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 System KCl−NaCl−H2O to 523.15 K, 40 MPa, and Ionic Strength from (0.1 to 5.8) mol·kg−1 Denis Zezin,* Thomas Driesner, and Carmen Sanchez-Valle Institute of Geochemistry and Petrology, ETH Zurich, Clausiusstrasse 25, 8092 Zurich, Switzerland S Supporting Information *

ABSTRACT: The densities of KCl−NaCl aqueous mixtures were determined at temperatures from (298.15 to 523.15) K, pressures up to 40 MPa, and over a range of compositions at ionic strengths from (0.1 to 5.8) mol·kg−1. A vibrating-tube densimeter used for the experimental measurements provides the accuracy on density better than 2·10−4 g·cm−3. The mean apparent molar volumes of the mixed electrolytes, Vϕmean, were calculated from the experimental data. At 523.15 K, the change ϕ in Vmean from saturated vapor pressure to 40 MPa is comparable to the change with temperature at 10 MPa from ambient conditions to 523.15 K. A Pitzer-type equation was fit to the data set and used to evaluate the individual partial molar volumes of NaCl and KCl in the solutions. The volume of mixing computed from the equation is always positive and displays a nearly symmetrical increase between the NaCl and KCl end-members. It also increases with increasing salt concentration and pressure, and decreases with increasing temperature. The results of this study permit a quantitative modeling of the properties of complex aqueous solutions and simulation of fluid-rock interaction processes occurring in geothermal and hydrothermal systems.

■

INTRODUCTION Multicomponent aqueous electrolyte mixtures are the most abundant type of fluids in the Earth’s crust.1 Geothermal systems or oilfield brines in sedimentary basins contain aqueous solutions characterized by a wide range of salinity and composition.2,3 Basin fluids may have salinity ranging from near zero to over 400 g·L−1 with a predominance of chlorides of Na, K, Ca, and Mg.4 Aqueous fluids of many hydrothermal environments, depending on physical-chemical conditions and sources, may also be highly concentrated and even saturated with chloride salts.5,6 Concentrated aqueous electrolyte solutions are also essential constituents of many chemical engineering processes, such as desalination, wastewater treatment, extractive distillation, fractional crystallization, scale formation in pipe lines and gas scrubbing.7 Quantitative modeling of geochemical and engineering processes involving multielectrolyte fluids requires knowledge of thermodynamic properties of such solutions which can be obtained through experimentation and measurements of relevant physicochemical properties. To date, such experimental data are mostly available for aqueous single electrolyte solutions only. In particular, the volumetric properties of aqueous chloride solutions of different alkali and alkali earth metals were measured accurately over a wide range of temperatures and pressures.8−14 A number of models for calculation of volumetric properties of single aqueous electrolytes at temperatures to about 573 K were proposed based on the experimental data.13−23 However, the properties of multielectrolyte solutions at elevated temperatures and at © 2014 American Chemical Society

pressures above the vapor pressure saturation curve are very limited. This lack of experimental data for mixed electrolyte aqueous solutions restricts modeling ability, thus predictions of fluid properties at geologically relevant conditions have to rely on semiempirical models for binary solutions.15−17,22,23 Accurate volumetric data would allow an improvement in the parametrization of the pressure dependence in thermodynamic models of aqueous electrolyte solutions containing mixtures of alkali and alkali earth chlorides. This would increase the reliability of quantitative models of the processes occurring in deep sedimentary basins, geothermal and hydrothermal systems, e.g., dissolution and precipitation of minerals, as well as corrosion and scale formation in wells and installations. Therefore, we have started an effort devoted to detailed investigation of the volumetric properties of multicomponent electrolyte solutions over a wide range of temperatures and pressures. In this paper, we report new experimental data on the volumetric properties of the system KCl−NaCl−H2O at temperatures from (298.15 to 523.15) K and pressures up to 40 MPa over a range of compositions at ionic strengths from (0.1 to 5.8) mol·kg−1. The data were obtained using a vibratingtube densimeter. This method for the precise determination of the density of fluids was first introduced by Kratky et al.24 and Received: September 24, 2013 Accepted: February 11, 2014 Published: February 25, 2014 736

dx.doi.org/10.1021/je400761c | J. Chem. Eng. Data 2014, 59, 736−749

Journal of Chemical & Engineering Data

Article

Picker et al.25 and has subsequently been developed further toward application at hydrothermal conditions.26,27 Previous studies of the properties of KCl−NaCl aqueous mixtures were performed by using the sinker method,28 pycnometer29−31 or vibrating-tube densimeters.14,32,33 The density of KCl and NaCl salt mixtures was measured at a pressure of 0.1 MPa at 298.15 K28−33 and from (303.15 to 368.15) K.11 Other recent density data14 collected for mixtures with the only mole fraction of KCl of 0.136 at four different values of ionic strength cover a range of pressures up to 68.5 MPa and temperatures from (283.15 to 473.15) K. From the results of this study performed at a broad range of compositions and ionic strengths at elevated temperature and pressure it is possible to evaluate the mean apparent molar volumes of aqueous electrolyte mixtures, as well as the partial molar volumes of the individual electrolytes. The pressure- and concentration-dependence of the mean apparent molar volume may in turn provide important information about the structure of a solution and ionic interactions occurring in aqueous liquids. Thus the derivatives of molar volume can indicate the strong solute−solvent interaction and solvent structure distortion affected by the type of a solute. The pressure dependence of activity coefficients of dissolved components can also be revealed from the variable pressure series of measurements.

