Prediction of the Standard State Partial Molar Volume of Aqueous

Oct 29, 2015 - (1) Applications of these processes require high temperature data where experimental data are scarce. The prediction of the standard st...
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Prediction of the Standard State Partial Molar Volume of Aqueous Electrolytes to High Temperatures and High Pressures Essmaiil Djamali,*,† Walter G. Chapman,† and Kenneth R. Cox† †

Department of Chemical and Biomolecular Engineering, Rice University, 6100 S. Main Street, Houston, Texas 77005, United States ABSTRACT: The unified theory of electrolytes (J. Phys. Chem. B 2009, 113, 2398−2403) is used for the prediction of the standard state partial molar volumes of aqueous chlorides and hydroxides of the alkali metals, alkali earth metals, and the first row transition metals to high temperatures and pressures. The only required input to the model is the thermodynamic properties from reference tables at 298.15 K and 0.1 MPa. Comparison of the predicted values for the standard state partial molar volumes of aqueous electrolytes from this study with the available experimental data indicates good agreements to well within the combined uncertainties of the experimental data and the present model up to 623.15 K and 400 MPa. The present model is also compared with the correlations of Sedlbauer−O’Connell−Wood (SOCW) and the revised equation of Helgeson, Kirkham, and Flowers (HKF), which has been incorporated in the SUPCRT92 software.

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INTRODUCTION Many efforts have been devoted to the study of thermodynamic properties of aqueous solution of electrolytes because of their scientific and practical relevance. This information is necessary in a number of technological and engineering applications. Fundamental understanding of industrial and natural processes requires reliable pressure and temperature dependence of chemical equilibria in aqueous solutions.1 Applications of these processes require high temperature data where experimental data are scarce. The prediction of the standard state partial molar volume, V2°, of electrolytes at high temperatures and high pressures is the main objective of the present manuscript. The standard state adopted for the thermal properties of solutes is infinite dilution. The standard state partial molar volume, V2°, is an important property because it directly relates to changes in chemical potential with pressure, as indicated by μi ο (T , p2 ) = μi ο (T , p1 ) +

∫p

p2

V iο(T , p′) dp′

1

used to obtain more high temperature volumetric information: the direct experimental determination and semi-empirical or theoretical predictions. The standard state partial molar volumes of aqueous electrolytes are experimentally accessible from volumetric studies. To be useful, such studies in aqueous solutions require extrapolation of experimental data to infinite (low) dilutions. Such low dilutions are difficult and subject to experimental uncertainties and also to the reliability of extrapolation procedures. This is particularly important in cases where the low concentration is above the region of validity of limiting laws such as the Debye− Hückel expression or when ionic association is important.6 Low dilutions are required because as the dielectric constant of water decreases with increasing temperature, dissolved electrolytes show nonideal behavior at low concentrations. Because of the difficulties involved in the direct determination of standard state properties of electrolytes under conditions of high temperature and pressure, considerable effort has been devoted to model the properties of ionic aqueous solutions over a wide range of temperature and pressure from information at lower temperatures and pressure. There are two comprehensive correlation models in the literature from which values for standard state partial molar volume for electrolytes to high temperatures and pressures can be calculated: the Sedlbauer−O’Connell−Wood (SOCW) model1 and the revised model of Helgeson, Kirkham and Flowers (HKF). 7 The revised HKF model has been

(1)

The chemistry of aqueous electrolyte solutions at high temperature differs considerably from that at room temperature, 298.15 K.2−4 For example, at 298.15 K many ion association reactions do not occur to a measurable extent and many ionic compounds can be considered to be strong electrolytes. But as temperature increases, and the dielectric constant of water decreases, ion association becomes more significant.5 Despite an increase in recent years of the experimental information available on the volumetric properties of aqueous electrolytes at high temperatures, the amount of available data is still very small compared to the actual number of electrolytes.1 Previously there have been two approaches © XXXX American Chemical Society

Special Issue: Memorial Issue in Honor of Anthony R. H. Goodwin Received: August 26, 2015 Accepted: October 20, 2015

A

DOI: 10.1021/acs.jced.5b00722 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

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incorporated into software SUPCRT92.8 Both models require four ion specific parameters regressed from experimental data. SOCW1 only reported parameters for alkali halides and hydroxide, while the revised HKF model7 is more inclusive. When possible, the values for the standard state partial molar volumes at high temperature and high pressure, calculated from SUPCRT928 and the SOCW model,1 are compared with the corresponding values predicted from this study.

