A Model Incorporating Ion Dissociation, Solute Concentration, and

Bing Liu, John L. Oscarson, Craig J. Peterson, and Reed M. Izatt. Industrial & Engineering Chemistry Research 2006 45 (9), 2929-2939. Abstract | Full ...
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Ind. Eng. Chem. Res. 2004, 43, 7635-7646

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A Model Incorporating Ion Dissociation, Solute Concentration, and Solution Density Effects To Describe the Thermodynamics of Aqueous Sodium Chloride Solutions in the Critical Region of Water John L. Oscarson,* Bing Liu, and Reed M. Izatt Departments of Chemistry and Biochemistry and Chemical Engineering, Brigham Young University, Provo, Utah 84602

A model, based on Helmholtz energy, describing the thermodynamics of NaCl solutions in the near-critical region of water has been developed and tested as a function of temperature (350402 °C), pressure (18-41 MPa), and solute concentration (0-5 m) using literature heat of dilution (∆dilH) data. This model is an extension of one developed by Anderko and Pitzer (Geochim. Cosmochim. Acta 1993, 57, 1657-1680) as modified by Oscarson et al. (Ind. Eng. Chem. Res. 2001, 40, 2176-2182). The present model includes terms for NaCl dissociation and ion-ion interactions. Density and ∆dilH values predicted using the model agree well with literature values over the temperature, pressure, and solute concentration ranges of the study. Apparent log K′, ∆rH, ∆rS, and ∆rCp values change significantly with the solute concentration, temperature, and solution density. The model was used to determine speciation in aqueous NaCl solutions under the conditions of the study. 1. Introduction There has been increasing interest in recent years in the use of supercritical water oxidation (SCWO) to achieve high destruction efficiencies for a wide variety of hazardous chemical wastes1-5 including munitions,6 polychlorinated biphenyls,7 aqueous organics,8-11 sewage,9 and sludges.11,12 The SCWO technology involves the oxidation of the organic components with oxygen or other oxidizing agents in a water medium at temperature (T) and pressure (P) values above the critical T (Tc; 374 °C) and critical P (Pc; 22.1 MPa) values13 of water. In practice, the oxidation is initiated at about 400 °C and 25 MPa.2 During combustion, T increases to about 650 °C. SCWO is significantly superior to subcritical wet-air oxidation (150-325 °C) in destruction efficiency and to controlled incineration (1000-3000 °C) in energy consumption and the avoidance of NOx formation.2,14 Major advantages of SCWO1,14 are (a) complete miscibility of oxygen and high solubility of organics in supercritical water, eliminating two-phase flow; (b) rapid oxidation of organics, requiring short residence times; (c) complete oxidation (>99.99%)14 of organics, requiring minimal treatment of the effluent; and (d) recovery of the excess heat of oxidation for use as an energy source. If the materials to be destroyed contain acid-forming components such as chlorine, fluorine, phosphorus, and/ or sulfur, corrosion can be a significant problem.15,16 If metallic elements are present in the compounds to be destroyed or in the solution as a result of corrosion of the construction material, plugging of the equipment may be a major concern.17 Corrosion is most marked at T values between 300 and 400 °C.18,19 Avoidance or minimization of corrosion and plugging requires knowledge of the reactions occurring and the species present in the sub- and supercritical water regions as a function * To whom correspondence should be addressed. Tel.: (801) 422-6243. Fax: (801) 422-0151. E-mail: [email protected].

of solute molality (m ) molality or molal), and solution P/density (F). This knowledge is also useful in understanding chemical reactions in other high-T aqueous systems such as those found in geochemical and hydrothermal processes,20 power plants using the steam cycle,21 and industrial chemistry.17 Few chemical systems have been studied in the T, P, and m ranges of the present study. Sodium chloride solutions have been the basis for several models22-27 of aqueous solution thermodynamics in the water critical region. Heat of dilution (∆dilH) values for NaCl solutions from 350 to 402 °C have been reported by Busey et al.28 and us.29 Wood and associates30,31 and Ho and coworkers32,33 have determined equilibrium constant (K) values from 306 to 400 °C using conductivity measurements for the reaction

Na+ + Cl- ) NaCl(aq)

(1)

These K values are valid at ionic strength (µ) ) 0. Other workers have calculated apparent equilibrium constants (K′) and investigated solutions in the critical region of water using molecular dynamics calculations.34-40 A quantitative understanding of speciation and chemical reactions in the water critical region requires a mathematical model that takes into account the various interactions that occur in the solution as a function of T, P, and m. Unfortunately, traditional models based on excess Gibbs energy (Gex) are ineffective in describing the thermodynamics of aqueous solutions above 350 °C.27,41 Anderko and Pitzer23 developed a model (AP) based on residual Helmholtz energy (Ares) that has been used to successfully correlate F and phase equilibrium values of relatively concentrated NaCl solutions in the water critical region. The AP model is based on the assumption that all of NaCl is associated. Therefore, in dilute solutions where the fraction of NaCl dissociated ) mNa+/(mNa+ + mNaCl(aq))] is large, the agree[FNaCl dis ment of the AP model with experimental thermodynamic data is poor. We24 added a term to the AP

10.1021/ie040112p CCC: $27.50 © 2004 American Chemical Society Published on Web 10/05/2004

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Ind. Eng. Chem. Res., Vol. 43, No. 23, 2004

Table 1. Comparison of Several Thermodynamic Models for Aqueous Electrolyte Solutions

model

Gibbs/ Helmholtz energy

advantages

limitations

Pitzer ion-interactiona

Gex(T,P,m)

correlates thermodynamic values well over wide T and m ranges and can be used to describe electrolyte mixtures

APb

Ares(T,F,m)

works in the near-critical region of water even at P values where F changes significantly with m

RIc

Ares(T,F,m)

most effective at low m values; includes term for solute dissociation

RIId

Ares(T,F,m)

effective in water near the critical region; includes terms for species dissociation and effect of ion concentration on Ares

increasingly less effective as temperatures increase above 300 °C at P values where solution F values change significantly with m no term for solute dissociation; cannot be used for calculating speciation; values of ∆dilH predicted by model at low m values are in poor agreement with experimental ∆dilH values does not account for changes in A ˆ of the ions with m; hence gives poor results at high m values applicability to other electrolytes has not been examined

a

Reference 42. b Reference 23. c Reference 29.

d

Present work.

