Volumetric Properties of Mixed Electrolyte Aqueous Solutions at

Article pubs.acs.org/jced

Volumetric Properties of Mixed Electrolyte Aqueous Solutions at Elevated Temperatures and Pressures. The Systems CaCl2−NaCl−H2O and MgCl2−NaCl−H2O to 523.15 K, 70 MPa, and Ionic Strength from (0.1 to 18) mol·kg−1 Denis Zezin,*,† Thomas Driesner,† Samuel Scott,† Carmen Sanchez-Valle,† and Thomas Wagner‡ †

Institute of Geochemistry and Petrology, ETH Zurich, Clausiusstrasse 25, 8092 Zurich, Switzerland Department of Geosciences and Geography, Division of Geology, P.O. Box 64 (Gustaf Hällströmin katu 2a), University of Helsinki, 00014 Helsinki, Finland

‡

S Supporting Information *

ABSTRACT: The densities of aqueous solutions in the systems CaCl2−NaCl−H2O and MgCl2−NaCl−H2O were determined experimentally at temperatures from (298.15 to 523.15) K, pressures up to 70 MPa and over a range of composition at ionic strengths from (0.1 to 18) mol·kg−1. The vibrating-tube densimeters used for the experimental measurements have an accuracy on density better than 9.9·10−5 g·cm−3. The mean apparent molar volumes of the mixtures calculated from the experimental data permitted a parametrization of the Pitzer equation for mixed electrolyte solutions within the entire range of temperatures, pressures, and compositions covered by this study. The parametrization of the Pitzer model for the pure binary salt aqueous solutions CaCl2−H2O and MgCl2−H2O was also refined based on new experimental and literature data. These models were used to evaluate the partial molar volumes and limiting partial molar volumes of components in aqueous mixtures of electrolytes. Using the refined models for the binary systems, Young’s mixing rule can also be used for evaluation of the mean apparent volume of electrolyte mixtures with accuracy similar to the Pitzer model and, consequently, for calculation of the densities of mixed salt solutions from the properties of binary electrolyte solutions. As an important application, we could show that the pressure effect on the estimates of the activity coefficients of components in complex aqueous electrolyte solutions can now be evaluated. Therefore, shifts in equilibrium calculations due to pressure can quantitatively be addressed when modeling geothermal, hydrothermal, or other natural or engineering aqueous systems at elevated temperatures and pressures.

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to 373.15 K and a pressure p = 0.6 MPa.6 The density of the system MgCl2−NaCl−H2O was reported at temperatures from (298.15 to 368.15) K and pressure p = 0.1 MPa9−11 and also from (296.02 to 371.82) K and p = 0.6 MPa.6 The only data set for MgCl2−NaCl aqueous mixtures at high temperatures up to 573.15 K and pressures up to 40 MPa12 was obtained by using a piezometer and is of low quality. Thus, the existing experimental data are not sufficient for accurate modeling of chemical equilibria of the aqueous systems containing these major dissolved chloride salts. The current contribution is the second of a series of papers reporting the experimental data on the volumetric properties of mixed electrolyte aqueous solutions at elevated temperatures and pressures. We present density measurements for ternary CaCl2−NaCl−H2O and MgCl2−NaCl−H2O systems at temperatures from (298.15 to 523.15) K, pressures up to 70 MPa, and ionic strengths from (0.1 to 18) mol·kg−1 at various proportions of components. As in the previous study of the

INTRODUCTION The volumetric properties of multicomponent aqueous systems are of central importance in the fields of hydrothermal geochemistry, petroleum, and geothermal reservoir engineering. A majority of aqueous solutions in high-temperature environments are represented by the mixtures of alkali and alkali earth chlorides and sulfates.1 NaCl is a dominant component of these solutions, whereas calcium and magnesium salts are also ubiquitous, with calcium sometimes exceeding sodium in concentrated brines with salinity higher than 20% in mass fraction.2 Despite the importance of multicomponent electrolyte solutions, very few experimental data are available for the properties of such solutions with more than one dissolved salt component. A substantial amount of data on the volumetric properties of binary (here and below, binary stands for pure salt-water systems) alkali and alkali earth chlorides was published; however, the data for ternary and more complex mixtures are limited and only cover a narrow range of temperatures and pressures. The density of the system CaCl2−NaCl− H2O was studied mostly at ambient conditions over a wide range of concentrations and ionic strengths.3−8 Only few studies reported the data at elevated temperatures to 308.15 K,3,7 and © XXXX American Chemical Society

Received: April 23, 2014 Accepted: July 4, 2014

A

dx.doi.org/10.1021/je500371u | J. Chem. Eng. Data XXXX, XXX, XXX−XXX

Journal of Chemical & Engineering Data

Article

of NaCl and CaCl2 in the CaCl2−NaCl mixtures and 3 mol·kg−1 and 3.01 mol·kg−1 of NaCl and MgCl2 in the MgCl2−NaCl mixtures, respectively.

KCl−NaCl−H2O system,13 the measurements were done by vibrating-tube densimetry, the most precise method for the determination of the density of fluids. New parametrizations in the framework of the Pitzer14 model are proposed for accurate calculations of molar volumes of binary electrolyte solutions and ternary mixtures. The volumetric data are also compared to those obtained from Young’s rule,15 employing only the properties of pure end-member binary solutions.

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RESULTS AND DISCUSSION The data treatment is analogous to that done for the KCl− NaCl−H2O system.13 The experimental results, T, p, molality, and the density difference between an experimental solution and pure water are presented in Table 2. The density was calculated from the measured period of vibration of the tube filled with water and reference NaCl solutions. The Hill equation of state for water18 and the consistent Archer equation for aqueous NaCl solution19 were employed in the calculations. The mean apparent molar volume of solute mixtures, the partial molar volume and the limiting molar volume of a solute in a medium are listed in Table 1S (Supporting Information). The mean apparent molar volume of electrolyte mixtures, Vϕmean, was calculated from the density of solutions as follows:

■

EXPERIMENTAL METHOD All aqueous solutions employed in experimental measurements were prepared by mass dilution from stock solutions of single electrolytes. The stock solutions were prepared with Milli-Q water (deionized water with resistivity 18.2 MΩ·cm at T = 298.15 K), crystalline anhydrous NaCl, and dihydrates of CaCl2 and MgCl2 (Table 1). The concentrations of the CaCl2 and Table 1. Sample Information Table chemical name sodium chloride

a

sodium chloride

b

calcium chloride dihydrateb magnesium chloride dihydrateb

source

initial mass fraction purity

Fisher Scientific

99.99

Fisher Scientific

> 99.5

Sigma-Aldrich

> 99.0

Sigma-Aldrich

> 99.0

treatment

ϕ = V mean

dried at 523.15 K for 24 h dried at 523.15 K for 24 h

1000(ρ0 − ρ) ∑j mj ·ρ ·ρ0

+

∑j mj ·Mj ∑j mj ·ρ

(1)

where ρ and ρ0 are the density (in g·cm−3) of solution and pure water, respectively, at temperature and pressure of interest; mj is the concentration (in mol·kg−1) and Mj is the molar weight of CaCl2 or MgCl2 and NaCl. The mean apparent molar volume of the electrolyte mixture decreases with temperature and increases with pressure over the range of conditions investigated (Figure 1). These trends of Vϕmean are similar to the behavior of KCl−NaCl−H2O mixtures.13 The mean apparent molar volume of electrolyte mixtures was approximated using the Pitzer approach14,20 formulated for the apparent molar volume of multicomponent systems:21

a

Used for calibration only. bUsed for preparation of experimental solutions.

MgCl2 stock solutions were determined by gravimetric analysis as well as calculated from the density measured at 298.15 K using an accurate density correlation available from the literature.16,17 The error on the concentration of NaCl solutions was less than 5·10−5 mol·kg−1; CaCl2 concentrations were determined to ± 6.4·10−2 mol·kg−1, MgCl2 concentrations were determined to ± 8.3·10−3 mol·kg−1. The errors on the CaCl2 and MgCl2 concentrations are significantly higher than those on NaCl because the crystalline salts used for preparation of solutions were dihydrates and of lower purity. The density of CaCl2−NaCl and MgCl2−NaCl aqueous mixtures was calculated from the measurements obtained using two different vibrating-tube densimeters: a custom-made DMA HP provided by Dr. Hans Stabinger GmbH, and a commercial DMA HP 4100 from Anton Paar. The first densimeter can operate at pressures up to 40 MPa and over an extended temperature range up to 523.15 K, compared to the pressure and temperature limits of 70 MPa and 473.15 K of the commercial instrument DMA HP 4100. Both instruments use the same principle of operation and measurements. By analogy with the custom-made densimeter, the values of the frequency of vibration of a tube filled with a sample solution measured with commercial DMA HP 4100 were used for the calculation of the density difference between the sample and reference solution as described in detail in our previous communication.13 The calibration of the densimeters was conducted daily at every temperature and pressure of interest. This resulted in significant improvement of the accuracy of density measurements achieved with the DMA HP 4100 instrument. The data were collected at temperatures of (298.15, 373.15, 423.15, 473.15 and 523.15) K, pressures up to 70 MPa, and concentrations of electrolytes up to 3.35 mol·kg−1 and 6 mol·kg−1

ϕ = V0 + V mean

1 ⎡⎢ v ⎛⎜ I ⎞⎟ A ln(1 + bI1/2) ∑ mi ⎢⎣ ⎝ b ⎠

+ RT {2 ∑ ∑ mc ma[Bcv, a + (∑ mc zc)Ccv, a] c

+

a

c

∑ ∑ mcmc′(2θcv,c′ + ∑ maψcv,c′ ,a) c

c′

a

⎤

+

∑ ∑ mama ′(2θav,a ′ + ∑ mcψav,a ′ ,c)}⎥ a

a′

c

⎥⎦

(2)

where V0 = ∑yiV0i , y is the molal fraction of NaCl in the mixture, V0i is the apparent molar volume of pure components at infinite dilution, mx is the molal concentration (in mol·kg−1), zx is the charge of respective anion a or cation c, Av is the Debye−Hückel limiting slope for the apparent molar volume, the constant b = 1.2 for 1:1 and 1:2 electrolytes, I is the ionic strength of a solution in mol·kg−1 calculated as (1/2)∑mizi, R = 8.314472 cm3·MPa·K−1·mol−1 is the gas constant, T is a temperature in K, Bvc,a and Cvc,a are the volumetric parameters obtained from the analogous correlations for pure binary solutions of electrolytes (see discussion below), and θvc,c′ and ψvc,c′,a are the mixing terms fitted to experimental data for the mixtures. The latter parameters account for mixing and may comprise both short-range and long-range effects for asymmetric mixing, for example, for cations of differing charge.22 In the case when a solution contains electrolytes with a common anion, the last term of eq 2 is zero. B



Article

Table 2. Results of Experimental Measurements of Density Difference Δρ of CaCl2−NaCl−H2O and MgCl2−NaCl−H2O Systems with Respect to Pure Water at Temperature T, Pressure p, and Molalities of Components mia T

p

m1

103·Δρ

m2 −1

K

MPa

mol·kg

298.14 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.16 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15

0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 10 10 10 10 10 10 10 10 10 10 10 10 10

