 0.88 2 104.56 ^ 1.13 2 112.88 ^ 1.26 2 121.59 ^ 1.26 2 130.71 ^ 1.26 2 139.87 ^ 1.63 2 148.16 ^ 2.76 2 153.93 ^ 3.39 2 155.14 ^ 7.15 2 149.87 ^ 10.67

2305.9 ^ 17.6 2211.3 ^ 6.3 2156.1 ^ 5.0 2130.1 ^ 5.0 2125.1 ^ 5.0 2134.7 ^ 5.0 2151.5 ^ 11.3 2166.9 ^ 12.6 2170.3 ^ 27.6 2148.1 ^ 36.4 284.5 ^ 43.9 32.2 ^ 66.5 188.3 ^ 120.5

222.06 ^ 1.5 220.77 ^ 1.2 220.30 ^ 1.2 220.78 ^ 1.1 222.24 ^ 1.1 224.72 ^ 1.1 228.18 ^ 1.2 232.63 ^ 1.3 238.24 ^ 1.6 245.59 ^ 2.2 256.36 ^ 3.5 274.90 ^ 6.4 2111.61 ^ 13.2

I ¼ 1:0 mol·kg21 0 214.725 ^ 0.006 25 213.753 ^ 0.006 50 213.003 ^ 0.006 75 212.404 ^ 0.006 100 211.916 ^ 0.009 125 211.514 ^ 0.012

77 78 80 82 85 87

002 ^ 38 504 ^ 25 442 ^ 38 676 ^ 50 128 ^ 75 764 ^ 100

63 57 53 49 47 44

852 ^ 314 597 ^ 264 241 ^ 289 953 ^ 326 108 ^ 414 283 ^ 490

2 48.16 ^ 1.13 2 70.12 ^ 0.88 2 84.18 ^ 0.88 2 94.01 ^ 1.00 2 101.88 ^ 1.26 2 109.20 ^ 1.38

2302.5 ^ 17.6 2205.9 ^ 6.3 2148.1 ^ 5.0 2119.2 ^ 5.0 2111.3 ^ 3.8 2116.3 ^ 5.0

221.20 ^ 1.5 219.84 ^ 1.4 219.27 ^ 1.3 219.57 ^ 1.3 220.78 ^ 1.3 222.86 ^ 1.4

P. Tremaine et al.

I ¼ 0:5 mol·kg21 0 214.684 ^ 0.009 25 213.717 ^ 0.006 50 212.973 ^ 0.006 75 212.382 ^ 0.009 100 211.903 ^ 0.009 125 211.512 ^ 0.012 150 211.193 ^ 0.015 175 210.943 ^ 0.015 200 210.727 ^ 0.018 225 210.563 ^ 0.018 250 210.429 ^ 0.021 275 210.310 ^ 0.030 300 210.187 ^ 0.045

90 93 96 100 103 106 109

579 ^ 126 575 ^ 151 742 ^ 176 039 ^ 201 391 ^ 251 621 ^ 377 458 ^ 602

41 38 34 32 32 35 45

254 ^ 741 016 ^ 544 857 ^ 837 480 ^ 1506 125 ^ 2636 710 ^ 4435 811 ^ 7615

2 116.57 ^ 1.38 2 123.97 ^ 1.38 2 130.79 ^ 1.88 2 135.65 ^ 3.14 2 136.23 ^ 5.27 2 129.37 ^ 8.54 2 111.04 ^ 14.31

2126.4 ^ 11.3 2131.0 ^ 13.8 2117.2 ^ 27.6 264.9 ^ 38.9 49.4 ^ 56.5 254.4 ^ 97.9 574.0 ^ 189.5

225.78 ^ 1.5 229.47 ^ 1.5 234.00 ^ 1.8 239.79 ^ 2.4 248.07 ^ 4.0 262.06 ^ 7.7 289.05 ^ 16.8

78 79 81 83 86 88 91 103 105

458 ^ 63 940 ^ 50 822 ^ 63 952 ^ 100 249 ^ 151 676 ^ 201 211 ^ 264 801 ^ 866 027 ^ 1293

65 59 55 52 50 49 47 63 89

346 ^ 226 476 ^ 490 630 ^ 552 974 ^ 640 923 ^ 766 108 ^ 904 363 ^ 1046 978 ^ 7866 441 ^ 14 644

2 47.99 ^ 1.63 2 68.62 ^ 1.63 2 81.04 ^ 1.76 2 88.99 ^ 2.01 2 98.87 ^ 2.38 2 99.37 ^ 2.76 2 103.60 ^ 3.01 2 72.68 ^ 15.56 2 27.20 ^ 27.49

2289.1 ^ 17.6 2187.9 ^ 6.3 2125.5 ^ 6.3 290.8 ^ 6.3 275.3 ^ 6.3 271.1 ^ 8.8 267.4 ^ 13.8 713.4 ^ 194.6 1384.5 ^ 390.4

219.05 ^ 2.3 217.52 ^ 2.3 216.68 ^ 2.3 216.56 ^ 2.3 217.11 ^ 2.4 218.24 ^ 2.6 219.78 ^ 2.7 229.98 ^ 14.1 232.66 ^ 32.0


150 211.181 ^ 0.015 175 210.907 ^ 0.018 200 210.680 ^ 0.021 225 210.490 ^ 0.021 250 210.323 ^ 0.024 275 210.160 ^ 0.036 300 29.975 ^ 0.054 I ¼ 3:0 mol·kg21 0 215.004 ^ 0.012 25 214.005 ^ 0.009 50 213.226 ^ 0.009 75 212.596 ^ 0.015 100 212.074 ^ 0.021 125 211.634 ^ 0.027 150 211.259 ^ 0.033 275 29.892 ^ 0.081 300 29.572 ^ 0.117

465

466

P. Tremaine et al. Table 13.2. Comparison of Kw for the dissociation of water from Marshall and Franck (1981) with those from Sweeton et al. (1974) at saturation vapor pressure t (8C)

log10 Kwa

log10 Kwb

Difference

0 25 50 75 100 125 150 175 200 225 250 275 300

214.941 213.993 213.272 212.709 212.264 211.914 211.642 211.441 211.302 211.222 211.196 211.224 211.301

2 14.938 2 13.995 2 13.275 2 12.712 2 12.265 2 11.912 2 11.638 2 11.432 2 11.289 2 11.208 2 11.191 2 11.251 2 11.406

2 0.003 þ 0.002 þ 0.003 þ 0.003 þ 0.001 2 0.002 2 0.004 2 0.009 2 0.013 2 0.014 2 0.005 þ 0.027 þ 0.105

a b

Sweeton et al. (1974). Marshall and Franck (1981).

Finally, the ionization of heavy water has been studied at elevated temperatures by Shoesmith and Lee (1976) and Mesmer and Herting (1978). The values of Mesmer and Herting (1978) are tabulated in Table 13.3. The effects of isotopic substitution on ionization constants have been described by Arnett and McKelvey (1969) and Laughton and Robertson (1969). 13.3.2. Compilation of Self-Consistent Tables for the Ionization of Acids and Bases In the sections that follow, tables have been reproduced from published compilations of experimental ionization constants that are consistent with the values for log10 Qw vs. I in Tables 13.1– 13.3, without refitting. Many, but not all of these, are from Oak Ridge National Laboratory and they incorporate critically compiled experimental data from other workers in the fitted results that are tabulated. Where such results do not exist, we have recalculated the data to be consistent with the values for log10 Qw in KCl media listed in Table 13.1. Our intention in presenting these results is to tabulate practical data for the ionization of acids and bases, so that values of log10 Q can be added to or subtracted from log10 Qw using the isocoulombic approach. As such, they are not critically evaluated ‘best’ data, but rather they are internally consistent ‘good’ data that are suitable for most applications.


467

Table 13.3. Thermodynamic quantities for the ionization of D2O at saturation pressure in KCl media from Mesmer and Herting (1978) t (8C)

log10 Qw

DH o (J·mol21)



I¼0 0 25 50 75 100 125 150 175 200 225 250 275 300

215.972 ^ 0.021 214.951 ^ 0.008 214.176 ^ 0.011 213.574 ^ 0.015 213.099 ^ 0.020 212.725 ^ 0.024 212.434 ^ 0.027 212.215 ^ 0.028 212.060 ^ 0.030 211.964 ^ 0.036 211.923 ^ 0.049 211.933 ^ 0.070 211.992 ^ 0.098

67 488 ^ 1632 60 040 ^ 879 54 308 ^ 628 49 455 ^ 711 44 852 ^ 795 39 999 ^ 753 34 602 ^ 837 28 242 ^ 1297 20 669 ^ 2134 11 590 ^ 3305 418 ^ 4602 213 389 ^ 6694 232 635 ^ 8368

2 58.58 ^ 5.86 2 84.89 ^ 2.97 2 103.39 ^ 2.01 2 117.86 ^ 2.22 2 130.62 ^ 2.26 2 143.13 ^ 2.34 2 156.31 ^ 2.47 2 170.83 ^ 2.97 2 187.02 ^ 4.60 2 205.85 ^ 7.11 2 227.19 ^ 10.04 2 252.71 ^ 12.97 2 286.19 ^ 16.74

2 347.3 ^ 46.0 2 257.3 ^ 27.6 2 207.1 ^ 20.1 2 185.4 ^ 13.4 2 185.8 ^ 11.3 2 202.9 ^ 16.7 2 233.5 ^ 25.5 2 276.6 ^ 33.1 2 331.0 ^ 46.0 2 399.6 ^ 54.4 2 489.5 ^ 66.9 2 636.0 ^ 71.1 2 933.0 ^ 87.9