Table 3. Adjusted Gibbs Free Energy of Ion at 298.15 K and 0.1 MPaa ΔhG⊕(298.15K, 0.1 MPa) H Li+ Na+ K+ Rb+ Cs+ Mg2+ Ca2+ Sr2+ Ba2+ Mn2+ Fe2+ Co2+ Ni2+ Cu2+ Zn2+ Cl− OH−b

CALCULATIONS AND RESULTS The standard state partial molar volume of an aqueous ion is predicted from eq 2:9 Table 1. Constants for Equations 11 and 15 values

a1 a2 a3 a4 a5 a6 a7 a8

−82.794 −27.896 0.8522 167.992 1.0464 −1758.264 19423.607 −6401.886

a

F1(D)[F3(D) − F3(Dr )] + ΔssV °(T , p)

(4)

and

(2)

ΔssV °(T , p) = RT (∂ln(d)/∂p)T

where the subscript r refers to the reference temperature of 298.15 K. It is important to note that in eq 2, the properties of the solute ion are required at only 298.15 K. F1(D) and F3(D) are functions of dielectric constant, D(T, p), of the solvent:10 ⎢ 1 − 1/D(T , p) ⎥ F1(D) = ⎢ ⎥ ⎣ 1 − 1/D(Tr , p) ⎦

Equation 6. bDjamali and Cobble.13

⎤⎛ ∂D ⎞ ⎥⎡ ⎢ 1 1 ⎥⎜ F3(D) = ⎢ ⎥⎢ ⎟ ⎣ 1 − D(Tr , p) ⎦⎣ D(T , p)2 ⎦⎝ ∂p ⎠T

V 2°(T , p) = V 2°(Tr , p) + ΔhG⊕(Tr , p) · − F1(D) ·ΔssV °(T , p)

−1524.895 −1345.271 −1329.072 −1357.468 −1363.027 −1368.646 −2800.158 −2861.631 −2894.662 −2947.423 −2815.695 −2801.908 −2796.728 −2793.442 −2802.939 −2802.744 514.560 673.077

+

■

parameters

Kj·mol−1

ions

(5)

where ΔssV° is the standard state correction from the hypothetically ideal 0.1 MPa gaseous ions being hydrated to the hypothetically ideal 1 m, (mol/kg), aqueous solution.9,11 The properties for pure water are obtained from the literature.12,10

(3)

Table 2. Reference State Thermodynamic Properties of Ions at 298.15 K and 0.1 MPa SM(cr) °

ΔfH°(aq)

ΔfG°(aq)

S2°(aq)

ΔfH°(g)

ΔfG°(g)

S°(g)

ΔhH°

ΔhG°

ions

J·mol·−1K−1a

Kj ·mol−1a

Kj ·mol−1a

J·mol−1·K−1a

Kj ·mol−1a

Kj ·mol−1b

J·mol−1·K−1c

Kj ·mol−1e

Kj ·mol−1e

H+ Li+ Na+ K+ Rb+ Cs+ Mg2+ Ca2+ Sr2+ Ba2+ Mn2+ Fe2+ Co2+ Ni2+ Cu2+ Zn2+ Cl−

d 29.12 1.21 64.18 76.78 85.23 32.68 41.42 52.30 62.80 32.01 27.28 30.04 29.87 33.15 41.63 d

0.00 −278.49 −240.12 −252.38 −251.17 −258.28 −466.85 −542.83 −545.80 −537.64 −220.75 −90.00 −58.20 −54.00 64.77 −153.89 −167.16

0.00 −293.31 −261.91 −283.27 −283.98 −292.02 −454.80 −553.58 −559.48 −560.77 −228.10 −91.50 −54.40 −45.60 65.49 −147.06 −131.23

0.00 13.40 59.00 102.50 121.50 133.05 −138.10 −53.10 −32.60 9.60 −73.60 −102.00 −113.00 −128.90 −99.60 −112.10 56.50

1536.20 685.78 609.36 514.26 490.10 457.96 2348.50 1925.90 1790.54 1660.38 2519.69 2749.93 2844.20 2931.39 3054.07 2782.78 −233.13