0.500 03 0.100 14 0.50048 1.02093 0.49908 1.00183 0.10007 3.00001 0.10089 1.00156 0.10023 0.50005 3.00476 1.00447 0.50141 3.00863 3.00338 1.05232 0.09999 0.50003 0.10014 0.50048 0.50041 0.00000 0.49910 1.00183 3.00338 0.10089 1.00156 0.00000 0.50005 3.00863 1.00097 1.00447 0.50141 3.00863 0.00000 1.00096 3.00476 0.48483 1.05232 0.10023 0.09999 0.10007 0.50048 0.50041 0.00000 0.49910 1.00183 3.00001 0.10089 1.00156 0.00000 0.50005 3.00476 1.00097 1.00447

mol·kg 0.100 3.001 0.010 0.011 0.100 0.100 0.100 0.101 0.200 0.208 0.500 0.500 0.500 0.501 1.000 1.002 1.791 3.009 1.000 0.100 3.001 0.010 0.050 0.099 0.100 0.100 0.101 0.200 0.208 0.490 0.500 0.500 0.501 0.501 1.000 1.002 1.005 1.006 1.791 2.908 3.009 0.500 1.000 0.100 0.010 0.050 0.099 0.100 0.100 0.101 0.200 0.208 0.490 0.500 0.500 0.501 0.501

−1

g·cm

T

−3

K

NaCl (1) + CaCl2(2) 28.73 423.16 231.63 423.14 21.04 423.15 41.77 423.15 28.76 423.15 47.72 423.15 13.04 423.15 116.70 423.15 22.04 423.15 56.77 423.15 47.67 423.15 62.60 423.15 143.91 423.15 81.26 423.15 102.31 423.15 180.98 423.15 232.01 423.15 257.67 423.15 88.69 423.15 28.67 423.15 231.18 423.15 20.94 423.15 24.52 423.15 9.14 423.15 28.66 423.15 47.55 423.15 116.21 423.15 21.99 423.15 56.62 423.15 43.27 423.16 62.35 423.16 143.37 423.16 80.51 423.16 80.98 423.16 101.95 423.16 180.28 423.14 85.67 423.15 120.07 423.15 231.17 423.15 236.22 423.15 256.79 423.15 47.55 423.15 88.49 423.15 13.04 423.15 20.85 423.15 24.36 423.15 9.13 423.15 28.51 423.15 47.29 423.15 115.75 423.15 21.85 423.15 56.33 423.15 43.15 423.15 62.15 423.15 142.91 423.15 80.30 423.15 80.67 423.15

C

p MPa 10 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40

m1 mol·kg

103·Δρ

m2 −1

1.052 32 0.499 87 0.10023 0.10011 0.50048 1.02090 3.35813 3.01468 0.50041 0.10030 1.00930 0.00000 1.00183 0.10007 0.50003 3.00001 0.50270 0.10089 1.00160 0.50005 3.00476 1.00447 0.50139 0.09999 3.00863 0.00000 3.00338 0.10014 0.10066 3.00210 3.02274 0.00000 1.00844 0.00000 1.05232 0.49987 0.10011 0.50048 1.02090 3.35813 3.01468 0.50041 0.10030 1.00930 0.00000 1.00183 0.10007 3.00001 0.50270 0.10089 1.00160 0.10023 0.50005 3.00476 1.00447 0.09999 3.00863

mol·kg 3.009 2.999 0.500 0.010 0.010 0.011 0.012 0.050 0.050 0.050 0.051 0.099 0.100 0.100 0.100 0.101 0.200 0.200 0.208 0.500 0.500 0.501 1.000 1.000 1.002 1.005 1.791 3.001 6.004 0.010 0.202 0.490 1.002 3.004 3.009 2.999 0.010 0.010 0.011 0.012 0.050 0.050 0.050 0.051 0.099 0.100 0.100 0.101 0.200 0.200 0.208 0.500 0.500 0.500 0.501 1.000 1.002

−1

g·cm−3 259.30 244.12 49.61 5.08 21.15 40.95 120.31 111.92 24.75 9.01 44.21 9.44 47.95 13.67 29.25 116.25 38.32 22.95 57.19 63.91 145.26 81.59 104.76 91.49 178.91 88.46 231.20 234.29 392.18 108.45 123.01 44.96 121.11 232.38 257.75 241.63 5.07 20.66 40.23 118.64 110.39 24.31 8.80 43.44 9.24 47.13 13.43 114.48 37.61 22.51 56.34 48.88 62.96 143.25 80.54 90.28 176.91



Article

Table 2. continued T

p

m1

m2

103·Δρ

T

p

m1

m2

103·Δρ

K

MPa

mol·kg−1

mol·kg−1

g·cm−3

K

MPa

mol·kg−1

mol·kg−1

g·cm−3

10 10 10 10 10 10 10 10 10 10 10 10 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40

0.50141 3.00863 0.00000 1.00096 3.00338 0.48483 0.10014 1.05232 0.10023 0.09999 0.10007 0.50003 0.50048 0.50041 0.00000 0.49910 1.00183 0.10007 0.50003 3.00001 0.10089 1.00156 0.00000 0.50005 3.00476 1.00097 1.00447 0.50141 0.09999 3.00863 0.00000 1.00096 3.00338 0.48483 1.05232 0.10023 0.10014 0.50048 0.50041 0.00000 0.49910 1.00183 0.10007 0.50003 3.00001 0.10089 1.00156 0.00000 0.50005 3.00476 1.00097 1.00447 0.50141 0.09999 3.00863 0.00000 1.00096 3.00338

1.000 1.002 1.005 1.006 1.791 2.908 3.001 3.009 0.500 1.000 0.100 0.100 0.010 0.050 0.099 0.100 0.100 0.100 0.100 0.101 0.200 0.208 0.490 0.500 0.500 0.501 0.501 1.000 1.000 1.002 1.005 1.006 1.791 2.908 3.009 0.500 3.001 0.010 0.050 0.099 0.100 0.100 0.100 0.100 0.101 0.200 0.208 0.490 0.500 0.500 0.501 0.501 1.000 1.000 1.002 1.005 1.006 1.791

40 40 40 40 40 40 40 40 40 40 40 40 70 70 70 70 70 70 70 70 70 70 70 70 70 70 70 70 70 70 70 70 70 70 70 70 70 70 70 70 2 2 2 2 2 2 2 2 5 5 5 5 5 5 5 5 5 5

3.00338 0.10014 0.00000 0.10066 0.50003 0.50139 3.00210 3.02274 0.00000 1.00844 0.00000 1.05232 0.10011 0.50048 1.02090 3.35813 3.01468 0.50041 0.10030 1.00930 0.00000 0.49985 1.00183 0.09998 3.00001 0.50270 0.10089 1.00160 3.00476 1.00447 3.00863 3.00338 0.00000 0.10066 3.00210 3.02274 0.00000 1.00844 0.00000 1.05232 0.50139 0.10007 0.50004 0.10023 0.49987 0.10014 0.09999 0.50005 0.50048 0.10100 1.02090 3.35813 3.01468 0.50041 0.10054 1.00930 1.00934 1.00130

1.791 3.001 3.004 6.004 0.100 1.000 0.010 0.202 0.490 1.002 1.005 3.009 0.010 0.010 0.011 0.012 0.050 0.050 0.050 0.051 0.099 0.099 0.100 0.100 0.101 0.200 0.200 0.208 0.500 0.501 1.002 1.791 3.004 6.004 0.010 0.202 0.490 1.002 1.005 3.009 1.000 0.100 0.100 0.500 2.999 3.001 1.000 0.500 0.010 0.010 0.011 0.012 0.050 0.050 0.050 0.051 0.051 0.099

228.81 231.87 229.98 389.14 28.73 103.39 106.82 121.23 44.42 119.33 87.20 255.27 4.96 20.32 39.42 116.66 108.44 23.78 8.65 42.55 9.27 28.01 46.28 13.12 112.54 36.94 22.12 55.25 140.99 79.08 174.32 225.86 227.05 385.63 104.99 119.37 43.64 117.50 85.89 252.24 115.16 15.65 33.03 55.33 261.77 251.81 100.95 71.14 23.80 6.09 45.87 131.38 122.98 27.81 10.38 49.24 49.27 53.20

298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.16 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.16 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15

NaCl (1) + CaCl2(2) 101.64 423.15 179.76 423.15 85.44 423.15 119.76 423.15 230.60 423.15 235.70 423.15 230.79 423.16 256.22 423.16 47.41 423.16 88.25 423.16 12.98 423.16 28.58 423.16 20.73 423.15 24.20 423.15 9.08 423.15 28.27 423.15 46.95 423.15 12.90 423.15 28.34 423.15 115.07 423.15 21.78 423.15 55.99 423.15 42.94 423.15 61.81 423.15 142.09 423.15 79.78 423.15 80.19 423.15 101.06 423.15 87.84 423.15 178.90 423.15 85.02 423.15 119.12 423.15 229.60 423.15 234.73 423.15 255.27 423.16 47.19 423.16 229.92 423.16 20.42 423.16 23.84 423.16 8.92 423.16 27.85 473.13 46.32 473.14 12.78 473.14 27.99 473.15 113.55 473.15 21.57 473.15 55.26 473.15 42.43 473.15 61.02 473.14 140.50 473.15 78.90 473.15 79.19 473.15 100.00 473.15 87.04 473.15 177.03 473.15 84.22 473.15 117.88 473.15 227.49 473.15

D



Article


p

m1

m2

103·Δρ

T

p

m1

m2

103·Δρ

K

MPa

mol·kg−1

mol·kg−1

g·cm−3

K

MPa

mol·kg−1

mol·kg−1

g·cm−3

40 40 40 40 70 70 70 70 70 70 70 70 70 70 2 2 2 2 2 2 2 2 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5

0.48483 1.05232 0.10023 0.10014 0.50048 0.50041 0.00000 0.10089 1.00156 0.00000 1.00097 0.00000 1.00096 0.48483 0.49987 0.10007 0.50003 0.10023 0.50005 0.50139 0.09999 0.10014 0.10011 0.50048 3.00210 1.01314 3.01468 0.10054 1.00934 0.00000 0.49994 1.00183 0.10002 3.00001 0.50272 0.10089 3.02274 1.00156 0.00000 3.00476 1.00097 3.00563 1.00447 0.10011 0.50139 1.00844 3.00863 0.00000 1.00096 3.00338 1.99123 0.10033 0.49994 1.05232 0.00000 0.10066 0.50005 0.10023

2.908 3.009 0.500 3.001 0.010 0.050 0.099 0.200 0.208 0.490 0.501 1.005 1.006 2.908 2.999 0.100 0.100 0.500 0.500 1.000 1.000 3.001 0.010 0.010 0.010 0.011 0.050 0.050 0.051 0.099 0.100 0.100 0.100 0.101 0.200 0.200 0.202 0.208 0.490 0.500 0.501 0.501 0.501 1.000 1.000 1.002 1.002 1.005 1.006 1.791 1.995 2.998 2.999 3.009 5.953 6.004 0.500 0.500

5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 20 20 20 20 20

0.00000 3.00001 0.10048 0.50272 0.99590 3.02274 0.00000 1.00100 3.00563 1.00255 0.50139 0.00000 0.49987 0.00000 1.00241 0.10023 0.10007 0.50005 0.09999 0.10014 0.50004 3.00863 0.10014 0.49987 0.50048 0.10100 1.02090 3.35813 3.01468 0.50041 0.10054 1.00934 1.00130 0.00000 3.00001 0.10048 0.50272 0.99590 3.02274 0.00000 1.00100 3.00563 1.00255 0.09999 0.00000 0.00000 1.00241 0.10007 0.50140 0.10023 0.50004 0.50005 3.00863 0.50048 0.10100 1.02090 3.35813 3.01468

0.099 0.101 0.200 0.200 0.201 0.202 0.490 0.501 0.501 0.999 1.000 1.005 2.999 3.004 3.006 0.500 0.100 0.500 1.000 3.001 0.100 1.002 3.001 2.999 0.010 0.010 0.011 0.012 0.050 0.050 0.050 0.051 0.099 0.099 0.101 0.200 0.200 0.201 0.202 0.490 0.501 0.501 0.999 1.000 1.005 3.004 3.006 0.100 1.000 0.500 0.100 0.500 1.002 0.010 0.010 0.011 0.012 0.050