59 036 ^ 3096 52 049 ^ 2134 46 903 ^ 1464 42 760 ^ 1004 38 995 ^ 962 35 146 ^ 1255 30 794 ^ 1841 25 648 ^ 2636 19 414 ^ 3640 11 799 ^ 5021 2385 ^ 6276 2 9623 ^ 8368 225 522 ^ 10042

2 82.42 ^ 10.04 2 105.14 ^ 6.69 2 120.08 ^ 4.60 2 130.42 ^ 3.10 2 138.91 ^ 2.72 2 146.90 ^ 3.26 2 155.27 ^ 4.52 2 164.85 ^ 6.28 2 175.73 ^ 8.37 2 188.28 ^ 10.88 2 203.34 ^ 13.81 2 221.33 ^ 17.15 2 243.93 ^ 20.50

2 330.1 ^ 50.6 2 235.6 ^ 36.4 2 180.7 ^ 31.8 2 154.4 ^ 28.5 2 149.8 ^ 27.2 2 162.3 ^ 30.1 2 187.9 ^ 35.6 2 225.5 ^ 41.8 2 276.1 ^ 50.2 2 338.9 ^ 58.6 2 418.4 ^ 71.1 2 539.7 ^ 79.5 2 748.9 ^ 92.0

I ¼ 1:0 mol·kg21 0 215.591 ^ 0.068 25 214.612 ^ 0.033 50 213.849 ^ 0.023 75 213.231 ^ 0.025 100 212.717 ^ 0.028 125 212.282 ^ 0.029 150 211.910 ^ 0.031 175 211.590 ^ 0.036 200 211.312 ^ 0.048 225 211.069 ^ 0.066 250 210.852 ^ 0.089 275 210.650 ^ 0.120 300 210.430 ^ 0.150

13.4. Inorganic Acids and Bases 13.4.1. Weak Acids at 25 8C and 100 kPa The properties of aqueous inorganic acids and bases at 25 8C are well understood, and they are discussed in depth in several authoritative texts, reviews and monographs, many of which date from the 1960s (see, e.g., Cotton and Wilkinson, 1988; Hepler and Hopkins, 1979). The introduction of modern titration calorimeters, flow micro-calorimeters and vibrating-tube densimeters resulted in a major increase in the number and quality of data for DH o, DS o, DCpo and DV o. Many of these derivative properties and the ‘best’ values for log10 K have been tabulated by Pettit and Powell (1997) and Smith and Martell (1997). Table 13.4 lists values at 25 8C from Larson et al. (1982).

468

P. Tremaine et al.

Table 13.4. Molal equilibrium constants and related thermodynamic properties for inorganic acid dissociation reactions in aqueous solution at 25 8C and 1 atm from Larson et al. (1982) Reaction H3PO4(aq) O Hþ(aq) þ H2PO2 4 (aq) þ H2PO2 4 (aq) O H (aq) 22 þ HPO4 (aq) þ HPO22 4 (aq) O H (aq) 32 þ PO4 (aq) þ HCO2 3 (aq) O H (aq) 22 þ CO3 (aq) þ HSO2 4 (aq) O H (aq) 22 þ SO4 (aq)

K1a

DH o DS o DCop DV o 21 21 21 21 21 (kJ·mol ) (J·K ·mol ) (J·K ·mol ) (cm3·mol21)

7.13 £ 1023

2 7.74

267.06

2128

2 16.3

6.31 £ 1028

3.6

2 126.82

2220

2 25.9

4.22 £ 10213

17.2

2179.2

2242

–

4.69 £ 10211

14.7

2 148.45

2250

2 28.7

2113.7

2300

2 21.0

1.05 £ 1022

222.6

13.4.2. Weak Acids at Temperatures up to 300 8C 13.4.2.1. Carbon Dioxide and Carbonic Acid The solution chemistry of aqueous carbon dioxide has been reviewed by Palmer and van Eldik (1983). At room temperature, a small fraction of the dissolved gas is hydrated, according to the reaction: CO2 ðaqÞ þ H2 OðlÞ O H2 CO3 ðaqÞ

ð13:44Þ

The relative concentration of the hydrated molecular form of ‘carbonic acid’ is now understood to be less than 1% of the total dissolved carbon dioxide. The relative concentration decreases with increasing temperature or ionic strength, and increases slightly with pressure in the kbar range. Thus, it is common practice to write ionization equilibria in terms of total dissolved neutral species: mCOp2 ¼ mCO2 þ mH2 CO3

ð13:45Þ

Aqueous carbon dioxide ionizes to form hydrogen carbonate (bicarbonate) and carbonate ions, which can be expressed in terms of the isocoulombic or ‘nearly’ isocoulombic neutralization reactions: COp2 ðaqÞ þ H2 OðlÞ O Hþ ðaqÞ þ HCO2 3 ðaqÞ

ð13:46Þ

2 22 HCO2 3 ðaqÞ þ OH ðaqÞ O CO3 ðaqÞ þ H2 OðlÞ

ð13:47Þ

The first ionization of COp2 ðaqÞ has been measured at temperatures and pressures up to 300 8C and 10 MPa by Patterson et al. (1982) in an EMF flow cell with no vapor phase, and up to conditions of 250 8C and 200 MPa by Read (1975) using a conductivity method. Patterson’s values of log10 Q1a, which incorporated Read’s results, are listed in Table 13.5 at I ¼ 0 and ionic strengths (in NaCl(aq)

t (8C)

log10 K1a (I ¼ 0)

log10 Q1a (I ¼ 0:1 mol·kg21)

log10 Q1a (I ¼ 0:5 mol·kg21)

log10 Q1a (I ¼ 1:0 mol·kg21)

log10 Q1a (I ¼ 3:0 mol·kg21)

log10 Q1a (I ¼ 5:0 mol·kg21)

0 25 50 75 100 125 150 175 200 225 250 275 300

2 6.569 ^ 0.007 2 6.349 ^ 0.005 2 6.279 ^ 0.005 2 6.305 ^ 0.008 2 6.397 ^ 0.012 2 6.539 ^ 0.015 2 6.721 ^ 0.018 2 6.938 ^ 0.021 2 7.189 ^ 0.023 2 7.470 ^ 0.024 2 7.783 ^ 0.027 2 8.125 ^ 0.038 2 8.498 ^ 0.060

26.348 ^ 0.006 26.119 ^ 0.004 26.037 ^ 0.004 26.048 ^ 0.007 26.122 ^ 0.011 26.242 ^ 0.014 26.399 ^ 0.017 26.588 ^ 0.019 26.804 ^ 0.021 27.045 ^ 0.022 27.306 ^ 0.025 27.582 ^ 0.037 27.864 ^ 0.059

26.214 ^ 0.006 25.983 ^ 0.004 25.895 ^ 0.005 25.895 ^ 0.008 25.952 ^ 0.011 26.052 ^ 0.013 26.184 ^ 0.015 26.344 ^ 0.017 26.527 ^ 0.018 26.727 ^ 0.019 26.939 ^ 0.022 27.153 ^ 0.034 27.356 ^ 0.056

26.165 ^ 0.009 25.938 ^ 0.005 25.849 ^ 0.005 25.842 ^ 0.008 25.889 ^ 0.011 25.974 ^ 0.013 26.088 ^ 0.014 26.227 ^ 0.016 26.384 ^ 0.017 26.555 ^ 0.017 26.731 ^ 0.020 26.902 ^ 0.032 27.052 ^ 0.053

26.162 ^ 0.039 25.958 ^ 0.025 25.873 ^ 0.016 25.853 ^ 0.014 25.873 ^ 0.014 25.917 ^ 0.014 25.979 ^ 0.015 26.053 ^ 0.016 26.135 ^ 0.017 26.218 ^ 0.019 26.293 ^ 0.023 26.347 ^ 0.033 26.361 ^ 0.052

26.239 ^ 0.074 26.061 ^ 0.050 25.982 ^ 0.034 25.954 ^ 0.027 25.951 ^ 0.024 25.960 ^ 0.023 25.975 ^ 0.021 25.993 ^ 0.021 26.008 ^ 0.024 26.016 ^ 0.030 26.005 ^ 0.038 25.961 ^ 0.051 25.864 ^ 0.071

log10 K2a (I ¼ 0)

log10 Q2a (I ¼ 0:1 mol·kg21)

log10 Q2a (I ¼ 0:5 mol·kg21)

log10 Q2a (I ¼ 1:0 mol·kg21)

log10 Q2a (I ¼ 3:0 mol·kg21)

log10 Q2a (I ¼ 5:0 mol·kg21)

210.627 ^ 0.005 210.337 ^ 0.003 210.180 ^ 0.004 210.117 ^ 0.008 210.120 ^ 0.017 210.171 ^ 0.028 210.255 ^ 0.039 210.365 ^ 0.049 210.491 ^ 0.056 210.630 ^ 0.063 210.777 ^ 0.073

210.181 ^ 0.007 2 9.869 ^ 0.007 2 9.687 ^ 0.007 2 9.593 ^ 0.008 2 9.559 ^ 0.015 2 9.568 ^ 0.026 2 9.606 ^ 0.037 2 9.661 ^ 0.046 2 9.725 ^ 0.053 2 9.788 ^ 0.059 2 9.838 ^ 0.069