τ2 =

Δρ = ρ − ρ0 = K(τ 2 − τ02)

Table 1. Sample Information Table

sodium chloride1 sodium chloride2 potassium chloride

Fisher Scientific Sigma Aldrich Sigma Aldrich

initial mass fraction purity 99.99 > 99.5 > 99.5

(2)

where τ, ρ, τ0, and ρ0 are the periods of vibration and densities of experimental and reference solution (Milli-Q water); K is the calibration constant determined experimentally at each temperature and pressure using two fluids with known densities. In this study, Milli-Q water and concentrated aqueous solution of NaCl (5.87 mol·kg−1, prepared from NaCl, mass fraction purity 99.99 %, Fisher Scientific) were used as standards for calibration ensuring that the density of experimental solutions is within calibration limits. The density of water and NaCl solution was calculated from the high-accuracy equations of state of Hill35 and Archer,22 respectively. Since Archer’s equation for NaCl is formulated based on Hill’s equation of state for water, the obtained results are internally consistent. The period of vibration of the tube was measured at static conditions with an accuracy of 0.01 μs. Prior to delivery to the densimeter, the solution was purged with helium (helium purity 5.0, PanGas) for 30 min at room temperature and subsequently degassed in-line using an X-Act degassing unit (Jour Research). The tube was first flushed with 40 mL of the sample solution, then the flow was stopped and the system was equilibrated at the temperature of interest. A series of measurements was done at variable pressure at static conditions. Between experiments with different solutions, the system was flushed with water until the period of vibration reached the reference value for pure water. Measurements were taken both on increasing and decreasing pressure paths, and the average value was recorded as a true one. The discrepancy was usually below 0.01 μs. Temperature was measured using a platinum resistance thermometer with accuracy of 0.01 K, pressure was measured using a pressure transmitter (WIKA, model 891.20.501, accuracy 0.05 %) calibrated against a Bourdon-type pressure gauge (Heise). The standard deviation of the density of solutions was evaluated based on the repeated measurements of the solution at all temperatures. These values better represent an experimental error than those calculated using error propagation analysis.

EXPERIMENTAL METHOD Most of the analyzed solutions 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) and crystalline anhydrous salts of NaCl and KCl (Table 1). The concentrated

source

(1)

where mt and Vt are the mass and volume of the tube and C is a constant dependent on the physical properties of the tube. It follows that the density of the solution of interest can be determined from the measured period of vibration of the tube filled with experimental and reference solutions with accurately known density according to the following relation:

■

chemical name

4π 2 (mt + ρVt ) C

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

a

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

solutions with ionic strength over 5 mol·kg−1 were prepared directly from salts and Milli-Q water. The error on the concentration of prepared solution is proportional to the concentration of salts and was estimated to be in the range from 3·10−6 mol·kg−1 for diluted solutions with ionic strength 0.1 mol·kg−1 to 5·10−5 mol·kg−1 for concentrated solutions with ionic strength above 5 mol·kg−1. The density difference Δρ between the KCl−NaCl aqueous solution and pure Milli-Q water was measured using a custommade vibrating-tube densimeter (DMA HP, Dr. Hans Stabinger GmbH) at temperatures of (298.15, 373.15, 423.15, 473.15, 523.15) K, pressure up to 40 MPa, and ionic strength from (0.1 to 5.8) mol·kg−1. The method permits determination of density from the period of oscillation of a U-shaped tube driven and measured using permanent magnets mounted on the tube.24,34 According to the theory of a vibrating tube, the squared period of vibration in the tube, τ2, is related to the density of the solution ρ:

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RESULTS AND DISCUSSION The results of this study are presented in Table 2 as density differences between an experimental solution and pure water which were calculated from the measured period of vibration of the tube using eq 2. The mean apparent molar volume of the electrolyte mixture, Vϕmean, is presented in Table 1S (Supporting Information); it was calculated from the density of the solutions as ϕ = V mean

1000(ρ0 − ρ) ∑j mjρρ0

+

∑j mjMj ∑j mjρ

(3) −1

where mj and Mj are the concentration (in mol·kg ) and molar mass of KCl or NaCl, ρ and ρ0 are the density (in g·cm−3) of solution and pure water, respectively. The uncertainties of the 737



Article

Table 2. Results of Experimental Measurements of Density Difference of Aqueous KCl−NaCl Mixtures Δρ with Respect to Pure Water at Temperature T, Pressure p, and Molalities of Components mia T

p

K

MPa

298.20 298.15 298.16 298.21 298.13 298.14 298.15 298.14 298.18 298.19 298.21 298.17 298.15 298.17 298.16 298.15 298.18 298.19 298.17 298.15 298.24 298.18 298.16 298.20 298.10 298.14 298.15 298.15 298.19 298.20 298.16 298.18 298.15 298.18 298.19 298.16 298.14 298.24 298.18 298.15 298.15 298.20 298.10 298.13 298.15 298.16 298.14 298.18 298.18 298.22 298.15 298.18 298.14 298.15 298.17 298.17 298.16 298.13

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 0.1 0.1 2 2 2 2 2 2 2 2 2 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

mNaCl mol·kg

−1

0.10395 0.10518 0.10676 0.10696 0.10756 0.10807 0.49988 0.99975 0.99991 1.00019 1.00035 1.00090 1.00092 1.00099 1.15326 2.99981 3.53342 3.58016 3.58072 3.58228 3.58557 0.10395 0.10676 0.10696 0.10756 0.10807 0.99975 0.99991 1.00019 1.00035 1.00090 1.00099 1.15326 3.53342 3.58016 3.58072 3.58228 3.58557 0.10395 0.10518 0.10676 0.10696 0.10756 0.10807 0.49988 0.99975 0.99991 1.00019 1.00035 1.00090 1.00092 1.00099 1.15326 2.99981 3.53342 3.58016 3.58072 3.58228

103·Δρ

mKCl mol·kg

−1

2.06402 0.00000 1.02732 0.65057 0.11055 3.58389 0.00000 0.33135 0.65012 1.03055 0.11100 1.03979 0.00000 2.23856 3.57740 0.00000 1.02020 0.10571 2.23660 0.33082 0.64398 2.06402 1.02732 0.65057 0.11055 3.58389 0.33135 0.65012 1.03055 0.11100 1.03979 2.23856 3.57740 1.02020 0.10571 2.23660 0.33082 0.64398 2.06402 0.00000 1.02732 0.65057 0.11055 3.58389 0.00000 0.33135 0.65012 1.03055 0.11100 1.03979 0.00000 2.23856 3.57740 0.00000 1.02020 0.10571 2.23660 0.33082

g·cm

T

−3

K

90.44 4.34 49.33 33.85 9.51 145.26 20.15 53.31 66.54 81.65 44.23 81.88 39.27 125.58 174.63 108.79 161.22 131.26 199.78 139.06 149.90 90.31 49.29 33.89 9.49 145.11 53.27 66.42 81.57 44.18 81.77 125.53 174.45 161.05 131.07 199.57 138.88 149.73 90.22 4.31 49.24 33.89 9.56 144.89 20.06 53.16 66.27 81.41 44.02 81.72 39.09 125.41 174.26 108.44 160.79 130.83 199.30 138.63