11.54 126.04 25.70 42.71 62.80 134.69 50.77 89.93 156.93 131.45 114.63 98.01 260.73 249.84 272.91 55.11 15.56 70.77 100.42 250.84 32.84 193.52 249.38 259.26 23.69 6.06 45.42 130.40 122.06 27.59 10.32 48.81 52.76 11.47 125.12 25.46 42.33 62.19 133.74 50.38 89.27 155.78 130.52 99.68 97.34 248.38 271.38 15.41 113.84 54.64 32.54 70.23 192.24 23.23 5.94 44.66 128.65 120.36

298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 373.15 373.15 373.15 373.15 373.15 373.15 373.15 373.15 373.15 373.15 373.15 373.15 373.15 373.15 373.15 373.15 373.15 373.15 373.15 373.15 373.15 373.15 373.15 373.15 373.15 373.15 373.15 373.15 373.15 373.15 373.15 373.15 373.15 373.15 373.15 373.15 373.15 373.15 373.15 373.15 373.15 373.15 373.15 373.15

NaCl (1) + CaCl2(2) 232.89 473.15 253.24 473.15 46.72 473.15 228.24 473.15 20.02 473.15 23.24 473.15 8.82 473.15 21.17 473.15 54.29 473.15 41.94 473.15 77.51 473.15 83.18 473.15 116.26 473.15 230.49 473.15 239.39 473.15 13.01 473.15 28.02 473.15 47.59 473.16 61.67 473.16 101.42 473.16 88.38 473.16 229.12 473.16 4.94 473.14 20.15 473.15 105.70 473.15 39.22 473.15 108.99 473.15 8.63 473.15 42.33 473.15 9.18 473.15 28.06 473.15 46.12 473.15 13.02 473.15 112.16 473.15 36.61 473.15 21.87 473.15 120.51 473.15 55.16 473.15 43.28 473.15 141.05 473.15 78.65 473.15 141.14 473.15 78.66 473.15 88.27 473.15 101.31 473.15 117.36 473.15 175.81 473.15 85.21 473.15 117.77 473.15 226.62 473.16 214.08 473.16 228.88 473.16 239.21 473.16 252.40 473.15 377.23 473.15 386.04 473.15 61.57 473.15 47.54 473.15

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Article


p

m1

m2

103·Δρ

T

p

m1

m2

103·Δρ

K

MPa

mol·kg−1

mol·kg−1

g·cm−3

K

MPa

mol·kg−1

mol·kg−1

g·cm−3

5 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20

0.00000 0.10023 0.50005 0.10011 0.50048 3.00210 1.01314 3.01468 0.10054 1.00934 0.00000 0.49994 1.00183 0.10002 3.00001 0.50272 0.10089 3.02274 1.00156 0.00000 3.00476 3.00563 1.00447 0.10011 0.50139 1.00844 3.00863 0.00000 3.00338 1.99123 0.10033 1.05232 0.00000 0.10066 1.00096 0.49987 1.00097 0.00000 0.10023 0.50005 0.50139 0.10014 0.10011 0.50048 3.00210 1.01314 3.01468 0.10054 1.00934 0.00000 0.49994 1.00183 0.10002 3.00001 0.50272 0.10089 3.02274 1.00156

3.004 0.500 0.500 0.010 0.010 0.010 0.011 0.050 0.050 0.051 0.099 0.100 0.100 0.100 0.101 0.200 0.200 0.202 0.208 0.490 0.500 0.501 0.501 1.000 1.000 1.002 1.002 1.005 1.791 1.995 2.998 3.009 5.953 6.004 1.006 2.999 0.501 3.004 0.500 0.500 1.000 3.001 0.010 0.010 0.010 0.011 0.050 0.050 0.051 0.099 0.100 0.100 0.100 0.101 0.200 0.200 0.202 0.208

20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40 70

0.10054 1.00934 1.00130 0.00000 0.10048 0.50272 0.99590 3.02274 0.00000 1.00100 3.00563 1.00255 0.09999 3.00863 0.00000 0.49987 0.10014 0.00000 1.00241 0.50003 0.50005 0.10023 0.50139 0.10007 0.50041 3.00001 0.49987 0.50048 0.10100 1.02090 3.35813 3.01468 0.10054 1.00934 1.00130 0.00000 0.10048 0.50272 0.99590 3.02274 0.00000 1.00100 3.00563 1.00255 0.09999 0.00000 0.10014 0.00000 1.00241 0.10023 0.50139 0.50003 0.50041 0.10007 3.00001 0.50005 3.00863 0.50048

0.050 0.051 0.099 0.099 0.200 0.200 0.201 0.202 0.490 0.501 0.501 0.999 1.000 1.002 1.005 2.999 3.001 3.004 3.006 0.100 0.500 0.500 1.000 0.100 0.050 0.101 2.999 0.010 0.010 0.011 0.012 0.050 0.050 0.051 0.099 0.099 0.200 0.200 0.201 0.202 0.490 0.501 0.501 0.999 1.000 1.005 3.001 3.004 3.006 0.500 1.000 0.100 0.050 0.100 0.101 0.500 1.002 0.010

10.13 48.02 51.85 11.35 25.06 41.71 61.28 131.90 49.70 88.01 153.89 128.85 98.35 189.99 96.15 256.67 246.85 245.80 268.65 31.95 69.21 53.83 112.36 15.13 27.18 123.43 252.40 22.58 5.72 43.44 125.79 117.64 9.78 46.72 50.47 11.03 24.33 40.64 59.72 128.93 48.59 86.03 150.62 126.21 96.20 94.10 242.74 241.80 269.33 52.52 109.94 31.04 26.39 14.69 120.61 67.54 186.43 21.77

373.16 373.15 373.15 373.15 373.15 373.15 373.15 373.15 373.15 373.15 373.15 373.15 373.15 373.15 373.15 373.15 373.15 373.15 373.15 373.15 373.15 373.15 373.15 373.15 373.15 373.15 373.15 373.15 373.15 373.15 373.15 373.15 373.15 373.15 373.15 373.15 373.16 373.16 373.15 373.15 373.15 373.15 373.15 373.15 373.15 373.15 373.15 373.15 373.15 373.15 373.15 373.15 373.15 373.15 373.15 373.15 373.15 373.15

NaCl (1) + CaCl2(2) 226.54 473.15 47.35 473.15 61.36 473.15 4.96 473.15 20.20 473.15 105.42 473.15 39.13 473.15 108.75 473.15 8.61 473.15 42.28 473.15 9.23 473.15 27.94 473.15 46.01 473.15 12.96 473.15 111.84 473.15 36.61 473.15 21.87 473.15 120.18 473.15 55.06 473.15 43.22 473.15 140.67 473.15 140.72 473.15 78.39 473.15 88.00 473.16 101.02 473.16 117.04 473.16 175.32 473.14 85.07 473.15 226.17 473.15 213.68 473.15 228.34 473.15 251.84 473.15 376.57 473.15 385.54 473.15 117.41 473.15 238.60 473.15 78.38 473.15 226.08 473.15 47.10 473.15 61.03 473.15 100.50 473.15 227.40 473.15 4.84 473.15 20.00 473.15 104.83 473.15 38.87 473.15 108.10 473.15 8.54 473.15 41.98 473.15 9.11 473.15 27.78 473.15 45.66 473.16 12.89 473.16 111.09 473.16 36.36 473.16 21.67 473.16 119.51 473.16 54.71 473.15

F



Article


p

m1

m2

103·Δρ

T

p

m1

m2

103·Δρ

K

MPa

mol·kg−1

mol·kg−1

g·cm−3

K

MPa

mol·kg−1

mol·kg−1

g·cm−3

20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40 70 70 70 70

0.00000 3.00476 1.00447 0.10011 1.00844 3.00863 0.00000 3.00338 1.99123 0.49987 1.05232 0.00000 1.00096 1.00097 3.00563 0.00000 0.10066 1.00096 0.10011 0.50048 3.00210 1.01314 3.01468 0.10054 1.00934 0.00000 0.49994 1.00183 0.10002 3.00001 0.50272 3.02274 1.00156 0.00000 0.10023 0.50005 3.00476 1.00097 1.00447 0.10011 0.50139 1.00844 3.00863 3.00338 0.49987 0.10014 1.05232 0.00000 0.10066 3.00563 0.10089 0.00000 1.99123 0.00000 0.10011 0.50048 3.00210 1.02093

0.490 0.500 0.501 1.000 1.002 1.002 1.005 1.791 1.995 2.999 3.009 5.953 1.006 0.501 0.501 3.004 6.004 1.006 0.010 0.010 0.010 0.011 0.050 0.050 0.051 0.099 0.100 0.100 0.100 0.101 0.200 0.202 0.208 0.490 0.500 0.500 0.500 0.501 0.501 1.000 1.000 1.002 1.002 1.791 2.999 3.001 3.009 5.953 6.004 0.501 0.200 1.005 1.995 3.004 0.010 0.010 0.010 0.011

70 70 70 70 70 70 70 70 70 70 70 70 70 70 70 70 70 70 70 70 70 70 70 70 70 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 10

0.10113 1.02090 3.35813 3.01468 0.10054 1.00934 1.00130 0.00000 0.09998 0.50272 0.99590 3.02274 0.00000 1.00100 3.00563 1.00255 0.10023 0.00000 0.50000 0.00000 1.00241 0.10048 0.50041 3.00001 3.00863 3.35813 0.10007 0.50005 0.50003 3.01468 0.50139 0.10011 1.00157 3.00001 0.50041 3.00476 0.49434 0.50048 1.02093 0.99588 3.02274 0.10023 0.09999 0.00000 3.00338 1.00241 0.50272 1.00097 0.10030 0.00000 1.00549 0.00000 0.10014 0.10089 1.05232 3.00863 0.00000 0.50041

0.011 0.011 0.012 0.050 0.050 0.051 0.099 0.099 0.100 0.200 0.201 0.202 0.490 0.501 0.501 0.999 0.999 1.005 2.999 3.004 3.006 0.200 0.050 0.101 1.002 0.012 0.100 0.500 0.100 0.050 1.000 0.010 0.100 0.101 0.050 0.500 3.012 0.010 0.011 0.201 0.202 0.500 1.000 1.005 1.791 3.006 0.200 0.501 0.050 0.490 1.000 0.099 3.001 0.200 3.009 1.002 3.004 0.050

5.55 42.14 122.53 114.57 9.43 45.31 49.11 10.63 14.16 39.37 58.02 125.68 47.24 83.80 147.06 123.31 94.06 91.76 247.96 237.26 259.71 23.71 25.49 117.44 182.39 149.17 18.72 81.30 38.86 140.17 128.85 7.60 62.78 143.37 33.61 176.15 285.32 28.90 54.29 73.00 152.92 63.35 113.24 110.13 270.15 298.76 50.37 102.53 12.55 57.84 148.58 13.08 274.26 30.55 298.39 213.99 272.46 33.06

373.15 373.15 373.15 373.15 373.15 373.15 373.15 373.15 373.15 373.15 373.15 373.15 373.15 373.15 373.16 373.16 373.16 373.14 373.15 373.15 373.15 373.15 373.15 373.15 373.15 373.15 373.15 373.15 373.15 373.15 373.15 373.15 373.15 373.15 373.15 373.15 373.15 373.15 373.15 373.15 373.15 373.15 373.15 373.15 373.15 373.15 373.15 373.15 373.15 373.16 373.16 373.16 373.16 373.16 373.15 373.15 373.15 373.15