model that accounts for the reaction shown in eq 1. This term was based on the equation for log K reported by Gruszkiewicz and Wood31 for the reaction in eq 1. Their equation for log K was based on electrical conductivity measurements.31 One of the assumptions of this revised model (RI) was that Ares of the ions at any finite concentration was equal to the Ares value of the ions at µ ) 0. The agreement of the RI model24 with measured ∆dilH values28,29 was much better than that of the AP model, especially at low concentrations. We now present a revision of the RI model that includes terms that account for the concentration effect of the ions in solution over the 0-5 m range. This new model (RII) has been tested using literature ∆dilH values.28,29 The goal of the present paper is to show the development of the RII model and to describe its usefulness in accounting for the thermodynamics of NaCl solutions as a function of solution F, T, and m in the water critical region. The P, T, and m ranges investigated were 17-40 MPa, 350-402 °C, and 0-5 m, respectively. 2. Model Development 2.1. General Procedure. Comparisons of the advantages and limitations of the Pitzer ion-interaction, AP, RI, and RII models for use in the water critical region are given in Table 1. The most widely accepted model used to describe the thermodynamics of aqueous electrolyte solutions is the Pitzer ion-interaction model.42 This model is based on Gex and accurately describes the thermodynamics of aqueous electrolyte solutions over wide m ranges at T values up to ∼350 °C. Archer22 used this model to correlate an extensive number of thermodynamic properties of NaCl solutions over a wide range of T, P, and m values. Levelt Sengers and co-workers27,41 have explained that the Pitzer ion-interaction model begins to fail to adequately describe aqueous solutions at 300 °C and is totally inadequate above 350 °C because it does not take into account the large changes in solution F with m in this T range. The AP model successfully correlates phase equilibria and fluid F values especially at high m values where little dissociation occurs. The assumption that no NaCl dissociates is based on the observation that electrolytes become more associated at high T and low F.23 However, at low m and/or high F values, the AP

is appreciable. A significant model fails because FNaCl dis limitation of the model is that the assumption of no NaCl dissociation precludes the calculation of speciation and corrosion potential. The RI model developed by Oscarson et al.24 gives good agreement with ∆dilH measurements at low m values. However, the agreement with ∆dilH data at high m values is only marginally better for the RI model than for the AP model. This poor agreement at high m values was expected because the partial molar Helmholtz energy (A ˆ ) of the ions is assumed to be constant and to be the same as that of the ions at µ ) 0. 2.2. RII Model. The RII model is shown in eq 2. The

Ares(T,F,xNaCl(aq),xNa+) ) AAP(T,F,xNaCl(aq)) + ∆Adiss(T,F,xNaCl(aq),xNa+) xNa+ + ∆AMSA(T,F,xNa+) (2) AAP term contains the expressions developed by Anderko and Pitzer.23 Addition of the ∆Adiss term,24 which allows the calculation of the change in A upon solute dissociation into ions in a hypothetical solution at µ ) 0, gives the RI model. The RII model includes the first two terms plus the ∆AMSA term, which accounts for the changes in Ares going from a hypothetical solution at µ ) 0 to a solution of a finite solute concentration. The AAP term includes theoretical expressions together with a perturbation term with adjustable parameters. The ∆Adiss term was calculated using a modification of the equation for log Km (see Table 2) as reported by Gruszkiewicz and Wood.31 In the RI model, the parameters in the log Km equation31 were used without modification. However, in the present work, the seven parameters in the log Km equation were modified as shown in Table 2. It was impossible to fit the ∆dilH data without these modifications. Both sets of parameters give similar log Km values. However, the different sets of parameters give significantly different temperature derivatives of log Km, resulting in different heat of reaction (∆rH) values for the reaction in eq 1. The F value used in the log Km equation should be the F value for water in the actual solution. We approximated this F value using eq 3 where Fhyp is the hypothetical F value

Fhyp ) (1 - xNaCl)Mw/V

(3)

Ind. Eng. Chem. Res., Vol. 43, No. 23, 2004 7637 Table 2. Comparison of the Parameters Found in This Study and Those Found in the Literature24,31 σ ) σ1 + σ2/T log Km ) a1 - a2/T + a3F + a4/F + a5 exp[a6(T - Tc) + a7F3]

equation for σ (eq 3) equation for log Km

param

literature value

ref

value used in this study

σ1 σ2 a1 a2 a3 a4 a5 a6 a7

5.695 × 10-10 m -5.513 × 10-8 m‚K 1.5089 1200 K -4.3583 × 10-4 m3‚kg-1 1291 kg‚m-3 -1.7768 -0.037829 K-1 -4.417 × 10-8 m9‚kg-3

24 24 31 31 31 31 31 31 31

7.936 × 10-10 m -6.076 × 10-8 m‚K 1.3644 1559 K -4.56164 × 10-4 m3‚kg-1 1948 kg‚m-3 -6.6093 -0.038415 K-1 -2.4621 × 10-8 m9‚kg-3

of water at the T, P, and m values of the solution, Mw is the molecular mass of water, and V is the molar volume of the solution. The ∆Adiss term is based on the assumption that only 1:1 association of Na+ and Cl- occurs. There is evidence based on Monte Carlo simulations and interpretation of experimental data that polynuclear clusters occur in concentrated supercritical electrolyte solution.43.44 If clusters are present, the speciation of NaCl solutions would be much more complex than the RII model predicts. The perturbation term and the adjustable parameters in the ∆Adiss and ∆AMSA terms allow the RII model to fit F and ∆dilH data even though the physical picture may not be correct. In principle, the ∆Adiss term could be changed to include the several reactions needed to describe the different polynear clusters and then the perturbation term could be changed to fit the data. Such a mathematical representation would be more complex and would still require a perturbation term. In this paper, the model was based on 1:1 Na+ and Classociation. The RII model has the same form as the RI model except that a term [∆AMSA(T,F,xi)] has been added that accounts for the change in A with m over the entire NaCl solubility range in the near-critical region of water. The added term, shown in eq 4, is a modification

∆AMSA ) -(2Γ3RTV/3πNa)(1 + 1.5σΓ)

(4)

of the mean spherical approximation term developed by Myers et al.45 The terms for σ, Γ, and κ are defined by eqs 5-7, respectively. Quantities in eqs 4-7 not defined

σ ) σ1 + σ2/T

(5)

Γ ) (1/2σ)[(1 + 2σκ)0.5 - 1] 2

2

∑xiZi ]

κ ) [(e Na /0RTV)

2 0.5

(6) (7)

earlier are as follows: xi is the mole fraction of either Na+ or Cl- in solution, R is the ideal gas constant, Na is Avogadro’s number, σ is half of the sum of the diameters of the Cl- and Na+ ions, σ1 and σ2 are parameters used by us to allow calculation of σ as a function of T, Γ is the MSA screening parameter, κ is the Debye screening length, e is the charge on an electron,  is the dielectric constant of water, 0 is the permittivity of free space, and Zi is the ion charge number. To better fit the heat data, the two parameters σ1 and σ2 used by Myers et al.45 were changed by us. It is noted that the σ1 and σ2 values were regressed by Myers et al.45 using data up to 300 °C. A comparison of

the σ1 and σ2 values used by us with those found in the literature is shown in Table 2. The value of  in eq 7 was calculated from the equation of Archer and Wang46 using the solution F value rather than the water F value at the T and P of interest. It is noted that the ∆AMSA term is based on a mean-field model, and therefore high accuracy is not expected near the water critical point. In the RI model, no parameters were adjusted by us. Parameters regressed by Anderko and Pitzer,23 Gruszkiewicz and Wood,31 and Myers et al.45 were used unchanged. In all, nine parameters were adjusted by us in the RII model (seven in the ∆Adiss term and two in the ∆AMSA term) in order to obtain a good fit of the data. These adjustments gave better T derivatives and probably helped in compensating for the inconsistencies in the  values used. Using both terms gave a better fit of the data than using only one of the terms and adding more adjustable parameters to that term. The ∆Adiss term makes a major contribution in the dilute region and has no composition-dependent terms, while the ∆AMSA term contributes nothing at infinite dilution but becomes more important as the concentration increases. 3. Model Application Equation 2 and its derivatives with respect to T and F allow the calculation of all of the thermodynamic properties of a NaCl solution in the water critical region. The derivatives of the first23 and second24 terms on the right-hand side of eq 2 are available. The derivatives of the third term with respect to T and F are given in eqs 8 and 9, respectively, where M h is the average molecular