29.917 ^ 0.016 29.582 ^ 0.016 29.376 ^ 0.015 29.255 ^ 0.016 29.191 ^ 0.017 29.166 ^ 0.024 29.165 ^ 0.033 29.177 ^ 0.040 29.192 ^ 0.046 29.196 ^ 0.050 29.174 ^ 0.059

29.831 ^ 0.021 29.480 ^ 0.019 29.257 ^ 0.019 29.118 ^ 0.019 29.035 ^ 0.019 28.989 ^ 0.023 28.966 ^ 0.030 28.954 ^ 0.036 28.942 ^ 0.040 28.914 ^ 0.043 28.852 ^ 0.051

29.870 ^ 0.039 29.472 ^ 0.019 29.204 ^ 0.021 29.020 ^ 0.027 28.891 ^ 0.028 28.797 ^ 0.028 28.725 ^ 0.028 28.661 ^ 0.028 28.592 ^ 0.030 28.501 ^ 0.035 28.365 ^ 0.046

2 10.052 ^ 0.067 29.614 ^ 0.032 29.308 ^ 0.033 29.088 ^ 0.044 28.924 ^ 0.048 28.796 ^ 0.046 28.689 ^ 0.042 28.590 ^ 0.042 28.485 ^ 0.043 28.355 ^ 0.057 28.176 ^ 0.080

0 25 50 75 100 125 150 175 200 225 250


Table 13.5. Equilibrium quotients for the first and second ionization of carbonic acid in aqueous NaCl media at saturation vapor pressure from Patterson 2 22 þ et al. (1982, 1984): CO2(aq) þ H2O(l) O Hþ(aq) þ HCO2 3 (aq), HCO3 (aq) O H (aq) þ CO3 (aq)

469

470

P. Tremaine et al.

media) up to 5.0 mol·kg21. The second ionization constant, which has been measured to 250 8C by Patterson et al. (1984), decreases with increasing temperature for reasons outlined earlier. 13.4.2.2. Phosphoric Acid The sodium salts of aqueous phosphoric acid are widely used as pH buffers in the boiler water of thermal electric power stations. Phosphoric acid ionizes according to the reactions: H3 PO4 ðaqÞ þ OH2 ðaqÞ O H2 PO2 4 ðaqÞ þ H2 OðlÞ

ð13:48Þ

2 22 H2 PO2 4 ðaqÞ þ OH ðaqÞ O HPO4 ðaqÞ þ H2 OðlÞ

ð13:49Þ

2 32 HPO22 4 ðaqÞ þ OH ðaqÞ O PO4 ðaqÞ þ H2 OðlÞ

ð13:50Þ

The first and second dissociation equilibria, reactions 13.48 and 13.49, have been determined potentiometrically at temperatures up to 300 8C by Mesmer and Baes (1974). Their values of log10 Q1a,OH and log10 Q2a,OH at ionic strengths in KCl(aq) up to 1.0 mol·kg21 are listed in Table 13.6. The third ionization constant is expected to decrease with increasing temperature. Values have been estimated by Lindsay (1990) and Shock and Helgeson (1988). 13.4.2.3. Hydrogen Sulfate Ion Sulfuric acid, H2SO4(aq), is considered to be a strong acid, which ionizes according to the reaction: þ H2 SO4 ðaqÞ O HSO2 4 ðaqÞ þ H ðaqÞ

ð13:51Þ

Colorimetric measurements of the pH of ammonia/sulfuric acid mixtures by Xiang et al. (1996) yielded values for the first dissociation constant of H2SO4(aq) from 350 to 400 8C. The hydrogen sulfate (‘bisulfate’) ion is a moderately strong acid, which is found in boilers and in the feed-train of nuclear and thermal electric power stations as an impurity from condenser leaks. The HSO2 4 ion is iso-electronic with 2 perchlorate ClO4 and, as a result, it can be used as a non-complexing ion for hightemperature experiments (Rudolph et al., 1997). The ionization of hydrogen sulfate has been studied as the reaction: þ 22 HSO2 4 ðaqÞ O H ðaqÞ þ SO4 ðaqÞ

ð13:52Þ

up to 250 8C by Dickson et al. (1990). The values for log10 Q2a at ionic strengths in NaCl(aq) up to 5.0 mol·kg21 are tabulated in Table 13.7.

t (8C)

0 25 50 75 100 125 150 175 200 225 250 275 300

H3PO4(aq) þ OH2(aq) O H2PO2 4 (aq) þ H2O(l)

22 2 H2PO2 4 (aq) þ OH (aq) O HPO4 (aq) þ H2O(l)

log10 K1a,OH (I ¼ 0)

log10 Q1a,OH (I ¼ 0:1 mol·kg21)





12.884 ^ 0.009 11.848 ^ 0.006 10.983 ^ 0.006 10.259 ^ 0.012 9.647 ^ 0.015 9.127 ^ 0.021 8.681 ^ 0.024 8.294 ^ 0.030 7.954 ^ 0.036 7.652 ^ 0.042 7.380 ^ 0.048 7.131 ^ 0.057 6.901 ^ 0.072

12.921 ^ 0.027 11.886 ^ 0.024 11.023 ^ 0.018 10.300 ^ 0.015 9.691 ^ 0.015 9.172 ^ 0.015 8.727 ^ 0.018 8.342 ^ 0.021 8.004 ^ 0.024 7.703 ^ 0.027 7.433 ^ 0.027 7.186 ^ 0.036 6.958 ^ 0.051

13.104 ^ 0.051 12.062 ^ 0.048 11.191 ^ 0.036 10.459 ^ 0.027 9.842 ^ 0.018 9.315 ^ 0.015 8.862 ^ 0.012 8.468 ^ 0.012 8.122 ^ 0.015 7.813 ^ 0.018 7.535 ^ 0.027 7.280 ^ 0.042 7.043 ^ 0.066

7.631 ^ 0.006 6.796 ^ 0.003 6.079 ^ 0.003 5.464 ^ 0.006 4.933 ^ 0.012 4.471 ^ 0.015 4.068 ^ 0.021 3.710 ^ 0.027 3.390 ^ 0.036 3.101 ^ 0.048 2.835 ^ 0.060 2.588 ^ 0.078 2.355 ^ 0.100

7.871 ^ 0.015 7.045 ^ 0.012 6.337 ^ 0.012 5.733 ^ 0.012 5.214 ^ 0.012 4.768 ^ 0.012 4.379 ^ 0.009 4.039 ^ 0.009 3.739 ^ 0.012 3.472 ^ 0.012 3.234 ^ 0.015 3.023 ^ 0.018 2.836 ^ 0.024

8.218 ^ 0.057 7.393 ^ 0.036 6.689 ^ 0.027 6.090 ^ 0.018 5.578 ^ 0.015 5.139 ^ 0.015 4.760 ^ 0.012 4.429 ^ 0.012 4.139 ^ 0.012 3.883 ^ 0.012 3.659 ^ 0.015 3.463 ^ 0.021 3.296 ^ 0.030


Table 13.6. Equilibrium quotients for the neutralization of H3PO4 and H2PO2 4 in aqueous KCl media at saturation vapor pressure from Mesmer and Baes (1974)

471

472 Table 13.7. Equilibrium quotients for the hydrogen sulfate ionization in aqueous NaCl media at saturation vapor pressure from Dickson et al. (1990): þ 22 HSO2 4 (aq) O H (aq) þ SO4 (aq) t (8C)

log10 K2a (I ¼ 0)

log10 Q2a (I ¼ 0:1 mol·kg21)

log10 Q2a (I ¼ 0:5 mol·kg21)

log10 Q2a (I ¼ 1:0 mol·kg21)

log10 Q2a (I ¼ 3:0 mol·kg21)

log10 Q2a (I ¼ 5:0 mol·kg21)

0 25 50 75 100 125 150 175 200 225 250

21.659 ^ 0.030 21.964 ^ 0.018 22.316 ^ 0.012 22.686 ^ 0.009 23.061 ^ 0.008 23.436 ^ 0.007 23.809 ^ 0.007 24.182 ^ 0.007 24.561 ^ 0.008 24.951 ^ 0.009 25.355 ^ 0.012

2 1.198 ^ 0.030 2 1.487 ^ 0.017 2 1.817 ^ 0.010 2 2.161 ^ 0.007 2 2.504 ^ 0.006 2 2.840 ^ 0.005 2 3.167 ^ 0.005 2 3.488 ^ 0.006 2 3.804 ^ 0.006 2 4.118 ^ 0.007 2 4.432 ^ 0.010

20.900 ^ 0.030 21.178 ^ 0.017 21.493 ^ 0.009 21.817 ^ 0.005 22.135 ^ 0.004 22.442 ^ 0.003 22.735 ^ 0.003 23.015 ^ 0.004 23.282 ^ 0.004 23.537 ^ 0.005 23.778 ^ 0.009

20.788 ^ 0.031 21.055 ^ 0.018 21.358 ^ 0.010 21.669 ^ 0.005 21.972 ^ 0.004 22.261 ^ 0.003 22.533 ^ 0.003 22.788 ^ 0.004 23.027 ^ 0.004 23.248 ^ 0.005 23.447 ^ 0.009

2 0.737 ^ 0.032 2 0.971 ^ 0.019 2 1.238 ^ 0.011 2 1.511 ^ 0.007 2 1.775 ^ 0.006 2 2.020 ^ 0.005 2 2.244 ^ 0.005 2 2.446 ^ 0.005 2 2.624 ^ 0.005 2 2.775 ^ 0.006 2 2.892 ^ 0.011