NaCl (1) + CaCl2(2) 42.94 473.15 139.81 473.15 77.84 473.15 87.57 473.15 116.38 473.15 174.36 473.15 84.61 473.15 225.05 473.15 212.62 473.15 237.66 473.15 250.77 473.15 375.40 473.15 116.89 473.15 77.74 473.15 140.02 473.15 225.09 473.15 384.27 473.15 115.82 473.15 4.88 473.15 19.79 473.15 103.65 473.15 38.41 473.16 106.93 473.16 8.46 473.16 41.37 473.16 8.98 523.14 27.40 523.14 45.21 523.14 12.69 523.14 110.02 523.15 36.00 523.15 118.26 523.15 54.15 523.15 42.53 523.15 46.60 523.15 60.39 523.15 138.53 523.15 77.23 523.15 77.13 523.15 86.74 523.15 99.54 523.15 115.36 523.15 172.92 523.15 223.34 523.15 235.93 523.15 225.72 523.15 249.05 523.15 373.16 523.15 382.08 523.15 138.61 523.15 21.43 523.15 83.87 523.15 211.02 523.15 223.42 523.16 4.73 523.16 19.53 523.16 102.14 523.16 37.88 523.15

G



Article


p

m1

m2

103·Δρ

T

p

m1

m2

103·Δρ

K

MPa

mol·kg−1

mol·kg−1

g·cm−3

K

MPa

mol·kg−1

mol·kg−1

g·cm−3

70 70 70 70 70 70 70 70 70 70 70 70 70 70 70 70 70 70 70 70 70 70 70 70 70 70 70 70 70 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5

3.01468 0.50041 0.10030 1.00934 0.00000 0.49985 1.00183 0.09998 3.00001 0.50272 0.10089 3.02274 1.00156 0.00000 3.00476 1.00447 0.48992 0.10023 1.00844 3.00863 0.00000 3.00338 1.99123 0.10051 0.50000 1.05232 0.00000 0.00000 0.10066 0.50139 0.09999 0.10014 0.49987 0.10011 0.50048 3.00210 1.02090 3.35813 3.01468 0.50041 0.10030 1.00930 0.00000 1.00183 0.10007 0.50003 3.00001 0.50270 0.10089 1.00160 0.10023 0.50005 3.00476 1.00447 3.00863 0.00000 3.00338 0.10066

0.050 0.050 0.050 0.051 0.099 0.099 0.100 0.100 0.101 0.200 0.200 0.202 0.208 0.490 0.500 0.501 0.979 0.999 1.002 1.002 1.005 1.791 1.995 2.995 2.999 3.009 5.953 3.004 6.004 1.000 1.000 3.001 2.999 0.010 0.010 0.010 0.011 0.012 0.050 0.050 0.050 0.051 0.099 0.100 0.100 0.100 0.101 0.200 0.200 0.208 0.500 0.500 0.500 0.501 1.002 1.005 1.791 6.004

10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20

0.10030 1.05232 0.10011 1.02093 3.35813 1.00157 0.10007 3.02274 0.00000 0.10023 3.00863 0.00000 0.10014 1.00241 0.49434 0.09999 3.01468 0.50003 0.10089 1.00097 0.50139 1.00549 3.00338 0.00000 3.00001 0.50272 0.00000 0.99588 3.00476 0.50048 0.50005 3.00863 0.00000 0.10030 0.10007 0.50005 0.50139 1.00241 1.05232 0.49434 0.50048 0.50003 1.00549 0.50041 3.00001 0.99588 3.02274 3.01468 1.00157 0.10089 3.00476 3.00338 0.50272 0.09999 0.10011 0.10014 1.02093 3.35813

0.050 3.009 0.010 0.011 0.012 0.100 0.100 0.202 0.490 0.500 1.002 1.005 3.001 3.006 3.012 1.000 0.050 0.100 0.200 0.501 1.000 1.000 1.791 3.004 0.101 0.200 0.099 0.201 0.500 0.010 0.500 1.002 3.004 0.050 0.100 0.500 1.000 3.006 3.009 3.012 0.010 0.100 1.000 0.050 0.101 0.201 0.202 0.050 0.100 0.200 0.500 1.791 0.200 1.000 0.010 3.001 0.011 0.012

12.31 295.26 7.34 53.25 146.92 61.74 18.32 150.70 57.09 62.38 211.24 108.61 271.19 295.49 282.20 111.64 137.22 38.14 30.02 101.03 126.99 146.56 267.05 269.36 141.35 49.47 12.89 71.78 173.87 28.32 79.89 206.50 264.02 11.87 17.68 77.67 123.86 289.85 289.63 276.73 27.28 35.66 142.99 31.92 137.64 69.63 146.77 133.49 59.78 29.06 169.65 261.70 47.95 108.82 7.04 265.93 51.51 142.98

373.15 373.15 373.15 373.15 373.15 373.15 373.15 373.15 373.15 373.15 373.15 373.15 373.15 373.15 373.15 373.15 373.15 373.15 373.15 373.15 373.15 373.15 373.15 373.15 373.15 373.15 373.15 373.16 373.16 423.15 423.15 423.15 423.15 423.15 423.15 423.15 423.15 423.15 423.15 423.15 423.15 423.15 423.15 423.15 423.15 423.15 423.15 423.15 423.15 423.15 423.15 423.15 423.15 423.15 423.15 423.15 423.15 423.15

NaCl (1) + CaCl2(2) 105.36 523.15 22.87 523.15 8.27 523.15 40.83 523.15 9.06 523.15 27.02 523.15 44.52 523.15 12.48 523.15 108.38 523.15 35.46 523.15 21.10 523.15 116.84 523.15 53.44 523.15 42.11 523.15 136.71 523.15 76.06 523.15 96.70 523.15 85.70 523.15 113.91 523.15 170.80 523.15 82.71 523.15 220.87 523.15 208.65 523.15 223.62 523.16 233.78 523.16 246.60 523.16 370.10 523.16 221.22 523.16 379.05 523.16 106.01 523.16 92.61 523.16 236.47 523.14 246.37 523.15 5.33 523.15 21.49 523.15 109.83 523.15 41.61 523.15 121.91 523.15 113.45 523.15 25.04 523.15 9.16 523.15 44.80 523.15 9.69 523.15 48.53 523.15 13.90 523.15 29.70 523.15 117.60 523.15 38.84 523.16 23.24 523.16 57.92 523.16 50.30 523.16 64.76 523.16 146.75 523.16 82.60 523.16 180.94 523.16 89.35 523.16 233.42 523.16 395.09 523.16

H



Article


p

m1

m2

103·Δρ

T

p

m1

m2

103·Δρ

K

MPa

mol·kg−1

mol·kg−1

g·cm−3

K

MPa

mol·kg−1

mol·kg−1

g·cm−3

5 5 5 5 5 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10

3.02274 0.00000 1.00844 0.00000 1.05232 0.10066 0.10023 0.10011 0.50048 3.00210 1.02090 3.35813 3.01468 0.50041 0.10030 1.00930 0.00000 1.00183 0.10007 3.00001 0.50270 0.10089 1.00160 0.00000 0.50005 3.00476 1.00447 0.50139 0.09999 3.00863 0.00000 3.00338 0.10014 0.49987 0.50003 3.02274 1.00844 0.00000

0.202 0.490 1.002 3.004 3.009 6.004 0.500 0.010 0.010 0.010 0.011 0.012 0.050 0.050 0.050 0.051 0.099 0.100 0.100 0.101 0.200 0.200 0.208 0.490 0.500 0.500 0.501 1.000 1.000 1.002 1.005 1.791 3.001 2.999 0.100 0.202 1.002 3.004

20 20 20 20 20 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40

0.00000 0.10023 0.00000 1.00097 0.00000 0.10030 0.50048 0.50041 0.00000 0.10007 0.10089 0.10014 0.00000 1.00241 3.00001 0.50005 0.50003 3.00476 0.49434 3.00863 0.10023 0.50139 0.00000 1.05232 0.10011 1.00157 1.00549 0.50272 3.00338 1.00097 3.02274 0.00000 3.01468 0.99588 0.09999 1.02093 3.35813

0.490 0.500 1.005 0.501 0.099 0.050 0.010 0.050 0.099 0.100 0.200 3.001 3.004 3.006 0.101 0.500 0.100 0.500 3.012 1.002 0.500 1.000 1.005 3.009 0.010 0.100 1.000 0.200 1.791 0.501 0.202 0.490 0.050 0.201 1.000 0.011 0.012

55.47 60.64 105.88 98.23 12.44 11.18 25.73 30.18 11.74 16.70 27.62 257.90 256.04 281.39 131.99 74.34 34.96 163.31 268.55 199.43 57.99 119.13 101.81 281.22 6.55 56.90 137.67 45.61 253.60 94.16 140.88 53.19 127.92 66.39 104.61 48.86 137.08

0.99911 3.00012 0.00000 1.00125 0.10007 0.20190 0.49980 2.99998 0.20014 0.00000 0.99911 0.50434 0.19961 0.00000 1.00005 3.00012 0.50040 0.10047 1.00053

0.1001 0.5005 1.0003 3.0093 3.0097 3.0098 3.0101 0.0998 0.1000 0.1000 0.1001 0.1017 0.4998 0.5000 0.5000 0.5005 0.5006 0.5039 0.9996

20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 40 40 40

0.00000 1.00005 3.00012 0.50040 0.10047 1.00053 0.10021 3.00001 0.20007 0.49992 1.00608 0.00000 0.10007 0.00000 0.49980 0.20190 2.99998 0.20014 0.00000

0.5000 0.5000 0.5005 0.5006 0.5039 0.9996 1.0000 1.0000 1.0005 1.0006 1.2355 3.0001 3.0097 1.0003 3.0101 3.0098 0.0998 0.1000 0.1000

41.85 77.61 141.31 60.03 45.99 113.56 84.01 173.05 87.38 97.45 130.12 213.81 217.36 80.74 227.97 220.00 112.77 16.53 8.66

423.16 423.16 423.16 423.16 423.16 423.14 423.15 423.15 423.15 423.15 423.15 423.15 423.15 423.15 423.15 423.15 423.15 423.15 423.15 423.15 423.15 423.15 423.15 423.15 423.15 423.15 423.15 423.15 423.15 423.15 423.15 423.15 423.15 423.15 423.15 423.16 423.16 423.16 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15

0.1 0.1 0.1 0.1 0.1 0.1 0.1 5 5 5 5 5 5 5 5 5 5 5 5

NaCl (1) + CaCl2(2) 124.69 523.16 45.61 523.16 122.26 523.16 234.51 523.16 260.07 523.16 394.22 523.14 50.05 523.15 5.23 523.15 21.35 523.15 109.35 523.15 41.37 523.15 121.28 523.15 112.98 523.15 24.99 523.15 9.11 523.15 44.61 523.15 9.55 523.15 48.29 523.15 13.81 523.15 117.12 523.15 38.64 523.16 23.19 523.16 57.67 523.16 45.35 523.16 64.46 523.16 146.27 523.16 82.22 523.16 105.59 523.16 92.23 523.16 180.21 523.16 89.07 523.16 232.65 523.16 235.72 523.16 245.62 523.16 29.52 523.16 124.17 523.16 121.78 523.17 233.74 NaCl (1) + MgCl2(2) 46.51 423.15 140.52 423.15 73.84 423.15 226.59 423.15 201.59 423.15 204.47 423.15 212.74 423.15 114.72 423.15 15.87 423.15 7.78 423.15 46.34 423.15 27.82 423.15 45.35 423.15 37.82 423.15 74.05 423.15 140.06 423.15 56.40 423.15 41.91 423.15 107.32 423.15