298.16 298.14 298.15 298.17 298.12 298.15 298.16 298.17 298.15 298.15 298.24 298.17 298.15 298.14 298.19 298.19 298.12 298.15 298.15 298.16 298.09 298.15 298.12 298.15 298.15 298.12 298.15 298.15 298.17 298.13 298.16 298.24 298.13 298.17 298.17 298.11 298.15 298.15 298.19 298.14 298.12 298.15 298.17 298.14 298.15 298.16 298.15 298.23 298.15 298.10 298.16 298.15 298.11 298.15 298.16 298.15 298.19 298.13

738

p

mNaCl −1

MPa

mol·kg

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 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 40 40 40 40 40 40 40 40 40 40

1.00035 1.00090 1.00092 1.00099 1.15326 2.99981 3.53342 3.58016 3.58072 3.58228 3.58557 0.10395 0.10518 0.10676 0.10696 0.10756 0.10807 0.49988 0.99975 0.99991 1.00019 1.00035 1.00090 1.00092 1.00099 1.15326 2.99981 3.53342 3.58016 3.58072 3.58228 3.58557 0.10676 0.10696 0.10756 0.10807 0.99975 0.99991 1.00019 1.00035 1.00090 1.00099 1.15326 3.53342 3.58016 3.58072 3.58228 3.58557 0.10518 0.10676 0.10696 0.10756 0.10807 0.49988 0.99975 0.99991 1.00019 1.00035

103·Δρ

mKCl −1

g·cm−3

0.11100 1.03979 0.00000 2.23856 3.57740 0.00000 1.02020 0.10571 2.23660 0.33082 0.64398 2.06402 0.00000 1.02732 0.65057 0.11055 3.58389 0.00000 0.33135 0.65012 1.03055 0.11100 1.03979 0.00000 2.23856 3.57740 0.00000 1.02020 0.10571 2.23660 0.33082 0.64398 1.02732 0.65057 0.11055 3.58389 0.33135 0.65012 1.03055 0.11100 1.03979 2.23856 3.57740 1.02020 0.10571 2.23660 0.33082 0.64398 0.00000 1.02732 0.65057 0.11055 3.58389 0.00000 0.33135 0.65012 1.03055 0.11100

43.83 81.36 38.93 125.11 173.81 108.05 160.32 130.45 198.75 138.20 149.08 89.59 4.28 48.82 33.59 9.60 143.92 19.80 52.69 65.77 80.60 43.61 80.83 38.63 124.37 172.97 107.30 159.41 129.63 197.70 137.36 148.21 48.59 33.27 9.43 143.20 52.37 65.36 80.30 43.29 80.36 123.71 172.14 158.48 128.79 196.79 136.54 147.37 4.22 48.28 33.05 9.30 142.62 19.54 52.08 64.99 79.90 43.02

mol·kg



Article

Table 2. continued T

p

mNaCl

mKCl

103·Δρ

T

p

mNaCl

mKCl

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 2 2 2 2 2 2 2 2 2 2 2 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 10 10 10 10 10 10 10

3.58557 0.10395 0.10518 0.10676 0.10696 0.10756 0.10807 0.49988 0.99975 0.99991 1.00019 0.10039 0.10678 0.10696 0.10713 0.10729 0.10731 0.99975 1.00017 1.00034 1.00035 1.00070 1.00495 1.01161 3.53342 3.58129 3.58159 3.58170 3.58228 3.58470 0.09977 0.10039 0.10678 0.10696 0.10713 0.10729 0.10731 0.49956 0.99975 1.00017 1.00034 1.00035 1.00070 1.00092 1.01161 2.99981 3.53342 3.58129 3.58159 3.58170 3.58228 3.58470 0.09977 0.10039 0.10678 0.10696 0.10713 0.10729 0.10731

0.64398 2.06402 0.00000 1.02732 0.65057 0.11055 3.58389 0.00000 0.33135 0.65012 1.03055 3.58061 2.23885 0.65057 0.11257 1.04510 0.65049 0.33135 1.03075 0.11086 0.11100 3.58334 0.00000 2.24089 1.02020 0.64988 0.11084 0.00000 0.33082 2.24416 0.00000 3.58061 2.23885 0.65057 0.11257 1.04510 0.65049 0.00000 0.33135 1.03075 0.11086 0.11100 3.58334 0.00000 2.24089 0.00000 1.02020 0.64988 0.11084 0.00000 0.33082 2.24416 0.00000 3.58061 2.23885 0.65057 0.11257 1.04510 0.65049

149.49 90.04 4.31 49.12 33.84 9.65 144.55 20.00 52.99 66.11 81.12 141.33 95.98 32.94 9.69 49.49 32.99 51.74 79.64 42.61 42.59 167.15 37.96 124.39 156.69 145.92 126.84 122.70 134.85 194.66 3.95 141.15 95.86 32.93 9.67 49.44 32.95 19.20 51.63 79.51 42.53 42.53 166.90 37.62 124.25 104.81 156.45 145.75 126.61 122.47 134.63 194.42 3.90 140.82 95.61 32.77 9.61 49.32 32.83

298.20 298.15 298.13 298.19 298.15 298.13 298.15 298.16 298.15 298.23

40 40 40 40 40 40 40 40 40 40

1.00090 1.00092 1.00099 1.15326 2.99981 3.53342 3.58016 3.58072 3.58228 3.58557

1.03979 0.00000 2.23856 3.57740 0.00000 1.02020 0.10571 2.23660 0.33082 0.64398

79.99 38.11 123.03 171.46 105.93 157.60 128.03 195.84 135.76 146.55

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

20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 40 40 40 40 40 40 40 40

0.09977 0.10039 0.10678 0.10696 0.10713 0.10729 0.10731 0.49956 0.99975 1.00017 1.00034 1.00035 1.00070 1.00092 1.01161 2.99981 3.53342 3.58129 3.58159 3.58170 3.58228 3.58470 0.10039 0.10678 0.10696 0.10713 0.10729 0.10731 0.99975 1.00017 1.00034 1.00035 1.00070 1.01161 3.53342 3.58129 3.58159 3.58170 3.58228 3.58470 0.09977 0.10039 0.10678 0.10696 0.10713 0.10729 0.10731 0.49956