[ [

] ]

∂Γ dσ +σ dT ∂T F ) ∆A F 3 1 + σT 2 (8) ∂Γ σ 1 ∂V 3 ∂∆AMSA ∂F T MSA 3 ∂Γ ) ∆A + + 3 ∂F T Γ ∂F T V ∂F T 2 1 + σT 2 (9) ∂κ dσ dσ (1 + 2σκ)0.5 σ +κ - 4Γ ∂Γ ∂T F dT dΓ (10) ) ∂T F 4σ ∂ ∂κ ∂T F 1 ) -0.5κ (11) + ∂T F  T σ2 dσ (12) )- 2 dT T

(

)

(

)

∂∆AMSA ∂T

MSA

( )

3 ∂Γ 1 3 + + Γ ∂T F T 2

( )

Γ

( )

( )

[( )

]

∂κ ∂Γ ∂F T ) ∂F T 2(1 + 2σκ)0.5

( )

( )

)T

( )

[( ) ]

( )

(∂F∂κ)

( )

[( )

(13)

( )]

∂V ∂ κ  +V 2V ∂F T ∂F T M h ∂V )- 2 ∂F T F

( )

(14) (15)

mass of the solution. The  value and its derivatives were determined using the calculated F at given T, P, and m values of the solution. The F value thus calculated is not consistent with that found using the Hill model.46

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This latter F value is used in the equation for  developed by Archer.46 Using the value for  found by incorporating the calculated (instead of the Hill) F value into the Archer equation leads to inconsistencies in the calculated ∆AMSA term. The F value of pure water calculated using our equation differs from that calculated using the Hill equation by about 7% at T and P values where water is highly compressible, and the ε value calculated using our F value is about 10% different than that found using the correct F value. In the T and P regions where water is less compressible, the differences in both F and ε are about 1%. Values of Ares and its derivatives can be calculated using eqs 2 and 8-15 and those given previously23,24 if F, T, and the concentrations of NaCl(aq), Na+, and Clare known. However, T, P, and m are the independent variables in the ∆dilH experiments; therefore, an iterative process is required to find F and concentrations of NaCl value is NaCl(aq), Na+, and Cl- (FNaCl dis ). The Fdis found by minimization of the Gibbs energy. At each value, the F value of the solution that gives FNaCl dis agreement between the P value of the experiment and the P value calculated by eq 16 is determined by an iterative process:

P ) F2 (∂A/∂F)T

(16)

are calculated, the remaining therOnce F and FNaCl dis modynamic properties of the solution can be determined using standard thermodynamic relationships. In the present study, measured ∆dilH and solution F values are used to regress the adjustable parameters in the model. Accomplishment of this task requires the calculation of the molar enthalpy, H, of each stream by

H ) -T 2

[

]

∂(A/T) ∂T

F,m

+ PV

(17)

The ∆dilH value can then be found by first subtracting the H value of water times the molar flow of the water in and the H of the solution in times the molar flow of solution in from the H value of the solution out times the molar flow of solution out and second dividing this quantity by the molar flow of NaCl. 4. Results and Discussion 4.1. Comparison of ∆dilH Values Predicted Using AP, RI, and RII Models with Literature Values. A comparison of experimental ∆dilH values taken from the literature28,29 with those calculated using eq 2 is given in Table 3. Figure 1 shows a comparison of the ability of the AP, RI, and RII models to fit ∆dilH data at three experimental conditions. Values of P are approximately the same in the three cases. As shown in Figure 1, the RII model fits the experimental data better than either is the RI or AP model. At conditions where FNaCl dis significant (i.e., low initial concentration, 0.1 m, and low T, 350 °C), as shown in Figure 1a, the RII model fits the experimental data slightly better than the RI model and both of these models fit the experimental data markedly better than the AP model. If the initial solute m (mi) is increased to 5 m so that moderate NaCl dissociation occurs at 350 °C (Figure 1b), the RII model still fits the data well. The fit of the RI model is poorer and that of the AP model is better than that at low mi

Table 3. Comparison of Experimental ∆dilH Values Taken from the Literature (lit) with Those Calculated (calc) Using Equation 2 T (°C)

mi a mf b P (mol‚kg-1 (mol‚kg-1 lit ∆dilH calc ∆dilH (MPa) of H2O) of H2O) (kJ‚mol-1) (kJ‚mol-1) ref

349.9 20.41 20.48 20.45 20.59 21.20 20.48 21.17 20.52 20.52 21.07 20.59 20.55 20.55 21.07 41.40 40.53 40.66 40.96 40.41 350 17.60 17.60 17.60 17.60 17.60 17.60 17.60 17.60 17.60 17.60 370 24.70 24.70 24.70 24.70 24.70 24.70 24.70 24.70 24.70 24.70 24.70 24.70 24.70 24.70 24.70 24.70 24.70 24.70 380 24.70 24.70 24.70 24.70 24.70 24.70 24.70 24.70 24.70 402.2 41.72 41.72 41.72 41.72 41.72 41.72 41.72 a

5.178 5.178 5.178 5.178 5.178 1.000 1.000 1.000 1.000 1.000 0.100 0.100 0.100 0.100 5.178 5.178 5.178 1.000 1.000 0.500 0.500 0.500 0.500 0.500 0.500 0.500 0.500 0.500 0.500 0.100 0.100 0.100 0.100 0.100 0.100 0.100 0.100 0.100 0.301 0.301 0.301 0.301 0.301 0.301 0.301 0.301 0.301 0.301 0.301 0.301 0.301 0.301 0.301 0.301 0.301 0.301 5.178 5.178 1.000 1.000 0.100 0.200 0.200

3.778 2.452 1.606 1.194 0.789 0.746 0.495 0.329 0.246 0.164 0.033 0.025 0.025 0.016 2.448 2.448 0.787 0.495 0.495 0.450 0.399 0.349 0.299 0.249 0.199 0.149 0.099 0.100 0.050 0.090 0.080 0.070 0.060 0.050 0.040 0.030 0.020 0.010 0.270 0.240 0.210 0.180 0.150 0.120 0.090 0.060 0.030 0.270 0.240 0.210 0.180 0.150 0.120 0.090 0.060 0.030 3.775 1.191 0.246 0.164 0.016 0.100 0.050