I



Article


p

m1

m2

103·Δρ

T

p

m1

m2

103·Δρ

K

MPa

mol·kg−1

mol·kg−1

g·cm−3

K

MPa

mol·kg−1

mol·kg−1

g·cm−3

5 5 5 5 5 5 5 5 5 5 5 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 40

0.10021 3.00001 0.00000 0.20007 0.49992 1.00608 0.00000 1.00125 0.10007 0.20190 0.49980 2.99998 0.20014 0.00000 0.99911 0.50434 0.19961 0.00000 1.00005 3.00012 0.50040 0.10047 1.00053 0.10021 3.00001 0.00000 0.20007 0.49992 1.00608 0.00000 1.00125 0.10007 0.20190 0.49980 2.99998 0.20014 0.00000 0.99911 0.50434 0.19961 0.00000 1.00005 3.00012 0.50040 0.10047 1.00053 0.10021 3.00001 0.00000 0.20007 0.49992 1.00608 0.00000 1.00125 0.10007 0.20190 0.49980 2.99998

1.0000 1.0000 1.0003 1.0005 1.0006 1.2355 3.0001 3.0093 3.0097 3.0098 3.0101 0.0998 0.1000 0.1000 0.1001 0.1017 0.4998 0.5000 0.5000 0.5005 0.5006 0.5039 0.9996 1.0000 1.0000 1.0003 1.0005 1.0006 1.2355 3.0001 3.0093 3.0097 3.0098 3.0101 0.0998 0.1000 0.1000 0.1001 0.1017 0.4998 0.5000 0.5000 0.5005 0.5006 0.5039 0.9996 1.0000 1.0000 1.0003 1.0005 1.0006 1.2355 3.0001 3.0093 3.0097 3.0098 3.0101 0.0998

40 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40 70 70 70 70 70 70 70 70 70 70 70 70 70 70 70 70 70 70 70 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5

0.99911 0.10074 0.50434 0.00000 0.19961 0.00000 1.00005 3.00012 0.50040 0.10047 1.00053 0.10021 3.00001 0.00000 0.20007 0.49992 1.00608 0.00000 0.10007 1.00125 0.20190 0.49980 2.99998 0.20014 0.00000 0.10074 0.50434 0.00000 0.19961 0.00000 1.00005 3.00012 0.50040 0.10047 1.00053 0.10021 3.00001 0.20007 0.49992 1.00608 0.00000 2.99998 0.20014 0.00000 0.99911 0.10074 0.50434 0.00000 0.19961 0.00000 1.00005 3.00012 0.50040 0.10047 1.00053 0.10021 3.00001 0.00000

0.1001 0.1008 0.1017 0.2000 0.4998 0.5000 0.5000 0.5005 0.5006 0.5039 0.9996 1.0000 1.0000 1.0003 1.0005 1.0006 1.2355 3.0001 3.0097 3.0093 3.0098 3.0101 0.0998 0.1000 0.1000 0.1008 0.1017 0.2000 0.4998 0.5000 0.5000 0.5005 0.5006 0.5039 0.9996 1.0000 1.0000 1.0005 1.0006 1.2355 3.0001 0.0998 0.1000 0.1000 0.1001 0.1008 0.1017 0.2000 0.4998 0.5000 0.5000 0.5005 0.5006 0.5039 0.9996 1.0000 1.0000 1.0003

46.01 12.78 28.25 17.06 48.45 41.09 76.30 139.27 59.02 45.23 111.84 82.64 170.62 79.30 85.97 95.89 128.05 210.76 214.28 236.70 216.89 224.84 110.70 16.05 8.37 12.50 27.59 16.54 47.23 40.16 74.77 136.75 57.77 44.11 109.57 80.78 167.73 84.11 93.90 125.66 207.02 125.71 19.35 10.45 52.65 15.20 32.40 20.17 55.97 48.08 86.85 154.89 67.92 52.56 126.77 95.00 189.78 91.46

298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15

NaCl (1) + MgCl2(2) 76.81 423.15 169.29 423.15 73.57 423.15 80.68 423.15 90.93 423.15 122.97 423.15 197.33 423.15 225.97 423.15 200.97 423.15 203.91 423.15 212.07 423.15 114.31 423.15 15.77 423.15 7.73 423.15 46.17 423.15 27.71 423.15 45.18 423.15 37.67 423.15 73.75 423.15 139.59 423.15 56.20 423.15 41.71 423.16 106.91 423.15 76.51 423.15 168.75 423.15 73.26 423.15 80.37 423.15 90.57 423.15 122.56 423.15 196.71 423.15 225.36 423.15 200.41 423.15 203.30 423.15 211.51 423.15 113.60 423.15 15.62 423.15 7.68 423.15 45.85 423.15 27.51 423.15 44.83 423.15 37.37 423.15 73.25 473.15 138.65 473.15 55.80 473.15 41.41 473.15 106.21 473.15 76.01 473.15 167.72 473.15 72.84 473.15 79.82 473.15 89.97 473.15 121.76 473.15 195.55 473.15 224.03 473.15 199.14 473.15 202.02 473.15 210.18 473.15 112.18 473.15

J



Article


p

m1

m2

103·Δρ

T

p

m1

m2

103·Δρ

K

MPa

mol·kg−1

mol·kg−1

g·cm−3

K

MPa

mol·kg−1

mol·kg−1

g·cm−3

40 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40 70 70 70 70 70 70 70 70 70 70 70 70 70 70 70 70 70 70 70 70 70 70 70 5 5 5 5 5 5 5 5 5 5 5 5 5

0.20014 0.00000 0.99911 0.50434 0.19961 0.00000 1.00005 3.00012 0.50040 0.10047 1.00053 0.10021 3.00001 0.00000 0.20007 0.49992 1.00608 0.00000 1.00125 0.10007 0.20190 0.49980 0.19961 2.99998 0.20014 0.00000 0.99911 0.50434 0.00000 1.00005 3.00012 0.50040 0.10047 1.00053 0.10021 3.00001 0.00000 0.20007 0.49992 1.00608 0.00000 1.00125 0.10007 0.20190 0.49980 0.50434 0.00000 2.99998 0.00000 0.99911 0.10074 0.19961 0.00000 3.00012 0.50040 0.10047 3.00001 0.00000

0.1000 0.1000 0.1001 0.1017 0.4998 0.5000 0.5000 0.5005 0.5006 0.5039 0.9996 1.0000 1.0000 1.0003 1.0005 1.0006 1.2355 3.0001 3.0093 3.0097 3.0098 3.0101 0.4998 0.0998 0.1000 0.1000 0.1001 0.1017 0.5000 0.5000 0.5005 0.5006 0.5039 0.9996 1.0000 1.0000 1.0003 1.0005 1.0006 1.2355 3.0001 3.0093 3.0097 3.0098 3.0101 0.1017 3.0001 0.0998 0.1000 0.1001 0.1008 0.4998 0.5000 0.5005 0.5006 0.5039 1.0000 1.0003

5 5 5 5 5 5 5 5 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20

0.20007 0.49992 1.00608 0.00000 1.00125 0.10007 0.20190 0.49980 2.99998 0.20014 0.00000 0.99911 0.10074 0.50434 0.00000 0.19961 0.00000 1.00005 3.00012 0.50040 0.10047 1.00053 0.10021 3.00001 0.00000 0.20007 0.49992 1.00608 0.00000 1.00125 0.10007 0.20190 0.49980 2.99998 0.20014 0.00000 0.99911 0.10074 0.50434 0.00000 0.19961 0.00000 1.00005 3.00012 0.50040 0.10047 1.00053 0.10021 3.00001 0.00000 0.20007 0.49992 1.00608 0.00000 1.00125 0.10007 0.20190 0.49980

1.0005 1.0006 1.2355 3.0001 3.0093 3.0097 3.0098 3.0101 0.0998 0.1000 0.1000 0.1001 0.1008 0.1017 0.2000 0.4998 0.5000 0.5000 0.5005 0.5006 0.5039 0.9996 1.0000 1.0000 1.0003 1.0005 1.0006 1.2355 3.0001 3.0093 3.0097 3.0098 3.0101 0.0998 0.1000 0.1000 0.1001 0.1008 0.1017 0.2000 0.4998 0.5000 0.5000 0.5005 0.5006 0.5039 0.9996 1.0000 1.0000 1.0003 1.0005 1.0006 1.2355 3.0001 3.0093 3.0097 3.0098 3.0101

98.81 109.47 144.87 236.99 263.64 241.24 243.69 251.66 124.69 19.13 10.70 52.47 14.99 32.41 20.00 55.49 47.96 86.05 153.71 67.33 52.08 125.80 94.24 188.42 90.56 98.00 108.57 143.74 235.13 261.82 239.38 241.77 249.74 122.99 18.73 10.13 51.29 14.72 31.48 19.59 54.48 46.81 84.73 151.66 66.25 51.07 123.96 92.78 185.98 89.15 96.49 106.91 141.74 227.42 258.69 236.54 238.89 246.75

298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.14 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 373.15 373.15 373.15 373.15 373.15 373.15 373.15 373.15 373.15 373.15 373.15 373.15 373.15

NaCl (1) + MgCl2(2) 15.46 473.15 7.62 473.15 45.23 473.15 27.19 473.15 44.25 473.15 36.94 473.15 72.31 473.15 137.00 473.15 55.07 473.15 40.89 473.15 104.79 473.15 75.01 473.15 165.81 473.15 71.84 473.15 78.78 473.15 88.81 473.15 120.23 473.15 193.31 473.15 221.63 473.15 196.93 473.15 199.79 473.15 207.84 473.15 43.30 473.15 110.23 473.15 15.02 473.15 7.33 473.15 44.19 473.15 26.50 473.15 36.15 473.15 70.91 473.15 134.65 473.15 53.97 473.15 40.05 473.15 103.04 473.15 73.57 473.15 163.10 473.15 70.40 473.15 77.23 473.15 87.12 473.15 118.13 473.15 190.29 473.15 218.30 473.15 193.93 473.15 196.69 473.15 204.77 473.15 27.49 473.15 203.28 473.15 111.23 473.15 8.18 473.15 44.97 473.15 12.07 473.15 46.39 473.15 39.25 473.15 137.16 473.15 56.94 473.15 43.13 473.15 167.62 473.15 76.07 473.15

K



Article


p

m1

m2

103·Δρ

T

p

m1

m2

103·Δρ

K

MPa

mol·kg−1

mol·kg−1

g·cm−3

K

MPa

mol·kg−1

mol·kg−1

g·cm−3

5 5 5 5 5 5 5 5 5 5 5 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20

0.20007 0.49992 1.00125 0.10007 0.20190 0.49980 1.00005 0.10021 1.00053 1.00608 0.20014 0.10021 1.00005 0.99911 0.10074 0.19961 3.00012 0.10047 3.00001 0.00000 1.00125 0.10007 0.20190 0.49980 2.99998 1.00608 1.00053 0.20007 0.00000 0.49992 0.50434 0.00000 0.50040 0.20014 0.00000 0.19961 0.10047 0.00000 0.50040 0.20014 3.00001 0.20007 1.00053 1.00005 2.99998 0.99911 0.10074 3.00012 0.00000 1.00608 1.00125 0.10007 0.20190 0.49980 0.00000 0.10021 0.49992 0.50434

1.0005 1.0006 3.0093 3.0097 3.0098 3.0101 0.5000 1.0000 0.9996 1.2355 0.1000 1.0000 0.5000 0.1001 0.1008 0.4998 0.5005 0.5039 1.0000 1.0003 3.0093 3.0097 3.0098 3.0101 0.0998 1.2355 0.9996 1.0005 0.5000 1.0006 0.1017 3.0001 0.5006 0.1000 0.1000 0.4998 0.5039 0.5000 0.5006 0.1000 1.0000 1.0005 0.9996 0.5000 0.0998 0.1001 0.1008 0.5005 1.0003 1.2355 3.0093 3.0097 3.0098 3.0101 0.1000 1.0000 1.0006 0.1017