0.00000 3.58061 2.23885 0.65057 0.11257 1.04510 0.65049 0.00000 0.33135 1.03075 0.11086 0.11100 3.58334 0.00000 2.24089 0.00000 1.02020 0.64988 0.11084 0.00000 0.33082 2.24416 3.58061 2.23885 0.65057 0.11257 1.04510 0.65049 0.33135 1.03075 0.11086 0.11100 3.58334 2.24089 1.02020 0.64988 0.11084 0.00000 0.33082 2.24416 0.00000 3.58061 2.23885 0.65057 0.11257 1.04510 0.65049 0.00000

3.89 140.25 95.16 32.61 9.59 49.08 32.68 19.06 51.15 78.85 42.15 42.14 165.81 37.23 123.30 103.78 155.23 144.54 125.56 121.37 133.59 193.03 139.63 94.72 32.41 9.53 48.83 32.52 50.82 78.47 41.86 41.87 165.11 122.74 154.49 143.82 124.87 120.78 132.81 192.17 3.84 139.10 94.33 32.31 9.46 48.63 32.37 18.79

298.24 298.17 298.15 298.15 298.19 298.16 298.12 298.15 298.15 298.16 298.14 373.15 373.15 373.15 373.15 373.15 373.15 373.15 373.15 373.15 373.15 373.15 373.15 373.15 373.15 373.15 373.15 373.15 373.15 373.15 373.15 373.15 373.15 373.15 373.15 373.15 373.15 373.15 373.15 373.15 373.15 373.15 373.15 373.15 373.15 373.15 373.15 373.15 373.15 373.15 373.15 373.15 373.15 373.15 373.16 373.15 373.15 373.15 373.15

739



Article


p

mNaCl

mKCl

103·Δρ

T

p

mNaCl

mKCl

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 2 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 10 10 10 10 10 10 10 10 10 10 10 10

0.49956 0.99975 1.00017 1.00034 1.00035 1.00070 1.00092 1.01161 2.99981 3.53342 3.58129 3.58159 3.58170 3.58228 3.58470 0.10678 0.10807 0.99991 1.00070 1.09150 3.53342 3.58159 3.58170 3.58268 0.09977 0.10678 0.10713 0.10729 0.10731 0.10807 0.50071 0.83000 0.99991 1.00017 1.00034 1.00070 1.00090 1.00495 1.01161 1.09150 2.99853 3.53342 3.58129 3.58159 3.58170 3.58268 3.58470 0.09977 0.10678 0.10713 0.10729 0.10731 0.10807 0.49988 0.83000 0.99991 1.00017 1.00034 1.00070

0.00000 0.33135 1.03075 0.11086 0.11100 3.58334 0.00000 2.24089 0.00000 1.02020 0.64988 0.11084 0.00000 0.33082 2.24416 2.23885 3.58389 0.65012 3.58334 0.65123 1.02020 0.11084 0.00000 0.11074 0.00000 2.23885 0.11257 1.04510 0.65049 3.58389 0.00000 0.08421 0.65012 1.03075 0.11086 3.58334 1.03979 0.00000 2.24089 0.65123 0.00000 1.02020 0.64988 0.11084 0.00000 0.11074 2.24416 0.00000 2.23885 0.11257 1.04510 0.65049 3.58389 0.00000 0.08421 0.65012 1.03075 0.11086 3.58334

19.20 51.45 79.27 42.43 42.40 166.53 37.50 123.94 104.47 156.00 145.37 126.30 122.10 134.23 193.96 99.50 148.12 67.36 172.79 70.43 162.28 131.83 127.48 131.94 4.18 99.28 10.16 51.44 34.48 147.80 20.35 37.09 67.25 82.41 44.53 172.51 82.81 39.77 128.17 70.29 108.86 161.87 150.16 131.62 127.13 131.62 199.73 4.18 98.92 10.05 51.24 34.28 147.22 20.21 36.92 66.91 82.00 44.36 171.94

373.15 373.15 373.15 373.15 373.15 373.15 373.15 373.15 373.15 373.15 373.15 373.14 373.15 373.15

40 40 40 40 40 40 40 40 40 40 40 40 40 40

0.99975 1.00017 1.00034 1.00035 1.00070 1.00092 1.01161 2.99981 3.53342 3.58129 3.58159 3.58170 3.58228 3.58470

0.33135 1.03075 0.11086 0.11100 3.58334 0.00000 2.24089 0.00000 1.02020 0.64988 0.11084 0.00000 0.33082 2.24416

50.62 78.04 41.61 41.61 164.48 36.78 122.24 102.71 153.75 143.14 124.22 120.08 132.16 191.37

423.15 423.15 423.15 423.15 423.15 423.15 423.16 423.17 423.15 423.15 423.15 423.15 423.15 423.14 423.16 423.15 423.15 423.15 423.15 423.15 423.15 423.15 423.15 423.16 423.15 423.15 423.15 423.15 423.15 423.16 423.16 423.15 423.16 423.16 423.15 423.15 423.15 423.15 423.16 423.16 423.15 423.15 423.15 423.15

20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 40 40 40 40 40 40 40

0.10807 0.50071 0.83000 0.99991 1.00017 1.00034 1.00070 1.00090 1.00495 1.01161 1.09150 2.99853 3.53342 3.58129 3.58159 3.58170 3.58268 3.58470 0.10678 0.10713 0.10729 0.10731 0.10807 0.83000 0.99991 1.00017 1.00034 1.00070 1.00090 1.01161 1.09150 3.53342 3.58129 3.58159 3.58170 3.58268 3.58470 0.09977 0.10678 0.10713 0.10729 0.10731 0.10807 0.49988

3.58389 0.00000 0.08421 0.65012 1.03075 0.11086 3.58334 1.03979 0.00000 2.24089 0.65123 0.00000 1.02020 0.64988 0.11084 0.00000 0.11074 2.24416 2.23885 0.11257 1.04510 0.65049 3.58389 0.08421 0.65012 1.03075 0.11086 3.58334 1.03979 2.24089 0.65123 1.02020 0.64988 0.11084 0.00000 0.11074 2.24416 0.00000 2.23885 0.11257 1.04510 0.65049 3.58389 0.00000