-10.099 -23.866 -37.708 -46.864 -58.580 -9.244 -20.944 -31.713 -38.800 -47.300 -25.281 -29.101 -29.432 -37.611 -15.613 -15.879 -36.591 -10.652 -10.805 -3.100 -6.920 -10.800 -15.600 -21.300 -21.160 -27.900 -36.000 -46.600 -62.000 -4.050 -8.740 -13.890 -19.550 -26.680 -34.550 -44.990 -59.270 -80.680 -3.070 -7.290 -12.180 -17.900 -25.000 -32.390 -41.350 -51.010 -64.270 -10.040 -23.270 -38.380 -55.910 -78.070 -103.560 -136.410 -175.810 -236.310 -13.101 -60.173 -52.453 -66.190 -58.903 -23.412 -43.861

-10.911 -25.658 -39.424 -48.000 -57.413 -7.649 -16.842 -26.668 -32.998 -40.910 -25.337 -31.733 -31.733 -39.779 -17.289 -17.436 -36.780 -10.103 -10.175 -2.872 -5.988 -9.426 -13.276 -17.723 -23.034 -29.792 -39.263 -39.052 -55.522 -3.620 -7.719 -12.343 -17.716 -24.202 -32.174 -42.632 -57.679 -83.744 -3.877 -8.141 -12.895 -18.352 -24.702 -32.419 -42.364 -56.424 -81.345 -14.633 -30.763 -48.716 -69.085 -92.264 -119.023 -150.954 -190.376 -245.512 -13.355 -62.399 -47.599 -59.907 -62.955 -21.012 -43.239

28 28 28 28 28 28 28 28 28 28 28 28 28 28 28 28 28 28 28 29 29 29 29 29 29 29 29 29 29 29 29 29 29 29 29 29 29 29 29 29 29 29 29 29 29 29 29 29 29 29 29 29 29 29 29 29 28 28 28 28 28 28 28

Initial NaCl concentration. b Final NaCl concentration.

values (Figure 1a). However, the fit using the RI model is better than that of the AP model. If T is increased to 380 °C, keeping P approximately constant (Figure 1c), FNaCl dis is small even at moderate concentrations. In this case, the AP model is more effective than the RI model but is moderately less effective than the RII model. The

Ind. Eng. Chem. Res., Vol. 43, No. 23, 2004 7639

Figure 2. Plot of ∆dilH (calculated) versus ∆dilH (literature) for NaCl solutions. The straight line represents the perfect agreement between calculated and literature values. Literature values are taken from Table 3. The dashed lines represent estimated uncertainties of the literature values as discussed in the text.

Figure 1. Plot of literature ([) and calculated (see inset) ∆dilH values as a function of the NaCl molality. Temperature and pressure conditions for the literature values: (a) 350 °C, 20.5 MPa; (b) 350 °C, 20.4-21.2 MPa; (c) 380 °C, 24.7 MPa.

results in Figure 1 are consistent with the assumptions upon which the models are based (Table 1). The AP model fits the experimental data best in regions under the conditions represented in parts b and c of Figure 1, where NaCl dissociation is low. The AP model fits the is large (Figure 1a). The RI data poorly where FNaCl dis model fits the experimental data best at low mi values (Figure 1a) because the ion properties are assumed to be those of ions at µ ) 0. The success of the RII model in fitting the experimental data over the entire T, P, and m ranges (Figure 1a-c) is due to inclusion of terms that account for species dissociation and ion-ion interaction as m increases. A comparison of the ability of the models to fit all experimental ∆dilH values taken from the literature (Table 3) is shown in Figure 2, where the ∆dilH values calculated using the three models are plotted versus literature ∆dilH values. The straight line of slope 1 and of intercept 0 represents perfect agreement between literature and calculated values. The dashed lines indicate the estimated uncertainty region of the measurements. This uncertainty results from the estimated uncertainties of the T and P values and of the heat measurements. Values of -∆dilH are largest when T is high and P is low. Values of T and P represented by

the points in the lower left-hand corner of Figure 2 meet this condition. At high T and low P, changes in F are large with small changes in either T or P. The inability to measure T and P precisely in this region results in increased uncertainties in the ∆dilH measurements. The agreement between the literature and RII model values presented in Figure 2 is good. This agreement is not as good at high -∆dilH values, where the uncertainty in the literature values is largest. Use of the AP model generally gives calculated -∆dilH values that are lower than the literature values, indicating that a significant fraction of the -∆dilH values is due to increased FNaCl values as the solution is diluted. The dis -∆dilH values calculated using the RI model are generally larger than the literature values. A possible explanation is that the partial molar enthalpy, H ˆ , values are larger for ions in dilute solutions than for those in concentrated solutions. The H ˆ values of the ions in the RI model are assumed to be those of the ions at µ ) 0. Additional explanations for the disagreement between ∆dilH values calculated using the RI model and those found in the literature have been given.24 4.2. Thermodynamic Values Calculated Using the RII Model. The RII model was used to calculate log K, ∆rH°, ∆rS°, and ∆rCp° values for the reaction given in eq 1 (standard state defined as µ ) 0; r refers to the reaction) as a function of T and F. The log K′ values and corresponding ∆rH, ∆rS, and ∆rCp values for the reaction given in eq 1 as a function of T, F, and m were also calculated. These latter thermodynamic values give insight into the interactions of the solute species with each other and with the solvent as functions of the experimental variables. Table 4 contains the thermodynamic (at µ ) 0) and apparent thermodynamic values as functions of P and m at 350, 375, and 400 °C. To give smooth curves in plots of the thermodynamic quantities as a function of T and to obtain ∆rCp° and ∆rCp values, values of ∆rG°, ∆rG, ∆rH°, ∆rH, -T∆rS°, and -T∆rS were also calculated at 30 and 40 MPa and at 0, 1.25, and 5 m at 5 °C intervals from 350 to 400 °C. These calculated values are available as Supporting Information. 4.2.a. Thermodynamic Values Valid at Infinite Dilution. In Figure 3, ∆rH°, ∆rG°, and -T∆rS° values at 30 and 40 MPa are plotted versus T (350-400 °C). The ∆rH° and T∆rS° values increase dramatically with T, while the corresponding changes in ∆rG° are much smaller and are dominated by the changes in -T∆rS°.