40 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40 70 70 70 70 70 70 70 70 70 70 70 70 70 70 70 70 70 70 70 70 70 70 70 70 70 5 5 5 5 5 5 5 5

2.99998 0.20014 0.00000 0.99911 0.10074 0.50434 0.00000 0.19961 0.00000 1.00005 3.00012 0.50040 0.10047 1.00053 0.10021 3.00001 0.00000 0.20007 0.49992 1.00608 0.00000 1.00125 0.10007 0.20190 0.49980 2.99998 0.20014 0.00000 0.99911 0.10074 0.50434 0.00000 0.19961 0.00000 1.00005 3.00012 0.50040 0.10047 1.00053 0.10021 3.00001 0.00000 0.20007 0.49992 1.00608 0.00000 1.00125 0.10007 0.20190 0.49980 1.00005 0.50040 2.99998 0.20014 0.10074 0.49992 0.49980 0.00000

0.0998 0.1000 0.1000 0.1001 0.1008 0.1017 0.2000 0.4998 0.5000 0.5000 0.5005 0.5006 0.5039 0.9996 1.0000 1.0000 1.0003 1.0005 1.0006 1.2355 3.0001 3.0093 3.0097 3.0098 3.0101 0.0998 0.1000 0.1000 0.1001 0.1008 0.1017 0.2000 0.4998 0.5000 0.5000 0.5005 0.5006 0.5039 0.9996 1.0000 1.0000 1.0003 1.0005 1.0006 1.2355 3.0001 3.0093 3.0097 3.0098 3.0101 0.5000 0.5006 0.0998 0.1000 0.1008 1.0006 3.0101 0.1000

120.06 18.13 9.72 49.90 14.22 30.56 18.94 52.97 45.43 82.54 148.29 64.35 49.70 120.83 90.29 182.02 86.69 93.91 104.18 138.28 227.17 253.50 231.37 233.76 241.56 117.03 17.46 9.31 48.32 13.67 29.50 18.23 51.29 43.89 80.15 144.55 62.45 48.07 117.61 87.63 177.77 84.17 91.21 101.21 134.66 221.66 247.22 225.76 228.16 235.83 100.97 79.81 143.08 23.46 18.65 126.46 281.87 13.16

373.15 373.15 373.15 373.15 373.15 373.15 373.15 373.15 373.15 373.15 373.15 373.15 373.15 373.15 373.15 373.15 373.15 373.15 373.15 373.15 373.15 373.15 373.15 373.15 373.15 373.15 373.15 373.15 373.16 373.16 373.16 373.16 373.16 373.16 373.16 373.14 373.14 373.14 373.14 373.14 373.15 373.15 373.15 373.15 373.15 373.15 373.15 373.15 373.15 373.15 373.15 373.15 373.15 373.15 373.15 373.15 373.15 373.16

NaCl (1) + MgCl2(2) 82.80 473.15 92.59 473.15 229.70 473.15 206.92 473.15 209.61 473.15 217.60 473.15 73.84 473.15 79.15 473.15 108.20 473.15 124.38 473.15 15.88 473.15 78.83 473.15 73.56 473.15 44.82 473.15 12.07 473.15 46.21 473.15 136.77 473.15 42.96 473.15 167.11 473.15 75.73 473.15 229.16 473.15 206.32 473.15 208.97 473.15 217.01 473.15 110.89 473.15 123.95 473.15 107.81 473.15 82.55 473.15 38.98 473.15 92.26 473.15 27.31 473.15 202.75 473.15 56.76 473.15 15.81 473.15 8.05 473.15 45.84 473.15 42.65 473.15 38.76 473.15 56.33 473.15 15.65 473.15 166.20 473.15 82.00 473.15 107.11 473.15 73.09 473.15 110.23 473.15 44.47 473.15 11.92 473.15 135.92 473.15 75.18 473.15 123.18 473.15 227.85 523.14 205.12 523.14 207.76 523.15 215.70 523.15 8.06 523.15 78.33 523.15 91.65 523.15 27.22 523.15

L



Article


p

m1

m2

103·Δρ

T

p

m1

m2

103·Δρ

K

MPa

mol·kg−1

mol·kg−1

g·cm−3

K

MPa

mol·kg−1

mol·kg−1

g·cm−3

20 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40 70 70 70 70 70 70 70 70 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5

0.00000 1.00608 3.00001 0.10021 1.00053 0.20014 0.99911 0.10074 0.19961 0.00000 3.00012 0.00000 0.20007 0.49992 1.00125 0.10007 0.20190 0.49980 0.50434 2.99998 0.00000 1.00005 0.10047 0.50040 0.00000 0.99911 0.10074 3.00012 0.00000 1.00125 0.10007 0.20190 0.49980 0.49980 1.00125 2.99998 0.20014 0.00000 0.10074 0.50434 0.00000 0.19961 0.00000 1.00005 3.00012 0.50040 0.10047 1.00053 0.10021 3.00001 0.00000 0.20007 0.49992 1.00608 0.00000 0.10007 0.99911 0.20190

3.0001 1.2355 1.0000 1.0000 0.9996 0.1000 0.1001 0.1008 0.4998 0.5000 0.5005 1.0003 1.0005 1.0006 3.0093 3.0097 3.0098 3.0101 0.1017 0.0998 0.1000 0.5000 0.5039 0.5006 3.0001 0.1001 0.1008 0.5005 1.0003 3.0093 3.0097 3.0098 3.0101 3.0101 3.0093 0.0998 0.1000 0.1000 0.1008 0.1017 0.2000 0.4998 0.5000 0.5000 0.5005 0.5006 0.5039 0.9996 1.0000 1.0000 1.0003 1.0005 1.0006 1.2355 3.0001 3.0097 0.1001 3.0098

5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20

0.50434 0.00000 0.19961 0.00000 3.00012 1.00053 0.10021 0.00000 0.20007 1.00608 0.10006 0.10047 0.99911 0.00000 0.20190 1.00125 3.00001 0.10006 0.20190 2.99998 0.20014 0.10074 1.00005 3.00012 0.50040 3.00001 0.00000 1.00125 0.00000 1.00053 0.99911 0.50434 0.00000 0.49980 0.19961 0.00000 0.10021 0.20007 0.00000 0.10047 0.49992 1.00608 0.20190 0.20014 0.10074 0.00000 3.00012 0.10006 0.49980 0.10047 1.00608 1.00125 2.99998 0.00000 1.00005 1.00053 0.10021 3.00001

0.1017 0.2000 0.4998 0.5000 0.5005 0.9996 1.0000 1.0003 1.0005 1.2355 3.0097 0.5039 0.1001 3.0001 3.0098 3.0093 1.0000 3.0097 3.0098 0.0998 0.1000 0.1008 0.5000 0.5005 0.5006 1.0000 3.0001 3.0093 0.5000 0.9996 0.1001 0.1017 1.0003 3.0101 0.4998 0.2000 1.0000 1.0005 0.1000 0.5039 1.0006 1.2355 3.0098 0.1000 0.1008 0.5000 0.5005 3.0097 3.0101 0.5039 1.2355 3.0093 0.0998 0.1000 0.5000 0.9996 1.0000 1.0000

39.15 24.53 66.34 57.59 175.10 145.42 110.48 106.88 114.61 165.52 271.33 62.18 62.52 266.96 273.82 294.81 212.72 267.88 270.34 140.91 23.00 18.30 99.32 172.55 78.41 209.76 263.54 291.20 56.53 143.16 61.35 38.27 105.09 278.40 65.15 24.00 108.64 112.72 12.87 61.08 124.49 163.05 264.30 22.15 17.63 54.72 168.14 261.91 272.26 59.13 158.78 284.96 137.14 12.36 96.42 139.29 105.48 204.78

373.16 373.15 373.15 373.15 373.15 373.15 373.15 373.15 373.15 373.15 373.15 373.15 373.15 373.15 373.15 373.15 373.15 373.15 373.15 373.15 373.15 373.15 373.15 373.15 373.16 373.15 373.15 373.15 373.15 373.15 373.15 373.15 373.15 423.13 423.14 423.15 423.15 423.15 423.15 423.15 423.15 423.15 423.15 423.15 423.15 423.15 423.15 423.15 423.15 423.15 423.15 423.15 423.15 423.15 423.15 423.15 423.15 423.20

NaCl (1) + MgCl2(2) 201.54 523.15 121.74 523.15 164.47 523.15 77.29 523.15 105.83 523.15 15.43 523.15 44.00 523.15 11.86 523.15 45.26 523.15 38.23 523.15 134.50 523.15 74.24 523.15 80.97 523.15 90.51 523.15 225.42 523.15 202.90 523.16 205.50 523.16 213.48 523.14 26.84 523.15 109.02 523.15 7.92 523.15 72.19 523.15 42.08 523.15 55.64 523.15 199.32 523.15 43.36 523.15 11.66 523.15 132.64 523.15 73.00 523.15 222.38 523.15 199.88 523.15 202.52 523.15 210.55 523.15 230.58 523.15 242.65 523.16 115.94 523.16 17.09 523.16 9.02 523.16 13.25 523.16 29.11 523.16 17.73 523.16 50.11 523.16 42.60 523.15 78.75 523.15 143.09 523.15 60.98 523.15 46.74 523.15 115.21 523.15 85.30 523.15 175.22 523.15 81.95 523.15 88.68 523.15 98.90 523.15 131.93 523.15 216.58 523.15 219.99 523.15 47.56 523.15 222.67 523.16

M



Article


p

m1

m2

103·Δρ

T

p

m1

m2

103·Δρ

K

MPa

mol·kg−1

mol·kg−1

g·cm−3

K

MPa

mol·kg−1

mol·kg−1

g·cm−3

10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 20 20 20 20 20 20 20 20 20

2.99998 0.20014 0.00000 0.99911 0.50434 0.00000 0.19961 0.00000 1.00005 3.00012 0.50040 0.10047 1.00053 0.10021 3.00001 0.00000 0.20007 0.49992 1.00608 0.00000 1.00125 0.10007 0.49980 0.10074 0.20190 1.00125 2.99998 0.20014 0.00000 0.99911 0.10074 0.50434 0.00000 0.19961

0.0998 0.1000 0.1000 0.1001 0.1017 0.2000 0.4998 0.5000 0.5000 0.5005 0.5006 0.5039 0.9996 1.0000 1.0000 1.0003 1.0005 1.0006 1.2355 3.0001 3.0093 3.0097 3.0101 0.1008 3.0098 3.0093 0.0998 0.1000 0.1000 0.1001 0.1008 0.1017 0.2000 0.4998

20 20 20 20 20 20 20 20 20 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40

0.00000 0.20007 0.00000 0.50040 0.49992 0.00000 0.19961 0.50434 0.99911 0.20014 3.00012 0.00000 0.10006 0.00000 1.00125 0.10074 0.99911 0.49980 0.20190 3.00001 2.99998 1.00005 0.50434 1.00608 1.00053 0.50040 0.49992 0.20007 0.19961 0.10047 0.00000 0.10021 0.00000 0.00000

1.0003 1.0005 0.2000 0.5006 1.0006 3.0001 0.4998 0.1017 0.1001 0.1000 0.5005 3.0001 3.0097 0.5000 3.0093 0.1008 0.1001 3.0101 3.0098 1.0000 0.0998 0.5000 0.1017 1.2355 0.9996 0.5006 1.0006 1.0005 0.4998 0.5039 0.1000 1.0000 1.0003 0.2000