146.25 20.05 36.59 66.35 81.41 43.92 170.83 81.85 39.14 126.83 69.39 107.49 160.00 148.49 130.03 125.58 130.03 197.82 97.66 9.84 50.49 33.75 145.37 36.28 65.84 80.88 43.55 169.83 81.20 126.03 68.91 158.94 147.59 129.12 124.62 129.12 196.59 4.04 97.08 9.79 50.16 33.52 144.62 19.64

373.15 373.15 373.15 373.15 373.15 373.15 373.15 373.15 373.15 373.15 373.15 373.15 373.15 373.15 373.16 423.15 423.15 423.15 423.15 423.15 423.15 423.14 423.15 423.13 423.15 423.15 423.15 423.13 423.15 423.15 423.16 423.13 423.16 423.13 423.15 423.15 423.15 423.16 423.13 423.16 423.15 423.16 423.13 423.15 423.15 423.14 423.14 423.15 423.15 423.14 423.14 423.14 423.15 423.15 423.14 423.15 423.12 423.15 423.16

740



Article


p

mNaCl

mKCl

103·Δρ

T

p

mNaCl

mKCl

103·Δρ

K

MPa

mol·kg−1

mol·kg−1

g·cm−3

K

MPa

mol·kg−1

mol·kg−1

g·cm−3

423.15 423.15 423.13 423.15 423.15 423.15 423.12 423.16 423.15 423.15 423.14 423.15 423.14 423.15 423.16 423.16 473.14 473.15 473.16 473.15 473.18 473.14 473.13 473.14 473.17 473.17 473.17 473.26 473.20 473.15 473.17 473.22 473.14 473.15 473.16 473.15 473.10 473.15 473.15 473.15 473.22 473.24 473.14 473.20 473.17 473.16 473.16 473.14 473.15 473.15 473.16 473.16 473.26 473.15 473.15 473.15 473.15 473.16 473.16

10 10 10 10 10 10 10 10 10 10 10 20 20 20 20 20 1.97 1.97 1.97 1.97 1.97 1.97 1.97 1.97 1.97 1.97 1.97 1.97 1.97 1.97 1.97 1.97 1.97 1.97 1.97 1.97 1.97 1.97 1.97 1.97 1.97 1.97 1.97 1.97 1.97 1.97 1.97 1.97 1.97 1.97 1.97 1.97 1.97 2 2 2 5 5 5

1.00090 1.00495 1.01161 1.09150 2.99853 3.53342 3.58129 3.58159 3.58170 3.58268 3.58470 0.09977 0.10678 0.10713 0.10729 0.10731 0.01064 0.01065 0.01065 0.01065 0.01066 0.01071 0.01075 0.01094 0.01186 0.01279 0.10654 0.10663 0.10670 0.10674 0.10678 0.10685 0.10756 0.11411 0.11452 0.78390 0.97791 0.99975 0.99991 1.00035 1.01002 1.01027 1.01033 1.01060 1.09150 1.15332 2.28490 3.58159 3.58228 3.58268 3.58481 3.58647 3.58656 0.10518 1.00495 3.58170 0.01064 0.01071 0.01094

1.03979 0.00000 2.24089 0.65123 0.00000 1.02020 0.64988 0.11084 0.00000 0.11074 2.24416 0.00000 2.23885 0.11257 1.04510 0.65049 0.64745 1.04555 1.72360 0.33261 2.23970 0.10055 0.64855 0.32983 3.58435 1.16224 3.58550 0.33076 1.72359 0.65159 1.04578 2.24084 0.11055 0.11184 3.57565 0.76820 0.30643 0.33135 0.65012 0.11100 1.04505 2.24076 0.65054 0.03171 0.65123 3.57746 2.23930 0.11084 0.33082 0.11074 1.12327 1.04538 2.24390 0.00000 0.00000 0.00000 0.64745 0.10055 0.32983

82.45 39.52 127.70 69.96 108.43 161.20 149.53 131.13 126.60 131.13 199.04 4.14 98.17 9.93 50.88 34.10 33.72 51.77 81.38 18.24 102.97 6.08 33.23 17.95 149.83 57.12 155.91 22.08 85.35 37.55 55.75 106.79 11.04 11.57 154.18 69.87 56.07 59.27 73.47 49.17 88.88 130.44 73.28 45.07 76.95 187.63 176.25 142.04 150.58 142.26 175.56 173.06 204.45 5.14 44.03 137.60 33.46 6.03 17.86

423.16 423.15 423.15 423.15 423.15 423.15 423.16 423.16 423.15 423.15 423.17 423.14 423.15 423.15 423.15

40 40 40 40 40 40 40 40 40 40 40 40 40 40 40

0.83000 0.99991 1.00017 1.00034 1.00090 1.00495 1.01161 1.09150 2.99853 3.53342 3.58129 3.58159 3.58170 3.58268 3.58470

0.08421 0.65012 1.03075 0.11086 1.03979 0.00000 2.24089 0.65123 0.00000 1.02020 0.64988 0.11084 0.00000 0.11074 2.24416

36.01 65.38 80.33 43.25 80.67 38.50 125.32 68.43 105.94 158.00 146.63 128.21 123.82 128.30 195.55

473.15 473.14 473.20 473.15 473.22 473.22 473.25 473.22 473.17 473.17 473.17 473.20 473.23 473.15 473.19 473.27 473.24 473.22 473.23 473.23 473.16 473.22 473.15 473.22 473.16 473.15 473.15 473.15 473.27 473.20 473.16 473.15 473.22 473.20 473.15 473.15 473.15 473.17 473.15 473.19 473.21 473.26 473.15

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 20 20 20 20 20 20 20 20 20 20 20 20 30

3.58481 3.58647 3.58656 0.01064 0.01065 0.01065 0.01065 0.01066 0.01071 0.01075 0.01094 0.01186 0.01279 0.09977 0.10654 0.10663 0.10670 0.10674 0.10678 0.10685 0.10756 0.11452 0.49988 0.78390 0.99975 0.99991 1.00035 1.00495 1.01002 1.01027 1.01033 1.09150 1.15332 2.28490 2.99853 3.58159 3.58170 3.58228 3.58268 3.58481 3.58647 3.58656 0.01064

1.12327 1.04538 2.24390 0.64745 1.04555 1.72360 0.33261 2.23970 0.10055 0.64855 0.32983 3.58435 1.16224 0.00000 3.58550 0.33076 1.72359 0.65159 1.04578 2.24084 0.11055 3.57565 0.00000 0.76820 0.33135 0.65012 0.11100 0.00000 1.04505 2.24076 0.65054 0.65123 3.57746 2.23930 0.00000 0.11084 0.00000 0.33082 0.11074 1.12327 1.04538 2.24390 0.64745