18 18 18 18 18 18 18 18 18 18 18 18 18 18 20 20 20 20 20 20 20 20 20 20 20 20 20 20 24 24 24 24 24 24 24 24 24 24 24 24 24 24 26 26 26 26 26 26 26 26 26 26 26 26 26 26

350

375

P (MPa)

T (°C)

5.000 3.000 2.000 1.000 0.500 0.200 0.100 0.050 0.020 0.010 0.005 0.002 0.001 0.000 5.000 3.000 2.000 1.000 0.500 0.200 0.100 0.050 0.020 0.010 0.005 0.002 0.001 0.000 5.000 3.000 2.000 1.000 0.500 0.200 0.100 0.050 0.020 0.010 0.005 0.002 0.001 0.000 5.000 3.000 2.000 1.000 0.500 0.200 0.100 0.050 0.020 0.010 0.005 0.002 0.001 0.000

m (mol‚kg-1)

0.82 0.79 0.83 0.95 1.07 1.21 1.30 1.38 1.49 1.55 1.61 1.67 1.71 1.79 0.82 0.78 0.81 0.92 1.04 1.17 1.26 1.34 1.44 1.51 1.56 1.62 1.66 1.74 1.02 1.05 1.14 1.35 1.52 1.67 1.77 1.86 1.98 2.06 2.13 2.20 2.25 2.35 1.01 1.03 1.11 1.29 1.46 1.62 1.73 1.82 1.93 2.00 2.06 2.13 2.17 2.26

log K′ (m basis) 69.5 91.8 114.2 154.0 178.8 188.7 189.7 189.5 189.3 189.2 189.2 189.2 189.3 189.4 68.3 88.9 108.6 141.9 163.0 173.7 176.3 177.4 178.1 178.3 178.5 178.6 178.7 178.8 75.2 112.9 157.9 250.3 313.0 336.8 332.1 323.3 314.7 311.1 309.2 308.0 307.6 306.5 73.7 107.4 144.8 216.1 267.6 300.7 310.9 315.6 318.3 319.2 319.6 319.9 320.0 320.1

∆rH (kJ‚mol-1) 127 162 199 265 307 326 329 331 332 333 334 336 336 338 125 158 190 245 281 301 307 310 313 315 316 318 319 320 136 194 265 412 512 552 546 534 523 519 518 517 518 518 133 185 245 358 441 495 513 522 528 531 533 534 535 537

∆rS (J‚mol-1‚K-1) 22 22 22 22 22 22 22 22 22 22 22 22 22 22 24 24 24 24 24 24 24 24 24 24 24 24 24 24 28 28 28 28 28 28 28 28 28 28 28 28 28 28 30 30 30 30 30 30 30 30 30 30 30 30 30 30

P (MPa) 5.000 3.000 2.000 1.000 0.500 0.200 0.100 0.050 0.020 0.010 0.005 0.002 0.001 0.000 5.000 3.000 2.000 1.000 0.500 0.200 0.100 0.050 0.020 0.010 0.005 0.002 0.001 0.000 5.000 3.000 2.000 1.000 0.500 0.200 0.100 0.050 0.020 0.010 0.005 0.002 0.001 0.000 5.000 3.000 2.000 1.000 0.500 0.200 0.100 0.050 0.020 0.010 0.005 0.002 0.001 0.000

m (mol‚kg-1) 0.81 0.77 0.79 0.89 1.00 1.13 1.22 1.31 1.40 1.47 1.52 1.58 1.61 1.69 0.80 0.76 0.78 0.87 0.97 1.10 1.19 1.27 1.36 1.43 1.48 1.54 1.57 1.64 1.00 1.01 1.08 1.24 1.39 1.55 1.66 1.75 1.85 1.92 1.98 2.05 2.08 2.17 1.00 0.99 1.05 1.20 1.34 1.49 1.59 1.68 1.78 1.85 1.90 1.97 2.00 2.08

log K′ (m basis) 67.3 86.3 103.9 132.3 150.2 160.3 163.2 164.6 165.4 165.8 166.0 166.1 166.2 166.4 66.3 84.0 99.8 124.4 139.8 148.9 151.7 153.1 154.0 154.3 154.5 154.7 154.8 154.9 72.2 102.8 134.5 191.6 232.9 261.4 271.5 276.6 279.8 280.8 281.4 281.8 281.9 282.1 70.9 98.8 126.3 173.3 206.8 230.4 238.9 243.3 246.0 247.0 247.5 247.8 247.9 248.1

∆rH (kJ‚mol-1) 123 153 182 229 260 279 285 289 292 294 295 297 298 299 122 149 175 216 243 260 266 270 273 275 276 278 278 280 131 178 228 319 386 433 451 460 467 470 472 474 475 477 128 171 215 290 345 384 399 408 414 416 418 420 421 423

∆rS (J‚mol-1‚K-1) 26 26 26 26 26 26 26 26 26 26 26 26 26 26 28 28 28 28 28 28 28 28 28 28 28 28 28 28 32 32 32 32 32 32 32 32 32 32 32 32 32 32 35 35 35 35 35 35 35 35 35 35 35 35 35 35

P (MPa) 5.000 3.000 2.000 1.000 0.500 0.200 0.100 0.050 0.020 0.010 0.005 0.002 0.001 0.000 5.000 3.000 2.000 1.000 0.500 0.200 0.100 0.050 0.020 0.010 0.005 0.002 0.001 0.000 5.000 3.000 2.000 1.000 0.500 0.200 0.100 0.050 0.020 0.010 0.005 0.002 0.001 0.000 5.000 3.000 2.000 1.000 0.500 0.200 0.100 0.050 0.020 0.010 0.005 0.002 0.001 0.000

m (mol‚kg-1) 0.80 0.75 0.76 0.85 0.95 1.07 1.15 1.23 1.33 1.39 1.44 1.50 1.53 1.60 0.79 0.74 0.75 0.83 0.92 1.04 1.12 1.20 1.30 1.36 1.41 1.46 1.49 1.57 0.99 0.98 1.03 1.16 1.29 1.44 1.53 1.62 1.72 1.78 1.84 1.90 1.93 2.01 0.97 0.96 1.00 1.11 1.23 1.36 1.45 1.54 1.63 1.70 1.75 1.81 1.84 1.92

log K′ (m basis) 65.3 81.9 96.2 117.8 131.2 139.3 141.9 143.2 144.0 144.4 144.6 144.7 144.8 145.0 64.5 80.0 93.1 112.3 124.0 131.2 133.5 134.7 135.5 135.8 136.0 136.2 136.3 136.4 69.7 95.3 119.4 159.1 186.8 206.3 213.4 217.1 219.4 220.2 220.6 220.9 221.0 221.2 68.0 90.8 111.2 142.8 164.4 179.4 184.9 187.8 189.6 190.2 190.5 190.8 190.9 191.0

∆rH (kJ‚mol-1)

120 146 169 205 229 244 250 253 257 258 260 261 262 263 119 143 164 196 217 230 236 239 242 244 245 247 247 249 126 166 204 268 313 346 359 366 371 374 376 377 378 380 124 159 191 242 277 303 313 319 324 326 327 329 330 331

∆rS (J‚mol-1‚K-1)