102.05 109.50 23.14 76.05 121.00 257.62 63.12 37.03 59.38 20.82 161.42 248.39 252.62 51.87 275.35 16.57 56.36 262.82 255.03 197.07 131.39 91.99 35.00 152.25 133.36 72.44 115.70 104.53 60.03 56.20 11.62 100.71 97.41 21.82

423.15 423.15 423.15 423.15 423.15 423.15 423.15 423.15 423.15 423.15 423.15 423.15 423.15 423.15 423.15 423.15 423.15 423.15 423.15 423.15 423.15 423.15 423.15 423.15 423.17 423.14 423.15 423.15 423.15 423.15 423.15 423.15 423.15 423.15

NaCl (1) + MgCl2(2) 115.43 523.16 16.90 523.16 8.93 523.16 47.33 523.16 28.96 523.16 17.58 523.16 49.76 523.16 42.25 523.16 78.35 523.16 142.49 523.15 60.68 523.15 46.49 523.15 114.65 523.15 84.90 523.15 174.45 523.15 81.55 523.15 88.32 523.15 98.49 523.15 131.27 523.15 215.66 523.16 241.77 523.16 219.09 523.16 229.75 523.16 13.19 523.16 221.79 523.16 239.87 523.16 114.34 523.16 16.69 523.16 8.77 523.16 46.83 523.16 13.00 523.16 28.66 523.16 17.33 523.16 49.26 523.17

mi is the molality of solute i; Δρ represents the measured difference in density of a solution with respect to water. Standard uncertainties u are u(T) = 0.01 K, u(p) = 0.0005·p, u(m2) = 0.0065·m2 for CaCl2, u(m2) = 0.0017·m2 for MgCl2, and the uncertainty on the concentration of NaCl depends on the uncertainty on the concentration of second electrolyte as u(m1) = 0.1·u(m2). The combined uncertainty U(Δρ) = (6.7·10−5, 3·10−5, 5.1·10−5, 9.9·10−5, and 6.2·10−5) g·cm−3 at T = (298.15, 373.15, 423.15, 473.15 and 523.15) K, respectively. The combined uncertainty is based on the standard deviation of the mean density difference of solutions evaluated from the repeated measurements of the solution at every temperature. a

The Pitzer theory suggests22 a temperature and pressure dependence of the mixing terms, and introduces the ionic v strength dependence of parameter θc,c′ for asymmetrical 2+ mixtures such as the mixtures with Ca −Na+ and Mg2+−Na+ ionic combinations of this study. Although various studies have attempted to evaluate the mixing terms θvc,c′ and ψvc,c′,a for the aqueous mixtures of electrolytes at T = 298.15 K,21,23,24 they did not find any significant improvement with the introduction of mixing terms and suggested the use of the Pitzer formulation for mixed electrolytes without these mixing parameters. Nevertheless, we performed the optimization of parameters using experimental data from this study and the literature.3−11 It was found that the introduction of mixing terms θvc,c′ and ψvc,c′,a improved the fit and the performance of eq 2. The temperature, pressure, and ionic strength dependencies were imposed on both parameters as follows: θcv, c ′ = a1 + T (a 2 + a3p + a4p2 + a5I −1)

ψcv, c ′ , a = a1 + T (a 2 + a3p + a4p2 + a5I −2)

(4)

where T is a temperature in K, p is a pressure in MPa, I is the ionic strength of an aqueous solution in mol·kg−1, ai are the parameters for calculation of mixing terms and consequent evaluation of the mean apparent molar volume of CaCl2−NaCl and MgCl2−NaCl aqueous mixtures at temperatures from (298.15 to 523.15) K and pressures from (0.1 to 70) MPa (eq 2) listed in Table 3. In total, 1061 measurements (673 from this study and 388 from the literature) were used for fitting of parameters for the CaCl2−NaCl−H2O system, and 834 measurements (463 from this study and 371 from the literature) were used for the MgCl2−NaCl−H2O system. For the latter system, a lower weight was assigned for the data sets of Qiblawey and Abu-Jdayil9 and Connaughton and Millero;11 the high-temperature data set of Melikov et al.12 was excluded from the fit. The root-mean-square deviations of the modeled values of Vϕmean from those determined from our experiments are 0.66 and 0.83 cm3·mol−1 for the

(3) N



Article

Table 3. Parameters for Mixing Terms of eq 2, θvc,c′ = a1 + v T(a2 + a3 p + a4 p2 + a5 I−1), and ψc,c′,a = a1 + T(a2 + a3 p + a4 2 −2 p + a5 I ), Obtained by Fitting of Experimental Data from This Study and Literature (T in K, p in MPa, I in mol·kg−1) CaCl2−NaCl−H2O a1·10 a2·106 a3·108 a4·1010 a5·105 3

MgCl2−NaCl−H2O

θvNa,Ca

ψvNa,Ca,Cl

θvNa,Mg

ψvNa,Mg,Cl

−0.358 12 2.8053 −1.2888 −0.761 60 −0.249 05

0.110 92 −0.670 00 0.411 26 0.152 07 0.264 12

−1.820 21 8.251 48 −4.081 71 3.307 44 −2.117 14

0.408 97 −1.904 95 1.250 87 −0.684 87 4.911 40

The volumetric properties of pure end-member binary salt solutions could be calculated using the available correlations based on the Pitzer framework.19,25 These correlations, however, lack internal consistency because different equations of state for water were used in the parametrization (i.e., Hill’s equation18 vs IAPWS-9526). In order to correct for this inconsistency, we reparameterized the equation for the volumetric properties of NaCl, CaCl2 and MgCl2 by adopting the widely used version of the Pitzer equation and the approach employed by Archer.20 All parameters were derived using the IAPWS-95 equation of state for the thermodynamic properties of water26 and the international formulation for the dielectric properties of water.27 The equations are summarized in the Supporting Information S2, supplemented by the regressed parameters (Table 2S). The volumetric virial parameters are set to follow a temperature and pressure

Figure 1. Pressure-dependence of Vϕmean for CaCl2−NaCl−H2O (a) and MgCl2−NaCl−H2O (b) systems for solutions containing 1 mol·kg−1 of NaCl mixed with 1 mol·kg−1 of CaCl2 or MgCl2. Symbols represent experimental measurements at temperatures ○, 298.15 K; △, 423.15 K; □, 473.15 K; and ◇, 523.15 K. Curves represent the approximation by a Pitzer equation (see text for details).

CaCl2−NaCl−H2O and MgCl2−NaCl−H2O systems, respectively. The model errors evaluated for individual data sets are listed in Table 4.

Figure 2. Apparent molar volume Vϕi of CaCl2 (a, b, c) and MgCl2 (d, e, f) in binary aqueous solutions as a function of electrolyte concentration. The experimental data (symbols) are compared with the models of Oakes et al. (CaCl2, dotted lines in panels a, b, c), Wang et al. (MgCl2, dotted lines in panels d, e, f), Mao and Duan (dotted-dashed lines), Rowland and May (dashed lines) and this study (solid lines) at various temperatures and pressures: (a,d) at 298.15 K, 0.1 MPa (upper curves, diamonds) and 70 MPa (lower curves, circles); (b, e) at 423.15 K, 5 MPa (upper curves, diamonds) and 70 MPa (lower curves, circles); (c, f) - 523.15 K, 5 MPa (upper curves, diamonds) and 40 MPa (lower curves, circles). O



Article

Figure 3. Mean apparent molar volume of CaCl2−NaCl (a, b, c) and MgCl2−NaCl (d, e, f) aqueous solute mixtures as a function of CaCl2 or MgCl2 concentration in a solution. Experimental data (symbols) are compared to the results of modeling using a Pitzer-type equation, eq 2, (full lines), and Young’s mixing rule, eq 5, (dashed lines) at temperatures of 373.15 K (a, d), 473.15 K (b, e), and 523.15 K (c, f) and p = 10 MPa. Symbols represent experimental measurements at ◇, 3 mol·kg−1 NaCl; □, 1 mol·kg−1 NaCl; △, 0.1 mol·kg−1 NaCl; ○, pure CaCl2 or MgCl2 binary solutions.

dependence of the form used by Archer20 for the NaCl−H2O system and Rowland and May25 for the MgCl2−H2O and CaCl2− H2O systems (eqs 6S and 7S in the Supporting Information, respectively). Furthermore, the second virial coefficient Bvc,a has an ionic strength dependence, whereas the third virial coefficient Cvc,a is set to be independent of ionic strength. The new parameters for the NaCl−H2O system were fitted to a synthetic data set representing Archer’s correlation for density of NaCl solution.19 Fitting of the parameters of the Pitzer equation for the CaCl2− H2O and MgCl2−H2O systems was done using the new experimental data from this study and available literature data.6,17,28−45 The Pitzer equation with our new set of parameters has better performance compared to those of Rowland and May,25 Mao and Duan,46 Oakes et al.,16 and Wang et al.47 (Figure 2). For the CaCl2−H2O system, our model performs significantly better than models of Oakes et al.16 and Mao and Duan,46 particularly at high pressures because the latter model is only valid to 60 MPa. However, the fit of Rowland and May25 was only slightly improved in the region of low concentrations of the electrolyte (Figure 2 panels a,b,c). For the MgCl2−H2O system, the equation of Wang et al.47 shows unphysical behavior, and that of Mao and Duan46 has more restricted pressure and molality limits of applicability (30 MPa and 3 mol·kg−1); the improvements over the model of Rowland and May25 are comparable to that for CaCl2−H2O binary system (Figure 2 panels d,e,f). Another approach for calculation of the mean apparent molar volume of solutes in a mixture of electrolytes is a simple Young’s mixing model.15 Using the properties of pure binary

electrolyte solutions, the mean apparent molar volume of the mixture of electrolytes can be calculated as follows: ϕ V mean =

∑ j

mjV jϕ ∑j mj

(5)

where mj is the molality of component j in a mixture, and Vϕj is the apparent molar volume of pure end-member aqueous electrolyte solution (CaCl2−H2O, MgCl2−H2O, or NaCl− H2O) at the same total molality as that of a mixture. We have found that this rule performs remarkably well for the systems of interest provided that internally consistent equations for the properties of binary end-members are used. The rootmean-square deviation of the mean apparent molar volume of electrolytes calculated using Young’s rule from that obtained from experiments is 0.85 cm3·mol−1 for CaCl2−NaCl−H2O solutions and 0.91 cm3·mol−1 for MgCl2−NaCl−H2O solutions. These values can be compared with 0.66 and 0.83 cm3·mol−1 for the Pitzer model and parameters regressed in this study. Thus, with the new parametrization of the Pitzer equations for binary NaCl−H2O, CaCl2−H2O, and MgCl2−H2O solutions presented in this work based on a consistent equation of state for the solvent (i.e., IAPWS-9526,27), the apparent molar volumes of electrolyte mixtures can be calculated from Young’s rule with an accuracy comparable to the Pitzer formulation for mixed solution with empirical interaction parameters (eq 2), but with no fitted mixing parameters needed. Figure 3 panels a−c present the experimental data and compare them to the results of calculations P



Article

Table 4. A Summary of Experimental Data Used for Fitting of Pitzer Model (eqs 2 to 4) and Corresponding Estimates of the Quality of the Fit ref 3 4 5 6 7 8 this this this this this 10 11 6 9 8 this this this this this

no. of points

study study study study study

110 66 97 72 35 8 114 164 144 139 112

study study study study study

18 23 72 250 8 101 87 95 100 80

Ta

p

RMSD

K

MPa

cm3·mol−1

0.1 0.1 0.1 0.6 0.1 0.1 0.1 to 70 2 to 70 5 to 70 5 to 70 5 to 40

0.42 0.23 0.70 0.66 0.72 0.16 0.45 0.49 0.32 0.84 1.04

0.1 0.1 0.6 0.1 0.1 0.1 to 70 5 to 70 5 to 70 5 to 70 5 to 40

0.31 1.70 0.39 2.48 0.17 0.49 0.44 0.49 0.95 1.44

CaCl2−NaCl−H2O 298, 308 298 298 296 to 372 278, 308 298 298 373 423 473 523 MgCl2−NaCl−H2O 298 288, 328, 368 296 to 372 298 to 318 298 298 373 423 473 523