2 0.806 ^ 0.032 2 1.010 ^ 0.019 2 1.250 ^ 0.011 2 1.495 ^ 0.006 2 1.730 ^ 0.005 2 1.946 ^ 0.005 2 2.140 ^ 0.004 2 2.309 ^ 0.005 2 2.450 ^ 0.005 2 2.560 ^ 0.006 2 2.629 ^ 0.012

P. Tremaine et al.


473

13.4.2.4. Hydrogen Sulfide It is not possible to study the ionization of hydrogen sulfide in electrochemical or conductivity cells that contain platinum electrodes. Suleimenov and Seward (1997) have circumvented this problem by determining the degree of ionization of H2S/HS2 buffers by UV – visible spectrophotometry at temperatures up to 350 8C. The resulting values for log10 K1a are listed in Table 13.8, for the reaction: H2 SðaqÞ O Hþ ðaqÞ þ HS2 ðaqÞ

ð13:53Þ

2

The further ionization of HS (aq) to form the sulfide ion: HS2 ðaqÞ O S22 ðaqÞ þ Hþ ðaqÞ

ð13:54Þ

has been shown to be negligible, even in very concentrated solutions of base (Rao and Hepler, 1977; Giggenbach, 1971). The destabilization of polyvalent ions in high-temperature water is expected to make S22(aq) even more unstable. 13.4.2.5. Nitric Acid The ionization constant of nitric acid has been determined at temperatures from 250 to 320 8C by Oscarson et al. (1992) by using flow calorimetry to determine enthalpies of dilution as a function of nitric acid molality for the ionization reaction: þ HNO3 ðaqÞ O NO2 3 ðaqÞ þ H ðaqÞ

ð13:55Þ

Table 13.8. First ionization constant of H2S (molal) and ionization constant of HNO3 from Suleimenov and Seward (1997) and Oscarson et al. (1992) H2S(aq) O Hþ(aq) þ HS2(aq)

t (8C)

25 50 100 150 200 250 275 300 319 350 a

p (MPa)

log10 K1a

log10 K1a (p ¼ psat a)

10 10 10 10 10 10

26.96 ^ 0.022 26.66 ^ 0.018 26.46 ^ 0.013 26.47 ^ 0.019 26.70 ^ 0.023 27.16 ^ 0.076

2 6.99 2 6.68 2 6.49 2 6.49 2 6.73 2 7.19

11

27.87 ^ 0.076

2 7.89

20

28.77 ^ 0.051

2 8.89

Saturation vapor pressure.

HNO3(aq) O Hþ(aq) þ NO2 3 (aq) p (MPa)

log10 K1a

10.3 11 11 12.8

21 21.42 21.92 22.39

474

P. Tremaine et al.

The results are consistent with earlier high-temperature conductance (Noyes, 1907) and solubility (Marshall and Slusher, 1975a,b) studies, which show that nitric acid becomes an increasingly weak acid at elevated temperature as do all acids, and that undissociated HNO3 is an important species above about 250 8C. Values for log10 K1a are reported in Table 13.8. Chlistunoff et al. (1999) have used UV – visible spectroscopy to determine equilibrium constants for the reactions by which HNO3(aq) converts to the more reduced species HNO2(aq) and NO(aq) in supercritical water. 13.4.2.6. Boric Acid Boric acid is used as a pH control agent and ‘chemical shim’ in the primary coolant of pressurized water reactors (PWRs), because of its high neutron crosssection. Its ionization behavior up to 300 8C has been determined by Mesmer et al. (1972) with potentiometric titrations in HECCs, and from 300 to 380 8C by Wofford et al. (1998) using colorimetric pH indicators. BðOHÞ3 ðaqÞ þ OH2 ðaqÞ O BðOHÞ2 4 ðaqÞ

ð13:56Þ

These data have been re-evaluated by Palmer et al. (2000), and these recalculated results for log10 Q1a,OH are tabulated in Table 13.9. In concentrated 2 solutions, borates form the species B2 ðOHÞ2 7 ðaqÞ; B3 ðOHÞ10 ðaqÞ and higher-order multinuclear clusters (Baes and Mesmer, 1986). These become less important as equilibrium species at elevated temperatures, and their formation constant values are given by Palmer et al. (2000).

Table 13.9. Equilibrium quotients for the ionization of boric acid at saturation vapor pressure (Palmer et al., 2000): B(OH)3(aq) þ OH2(aq) O BOH2 4 (aq) t (8C)





0 25 50 75 100 125 150 175 200 225 250 275 300

5.4438 4.756 4.184 3.706 3.305 2.969 2.687 2.451 2.254 2.093 1.965 1.866 1.796

5.423 4.736 4.164 3.687 3.287 2.952 2.670 2.434 2.238 2.077 1.949 1.850 1.781

5.357 4.672 4.102 3.627 3.229 2.896 2.617 2.383 2.190 2.033 1.908 1.814 1.750

5.285 4.602 4.035 3.564 3.171 2.843 2.570 2.343 2.158 2.010 1.895 1.814 1.764


475

13.4.2.7. Silicic Acid The ionization of silicic acid is one of the most important reactions in geochemistry, as it is responsible for the enhanced solubility of quartz and other silicate minerals at high pH. Busey and Mesmer (1977) used potentiometric titrations to determine log10 Q1a,OH for the reaction: SiðOHÞ4 ðaqÞ þ OH2 ðaqÞ O SiOðOHÞ2 3 ðaqÞ þ H2 OðlÞ

ð13:57Þ

The results are listed in Table 13.10 at ionic strengths in NaCl(aq) up to 5.0 mol·kg21. Silicates also form the multimeric clusters in concentrated solutions (Baes and Mesmer, 1986). Like the polynuclear borates, polysilicates are less stable at elevated temperatures. 13.4.3. Weak and ‘Almost Strong’ Acids and Bases at Temperatures to Supercritical Conditions 13.4.3.1. Hydrochloric Acid Like nitric acid, HCl(aq) becomes a weak acid at elevated temperatures and pressures. Heat of dilution studies (Holmes et al., 1987) have shown that the association of hydrochloric acid under subcritical conditions becomes important at temperatures above about 250 8C. The degree of ionization of HCl(aq) in the supercritical region has been studied by a number of authors using conductance methods. Recent high-resolution conductance measurements by Ho et al. (2001) have resolved earlier discrepancies, and values of 2log10 K1a for the association reaction: Hþ ðaqÞ þ Cl2 ðaqÞ O HClðaqÞ

ð13:58Þ

from this work are presented in Table 13.11. Mesmer et al. (1988, 1991) have used a treatment based on a fit of the density model to earlier experimental data to describe the factors that affect the association of HCl(aq) in the sub- and supercritical regions. 13.4.3.2. Alkali Metal Hydroxides The ionization properties of the alkali metal hydroxides LiOH, NaOH and KOH are of much importance because LiOH(aq) is used under subcritical conditions to control the pH of the primary coolant circuits in nuclear reactors, while NaOH(aq) and KOH(aq) are common components of geologic fluids that formed under supercritical conditions. Conductance measurements by a number of groups have shown that association increases at elevated temperatures for reasons similar to those for HCl(aq) (Mesmer et al., 1991). Tables 13.12 and 13.13 list values for the

476 Table 13.10. Equilibrium quotients for the silicic acid ionization in aqueous NaCl media at saturation vapor pressure from Busey and Mesmer (1977): Si(OH)4(aq) þ OH2(aq) O SiO(OH)2 3 (aq) þ H2O(l) t (8C)






0 25 50 75 100 125 150 175 200 225 250 275 300

4.662 ^ 0.049 4.168 ^ 0.033 3.767 ^ 0.025 3.438 ^ 0.022 3.165 ^ 0.022 2.937 ^ 0.022 2.746 ^ 0.021 2.585 ^ 0.021 2.448 ^ 0.022 2.332 ^ 0.024 2.233 ^ 0.027 2.149 ^ 0.031 2.078 ^ 0.037

4.793 ^ 0.045 4.297 ^ 0.026 3.893 ^ 0.014 3.562 ^ 0.010 3.286 ^ 0.010 3.056 ^ 0.010 2.861 ^ 0.010 2.696 ^ 0.010 2.556 ^ 0.011 2.436 ^ 0.014 2.333 ^ 0.018 2.245 ^ 0.023 2.169 ^ 0.030

4.865 ^ 0.046 4.367 ^ 0.027 3.961 ^ 0.016 3.627 ^ 0.012 3.348 ^ 0.012 3.115 ^ 0.013 2.917 ^ 0.013 2.749 ^ 0.013 2.605 ^ 0.013 2.481 ^ 0.015 2.374 ^ 0.018 2.281 ^ 0.023 2.200 ^ 0.029

5.072 ^ 0.051 4.565 ^ 0.031 4.150 ^ 0.018 3.805 ^ 0.012 3.516 ^ 0.011 3.270 ^ 0.011 3.059 ^ 0.011 2.876 ^ 0.011 2.717 ^ 0.011 2.577 ^ 0.012 2.452 ^ 0.015 2.341 ^ 0.019 2.241 ^ 0.024

5.266 ^ 0.059 4.750 ^ 0.039 4.324 ^ 0.026 3.968 ^ 0.019 3.666 ^ 0.015 3.407 ^ 0.014 3.181 ^ 0.013 2.984 ^ 0.013 2.808 ^ 0.013 2.651 ^ 0.016 2.509 ^ 0.020 2.379 ^ 0.025 2.259 ^ 0.031