Table 4. Calculated log K′, ∆H, and ∆S Values Associated with the Reaction Na+ + Cl- ) NaCl(aq) as a Function of the Temperature, Pressure, and Concentration (at m ) 0, log K′ ) log K; ∆rH ) ∆rH°, and ∆rS ) ∆rS°)

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5.000 3.000 2.000 1.000 0.500 0.200 0.100 0.050 0.020 0.010 0.005 0.002 0.001 0.000 5.000 3.000 2.000 1.000 0.500 0.200 0.100 0.050 0.020 0.010 0.005 0.002 0.001 0.000

1.17 1.22 1.31 1.52 1.71 1.91 2.04 2.14 2.24 2.31 2.37 2.43 2.47 2.55 1.16 1.20 1.28 1.46 1.63 1.82 1.93 2.03 2.13 2.20 2.25 2.32 2.35 2.43

79.6 112.6 147.5 213.6 270.4 320.1 341.0 352.5 359.8 362.3 363.6 364.4 364.8 365.1 78.1 108.2 138.7 194.1 240.0 278.6 294.3 302.9 308.3 310.1 311.1 311.7 311.9 312.1

141 190 244 346 434 512 546 565 577 583 586 588 589 591 138 184 230 316 388 449 474 489 499 503 505 507 508 510

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400

30 30 30 30 30 30 30 30 30 30 30 30 30 30 32 32 32 32 32 32 32 32 32 32 32 32 32 32

5.000 3.000 2.000 1.000 0.500 0.200 0.100 0.050 0.020 0.010 0.005 0.002 0.001 0.000 5.000 3.000 2.000 1.000 0.500 0.200 0.100 0.050 0.020 0.010 0.005 0.002 0.001 0.000

1.22 1.32 1.49 1.86 2.20 2.59 2.85 3.06 3.26 3.36 3.44 3.52 3.56 3.66 1.21 1.29 1.43 1.75 2.04 2.34 2.52 2.67 2.81 2.89 2.96 3.03 3.08 3.17

86.9 139.0 210.6 374.6 557.4 845.7 1044.5 1179.3 1272.8 1306.0 1323.0 1333.2 1336.6 1342.1 84.8 130.5 188.3 315.1 442.5 590.1 671.3 723.4 759.5 772.7 779.2 783.2 784.5 786.8

152 232 341 592 870 1306 1606 1811 1953 2005 2031 2048 2054 2064 149 219 307 502 696 921 1046 1126 1182 1203 1214 1221 1224 1229

34 34 34 34 34 34 34 34 34 34 34 34 34 34 36 36 36 36 36 36 36 36 36 36 36 36 36 36

5.000 3.000 2.000 1.000 0.500 0.200 0.100 0.050 0.020 0.010 0.005 0.002 0.001 0.000 5.000 3.000 2.000 1.000 0.500 0.200 0.100 0.050 0.020 0.010 0.005 0.002 0.001 0.000

1.20 1.26 1.39 1.66 1.91 2.16 2.32 2.44 2.56 2.64 2.70 2.76 2.81 2.89 1.19 1.24 1.34 1.58 1.80 2.03 2.16 2.27 2.38 2.45 2.51 2.58 2.62 2.70

82.9 123.5 171.4 271.2 365.5 459.6 504.4 530.8 548.3 554.4 557.6 559.5 560.1 561.1 81.2 117.6 158.2 238.5 310.7 377.2 406.5 422.9 433.6 437.3 439.2 440.3 440.7 441.2

146 208 281 435 579 724 794 835 864 874 880 884 886 889 143 198 261 385 496 599 645 672 690 697 700 703 705 707

38 38 38 38 38 38 38 38 38 38 38 38 38 38 40 40 40 40 40 40 40 40 40 40 40 40 40 40

Figure 3. Plot of energy (∆rG°, ∆rH°, -T∆rS°) for the reaction Na+ + Cl- ) NaCl(aq) versus temperature at 30 and 40 MPa.

This increase in -∆rG° with T results in corresponding significant increases in the log K values. These changes follow the same qualitative trends with T reported earlier for ion association reactions in water.47-49 The thermodynamic values shown in Figure 3 are valid at constant P, while those in earlier plots47-49 were valid at P values just above the water vapor pressure at each T value. The trends in ∆rH° and -T∆rS° were explained50 in terms of the solute-solvent and solutesolute interactions. The basis of the explanation was that, as T increases, hydrogen bonding and Η2Ο decrease, resulting in the bulk water changing from a highly organized network to a system consisting predominantly of single water molecules. As the reaction proceeds, water molecules bound to the ions are released to the bulk water. As a result, these released water molecules attain higher H and entropy (S) values than they had in the bound state. At low T values, the compressibility of water is low. Hence, the H and S values of the bulk water molecules are nearly independent of P. However, at the T and P values of the present study, the compressibility of water is high and increases with increasing T at a constant P but decreases with increasing P at a constant T. Thus, F and hydrogen bonding are strong functions of P. Hence, the changes in ∆rH° and ∆rS° with T are smaller at 40 MPa than at 30 MPa, as shown in Figure 3. The results in Figure 3 show that ∆rH° and T∆rS° increase with increasing T at a constant P and decrease with increasing P at a constant T. Because T∆rS° is larger than ∆rH°, -∆rG° (log K) increases with increasing T and decreasing P. Mesmer et al.51 observed that log K values are linear functions of log FH2O at constant T, where FH2O is the density of pure water at the T and P of the system. Marshall52 argued that the negative slopes of such linear functions are equal to the number of water molecules released to the bulk water upon ion association. The RI and RII models predict this trend and are therefore consistent with the observation of Marshall. In Figure 4, ∆rG°, ∆rH°, and -T∆rS° values at 350, 375, and 400 °C are plotted as functions of FH2O. The decrease in ∆rH° and T∆rS° with increasing FH2O is the result of the increasing random motion of the bulk water molecules as T increases and P decreases. The bulk water molecules have higher H and S values than do the water molecules associated with the ions. A large fraction of the increase of ∆rH° and T∆rS° upon ion

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Figure 5. Plot of ∆rCp for the reaction Na+ + Cl- ) NaCl(aq) versus temperature (°C) at NaCl concentrations of 0, 1.25, and 5 m at 30 and 40 MPa. Figure 4. Plot of energy (∆rG°, ∆rH°, -T∆rS°) for the reaction Na+ + Cl- ) NaCl(aq) versus density of water.