1516.94 667.81 578.61 500.30 477.00 445.74 2339.95 1918.09 1783.07 1654.37 2503.46 2730.35 2825.68 2913.25 3037.65 2773.21 −239.35

108.95 133.02 147.95 154.58 164.33 169.84 148.57 154.81 164.56 170.16 173.64 180.16 179.37 177.90 175.44 160.92 153.36

−1536.20 −964.27 −849.48 −766.64 −741.27 −716.24 −2815.35 −2468.73 −2336.34 −2198.02 −2740.44 −2839.93 −2902.40 −2985.39 −2989.30 −2936.67 65.97

−1516.94 −961.12 −840.51 −783.57 −760.98 −737.76 −2794.75 −2471.67 −2342.55 −2215.14 −2731.56 −2821.85 −2880.08 −2958.85 −2972.16 −2920.27 108.12

NBS tables.16 bΔfG° = ΔfH°−TΔfS°. cFor monovalent ions JANAF tables,18 for divalent ion from Djamali.17 dS°(H2, g) = 130.684 j·mol−1·K−1, and S° (Cl2, g) = 223.066 j·mol−1·K−1, from NBS tables.16 eΔhX° = ΔfX°(aq) − ΔfX°(g, ion), where X° = H° and G°.

a

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Figure 1. Comparison of the predicted values for the standard state partial molar volume of NaCl(aq) with the literature at different pressures (20 MPa (a), 40 MPa (b), 100 MPa (c), psat (d)): ○, Majer et al.;19 □, Hilbert;20 ×, Grant-Tayler;21 ···, correlation of SOCW;1 ---, SUPCRT92; , this study (eq 2).

Table 4. Standard State Partial Molar Volumes (cm3/mol) of NaCl(aq) at psat

a

T/K

p/MPa

V2°a

V2°b

V2°c

V2°d

V2°e

323.15 348.15 373.15 398.15 423.15 448.15 473.15 498.15 523.15 548.15 573.15 598.15 623.15

0.1 0.1 0.1 0.2 0.5 0.9 1.6 2.6 4.0 5.9 8.6 12.0 16.5

18.5 17.2 15.4 12.9 9.4 4.3 −3.5 −15.8 −36.7 −75.5 −158.1 −381.3 −1433.9

17.5 17.2 16.0 13.9 10.5 5.5 −1.9 −13.2 −31.1 −61.8 −120.6 −260.7 −823.1

17.9 17.9 16.9 14.8 11.6 6.7 −0.4 −11.0 −28.1 −57.7 −114.9 −256.0

17.4 17.4 16.5 14.7 11.8 7.5 1.2 −8.5 −24.3 −51.4 −100.2 −198.8 −496.1

18.2 18.2 16.8 15.0 12.4 7.5 0.4

Figure 2. Comparison of the predicted values for the standard state partial molar volume of NaCl(aq) with the literature at 548.15 K and pressures up to 400 MPa: ◊, Hilbert;21 △, Majer et al.;19 ○, Majer et al.;24 □, Sedlbauer et al.;25 ---, correlation of Pitzer et al.;26 ···, correlation of Archer;22 , this study.

Equation 2. bCorrelation of SOCW.1 cCorrelation of Archer.22 SUPCRT92.8 eEllis.23

d

loss of the solvent molecules in the primary solvation shell (inside the effective electrostatic radius). The CH and CS constants are solute specific and have been shown to be independent of T and p.9,13,14 These constants are known for some solutes of interest and previously were fixed from experimental data. In the following, we apply a new method of calculating the constants from information at 298.15 K. The value for the Gibbs free energy of hydration of the ion, ΔhG°(Tr,p), is calculated from the standard state Gibbs free energy of formations, ΔfG°(Tr, p) at the reference temperature Tr, 298.15 K:

The adjusted Gibbs free energy of the ion at the reference temperature, ΔhG⊕(Tr, p), is given by eq 6: Δh G⊕(Tr , p) = Δh G°(Tr , p) − C H + CSTr ⎛ m°drTrR ⎞ − RTr ln⎜ ⎟ ⎝ p° ⎠

(6)

where m° is equal to 1 mol/kg, dr is the density of the pure solvent in (g/cm3)12 at the reference temperature of 298.15 K, p° is equal to 0.1 MPa, and R is the ideal gas constant. The constants CH and CS in eq 6 represent the enthalpy and entropy