173.74 171.28 207.15 32.70 50.49 79.38 17.86 100.58 5.88 32.46 17.43 146.68 55.63 4.65 152.39 21.49 83.19 36.50 54.31 104.14 10.74 150.95 22.04 68.18 57.49 71.42 47.70 42.67 86.81 132.17 71.23 74.82 183.80 172.61 116.03 138.49 134.07 146.80 138.68 171.78 169.12 205.17 32.23

741



Article


p

mNaCl

mKCl

103·Δρ

T

p

mNaCl

mKCl

103·Δρ

K

MPa

mol·kg−1

mol·kg−1

g·cm−3

K

MPa

mol·kg−1

mol·kg−1

g·cm−3

473.15 473.15 473.16 473.16 473.15 473.15 473.15 473.17 473.15 473.14 473.19 473.18 473.14 473.17 473.16 473.19 473.26 473.19 473.15 473.18 473.21 473.14 473.16 473.15 473.16 473.20 473.24 473.14 473.16 473.16 473.16 473.15 473.16 473.15 473.15 473.25 473.17 473.18 473.15 473.23 473.17 473.17 473.16 473.16 473.17 473.18 473.15 473.18 473.25 473.17 473.16 473.17 473.17 473.15 473.18 473.15 473.16 473.15 473.15

5 5 5 5 5 5 5 5 5.84 5.84 5.84 5.84 5.84 5.84 5.84 5.84 5.84 5.84 5.84 5.84 5.84 5.84 5.84 5.84 5.84 5.84 5.84 5.84 5.84 5.84 5.84 5.84 5.84 5.84 5.84 5.84 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10

0.09977 0.49988 0.99975 0.99991 1.00495 2.99853 3.58170 3.58228 0.01065 0.01065 0.01065 0.01066 0.01075 0.01186 0.01280 0.10654 0.10663 0.10670 0.10674 0.10678 0.10685 0.10756 0.11452 0.78390 1.00035 1.01002 1.01027 1.01033 1.09150 1.15332 2.28490 3.58159 3.58268 3.58481 3.58647 3.58656 0.01064 0.01065 0.01065 0.01065 0.01066 0.01071 0.01075 0.01094 0.01186 0.01279 0.09977 0.10654 0.10663 0.10670 0.10674 0.10678 0.10685 0.10756 0.11452 0.49988 0.78390 0.99975 0.99991

0.00000 0.00000 0.33135 0.65012 0.00000 0.00000 0.00000 0.33082 1.04555 1.72360 0.33261 2.23970 0.64855 3.58435 1.16220 3.58550 0.33076 1.72359 0.65159 1.04578 2.24084 0.11055 3.57565 0.76820 0.11100 1.04505 2.24076 0.65054 0.65123 3.57746 2.23930 0.11084 0.11074 1.12327 1.04538 2.24390 0.64745 1.04555 1.72360 0.33261 2.23970 0.10055 0.64855 0.32983 3.58435 1.16224 0.00000 3.58550 0.33076 1.72359 0.65159 1.04578 2.24084 0.11055 3.57565 0.00000 0.76820 0.33135 0.65012

4.79 22.72 58.94 73.12 43.81 118.57 136.95 149.86 51.45 80.82 18.12 102.47 33.11 149.11 56.72 155.17 21.94 84.80 37.33 55.45 106.13 10.93 153.34 69.46 48.83 88.35 134.74 72.81 76.42 186.68 175.36 141.22 141.42 174.61 172.23 208.45 33.26 51.07 80.17 18.07 101.70 6.00 32.89 17.71 148.37 56.25 4.74 154.43 21.79 83.96 36.87 54.91 105.22 10.86 152.65 22.47 68.95 58.40 72.47

473.22 473.24 473.30 473.24 473.17 473.20 473.17 473.21 473.25 473.23 473.29 473.26 473.22 473.25 473.28 473.16 473.23 473.23 473.16 473.16 473.15 473.30 473.27 473.20 473.15 473.23 473.22 473.16 473.15 473.16 473.15 473.21 473.23 473.27 473.22 473.24 473.29 473.24 473.19 473.21 473.27 473.25 473.36 473.29 473.22 473.24 473.29 473.23 473.23 473.30 473.30 473.24 473.22 473.21 473.23 473.30 473.15 473.17 473.17

30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 39.85 39.85 39.85 39.85 39.85 39.85 39.85 39.85 39.85 39.85 39.85 39.85 39.85 39.85 39.85 39.85 39.85 39.85 39.85 39.85 39.85 39.85 40 40 40

0.01065 0.01065 0.01065 0.01066 0.01071 0.01075 0.01094 0.01186 0.01279 0.10654 0.10663 0.10670 0.10674 0.10678 0.10685 0.10756 0.11452 0.78390 0.99975 0.99991 1.00035 1.01002 1.01027 1.01033 1.09150 1.15332 2.28490 3.58159 3.58170 3.58228 3.58268 3.58481 3.58647 3.58656 0.01065 0.01065 0.01065 0.01066 0.01075 0.01186 0.01279 0.10654 0.10663 0.10670 0.10674 0.10678 0.10685 0.11452 0.78390 1.01002 1.01027 1.15332 2.28490 3.58481 3.58647 3.58656 0.01064 0.01071 0.01094

1.04555 1.72360 0.33261 2.23970 0.10055 0.64855 0.32983 3.58435 1.16224 3.58550 0.33076 1.72359 0.65159 1.04578 2.24084 0.11055 3.57565 0.76820 0.33135 0.65012 0.11100 1.04505 2.24076 0.65054 0.65123 3.57746 2.23930 0.11084 0.00000 0.33082 0.11074 1.12327 1.04538 2.24390 1.04555 1.72360 0.33261 2.23970 0.64855 3.58435 1.16224 3.58550 0.33076 1.72359 0.65159 1.04578 2.24084 3.57565 0.76820 1.04505 2.24076 3.57746 2.23930 1.12327 1.04538 2.24390 0.64745 0.10055 0.32983