P. Tremaine et al.


477

Table 13.11. Molal ion association constants of aqueous HCl solutions from Ho et al. (2001): Hþ(aq) þ Cl2(aq) O HCl(aq) t (8C) 200 300 300 350 350 370 370 380 380 380 390 390 390 400 400 400 410

p (MPa)

rw (g·cm23)

10.02 10.17 10.26 27.80 26.16 28.89 27.82 31.15 28.59 27.55 30.46 28.25 27.24 30.76 29.55 28.82 30.56

0.871 0.7159 0.7161 0.6365 0.6301 0.5724 0.5651 0.5441 0.5198 0.5067 0.4772 0.4267 0.3823 0.3876 0.3373 0.301 0.27

2log10 K1a 0.43 ^ 0.23 0.97 ^ 0.05 0.68 ^ 0.23 1.68 ^ 0.014 1.83 ^ 0.003 2.29 ^ 0.03 2.64 ^ 0.06 3.07 ^ 0.06 3.10 ^ 0.03 3.00 ^ 0.05 3.42 ^ 0.24 3.87 ^ 0.15 3.94 ^ 0.25 4.15 ^ 0.31 4.38 ^ 0.22 4.97 ^ 0.2 5.12 ^ 0.4

reactions: Liþ ðaqÞ þ OH2 ðaqÞ O LiOHðaqÞ

ð13:59Þ

Naþ ðaqÞ þ OH2 ðaqÞ O NaOHðaqÞ

ð13:60Þ

Kþ ðaqÞ þ OH2 ðaqÞ O KOHðaqÞ

ð13:61Þ

reported from the recent conductance measurements by Ho et al. (2000b). While it is beyond the scope of this work, we note that the association of alkali metal chlorides, LiCl(aq), NaCl(aq) and KCl(aq) is also very important under Table 13.12. The molal ion association constants of aqueous NaOH solutions and aqueous KOH solutions from Ho et al. (2000a,b) t (8C)

100 200 300 350 370 380 390 405

Naþ(aq) þ OH2(aq) O NaOH(aq)

Kþ(aq) þ OH2(aq) O KOH(aq)

p (MPa)

rw (g·cm23)

2 log10 K1b

p (MPa)

rw (g·cm23)

2log10 K1b

9.94 15.39 9.69 23.93 25.83 – 28.71 31.25

0.9629 0.8748 0.7148 0.621 0.5484 – 0.4385 0.346

0.28 ^ 0.19 0.66 ^ 0.13 0.89 ^ 0.3 1.65 ^ 0.01 1.83 ^ 0.02 – 2.46 ^ 0.1 2.9 ^ 0.13

13.7 15.63 16.55 28.28 27.74 27.19 28.18 31.31

0.9646 0.875 0.7288 0.6383 0.5642 0.5002 0.422 0.348

20.3 ^ 0.3 0.4 ^ 0.18 0.58 ^ 0.4 1.08 ^ 0.4 1.29 ^ 0.3 2.01 ^ 0.3 2.11 ^ 0.1 2.85 ^ 0.1

478

P. Tremaine et al. Table 13.13. The molal ion association constants of aqueous LiOH solutions from Ho et al. (2000a,b): Liþ(aq) þ OH2(aq) O LiOH(aq) t (8C) 50 100 150 200 250 300 300 300 350 350 370 380 390 400 400 410

p (MPa)

rw (g·cm23)

2 log10 K1b

4.40 4.88 9.40 9.91 11.02 9.52 10.39 12.87 23.86 27.44 28.79 29.85 28.88 32.49 30.57 32.20

0.9899 0.9606 0.9220 0.8709 0.8069 0.7144 0.7164 0.7216 0.6206 0.6352 0.5715 0.5323 0.4433 0.4328 0.3794 0.3273

0.53 ^ 0.17 1.03 ^ 0.17 1.29 ^ 0.19 1.28 ^ 0.1 1.41 ^ 0.15 1.36 ^ 0.04 1.56 ^ 0.1 1.60 ^ 0.02 2.00 ^ 0.03 1.81 ^ 0.07 2.49 ^ 0.06 2.67 ^ 0.15 3.18 ^ 0.03 3.10 ^ 0.23 3.48 ^ 0.03 3.75 ^ 0.2

supercritical conditions and must be considered in speciation calculations (Mesmer et al., 1991). 13.4.4. Representation of Inorganic Acid – Base Ionization Constants by the ‘Density’ Model Many of the ionization constants for inorganic acids and bases have been represented by fitting an expanded form of the ‘density’ model, Eq. 13.20. Table 13.14 lists parameters for the general equation: log10 K ¼ q1 þ q2 =T þ q3 ln T þ q4 T þ q5 T 2 þ q6 =T 2 þ ðq7 þ q8 T þ q9 =TÞ log10 rw

ð13:62Þ

as reported in the original papers cited. Here T is the temperature in kelvin and qn are fitting parameters for each acid. Where fits were not reported we have fitted Eq. 13.62 to the reported values of log10 K as tabulated. 13.5. Carboxylic Acids and Phenols 13.5.1. Background Many techniques such as those described earlier have been used to determine the ionization of aliphatic and aromatic carboxylic acids, and the thermodynamic properties of the reaction ðDr Cp ; Dr HÞ: It is not the task of this chapter to

q1 £ 1022

Acids a,b

CO2(aq) H3PO4b,c H2PO2b,d 4 HSO2b,e 4 H2Sf HNO3g B(OH)3b,h Si(OH)4b,i HClj HClk LiOHl NaOHm KOHn

25.22461 22.53198 22.46045 5.627097 7.82439 25.41813 20.362605 20.184014 0.0195 0.02638 0.02094 0.02068 0.02302

q2 £ 1024 2.96882 1.76558 1.71569 2 1.327375 2 2.05657 3.73852 0.364518 0.234669 2 0.13033 2 0.15188 2 0.079365 2 0.065661 2 0.095472

q3 £ 1021

q4 £ 102

8.18401 3.94277 3.77345 210.25154 214.2742 7.5445 0.505527 0.257979 0 0 0 0 0

2 8.96488 2 3.25405 2 3.22082 24.77538 36.1261 0 0 0 0 0 0 0 0

CO2(aq) þ H2O(l) O Hþ(aq) þ HCO2 3 (aq). Fitted at saturation vapor pressure. c H3PO4(aq) þ OH2(aq) O H2PO2 4 (aq) þ H2O(l). 22 d 2 H2PO2 4 (aq) þ OH (aq) O HPO4 (aq) þ H2O(l). 22 e þ HSO2 4 (aq) O H (aq) þ SO4 (aq). f þ 2 H2S(aq) O H (aq) þ HS (aq). g HNO3(aq) O Hþ(aq) þ NO2 3 (aq). h B(OH)3(aq) þ OH2(aq) O BOH2 4 (aq). i Si(OH)4(aq) þ OH2(aq) O SiO(OH)2 3 (aq) þ H2O(l). j þ H (aq) þ Cl2(aq) O HCl(aq) (for 200– 410 8C). k þ H (aq) þ Cl2(aq) O HCl(aq) (for 200– 600 8C). l Liþ(aq) þ OH2(aq) O LiOH(aq). m Naþ(aq) þ OH2(aq) O NaOH(aq). n þ K (aq) þ OH2(aq) O KOH(aq).

q5 £ 104 0 0 0 2 1.117033 2 1.6722 0 0 0 0 0 0 0 0

q6 £ 1025

q7 £ 1021

q8 £ 102

q9 £ 1023

t (8C)

2 20.4679 28.10134 28.97579 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 3.1264 1.64914 0 2 0.9876 2 0.9078 2 0.8192 2 1.2432 2 0.9862

0 0 0 0 0 0 2 2.3917 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 1.3852 5.8769 3.9935

0 – 300 0 – 300 0 – 300 0 – 250 25 – 350 250– 319 5 – 380 0 – 300 200– 410 200– 600 50 – 600 100– 600 100– 600


Table 13.14. Fitting parameters for the ionization constants log10 K of inorganic acids and bases according to Eq. 13.62

a

b

479

480 Table 13.15. Equilibrium quotients for the ionization of acetic acid in aqueous NaCl media at saturation vapor pressure from Mesmer et al. (1989): CH3COOH(aq) O Hþ(aq) þ CH3COO2(aq) t (8C)

log10 K1aa (I ¼ 0)

log10 Q1a (I ¼ 0:1 mol·kg21)

log10 Q1a (I ¼ 0:5 mol·kg21)

log10 Q1a (I ¼ 1:0 mol·kg21)

log10 Q1a (I ¼ 3:0 mol·kg21)

log10 Q1a (I ¼ 5:0 mol·kg21)

0 25 50 75 100 125 150 175 200 225 250 275 300

24.780 ^ 0.004 24.757 ^ 0.002 24.787 ^ 0.003 24.851 ^ 0.005 24.942 ^ 0.007 25.056 ^ 0.011 25.190 ^ 0.015 25.346 ^ 0.018 25.522 ^ 0.020 25.719 ^ 0.022 25.938 ^ 0.026 26.179 ^ 0.034 26.443 ^ 0.049

2 4.581 ^ 0.007 2 4.547 ^ 0.006 2 4.564 ^ 0.005 2 4.613 ^ 0.005 2 4.684 ^ 0.006 2 4.774 ^ 0.006 2 4.881 ^ 0.007 2 5.005 ^ 0.009 2 5.147 ^ 0.012 2 5.311 ^ 0.016 2 5.501 ^ 0.021 2 5.725 ^ 0.028 2 5.995 ^ 0.039