Δh G°(Tr , p) = Δf G°(Tr , p ; aq) − Δf G°(Tr , p ; g ) C

(7)

DOI: 10.1021/acs.jced.5b00722 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

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pr), at 298.15 K and 0.1 MPa. These relationships are summarized below for mono- and divalent ions:

Table 5. Comparison of the Standard State Partial Molar Volume (cm3/mol) of LiCl(aq) with the Literature at 32 MPa T/K

V2oa

σb

V2oc

V2od

298.15 348.15 398.15 448.15 498.15 548.15 573.15

18.1 17.6 13.8 6.0 −5.8 −35.9 −64.7

1.0 1.0 1.0 1.5 2.0 4.0 7.0

18.2 17.1 13.4 6.2 −7.9 −37.4 −65.8

18.9 16.9 13.4 6.7 −7.1 −40.6 −77.2

a c

27 b

CS,H+ = C H,H+ = 0

27

Majer et al. Estimated uncertainties are from Majer et al. Correlation of the SOCW.1 dThis study.

Table 6. Comparison of Experimental and Calculated Standard State Partial Molar Volumes (cm3/mol) of KCl(aq) T/K

p/MPa

V2°a

σa

V2°b

V2°c

V2°d

367.99 369.72 368.49 368.49 479.10 479.43 523.14 524.15 572.54 572.18 571.61 571.61

9.82 19.64 49.10 78.56 19.64 49.10 9.82 78.56 9.82 19.64 49.10 78.56

26 27 28 28 4 15 −36 6 −110 −89 −41 −15

2 2 2 2 10 6 15 7 30 30 25 15

26 28 31 31 12 15 −13 7 −99 −73 −21 −1

26.7 27.1 28.5 29.7 9.2 14.7 −19.5 7.7 −113.0 −77.6 −31.5 −12.3

26.3 27.4 28.4 28.9 9.1 14.2 −22.7 7.0 −141.2 −94.2 −37.8 −15.4

Values for ΔsolG°(Tr, p) are calculated from eq 8: r

V 2◦(Tr , p) dp′

C H,Cl− = a 2

(11)

CS,M+ = a3S2°(M+, aq) − [S2°(M+, g) − S2°(H+, g)]

(12)

CS,M2+ = a4 + a5S2°(M2 +, aq) − S2°(M2 +, g)

(13)

⎡ Δ H° + ⎤ C H,M+ = a6 log⎢ h M ⎥ ⎣ Δh HH° + ⎦

(14)

⎡ −Δh HMCl ° 2⎤ ⎥ C H,M2+ = a 7 + a8 log⎢ RT ⎣ ⎦

(15)

(16)

These standard state enthalpies and entropies for aqueous electrolytes at 298.15 K are from NBS tabulations,17 and the corresponding values for the simple gaseous ions are from JANAF tables.18 The constants, ai, in eqs 10 to 15 for simple mono- and divalent ions are summarized in Table 1. The reference state thermodynamic properties of some representative mono- and divalent ions for calculation of the values of Gibbs free energies and enthalpies of hydration at 298.15 K and 0.1 MPa are given in Table 2. The corresponding aqueous entropies of the ions from NBS tables17 are also given in Table 2. These enthalpies of hydration and aqueous entropies of the ions are used with eqs 12 to 16 to calculate the required values for the constants CH and CS (see eq 6). Finally, the values of ΔhG⊕(298.15K, 0.1 MPa) for the representative mono- and divalent ions are given in Table 3. The values in Table 3 for the adjusted Gibbs free energies of hydration, ΔhG⊕(298.15K, 0.1 MPa), when used with eq 2, allow prediction of the standard state partial molar volumes of chlorides and hydroxide of the alkali metal, alkali earth metal, and the first row transition metal ions to high temperatures and pressures. We present a comparison of the predicted values for the standard state partial molar volumes of the representative electrolytes from eq 2 with the experimental values, when available, and the representative models from literature up to 623.15 K and 400 MPa. The standard state partial molar volumes, V2°, for an aqueous solution of sodium chloride, NaCl(aq), at high temperatures and pressures are reported by many investigators. In Figure 1, the predicted values of V°2 for NaCl(aq) from eq 2 are compared with the corresponding experimental values at temperatures up to 623.15 K and pressures from steam saturation, psat, to 100 MPa. At all temperatures, the comparison indicates good agreement between the predicted values of standard state partial molar volumes of NaCl(aq) from this study and the corresponding experimental values from Majer et al.19 at 20 MPa, 40 MPa, and Hilbert at 100 MPa.20 Any differences are well within the uncertainties in (∂D/∂p)T (see eq 4) and uncertainties of the experimental data, most of which were