49.89 78.54 17.65 99.60 5.78 32.04 17.17 145.21 54.96 151.12 21.16 82.28 36.06 53.70 103.16 10.56 149.43 67.22 56.65 70.47 47.05 85.68 131.05 70.37 73.87 182.05 170.80 136.91 132.50 145.04 137.10 169.90 167.51 203.14 49.42 77.88 17.29 98.74 31.64 144.03 54.52 150.06 20.98 81.70 35.75 53.20 102.31 148.26 66.52 84.76 129.84 180.66 169.41 168.42 165.99 201.48 31.89 5.72 16.98

742



Article


p

mNaCl

mKCl

103·Δρ

T

p

mNaCl

mKCl

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 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 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10

1.00035 1.00495 1.01002 1.01027 1.01033 1.09150 1.15332 2.28490 2.99853 3.58159 3.58170 3.58228 3.58268 0.01075 0.01186 0.09977 0.10395 0.10654 0.10676 0.10678 0.10713 0.10729 0.10731 0.10756 0.10807 0.11451 0.49988 0.99991 1.00035 1.00070 1.00090 1.00099 1.00495 1.01161 2.99853 3.58159 3.58170 3.58464 3.58470 3.58557 0.01075 0.01186 0.09977 0.10395 0.10654 0.10676 0.10678 0.10729 0.10731 0.10756 0.10807 0.11451 0.49988 0.99991 1.00035 1.00070 1.00090 1.00099 1.00495

0.11100 0.00000 1.04505 2.24076 0.65054 0.65123 3.57746 2.23930 0.00000 0.11084 0.00000 0.33082 0.11074 0.64855 3.58429 0.00000 2.06402 3.58550 1.02732 2.23885 0.11257 1.04510 0.65049 0.11055 3.58389 3.57558 0.00000 0.65012 0.11100 3.58334 1.03979 2.23856 0.00000 2.24089 0.00000 0.11084 0.00000 1.12325 2.24416 0.64398 0.64855 3.58429 0.00000 2.06402 3.58550 1.02732 2.23885 1.04510 0.65049 0.11055 3.58389 3.57558 0.00000 0.65012 0.11100 3.58334 1.03979 2.23856 0.00000

48.45 43.40 87.80 133.95 72.27 75.88 185.89 174.60 117.71 140.35 135.93 148.78 140.57 38.74 168.25 5.99 112.61 173.71 63.30 121.20 13.51 64.11 44.67 13.29 176.32 173.97 27.46 84.56 57.72 204.91 101.57 153.85 52.00 153.11 134.61 159.75 155.55 196.61 230.57 180.81 37.93 165.88 5.84 110.99 171.43 62.26 119.53 63.14 44.05 13.06 174.01 171.57 26.88 83.22 56.67 202.38 100.07 151.70 51.01

473.15 473.16 473.15 473.17 473.16 473.16 473.15 473.16 473.15 473.16 473.15 473.16 473.15 523.17 523.15 523.16 523.17 523.16 523.16 523.16 523.16 523.17 523.16 523.16 523.15 523.19 523.19 523.16 523.14 523.18 523.16 523.18 523.17 523.16 523.20 523.20 523.16 523.16 523.16 523.19 523.17 523.17 523.16 523.17 523.16 523.19 523.15 523.16 523.22 523.17 523.16 523.15 523.20 523.15 523.17 523.18 523.17 523.16 523.21

40 40 40 40 40 40 40 40 40 40 40 40 40 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 40 40 40 40 40 40 40 40

0.09977 0.10756 0.49988 0.99975 0.99991 1.00035 1.00495 1.09150 2.99853 3.58159 3.58170 3.58228 3.58268 0.11451 0.49988 0.99991 1.00035 1.00070 1.00090 1.00099 1.00495 1.01161 2.99853 3.58159 3.58170 3.58464 3.58470 3.58557 0.01075 0.01186 0.10395 0.10654 0.10676 0.10678 0.10713 0.10729 0.10731 0.10756 0.10807 0.11451 0.99991 1.00035 1.00070 1.00090 1.00099 1.01161 3.58159 3.58170 3.58464 3.58470 3.58557 0.01075 0.01186 0.09977 0.10395 0.10654 0.10676 0.10678 0.10729

0.00000 0.11055 0.00000 0.33135 0.65012 0.11100 0.00000 0.65123 0.00000 0.11084 0.00000 0.33082 0.11074 3.57558 0.00000 0.65012 0.11100 3.58334 1.03979 2.23856 0.00000 2.24089 0.00000 0.11084 0.00000 1.12325 2.24416 0.64398 0.64855 3.58429 2.06402 3.58550 1.02732 2.23885 0.11257 1.04510 0.65049 0.11055 3.58389 3.57558 0.65012 0.11100 3.58334 1.03979 2.23856 2.24089 0.11084 0.00000 1.12325 2.24416 0.64398 0.64855 3.58429 0.00000 2.06402 3.58550 1.02732 2.23885 1.04510

4.50 10.42 21.42 56.03 69.69 46.42 41.49 73.04 113.44 135.50 131.10 143.58 135.66 167.64 25.93 80.76 54.86 198.01 97.32 147.98 49.37 147.44 128.91 153.52 149.26 189.64 222.98 173.89 35.86 159.06 105.76 164.33 59.01 114.03 12.22 59.79 41.21 12.17 166.75 164.59 78.79 53.38 194.33 95.03 144.93 144.43 150.18 145.99 186.04 219.01 170.29 35.03 156.59 5.22 103.83 161.68 57.79 111.99 58.60

473.15 473.15 473.22 473.22 473.12 473.16 473.19 473.17 473.15 473.15 473.15 473.17 473.15 523.05 523.12 523.15 523.16 523.13 523.16 523.15 523.15 523.13 523.14 523.14 523.16 523.12 523.15 523.15 523.14 523.15 523.12 523.16 523.14 523.13 523.15 523.15 523.16 523.15 523.14 523.18 523.06 523.11 523.15 523.16 523.15 523.15 523.16 523.15 523.14 523.15 523.16 523.13 523.16 523.16 523.15 523.16 523.12 523.15 523.15

743



Article


p

mNaCl

mKCl

103·Δρ

T

p

mNaCl

mKCl

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 20 20 20 20 20 20 20 20 20 20 20 20

1.01161 2.99853 3.58159 3.58170 3.58464 3.58470 3.58557 0.01075 0.01186 0.09977 0.10395 0.10654 0.10676 0.10678 0.10713 0.10729 0.10731 0.10756 0.10807