24.518 ^ 0.017 24.469 ^ 0.016 24.472 ^ 0.014 24.506 ^ 0.012 24.560 ^ 0.010 24.629 ^ 0.010 24.710 ^ 0.010 24.802 ^ 0.011 24.904 ^ 0.013 25.015 ^ 0.014 25.136 ^ 0.016 25.266 ^ 0.022 25.403 ^ 0.037

24.548 ^ 0.022 24.484 ^ 0.021 24.474 ^ 0.018 24.494 ^ 0.015 24.533 ^ 0.013 24.586 ^ 0.012 24.647 ^ 0.013 24.716 ^ 0.014 24.791 ^ 0.016 24.868 ^ 0.017 24.947 ^ 0.019 25.021 ^ 0.027 25.081 ^ 0.046

2 4.858 ^ 0.026 2 4.737 ^ 0.021 2 4.675 ^ 0.017 2 4.643 ^ 0.014 2 4.630 ^ 0.012 2 4.628 ^ 0.011 2 4.633 ^ 0.012 2 4.643 ^ 0.013 2 4.653 ^ 0.015 2 4.662 ^ 0.016 2 4.665 ^ 0.018 2 4.653 ^ 0.025 2 4.609 ^ 0.043

2 5.275 ^ 0.042 2 5.086 ^ 0.034 2 4.965 ^ 0.027 2 4.877 ^ 0.022 2 4.811 ^ 0.018 2 4.757 ^ 0.017 2 4.712 ^ 0.018 2 4.673 ^ 0.021 2 4.639 ^ 0.023 2 4.605 ^ 0.024 2 4.571 ^ 0.027 2 4.528 ^ 0.037 2 4.465 ^ 0.065

a

Values for log10 K1a are from Model II (Mesmer et al., 1989); values for Q1a at finite ionic strength are from Model I. P. Tremaine et al.


481

Table 13.16. Equilibrium quotients for the dissociation of formic acid in aqueous NaCl media at saturation vapor pressure from Bell et al. (1993): HCOOH(aq) O Hþ(aq) þ HCOO2(aq) t (8C) 25 50 75 100 150 200

log10 K1a (I ¼ 0) 23.755 ^ 0.002 23.781 ^ 0.003 23.849 ^ 0.003 23.951 ^ 0.005 24.233 ^ 0.011 24.591 ^ 0.019

log10 Q1a (I ¼ 0:1 mol·kg21)

log10 Q1a (I ¼ 0:5 mol·kg21)

log10 Q1a (I ¼ 1:0 mol·kg21)

log10 Q1a (I ¼ 5:0 mol·kg21)

23.544 ^ 0.003 23.556 ^ 0.003 23.607 ^ 0.003 23.690 ^ 0.004 23.922 ^ 0.009 24.215 ^ 0.018

23.465 ^ 0.007 23.457 ^ 0.007 23.485 ^ 0.006 23.554 ^ 0.005 23.735 ^ 0.007 23.962 ^ 0.015

23.480 ^ 0.008 23.461 ^ 0.008 23.477 ^ 0.007 23.521 ^ 0.006 23.664 ^ 0.007 23.846 ^ 0.014

23.980 ^ 0.015 23.879 ^ 0.011 23.809 ^ 0.009 23.764 ^ 0.009 23.714 ^ 0.015 23.683 ^ 0.024

enumerate all the reported experimental data, but rather to give reliable values of the dissociation constants and related thermodynamic properties of major carboxylic acids at elevated temperatures. Experimental values above 100 8C have been reported for several aliphatic carboxylic acids (acetic, formic, oxalic, malonic, succinic and citric acid) and one aromatic acid (benzoic). Most of these data were measured in the last decade at Oak Ridge National Laboratory by using the HECC. In each case presented here, the fits to their data and the equations generated for log10 K included other critically evaluated thermodynamic data (such as Dr Cpo ; DrH o, etc.). Details are described in the original literature. The values are reported in Tables 13.15–13.17 at saturation vapor pressure, as a function of temperature. The ionic strength corresponds to infinite dilution, except for acetic acid and formic acid, which are listed at several ionic strengths. These data were generated from fits of the general Eq. 13.62 to the experimental data, with values of the fitting parameters reported in Table 13.18. None of the measurements cited in Table 13.18 extended to temperatures high enough to fit statistically significant values for the ‘density’ terms q7, q8 and q9. We also note the results of Ellis (1963), who measured the acid dissociation constants for acetic, propionic, n-butyric and benzoic acids using conductance methods, at temperatures up to 225 8C. 13.5.1.1. Acetic and Formic Acids Acetic and formic acids are the most thoroughly studied carboxylic acids at elevated temperatures, both because of their simplicity and thermal stability and because of their importance to the electric power industry as corrosive trace contaminants in boiler water. For acetic acid, the results from Mesmer et al. (1989) represent the first potentiometric study of an organic acid at high temperatures. The ionization constants of the reaction: CH3 COOHðaqÞ O CH3 COO2 ðaqÞ þ Hþ ðaqÞ

ð13:63Þ

were carefully determined in NaCl media to 5 mol·kg21 from 50 to 250 8C by potentiometry. The values reported in Table 13.15 were generated from their

t (8C)

Oxalic acid log10 K1a

0 25 50 75 100 125 150 175 200 250

a b

Malonic acid log10 K2a

a

log10 K1a

b

Succinic acid log10 K2a

log10 K1a

log10 K2ac

24.199 ^ 0.018 24.264 ^ 0.014 24.399 ^ 0.012 24.574 ^ 0.014 24.780 ^ 0.019 25.015 ^ 0.020 25.280 ^ 0.024 25.580 ^ 0.031 – – Citric acid

log10 K1ad

log10 K2ad

log10 K3ad

log10 Kae

log10 Kaf

23.232 ^ 0.005 23.127 ^ 0.002 23.095 ^ 0.003 23.103 ^ 0.005 23.135 ^ 0.008 23.186 ^ 0.013 23.255 ^ 0.018 – 23.456 ^ 0.031 – –

24.841 ^ 0.003 24.759 ^ 0.001 24.758 ^ 0.003 24.801 ^ 0.009 24.871 ^ 0.018 24.962 ^ 0.029 25.072 ^ 0.042 – 25.357 ^ 0.070 – –

26.394 ^ 0.003 26.397 ^ 0.002 26.481 ^ 0.004 26.607 ^ 0.006 26.759 ^ 0.009 26.931 ^ 0.010 27.120 ^ 0.012 – 27.556 ^ 0.015 – –

24.258 ^ 0.009 24.206 ^ 0.006 24.233 ^ 0.005 24.304 ^ 0.005 24.401 ^ 0.006 24.520 ^ 0.006 24.657 ^ 0.007 24.815 ^ 0.008 24.993 ^ 0.010 25.195 ^ 0.013 25.421 ^ 0.016

24.210 ^ 0.007 24.205 ^ 0.004 24.237 ^ 0.004 24.300 ^ 0.004 24.390 ^ 0.005 24.505 ^ 0.005 24.644 ^ 0.006 24.804 ^ 0.007 24.986 ^ 0.009 25.191 ^ 0.014 25.418 ^ 0.027

c d

Kettler et al. (1995a). Beńe´zeth et al. (1997).

25.671 ^ 0.003 25.697 ^ 0.001 25.805 ^ 0.002 25.958 ^ 0.006 26.138 ^ 0.012 – – – – –

c

2 1.443 ^ 0.057 2 1.401 ^ 0.052 2 1.447 ^ 0.047 2 1.540 ^ 0.046 2 1.664 ^ 0.050 2 1.811 ^ 0.051 – – – –

Kettler et al. (1998). Kettler et al. (1992).

22.897 ^ 0.007 22.852 ^ 0.003 22.879 ^ 0.005 22.941 ^ 0.012 23.024 ^ 0.024 – – – – –

b

24.275 ^ 0.005 25.674 ^ 0.002 24.210 ^ 0.003 25.638 ^ 0.001 24.188 ^ 0.004 25.681 ^ 0.002 – – 24.248 ^ 0.007 25.919 ^ 0.010 – – 24.420 ^ 0.010 26.278 ^ 0.022 – – 24.678 ^ 0.014 26.702 ^ 0.037 25.005 ^ 0.021 27.159 ^ 0.054 Benzoic acid

e f

Kettler et al. (1995b) (from their cited Eq. 10). Kettler et al. (1995b) (from their cited Eq. 13).