Figure 4. Excess partial molar volume of solutes in (a) the CaCl2− NaCl−H2O and (b) the MgCl2−NaCl−H2O systems as a function of 0 pressure calculated as Vex i = V̅ i − V i from eqs 6 and 7. The solutes, CaCl2 or MgCl2 (dot-dashed lines) and NaCl (dashed lines), are in an aqueous solution containing 1 and 3 mol·kg−1 (bold and light lines, respectively) of CaCl2 or MgCl2 and 1 mol·kg−1 of NaCl at temperature T = 523.15 K.

a

Listed are the rounded values of T; RMSD is the root-mean-square deviation.

of the mean apparent molar volume of the mixture of solutes obtained from Young’s rule (eq 5) and the Pitzer equation (eq 2). The partial molar volume V̅ i and the limiting partial molar volume V i0 of a component in an aqueous electrolyte mixture were further calculated by consequent differentiation of eq 2:48 ⎛ ∂V ϕ ⎞ ϕ Vi̅ = (mi + mj)⎜⎜ mean ⎟⎟ + V mean ⎝ ∂mi ⎠

(6)

⎛ ∂V ϕ ⎞ + V jϕ V i0 = mj ≠ i⎜⎜ mean ⎟⎟ ⎝ ∂mi ⎠m = 0

(7)

i

1 mol·kg−1 of NaCl at 523.15 K is presented in Figure 4. This dependence, approximated by a polynomial equation and integrated with respect to pressure, provides a ratio of the mean activity coefficient of each electrolyte at different pressures. Thus, in the case of the CaCl2−NaCl−H2O solutions, the activity coefficient of CaCl2, γCaCl2, increases with pressure rising from saturated water vapor pressure to 70 MPa at T = 523 K and mNaCl = 1 mol·kg−1 by 9 and 17% at 1 and 3 mol·kg−1 CaCl2, respectively. The activity coefficient of NaCl in these solutions, γNaCl, changes only by 1−3%. The activity coefficient of MgCl2 in the MgCl2−NaCl−H2O system shows an effect that is opposite to CaCl2, and decreases with increasing pressure by 15 and 16%, whereas γNaCl changes by 3% and 6% at 1 and 3 mol·kg−1 MgCl2 in a solution, respectively. The effect of pressure on the activity coefficients was also previously estimated for seawater and the system Na−Ca−Cl−SO4− H2O.24,49−51 For example, it was calculated24 that the change of activity coefficient depends on the type of solute, and that γi increases by 5% to 30% when pressure increases from 0.1 MPa to 50 MPa. Although this partly compensates the decrease of activity coefficient with increasing temperature, neglecting the effect of pressure can introduce significant errors in calculations of the distribution of species in aqueous solutions and mineral solubility at elevated temperatures and pressures.

Vϕj ,

where the apparent molar volume of the second dissolved component in ternary mixture, was calculated from the Pitzertype correlations for binary mixtures parametrized in this study (Supporting Information S2). The values of V̅ i and V i0 are presented in the Supporting Information S1. The essential benefit of the presented correlations is that we now are able to evaluate quantitatively the effect of pressure on the activity coefficient of electrolyte in multicomponent mixtures over a wide range of temperatures covered by experimental studies, that is, at T = (298.15 to 523.15) K. The excess 0 partial molar volume of a solute in a mixture, Vex i = V̅ i − V i , can be used to evaluate the pressure derivative of the natural logarithm of the activity coefficient as follows: ⎛ ∂ lnγi ⎞ V ex = i ⎜ ⎟ RT ⎝ ∂P ⎠T , m

■

CONCLUSIONS This study provides new experimental data of the volumetric properties of mixed aqueous CaCl2−NaCl and MgCl2−NaCl solutions. The data obtained for wide ranges of temperature, pressure and composition complemented by the literature data

(8)

Vex i

The pressure dependence of calculated from eqs 6 and 7 for solutions containing 1 and 3 mol·kg−1 of CaCl2 or MgCl2 and Q



Article

298.15 and 308.15 K and at 0.1 MPa. J. Chem. Eng. Data 1990, 35, 304−309. (4) Kumar, A.; Atkinson, G.; Howell, R. D. Thermodynamics of Concentrated Electrolyte Mixtures. II. Densities and Compressibilities of Aqueous NaCl−CaCl2 at 25 °C. J. Solution Chem. 1982, 11, 857− 870. (5) Zhang, H.; Chen, G.; Han, S. Viscosity and Density of H2O + NaCl + CaCl2 and H2O + KCl + CaCl2 at 298.15 K. J. Chem. Eng. Data 1997, 42, 526−530. (6) Saluja, P. P. S.; Jobe, D. J.; LeBlanc, J. C.; Lemire, R. J. Apparent Molar Heat Capacities and Volumes of Mixed Electrolytes: [NaCl(aq + CaCl2(aq)], [NaCl(aq) + MgCl2(aq)], and [CaCl2(aq) + MgCl2(aq)]. J. Chem. Eng. Data 1995, 40, 398−406. (7) Kumar, A.; Atkinson, G. Thermodynamics of Concentrated Electrolyte Mixtures. 3. Apparent Molal Volumes, Compressibilities, and Expansibilities of NaCl−CaCl2, Mixtures from 5 to 35 °C. J. Phys. Chem. 1983, 87, 5504−5507. (8) Millero, F. J.; Laferriere, A. L.; Chetirkin, P. V. The Partial Molal Volumes of Electrolytes in 0.725 M Sodium Chloride Solutions at 25.°C. J. Phys. Chem. 1977, 81, 1737−1745. (9) Qiblawey, H.; Abu-Jdayil, B. Viscosity and Density of the Ternary Solution of Magnesium Chloride + Sodium Chloride + Water from (298.15 to 318.15) K. J. Chem. Eng. Data 2010, 55, 3322−3326. (10) Millero, F. J.; Connaughton, L. M.; Vinokurova, F.; Chetirkin, P. V. PVT Properties of Concentrated Aqueous Electrolytes. III. Volume Changes for Mixing the Major Sea Salts at I = 1.0 and 3.0 at 25 °C. J. Solution Chem. 1985, 14, 837−851. (11) Connaughton, L. M.; Millero, F. J. The PVT Properties of Concentrated Aqueous Electrolytes. VIII. The Volume Changes for Mixing the Major Sea Salts at an Ionic Strength of 3.0 from 5 to 95 °C. J. Solution Chem. 1987, 16, 491−502. (12) Melikov, R. A.; Aliev, N. M.; Imanov, S. Y. Experimental Study of Aqueous (NaCl−MgCl2−H2O) Solutions Densities at Pressures up to 40 MPa and Temperatures up to 573.15 K. Izv. Vyss. Uchebn. Zaved., Neft. Gaz 1995, 2, 44−46. (13) Zezin, D.; Driesner, T.; Sanchez-Valle, C. Volumetric Properties of Mixed Electrolyte Aqueous Solutions at Elevated Temperatures and Pressures. The System KCl−NaCl−H2O to 523.15 K, 40 MPa, and Ionic Strength from (0.1 to 5.8) mol·kg−1. J. Chem. Eng. Data 2014, 59, 736−749. (14) Pitzer, K. Thermodynamics of Electrolytes. I. Theoretical Basis and General Equations. J. Phys. Chem. 1973, 77, 268−277. (15) Young, T. F.; Smith, M. B. Thermodynamic Properties of Mixtures of Electrolytes in Aqueous Solutions. J. Phys. Chem. 1954, 58, 716−724. (16) Oakes, C. S.; Simonson, J. M.; Bodnar, R. J. Apparent Molar Volumes of Aqueous Calcium Chloride to 250 °C, 400 bar, and from Molalities of 0.242 to 6.150. J. Solution Chem. 1995, 24, 897−916. (17) Obšil, M.; Majer, V.; Hefter, G.; Hynek, V. Volumes of MgCl2(aq) at Temperatures from 298 to 623 K and Pressures up to 30 MPa. J. Chem. Thermodyn. 1997, 29, 575−593. (18) Hill, P. G. A Unified Fundamental Equation for the Thermodynamic Properties of H2O. J. Phys. Chem. Ref. Data 1990, 19, 1233−1274. (19) Archer, D. G. Thermodynamic Properties of the NaCl + H2O System II. Thermodynamic Properties of NaCl(aq), NaCl·2H2O(cr), and Phase Equilibria. J. Phys. Chem. Ref. Data 1992, 21, 793−829. (20) Archer, D. G.; Carter, R. W. Thermodynamic Properties of the NaCl + H2O System. 4. Heat Capacities of H2O and NaCl(aq) in Cold-Stable and Supercooled States. J. Phys. Chem. B 2000, 104, 8563−8584. (21) Krumgalz, B. S.; Pogorelsky, R.; Pitzer, K. S. Ion Interaction Approach to Calculations of Volumetric Properties of Aqueous Multiple-Solute Electrolyte Solutions. J. Solution Chem. 1995, 24, 1025−1038. (22) Pitzer, K. S. Ion Interaction Approach: Theory and Data Correlation. In Activity Coefficients in Electrolyte Solutions; Pitzer, K. S., Ed.; CRC Press: Boca Raton, 1991; pp 279−434.

were used for parametrization of a Pitzer mixing model that describes the volumetric properties of multicomponent solutions over the entire T−p composition domain used in experiments. The parameters for the Pitzer equation for the binary systems CaCl2−H2O, MgCl2−H2O, and NaCl−H2O were also refined using the IAPWS-95 equation of state for water and density data from this study and the literature. Therefore, the new parameter set of the Pitzer model is internally consistent, thus eliminating the errors related to the involvement of various equations for water and models for Debye−Hückel coefficients. With modified parameters for the binary systems, the mean apparent molar volume of CaCl2− NaCl−H2O and MgCl2−NaCl−H2O mixtures, and the density of these electrolyte solutions can be calculated using Young’s rule with an accuracy comparable to the Pitzer equation at temperatures up to 523.15 K and pressures up to 70 MPa. Furthermore, the new experimental data on the properties of complex aqueous solutions from this study supplemented by a mixing model permit evaluation of the partial molar volumes of components in solutions containing multiple dissolved chlorides. This accounts for the effect of pressure on the activity coefficients of dissolved solutes and, consequently, on equilibrium calculations in geological processes and settings involving aqueous fluid systems at elevated temperatures and pressures, such as fluid reservoirs, hydrothermal fluid flow, and formation of ore deposits, sedimentary basins, and geothermal systems.

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ASSOCIATED CONTENT

S Supporting Information *

S1 (Table 1S). A table listing the mean apparent molar volume of aqueous CaCl2−NaCl and MgCl2−NaCl mixtures, partial molar volumes of components and limiting partial molar volumes of solutes in ionic media calculated from the obtained experimental data. S2. A summary of the formulations of Pitzer equations for binary NaCl−H2O, CaCl2−H2O and MgCl2− H2O systems from the works of Archer20 and Rowland and May25 supplemented by the new parameters regressed to data from this study and the literature tabulated in Table 2S. This material is available free of charge via the Internet at http:// pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*Tel.: +41 44 632 80 73. E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The authors sincerely thank Dr. Hans Stabinger for providing the densimeter and encouragement for the project.

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REFERENCES

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S


Volumetric Properties of Mixed Electrolyte Aqueous Solutions at

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