association at high T values is due to the increase in the H and S values of the water molecules as they are released. As FH2O increases, the bulk water molecules become more limited in their motion and thus have lower H and S values that approach those of the bound water molecules. Because the H and S values of the bound water molecules and their change with T are expected to be small, the changes in H and S upon release are largely determined by the H and S of the bulk water molecules. These effects have important implications for the speciation in aqueous solutions of NaCl at near-critical conditions. Ionic species become more associated with increasing T and with decreasing FH2O. This increased association under these T and P conditions is partially due to the decrease in H2O.46 As the Tc of water is approached from lower T values at a constant P (at or moderately above the Pc), this increase in association accelerates as a result of the coupled effects of the increase in T and the dramatic decrease in FH2O. At much higher P values, FH2O does not change as much with T and the ions are less associated than those at lower P values. Hence, the K values exhibit large variations with P at constant T in the near-critical region of water. Because P is seldom constant in chemical processes involving aqueous solutions in the supercritical region, it is essential to know how K values change with P in order to obrtain accurate speciation. This knowledge is particularly important in understanding the water chemistry that occurs at high T over a wide P range. Values of ∆rCp° valid at m ) 0 and ∆rCp are plotted as a function of T at 30 and 40 MPa in Figure 5. The inset shows only the ∆rCp values. The ∆rCp° values follow the same trends with T and P as do the ∆rH° and T∆rS° values (see Figure 3); however, the relative changes in the ∆rCp° values with T and P are significantly greater, illustrating the sensitivity of ∆rCp° to solute-solvent interactions. Two examples illustrate this sensitivity. First, the ratio of ∆rH° at 350 °C and 30 MPa to ∆rH° at 400 °C and 30 MPa is 10, while the corresponding ratio of ∆rCp° values is 46. Second, the ratio of ∆rH° at 400 °C and 30 MPa to ∆rH° at 400 °C and 40 MPa is 4, while the corresponding ratio of ∆rCp° values is 12. Values of ∆rCp° are the result of the summation of two terms. The first term is the difference in the Cp values of the products minus the Cp values of the

reactants in the reaction shown in eq 1, assuming that no water molecules are involved in the reaction. The contribution of this term is expected to be relatively small and relatively constant with T and P. An approximation of this term can be obtained by using the Cp values for reactants and products in the gas-phase reaction Na+(g) + Cl- (g) ) NaCl(g) to calculate the ∆rCp° values. At 350 and 400 °C, the resulting gas phase ∆rCp° values are 35 and 45 J‚mol-1‚K-1, respectively.53 The ratio of these values is 1.3, compared to 46 for the same reaction in an aqueous solution at 30 MPa, indicating that the contribution of the first term to the overall ∆rCp° value is small. The second term is due to the large increase in the Cp values of the water molecules as they are released from the ions to the solvent as the reaction occurs. The Cp value for a free water molecule in the bulk solvent at these conditions changes dramatically with T and P. Because the Cp value of a bound water molecule is expected to be small and nearly constant, the ∆rCp value for the transfer of a bound water molecule to the bulk water at the conditions of release is dominated by the bulk water Cp values. The bulk water Cp values at 30 MPa are 115 and 466 J‚mol-1‚K-1 at 350 and 400 °C, respectively.13 At 400 °C and 40 MPa, the Cp value is 157 J‚mol-1‚K-1. This large change in the Cp values of bulk water going from 350 to 400 °C at constant P and from 30 to 40 MPa at constant T are consistent with the large changes in the ∆rCp° values for the reaction (Figure 3). Thus, the second term dominates the changes in ∆rCp° with T and P. 4.2.b. Thermodynamic Values as a Function of the Solute Concentration. The log K′ values for the reaction in eq 1 are plotted in Figure 6 as a function of m0.5 and P at 350, 375, and 400 °C. This plot shows significant trends. First, at all T values, the log K′ values decrease initially with increasing m and level off at high m values. At 350 °C, the log K′ values increase slightly at the highest m values compared to the second highest m values. At 375 °C, the log K′ values are essentially the same at the two highest m values. At 400 °C, the log K′ values continue to decrease through the m range studied. Second, as T increases, the log K′ values become larger at a given m and P values. This increase due to T is greatest at m ) 0 and decreases with increasing m. Third, as P increases at the same T and m, the log K′ values decrease. The decrease in the log K′ values with P is most pronounced at high T and low m. The decrease in the log K′ values due to increasing P becomes smaller as T decreases and m increases. In

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Figure 6. Plot of log K′ for the reaction Na+ + Cl- ) NaCl(aq) versus m0.5 (NaCl) and pressure (MPa) at 350, 375, and 400 °C.

Figure 8. Plot of ∆rS (J‚mol-1‚K-1) for the reaction Na+ + Cl- ) NaCl(aq) versus m0.5 (NaCl) and pressure (MPa) at 350, 375, and 400 °C.

Figure 9. Plot of water compressibility13 versus temperature (°C) at 30 MPa. The inset shows the compressibility up to 350 °C. Figure 7. Plot of ∆rH (kJ‚mol-1) for the reaction Na+ + Cl- ) NaCl(aq) versus m0.5 (NaCl) and pressure (MPa) at 350, 375, and 400 °C.

Figures 7 and 8, respectively, the ∆rH and ∆rS values are plotted as functions of m0.5 and P at 350, 375, and 400 °C. These plots show trends similar to those found in the log K′ values. Changes in F as a function of T, P, and m provide a plausible explanation for the trends in Figures 6-8. At 25 °C, water is essentially incompressible, as shown by the 1% change in FH2O as P increases from 0.1 to 40 MPa.13 The F values of NaCl solutions at 25 °C are close to those calculated by assuming that volumes are additive. The F value of a 5 m NaCl solution at 25 °C and 0.1 MPa is 1.166 g‚cm-3, while the calculated F value of the same solution is 1.136 g‚cm-3 if volumes are assumed to be additive. As T increases at constant P, the compressibility of water increases as the critical point of water is approached, as shown in Figure 9. This increase is significant at T values above 100 °C but becomes dramatic at T values above 350 °C. As water becomes more compressible, the F values for solutions resulting from the addition of NaCl are much higher than those calculated assuming that volumes are

Figure 10. Plot of solution density23 versus NaCl molality. T ) 400 °C. P ) 30 MPa.

additive. A comparison of experimental F values of NaCl solutions at 400 °C and 30 MPa with those obtained assuming that volumes are additive is shown in Figure 10. The trend shown in Figure 10 can be understood in terms of the strong attraction between water and each of the solute species, Na+, Cl-, and NaCl(aq). The resulting decrease in the solution volume is most