P. Tremaine et al.

0 25 50 75 100 125 150 175 200 225 250

a

482

Table 13.17. Equilibrium constants for the ionization of other carboxylic acids in aqueous NaCl media at saturation vapor pressure: H3A(aq) O Hþ(aq) þ H2A2(aq), H2A2(aq) O Hþ(aq) þ HA22(aq), HA22(aq) O Hþ(aq) þ A32(aq)

Acids Formic (K1a) Acetic (K1a)a Acetic (K1a)b Oxalic (K1a) Oxalic (K2a) Malonic (K1a) Malonic (K2a) Succinic (K1a) Succinic (K2a) Citric (K1a) Citric (K2a) Citric (K3a) Benzoic (K1a) a b

q1 3.879698 23.7944 2350.02 2603.83815 2614.33493 2607.587 2607.931 233.482 69.337 2629.084 2620.292 2609.333 2615.1048

q2

q3

2 1135.860 0 2 1010 0 18 325 55.327 34 240.02 94.9734 35 232.02 94.9734 34 561 94.9734 34 324 94.9734 0 6.1233 2 3314.45 2 11.208 35 073 98.6106 34 692 97.0050 34 388 94.9734 34 570.79 96.26395

q4

q5

20.0128286 0 0 0 20.063513 0 20.097611 0 20.07605 2 2.3861 £ 1025 20.093516 0 20.099240 0 20.018835 0 0 0 20.097611 0 20.097611 0 20.097611 0 20.097611 0

q6 373 2 1 110 2 2 170 2 2 170 2 2 170 2 2 170

2 2 170 2 2 170 2 2 170 2 2 170

q7 0 740 500 870 870 870 870 0 0 870 870 870 870

q9

q10

t (8C)

0 0 0 25 – 200 7.2484 2 780.44 2 4.6798 £ 107 0 – 300 0 0 0 0 – 300 0 0 0 0 – 125 0 0 0 0 – 175 0 0 0 0 – 100 0 0 0 0 – 100 0 0 0 0 – 250 0 0 0 0 – 250 0 0 0 0 – 200 0 0 0 0 – 200 0 0 0 0 – 200 0 0 0 0 – 250


Table 13.18. Fitting parameters for the ionization constant log10 Ka of organic acids at saturation vapor pressure according to Eq. 13.62

Model I (see text). Model II (see text).

483

484

P. Tremaine et al.

‘Model I’, which is the following version of the density model: log10 K1a ¼ q1 þ q2 =T þ q6 =T 2 þ q10 =T 3 þ ðq7 þ q9 =TÞ ln rw

ð13:64Þ

These authors also gave a second model, Model II, based on the expression of DCpo of the form a1 þ a2 T þ a3 =T 2 which is described in the original paper. The values reported in Table 13.15 at infinite dilution were generated from log10 K1a ¼ q1 þ q2 =T þ q3 ln T þ q4 T þ q6 =T 2

ð13:65Þ

Excellent fits of the results of Mesmer et al. (1989) were obtained with both models. The acid dissociation constants for the ionization of formic acid: HCOOHðaqÞ O Hþ ðaqÞ þ HCOO2 ðaqÞ

ð13:66Þ

were measured by Bell et al. (1993) using the same approach as for acetic acid, described above. The molal equilibrium quotients and thermodynamic properties obtained by these authors are reported in Table 13.16 as a function of temperature and ionic strength. The infinite dilution constants are generated from Eq. 13.62 together with the parameters reported in Table 13.18. 13.5.1.2. Polybasic Carboxylic acids and Benzoic Acid The ionization of several polybasic carboxylic acids have been measured at elevated temperatures. These acids are generally less stable than monobasic acids at elevated temperatures and ionize according to the stepwise equations: H3 AðaqÞ O Hþ ðaqÞ þ H2 A2 ðaqÞ

K1a

ð13:67Þ

H2 A2 ðaqÞ O Hþ ðaqÞ þ HA22 ðaqÞ K2a

ð13:68Þ

HA22 ðaqÞ O Hþ ðaqÞ þ A32 ðaqÞ

ð13:69Þ

K3a

The ionization equilibria of oxalic, malonic, succinic and citric acid have been studied by Kettler et al. (1992, 1995a, 1998) and Beńe´zeth et al. (1997). Values for log10 Ka at infinite dilution are reported in Table 13.17. The fitting parameters used to reproduce the experimental results are listed in Table 13.18. Although the density model was used for the fit, the density term, q9, which dominates at high temperature, was often set to zero because the data did not extend to high enough temperatures for this term to be significant. Measurements on benzoic acid ionization have been made by emf, conductance and UV – visible spectrophotometric methods. Benzoic acid contains both a phenyl and aryl carboxylic acid group. The carboxylic acid group ionizes according to the reaction: C6 H5 COOHðaqÞ O C6 H5 COO2 ðaqÞ þ Hþ ðaqÞ

ð13:70Þ


485

Equilibrium constants have been measured by Kettler et al. (1995b) using potentiometric titration methods. Values of log10 Ka and fitting parameters are listed in Tables 13.17 and 13.18, respectively. 13.6. Amines and Alkanol Amines 13.6.1. Effects of Amine Structure on Ionization and the Formation of Carbamates Amines and alkanolamines have seen wide application in the energy industry as ‘all volatile’ additives for boiler-water pH control and as ‘chemical solvents’ for removing carbon dioxide and other acid gases from natural gas and combustion gases. Boiler pH control applications typically involve dilute solutions of a few parts per million at temperatures from 25 to 350 8C, while gas treatment applications require concentrated solutions in excess of 1 mol·kg21 at temperatures from 25 to 150 8C. Factors influencing the ionization constants of amines have been reviewed by Jones and Arnett (1974). Briefly, amines and alkanolamines consist of three alkyl, alkanol or hydrogen substituent groups covalently bound to a central nitrogen atom. Together with the unbonded lone pair of valence electrons, these groups give the amine a tetrahedral structure. The basicity of the amine is controlled by the availability of the valence band electrons for chemical bonding to Hþ(aq). Electron donor substituent groups enhance the basicity and increase Kb, while electronwithdrawing groups reduce the magnitude of Kb. Steric effects (i.e., crowding effects) due to interactions among the three substituent groups may also suppress the value of Kb. This is particularly true for tertiary amines. Steric effects are also affected by hydration. Because of these competing factors, the relative base strengths of primary, secondary and tertiary amines at 25 8C follow the sequence: NH3 ðaqÞ , RNH2 ðaqÞ , RR0 NHðaqÞ . RR0 R00 NðaqÞ In addition to the ionization reaction: RR0 R00 NðaqÞ þ Hþ ðaqÞ O ½RR0 R00 NHþ ðaqÞ

ð13:71Þ

ammonia, primary and secondary amines can also react with carbon dioxide to form carbamic acid according to the reaction: H2 CO3 ðaqÞ þ RR0 NHðaqÞ O RR0 NCOO2 ðaqÞ þ Hþ ðaqÞ þ H2 OðlÞ

ð13:72Þ

Carbamate formation, which is a reversible reaction, does not occur in the dilute solutions used in boiler treatment applications, and is less favored at elevated temperatures (Roberts and Tremaine, 1985). Indeed, the decreasing stability with increasing temperature allows carbamate formation to be used in reversible cyclic

486

P. Tremaine et al.

processes to trap CO2 (Astarita et al., 1983). The use of sterically hindered secondary amines with bulky alkyl and alkanol substituents can prevent carbamate formation in processes where it is detrimental. 13.6.1.1. Ammonia Ammonia is an extremely important base in hydrothermal technology, because of its high solubility, volatility, pH buffer properties and ability to form complexes with metal ions. For example, it is among the most wisely used bases in ‘all-volatile’ treatments of boiler water (‘AVT’), and is also present in boiler water as a breakdown product of hydrazine (which is added as a reducing agent). Ammonia’s properties as a complexing agent form the basis of the Sherritt– Gordon hydrometallurgical process, in which copper, nickel and cobalt are extracted directly from crushed ore in large zircalloy pressure vessels, as metal– amine complexes. The ionization of ammonia has been studied by a number of authors, beginning with the pioneering work of Noyes (1907). Conductance measurements by Quist and Marshall (1968b) extended the data up to 700 8C. Hitch and Mesmer (1976) used a flow-cell potentiometric titration technique to determine log10 Q1b vs. ionic strength at temperatures up to 300 8C. The potentiometric values measured for the neutralization reaction: 2 NH3 ðaqÞ þ H2 OðlÞ O NHþ 4 ðaqÞ þ OH ðaqÞ

ð13:73Þ

by Hitch and Mesmer (1976) are summarized in Table 13.19. Values for the variation of log10 K1b with temperature and pressure have been used by Mesmer et al. (1988, 1991) to derive parameters for the density model to describe ammonia ionization at temperatures up to 800 8C. 13.6.1.2. Amines and Alkanolamines In addition to ammonia, morpholine, cyclohexylamine, ethanolamine and dimethylamine are the most widely used amines for ‘AVT’ boiler-water additives by the electric power industry, particularly nuclear plants. Thermodynamic constants for all three systems under boiler conditions have been determined by potentiometric titrations (Mesmer and Hitch, 1977; Beńe´zeth et al., 2001) and from estimates based on experimental values of V o (Tremaine et al., 1997; Shvedov and Tremaine, 1997). Values for log10 Q1b,H for the neutralization reactions: R2 NHðaqÞ þ Hþ ðaqÞ O R2 NHþ 2 ðaqÞ

ð13:74Þ

are listed in Table 13.20. The use of amines to control the pH of boiler water is designed to minimize the corrosion of carbon steel components of the boiler and feed-train before and after boiling. As a result, there is much interest in balancing the effects of


487

Table 13.19. Equilibrium quotients for the ionization of ammonia in aqueous KCl media at saturation vapor pressure from Hitch and Mesmer (1976): NH3(aq) þ H2O(l) O NHþ 4 (aq) þ OH2(aq) t (8C) 0 25 50 75 100 125 150 175 200 225 250 275 300

log10 K1b (I ¼ 0) 24.864 ^ 0.006 24.752 ^ 0.003 24.732 ^ 0.004 24.772 ^ 0.009 24.856 ^ 0.014 24.976 ^ 0.019 25.128 ^ 0.024 25.311 ^ 0.028 25.525 ^ 0.031 25.770 ^ 0.031 26.047 ^ 0.032 26.355 ^ 0.039 26.694 ^ 0.058

log10 Q1b (I ¼ 0:1 mol·kg21)

log10 Q1b (I ¼ 0:5 mol·kg21)

log10 Q1b (I ¼ 1:0 mol·kg21)

log10 Q1b (I ¼ 3:0 mol·kg21)