Figure 3. Comparison of the predicted values for the standard state partial molar volume of LiCl(aq) and KCl(aq) with the literature at psat: ---, SUPCRT92;8 ···, SOCW;1 , this study.

p

(10)

Δh H °(Tr , pr ) = Δf H °(Tr , pr ; aq) − Δf H °(Tr ; g )

Gilyarov et al.28 bPabalan and Pitzer correlation.29 cCorrelation of the SOCW.1 dThis study.

∫p

Cs,Cl‐ = a1

The values for ΔhH°(Tr, pr) are calculated from the standard state enthalpies of formation at 298.15 K and 0.1 MPa with the assumption that the gaseous ion behaves ideally:

a

Δf G◦(Tr , p) = Δf G◦(Tr , pr ) +

(9)

(8)

where pr is the reference pressure 0.1 MPa, V°2 is the standard state partial molar volume at 298.15 K.15 The values for the Gibbs free energies of formation, ΔfG°(Tr, pr), at 298.15 K and 0.1 MPa are from standard reference tables.16 Recently, it was discovered17 that the required constant of the model, CH and CS, in eq 6, are linearly related to the standard state enthalpy of hydration, ΔhH°(Tr, pr), and the standard state partial molar entropy of the aqueous ion, S2°(Tr, D

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Figure 4. Comparison of the predicted values for the standard state partial molar volume of MOH(aq) (M = Li+, Na+, K+, Cs+) with the literature at psat: ○, Corti et al.;30 □, Millero;15: ---, SUPCRT92;8 ···, SOCW;1 , this study.

SUPCRT92.8 At 20 MPa, the standard state partial molar volume of NaCl(aq), calculated from the SOCW model1 is in good agreement with the predicted value from this study; however, a large difference is observed with the related value for V°2 calculated from SUPCRT928 above 523.15 K. Furthermore, it should be noted that the good agreement with the corresponding experiment and the calculated values of V2° for NaCl(aq) from the SOCW1 model and SUPCRT928 is expected since the parameters of their models were regressed from the available experimental data at the time. The predicted values for standard state partial molar volume of NaCl(aq) at steam saturated pressure, psat, from this study are compared in Figure 1d and Table 4 with the corresponding values from the literature. Compared with higher pressure data, relatively larger differences are observed between the predicted values from this study and the calculated values of V2° for NaCl(aq) from the models of the SOCW1 and SUPCRT928 at steam saturated pressure and at temperatures greater than 473.15 K. These differences at psat and T ≥ 473.15 K are not surprising, since experimental values for the volumetric properties of NaCl(aq) in this interval are scarce. The close agreement between the calculated values of V°2 for NaCl(aq) from the SOCW model1 and that of Archer22 in Table 4 occurs mainly because the parameters of both models were regressed from the same set of experimental data, especially at higher temperatures. Figure 2 summarizes a comparison between the predicted values from this study (eq 2) for the partial molar volumes of NaCl(aq) and the corresponding values from the literature at 548.15 K and up to the extreme pressure of 400 MPa. The predicted values from this study for the standard state partial molar volumes of LiCl(aq) and KCl(aq) at different pressures and up to 623.15 K are compared with the

Figure 5. Comparison of the predicted values for the standard state partial molar volume of NaOH(aq) with the literature at temperatures up to 623.15 K: (○, 7 MPa), Corti and Simonson;32 (×, 10 MPa), Hnedkovsky et al.;31 (●, 30 MPa), Corti and Simonson;32 , This study.

determined from volumetric properties in relatively concentrated solutions (m ≥ 0.1 mol/kg). The predicted values of V°2 for NaCl(aq) from this study are also in good agreement with the corresponding values reported by Grant-Tayler21 up to 598.15 K. At 623.15 K and 20 MPa, a large difference is observed between the predicted value of V°2 for NaCl(aq) from this study and the related value reported by Grant-Tayler.21 The difference may be due to possible corrosion of the unlined pressure vessel employed by Grant-Tayler21 at such a high temperature. Figure 1 also summarizes a comparison between the predicted values of V2° for NaCl(aq) from eq 2 and the values calculated from the correlations of the SOCW 1 and E

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Figure 6. Comparison of the predicted values for the standard state partial molar volume of CaCl2(aq) (a,b) and BaCl2(aq) (c,d) with the literature at psat and 40 MPa, respectively: ○, Oakes et al.;33 □, Ellis;37 ···, correlation of Holmes et al.;34 ---, SUPCRT92;8 , this study.