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marked at conditions where the compressibility of water is highest, i.e., at high T and low P. In our study, this condition is met at 400 °C and 30 MPa (Figure 9). The solution has lower compressibility at high m values than at low m values because both the water and the solute species are closer together in the former case. As the F value of a solution increases as a result of increased m, the effect on log K′ is similar to that found in log K when F is increased as a result of increased P at constant T (Figure 6). The decrease in the log K′ values with increasing m at constant T and P can be explained in terms of the corresponding increases in F. As F increases, H2O increases46 and the attraction between the Na+ and Cl- through a distance decreases. In addition, solvated water molecules are released upon ion association, and these freed water molecules can be considered products of the association reaction. The decrease in the log K′ values with solution F is a result of the increase in H2O and of the increase in the concentration of the released water molecules.51 The correct log K′ value would include water as a product of the reaction specified in eq 1. Following the usual convention, we have not included water as a product of the reaction. The result of not including water is that, at high m values, F and, hence, log K′ values change very little with P (see Figure 6 and the discussion related thereto). An alternative explanation is based on the observation that, as the solute concentration increases, the critical point of the solution increases dramatically.54,55 For example, Tc and Pc of 0.1, 0.5, and 5 m NaCl solutions are 379 °C and 23 MPa; 400 °C and 28 MPa; and 611 °C and 84 MPa, respectively.54,55 Therefore, at the higher m values in Figure 6, the solutions are subcritical and the effects of T and m are small and similar to the behavior of aqueous solutions well below the critical point of water. This increase in the critical point of the solution with m is consistent with the large initial decrease in log K′ with m at 400 °C, where the solution goes from supercritical to subcritical, and the relatively smaller change at 350 °C, where the solution is subcritical over the entire m range (Figure 6). The changes of ∆rH and ∆rS with T, P, and m are strong functions of the number of water molecules released upon ion association and the differences between H or S values for the bound water molecules and H or S values for the free water molecules. As the F value of the solution increases, the structure of the water becomes more ordered, resulting in a higher H2O value with fewer water molecules being influenced by the charges on the ions. This increased structure in the bulk water also results in lower H and S values for released water molecules as compared to the values found at lower F values. The net result is that the changes in H and S, upon release of each water molecule, decrease as F increases. The compounding effect of the decrease in the number of water molecules released and the decrease in the changes in H and S per water molecule upon release results in the dramatic decrease in ∆rH and ∆rS with increasing m, as shown in Figures 7 and 8. The explanation for the convergence of both ∆rH and ∆rS at higher m values is the same as that given for log K′. As shown in Figure 5, the same general trends with T, P, and m as are found for ∆rH (Figure 7) and ∆rS (Figure 8) exist for ∆rCp values. As shown in Figure 11, ∆rCp is more sensitive than either ∆rH (Figure 7) or ∆rS

Figure 11. Plot of normalized ∆rCp, ∆rH, and ∆rS values versus NaCl molality.

NaCl Figure 12. Plot of a fraction of NaCl dissociated (Fdis ) versus NaCl solution density at 350, 375, and 400 °C and at 0.05, 0.5, and 5 m NaCl.

(Figure 8) to the changes in T, P, and m for the reasons stated above. This reinforces the argument given earlier to explain why the changes with T and P are much smaller at high m values, where the changes in F due to T and P are small. 4.2.c. Speciation. In Figure 12, FNaCl dis is plotted vs F at 350, 375, and 400 °C and 5, 0.5, and 0.05 m. The value is seen to increase significantly with F at FNaCl dis given T and m. At high m values, F and, therefore, NaCl FNaCl dis change little with T. At low m values, F and Fdis change dramatically with T. As m decreases, the change of FNaCl with T and F becomes larger. For example, at dis varies from about 0.12 to 0.66 as F 0.05 m, FNaCl dis increases from about 0.35 to 0.65 g‚cm-3. The results in Figure 12 illustrate dramatically the important role of F in determining FNaCl dis . 5. Conclusions The RII model developed in this study fits ∆dilH and F data for sodium chloride solutions over the T, P, and m ranges of 350-402 °C, 18-40 MPa, and 0-5 m, respectively. Values of ∆dilH provide a stringent test of the model because the equation that defines the model must be differentiated with respect to T in order to predict the heat data. This study has extended our previous work29 into ranges of T and P where large changes in F occur. The trends in the ∆rG, ∆rH, ∆rS, and ∆rCp values predicted

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using this model are consistent with those reported earlier47 up to T ) 350 °C. These trends are also consistent with the explanations of solute-solute and solute-solvent interactions given earlier by us.50 Several important industrial, waste-destruction, and geochemical processes involve aqueous solutions near the water critical point. Our results illustrate that knowledge of speciation in high-T aqueous solution reactions is necessary in order to understand these processes. Once the chemistry is quantitatively understood, the conditions and reagents necessary to minimize corrosion can be designed into the SCWO process. values vary over a wide range depending on The FNaCl dis T, P, and m. The F values of the solution are needed to describe the speciation at given sets of these conditions. It becomes increasingly difficult to obtain accurate F values using Gex models as T increases above 300 °C.27,41 Use of the AP model gives F values close to those obtained experimentally, but it cannot be used to calculate speciation because a basic assumption of the model is that no dissociation occurs. (See Table 1.) The RII model avoids the difficulties of the AP and RI models by incorporating terms for both ion dissociation and ion-ion interaction, resulting in good agreement between experimental and calculated ∆dilH values over wide T, P, and m ranges. It would be desirable to model aqueous systems containing ions other than Na+ and Cl-. It is especially important to study chemical reactions involving electrolytes other than 1:1. The approach used in the present study should lead to a model that will describe quantitatively a wide variety of electrolyte systems that are common in geochemical, waste-destruction, and industrial processes. Acknowledgment This material is based on work supported by the U.S. Army Research Office under Grant DAAA19-01-1-0027. Supporting Information Available: ∆G°, ∆G, ∆H°, ∆H, ∆Cp°, and ∆Cp values at 30 and 40 MPa and at 0, 1.25, and 5 m at 5 °C intervals from 350 to 400 °C. This material is available free of charge via the Internet at http://pubs.acs.org. Literature Cited (1) Shaw, R. W.; Brill, T. B.; Clifford, A. A.; Eckert, C. A.; Franck, E. U. Supercritical Water, A Medium for Chemistry. Chem. Eng. News 1991, 69, 26. (2) Tester, J. W.; Holgate, H. R.; Armellini, F. J.; Webley, P. A.; Killilea, W. R.; Hong, G. T.; Barner, H. E. Supercritical Water Oxidation Technology. Process Development and Fundamental Research. In Emerging Technologies in Hazardous Waste Management III; Tedder, D. W., Pohland, F. G., Eds.; American Chemical Society: Washington, DC, 1993. (3) Gloyna, E. F.; Li, L. Supercritical Water Oxidation Research and Development Update. Environ. Prog. 1995, 14, 182-192. (4) Modell, M. Supercritical-Water Oxidation. In Standard Handbook of Hazardous Waste Treatment and Disposal; Freeman, H. M., Ed.; McGraw-Hill Book Co.: New York, 1989; pp 8.1538.168. (5) Griffith, J. W. Design and Operation of the First Supercritical Wet Oxidation Industrial Waste Destruction Facility, 1995. Chem. Oxid. 1997, 5, 22-38. (6) Spritzer, M. H.; Hazelbeck, D. A.; Downey, K. W. Supercritical Water Oxidation of Chemical Agents, and Solid Propellants. J. Energ. Mater. 1995, 13, 185-212. (7) Weber, R.; Yoshida, S.; Miwa, K. PCB Destruction in Subcritical and Supercritical WatersEvaluation of PCDF Forma-

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Received for review April 8, 2004 Revised manuscript received August 9, 2004 Accepted August 23, 2004 IE040112P