24.648 ^ 0.007 24.526 ^ 0.003 24.495 ^ 0.004 24.521 ^ 0.008 24.587 ^ 0.013 24.685 ^ 0.017 24.814 ^ 0.022 24.969 ^ 0.026 25.151 ^ 0.028 25.357 ^ 0.028 25.584 ^ 0.029 25.827 ^ 0.037 26.079 ^ 0.056

24.517 ^ 0.021 24.392 ^ 0.011 24.353 ^ 0.008 24.368 ^ 0.011 24.420 ^ 0.014 24.502 ^ 0.016 24.610 ^ 0.019 24.741 ^ 0.022 24.895 ^ 0.024 25.067 ^ 0.025 25.252 ^ 0.025 25.441 ^ 0.032 25.622 ^ 0.051

24.460 ^ 0.046 24.336 ^ 0.026 24.296 ^ 0.015 24.306 ^ 0.014 24.351 ^ 0.017 24.422 ^ 0.018 24.516 ^ 0.020 24.633 ^ 0.022 24.768 ^ 0.023 24.918 ^ 0.023 25.077 ^ 0.023 25.233 ^ 0.029 25.371 ^ 0.047

24.401 ^ 0.163 24.291 ^ 0.104 24.253 ^ 0.066 24.256 ^ 0.048 24.284 ^ 0.044 24.330 ^ 0.044 24.393 ^ 0.044 24.470 ^ 0.042 24.559 ^ 0.040 24.654 ^ 0.039 24.747 ^ 0.043 24.825 ^ 0.054 24.870 ^ 0.075

buffering properties and volatility. Ionization constants and Henry’s law constants (volatility) of several other amines and alkanolamines have been determined at elevated temperatures (Balakrishnan, 1988; Lewis and Wetton, 1987). Values of log10 K1b,H, determined by Balakrishnan using conductivity measurements at temperatures up to 275 8C, are listed in Table 13.21 for seven amines and Table 13.20. Equilibrium constants for morpholine, cyclohexylamine and dimethylamine at infinite dilution from Ridley et al. (2000), Mesmer and Hitch (1977) and Beńe´zeth et al. (2001), respectively log10 K1b,H

t (8C) Morpholine 0 25 50 75 100 125 150 175 200 225 250 275 300

a

9.110 ^ 0.006 8.491 ^ 0.003 7.954 ^ 0.005 7.064 ^ 0.010 6.345 ^ 0.017 5.738 ^ 0.026 5.202 ^ 0.038 4.694 ^ 0.060

C4H8ONH(aq) þ Hþ(aq) O C4H8ONHþ 2 (aq). C6H11NH2(aq) þ Hþ(aq) O C6H11NHþ 3 (aq). c (CH3)2NH(aq) þ Hþ(aq) O (CH3)2NHþ 2 (aq). a

b

Cyclohexylamineb

Dimethylaminec

11.561 ^ 0.035 10.606 ^ 0.034 9.796 ^ 0.033 9.096 ^ 0.033 8.484 ^ 0.033 7.945 ^ 0.032 7.463 ^ 0.033 7.034 ^ 0.032 6.647 ^ 0.031 6.298 ^ 0.035 5.982 ^ 0.050 5.697 ^ 0.079 5.438 ^ 0.120

11.56 ^ 0.02 10.77 ^ 0.02 10.06 ^ 0.02 9.42 ^ 0.02 8.83 ^ 0.03 8.28 ^ 0.03 7.76 ^ 0.04 7.28 ^ 0.05 6.83 ^ 0.05 6.41 ^ 0.06 6.00 ^ 0.07 5.63 ^ 0.08 5.29 ^ 0.10

488

Table 13.21. Ionization constants for seven amines expressed as log10 K1b,H for the reaction BHþ(aq) O B(aq) þ Hþ(aq) from Balakrishnan (1988) log10 K1b,H

t (8C)

25 50 75 100 125 150 175 200 225 250 275

MPA

AMP

EAE

DEAE

PYR

PIP

QUI

9.91 ^ 0.04 9.29 ^ 0.05 8.54 ^ 0.11 7.99 ^ 0.07 7.50 ^ 0.06 7.04 ^ 0.06 6.65 ^ 0.07 6.27 ^ 0.07 5.94 ^ 0.08 5.56 ^ 0.12 5.06 ^ 0.18

9.64 ^ 0.04 8.93 ^ 0.05 8.34 ^ 0.05 7.81 ^ 0.05 7.33 ^ 0.03 6.91 ^ 0.04 6.53 ^ 0.04 6.15 ^ 0.03 5.83 ^ 0.03 5.52 ^ 0.04 5.23 ^ 0.03

9.88 ^ 0.10 9.25 ^ 0.03 8.79 ^ 0.04 8.22 ^ 0.05 7.78 ^ 0.07 7.33 ^ 0.03 6.93 ^ 0.02 6.60 ^ 0.06 6.27 ^ 0.03 5.95 ^ 0.05 5.65 ^ 0.13

9.85 ^ 0.15 9.18 ^ 0.04 8.71 ^ 0.02 8.45 ^ 0.04 7.94 ^ 0.03 7.52 ^ 0.01 7.04 ^ 0.02 6.70 ^ 0.03 6.39 ^ 0.03 6.10 ^ 0.03 5.82 ^ 0.09

11.27 ^ 0.08 10.51 ^ 0.03 9.80 ^ 0.02 9.24 ^ 0.02 8.73 ^ 0.02 8.25 ^ 0.02 7.82 ^ 0.03 7.40 ^ 0.02 7.06 ^ 0.02 6.68 ^ 0.04 6.37 ^ 0.08

11.02 ^ 0.02 10.27 ^ 0.03 9.69 ^ 0.02 9.12 ^ 0.02 8.63 ^ 0.02 8.16 ^ 0.03 7.74 ^ 0.02 7.34 ^ 0.02 6.98 ^ 0.03 6.60 ^ 0.06 6.28 ^ 0.09

11.11 ^ 0.07 10.37 ^ 0.07 9.90 ^ 0.04 9.38 ^ 0.03 8.91 ^ 0.04 8.46 ^ 0.03 8.04 ^ 0.01 7.69 ^ 0.03 7.38 ^ 0.04 7.04 ^ 0.02 6.83 ^ 0.04

MPA: 3-methoxypropylamine, CH3OCH2CH2CH2NH2; AMP: 2-amino-2-methyl-1-propanol, (CH3)2C(NH2)CH2OH; EAE: 2-ethylaminoethanol, C2H5NHCH2CH2OH; DEAE: 2-diethylaminoethanol, (C2H5)2NCH2CH2OH; PYR: pyrrolidine, C4H9N; PIP: piperidine, C5H11N; QUI: quinuclidine, C7H13N. P. Tremaine et al.


489

alkanolamines: 3-methoxypropylamine (MPA), 2-amino-2-methyl-1-propanol (AMP), 2-ethylaminoethanol (EAE), 2-diethylaminoethanol (DEAE), pyrrolidine, piperidine and quinuclidine. 13.7. Other Sources of Data Values for the ionization constants of many acids and bases at 25 8C are listed in compilations by Pettit and Powell (1997), Smith and Martell (1997), Christensen et al. (1976) and Oscarson et al. (1992). Some high-temperature values are included. Proprietary databases of high-temperature ionization constants are maintained and developed for electric power industry applications by EPRI (Alexander and Liu, 1989) and for more general chemical industry applications by OLI Systems Inc. (Anderko, 1995). A large database and computer code for calculating the thermodynamic properties of inorganic ions and their reactions at elevated temperature and pressure is incorporated in the public database SUPCRT92 (Johnson et al., 1992). This is based on the HKF equation of state, and primarily on experimental data available before the late 1980s. Many of the standard partial molar heat capacity and volume data at that time were limited to temperatures below 50 8C, and the HKF extrapolations are not always in agreement with later experiments. The papers on which the program is based (Shock and Helgeson, 1988) are a good source of literature related to experimental studies. The HKF equation of state has also been used to predict the ionization and complexation constants of many organic species under hydrothermal conditions (Shock and Helgeson, 1990; Shock et al., 1992; Shock and Koretsky, 1993, 1995; Amend and Helgeson, 1997). Because the HKF model has no theoretical basis for neutral species, high-temperature values of log10 K should be treated with caution unless the results have been obtained by direct fitting of high-temperature experimental data for the species in question. These papers are exhaustively referenced and are a valuable guide to the literature. Finally, a number of authors have reported functional-group additivity models for organic species from which heat capacity and volume functions can be calculated. We particularly note the treatments by Sedlbauer et al. (2000) and Plyasunov et al. (2000a,b), which appear to provide reliable extrapolations of log10 K for many reactions up to about 250 8C. References Alexander, J.H. and Liu, L., Users Manual, Vol. I. EPRI Report NP-5561-CCM, 1989. Amend, J.P. and Helgeson, H.C., J. Chem. Soc., Faraday Trans., 93, 1927–1941 (1997). Anderko, A., 18th OLI Users Conference, Morristown, NJ, October 10, 1995. Anderson, G.M., Castet, S., Schott, J. and Mesmer, R.E., Geochim. Cosmochim. Acta, 55, 1769– 1779 (1991).

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