Table 7. Standard State Partial Molar Volume for MgCl2(aq) at Different T, p

Figure 7. Comparison of the predicted values for the standard state partial molar volume of MgCl2(aq) with the literature at 10 MPa (a) and 30 MPa (b): ○, Obsil et al. (uncorrected for ion pairing);36 ●, Obsil et al. (corrected for ion pairing, see text);35 □, Ellis37 (2 MPa); ···, correlation of Holmes et al.;34 ---, SUPCRT92;8 , this study (see also Table 7).

a

T

p

V2oa

V2ob

V2oc

K

Mpa

cm3 mol−1

cm3 mol−1

cm3 mol−1

369.36 450.04 517.04 572.71 369.36 450.04 517.04 572.67

10.22 10.14 10.29 10.42 30.30 30.52 30.27 30.28

7.8 −24.3 −106.2 −326.8 10.5 −17.3 −71.1 −217.4

8.6 −19.3 −93.2

7.2 −20.4 −97.45 −394.7 11.1 −11.9 −68.2 −221.2

11.3 −12.1 −73.1

Obsil et al.35 bHolmes et al.34 cThis study.

agreement to well within the stated uncertainty of the experimental data at all temperatures and pressures reported by Gilyarov et al.28 The predicted values of V°2 for KCl(aq) from this study are also compared with the Pabalan and Pitzer correlation29 in Table 6. Again, a good agreement is observed between the predicted values of V°2 for KCl(aq) from eq 2 and the related values calculated from the Pabalan and Pitzer correlation.29 However, the Pabalan and Pitzer correlation29 requires 15 parameters to calculate V2° for KCl(aq) while the present model needs data at only 298.15 K. At the steam saturated pressure, a better agreement is observed with the SOCW model;1 however, large differences between the results from this study and those of the corresponding values calculated from the SUPCRT928 model is seen for both LiCl(aq) and KCl(aq) at T ≥ 373.15 K (Figure 3). In Figure 4, the standard state partial molar volumes of hydroxide of alkali metal MOH (M= Li+, Na+, K+, Cs+) at psat

corresponding values from the literature in Tables 5 and 6 as well as Figure 3. In Table 5, the predicted values of V2° for LiCl(aq) from this study at 32 MPa are compared with the corresponding experimental values reported by Majer et al.27 The comparison indicates an excellent agreement between the predicted values from this study and Majer et al.27 data up to 548.15 K. However, at 573.15 K and 32 MPa, a modest disagreement is observed between the two sets of data. This difference perhaps is partly due to lack of ion pair association in the Majer et al. model27 at such a high temperature. Table 6 summarizes a comparison of the predicted values of V°2 for KCl(aq) from this study and the experimental values from Gilyarov et al.28 at temperatures up to 572.61 K and pressures from 9.82 MPa to 78.56 MPa. The comparison shows good F

DOI: 10.1021/acs.jced.5b00722 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

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and pressures (eq 2). The model requires as input only the solute specific thermodynamic properties at the reference temperature 298.15 K and reference pressure 0.1 MPa and available auxiliary data related to the solvent as functions of temperature and pressure. It is used to predict the standard state partial molar volumes for chlorides and hydroxides of the alkali metals, alkali earth metals, and the first row transition metals to high temperatures and pressures. The predicted standard state partial molar volumes from this study are in very good agreement with the available literature. The present model compares well with the SOCW correlation1 results for monovalent ions above steam saturated pressures at all temperatures considered (as shown in Figures 1 and 4). However, it should be noted that experimental data for steam saturated pressures above 473.15 K are limited. Lack of available data in the literature may in part explain the differences observed between the predicted values for V°2 at psat (T ≥ 523.15 K) from this study and the corresponding values calculated from the SOCW model.1 The predicted values for the standard state partial molar volumes of MCl2(aq) (M = Mg, Ca, Ba) from this study are in excellent agreement with the corresponding values calculated from Holmes et al. correlation.34 Comparison of the predicted values for V2° of electrolytes from SUPCRT928 with the available experimental data from the literature and the corresponding values from this study indicates a large disagreement, especially at temperatures above 473.15 K (Figures 1a, 3, 4, 6, and 7).

predicted from this study (eq 2) are compared with the corresponding values from the literature. The comparison indicated an excellent agreement with the related values from the experiment reported by Millero15 and Corti et al.30 and those calculated from the SOCW model1 up to 598.15 K, to well within the combined uncertainties of the models. At temperatures above 523.15 K, large differences are observed between the results from this study and those of the corresponding values calculated from SUPCRT928 (Figure 4). It is also noted that the parameters of the SUPCRT928 were regressed from the experimental data up to 523.15 K. Figure 5 summarizes a comparison of the predicted values of V°2 for NaOH(aq) from this study with the corresponding experimental data reported by Hnedkovsky et al.31 at 10 MPa up to 573.15 K and by Corti and Simonson32 at 7 MPa and 30 MPa up to 623.15 K. The comparison indicates good agreement between the experiment and the predicted values of V°2 from eq 2 for NaOH(aq) up to 598.15 K. At 623.15 K and 30 MPa, the difference between the predicted value of V°2 for NaOH(aq) from this study and the experimental value reported by Corti and Simonson32 can be explained by lack of ion pair association in their model. Finally, in Figures 6 and 7, the predicted standard state partial molar volumes of alkali earth metal chlorides MCl2(aq) (M = Ca2+, Ba2+, Mg2+) from this study, at psat and 40 MPa, are compared with the corresponding values from the literature. The comparison for CaCl2(aq) indicates good agreement with the Oakes et al.33 data at both psat and 40 MPa (Figure 6a,b). The predicted values for V°2 of BaCl2(aq), from this study at psat and 40 MPa, are also in excellent agreement with the correlation of Holmes et al.34 (Figure 6c,d). However, large differences are noted when comparing the results from this study, for both CaCl2(aq) and BaCl2(aq), with the related values calculated from SUPCRT92,8 especially, at temperatures greater than 423.15 K. Similarly, in Figure 7 and Table 7, the predicted values of V2° for MgCl2(aq) from this study are compared with the experimental values from Obsil et al.35,36 at 10 MPa and 30 MPa and Ellis37 at 2 MPa. Obsil et al.35 later corrected their reported values up to 573.1 K for the contribution due to the first association between Mg2+(aq) ion and Cl−(aq). They estimated the equilibrium constant and volume for the chloride complex formation (MgCl+(aq)). The agreement between the predicted values for V2° of MgCl2(aq) from this study and the corrected values of V2° for the first step association of Mg2+(aq) ion and Cl−(aq) by Obsil et al.35 is reasonably good, well within the estimated uncertainties of the experimental values at all the temperatures and the pressures considered. Furthermore, in Figure 7, the predicted values for V°2 of MgCl2(aq) from this study are also compared with the corresponding values from the correlation of Holmes et al.34 and SUPCRT92.8 Excellent agreement is seen between the predicted values for V2° of MgCl2(aq) from this study and the correlation of Holmes et al.34 up to highest temperature of their study, 523.15 K. However, large differences are observed when comparing the predicted V2° of MgCl2(aq) from this study with the corresponding values calculated from SUPCRT928 at both 10 and 30 MPa. The agreement between the calculated values for V°2 of MgCl2(aq) from SUPCRT928 at 573 K and 10 MPa with the uncorrected related value of Obsil et al.36 is fortuitous.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Funding

The authors acknowledge RPSEA / DOE 10121-4204-01 for their financial support. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The authors acknowledge Donald G. Archer for providing us with the software for calculating dielectric properties of water. REFERENCES

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CONCLUSION A model is presented for prediction of the standard state partial molar volumes of aqueous electrolytes to high temperatures G

DOI: 10.1021/acs.jced.5b00722 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

Journal of Chemical & Engineering Data

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DOI: 10.1021/acs.jced.5b00722 J. Chem. Eng. Data XXXX, XXX, XXX−XXX