2.24089 0.00000 0.11084 0.00000 1.12325 2.24416 0.64398 0.64855 3.58429 0.00000 2.06402 3.58550 1.02732 2.23885 0.11257 1.04510 0.65049 0.11055 3.58389

151.10 132.55 157.49 153.23 194.03 227.70 178.22 36.92 162.08 5.59 108.10 167.49 60.46 116.47 12.83 61.25 42.39 12.56 170.01

523.16 523.16 523.17 523.19 523.15 523.17 523.16 523.15 523.19 523.16 523.16 523.20 523.16 523.16 523.15 523.21 523.19 523.16

40 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40

0.10731 0.10756 0.10807 0.11451 0.49988 0.99991 1.00035 1.00070 1.00090 1.00099 1.00495 1.01161 2.99853 3.58159 3.58170 3.58464 3.58470 3.58557

0.65049 0.11055 3.58389 3.57558 0.00000 0.65012 0.11100 3.58334 1.03979 2.23856 0.00000 2.24089 0.00000 0.11084 0.00000 1.12325 2.24416 0.64398

40.26 11.87 164.06 161.99 24.49 77.16 52.10 191.31 93.25 142.41 46.82 142.01 123.53 147.49 143.27 183.07 215.76 167.28

523.17 523.15 523.15 523.15 523.15 523.17 523.15 523.15 523.16 523.15 523.16 523.17 523.16 523.16 523.20 523.15 523.15 523.17 523.16

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(mi) = 0.000012·m. The combined uncertainty U(Δρ) = (1.9·10−4, 2.1·10−4, 1.2·10−4, 3.6·10−5, and 1.7·10−4) 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 all temperatures. a

plots combine the data collected at a temperature of 298.15 K and pressure of 0.1 MPa at concentrations of NaCl of 0.1, 1, and 3.5 mol·kg−1. The data at 0 mol·kg−1 of KCl represent the experimental measurements of a binary NaCl−H2O solution. The temperature-dependence of Vϕmean is shown in Figure 2 for a pressure of 10 MPa. The values of Vϕmean were found to be independent or even have a broad maximum at temperatures between (298.15 and 373.15) K, and start progressively decreasing with temperature rising over 373.15 K (Figure 2). Such behavior of Vϕmean is characteristic for pure electrolytes, for example, NaCl.36 Similarly, the mean apparent molar volume of mixed solutes decreases with temperature more rapidly for more diluted solutions as compared to concentrated mixtures approaching the trends of limiting values of molar volume at infinite dilution. Figure 3 shows the pressure-dependence of the isotherms of two samples containing 1 mol·kg−1 KCl and 0.1 mol·kg−1 and 3.58 mol·kg−1 NaCl, respectively (similar trends were observed for other samples). The pressure effect on Vϕmean is opposite to the effect of temperature; that is, Vϕmean increases with pressure in the range of studied conditions. The increase of Vϕmean with pressure becomes more significant at higher temperatures and lower concentrations. It is worth noting that although the effects of temperature and pressure on Vϕmean are opposite, they are remarkably comparable by magnitude: at the highest investigated temperature of 523.15 K, the pressure effect is similar to the temperature effect on Vϕmean along the vapor saturation curve from ambient conditions to this temperature. The strong pressure effect results from the much higher compressibility of the aqueous mixtures at elevated temperatures and indicates that caution should be applied when employing thermodynamic models that are not constrained by experimental data at even higher temperatures.

calculated apparent molar volume are significantly dependent on the concentration of salts in solutions. Although the uncertainty of apparent molar volume in concentrated solutions having ionic strength above 5 mol·kg−1 is usually below 0.05 cm3·mol−1, the error may reach 1−2 cm3·mol−1 in dilute solutions with ionic strength under 0.2 mol·kg−1. Figure 1 presents the comparison of Vϕmean obtained in this study to those calculated from some of the density data available in the literature.11,28,30,32,33 The data are presented as a variation of Vϕmean with the concentration of KCl added to a solution at constant concentration of NaCl. The presented

Figure 1. Mean apparent molar volume of KCl−NaCl aqueous mixtures as a function of the concentration of KCl added to a solution at constant concentration of NaCl of 0.1 mol·kg−1 (squares), 1 mol· kg−1 (triangles), and 3.5 mol·kg−1 (circles). Symbols represent experimental measurements: ▽, ref 11; gray diamond, ref 28; gray down triangle, ref 30; gray triangle, square, circle, ref 32; △, □, ○, ref 33; ■, ▲, ●, this study. Lines are provided for eye guidance only. 744



Article

Figure 3. The pressure-dependence of Vϕmean for the isothermal data of two sample solutions at mKCl = 1 mol·kg−1 mixed with 0.1 mol·kg−1 (a) and 3.58 mol·kg−1 of NaCl (b). Symbols represent experimental measurements at ○, 373.15 K; ◇, 423.15 K; □, 473.15 K; △, 523.15 K. Lines are provided for eye guidance only.

electrolytes, m is the total molality in mol·kg−1,R is the gas constant, T is a temperature in K, Bvi , Cvi , θ2,3 and ψ2,3 are adjustable parameters. It is important to note that we used the Pitzer formulation solely as a mathematical framework for fitting. Although we had tried to use the virial coefficients for the binary solutions, Bvi and Cvi , calculated from the correlations of Mao and Duan,23 and fit only two interaction parameters θ2,3 and ψ2,3, the resulting equation could not describe the experimental data with sufficient accuracy. Therefore, in our model, the fitted parameters Bvi and Cvi are not the true virial coefficients of end-member binary solutions, but adjustable parameters along with θ2,3 and ψ2,3. With this approach it was possible to reproduce the experimental data with high accuracy permitting further derivation of partial molar volumes of components in the mixture. The comparison of the preliminary fit of obtained experimental data in this study to the previously published results11,28−33 showed a good correlation at temperature 298.15 K, thus we decided to include those data in the general fit. Initially, fitting was done at constant temperature and pressure. We found that only three parameters are independent and sufficient (Bv1, Bv2, and θ2,3), whereas others are correlated (Cv1, Cv2, and ψ2,3). The consequent fitting showed that the former parameters exhibited a clear pressure dependence; thus they were fitted to a linear pressuredependent equation: F = a1 + a2p, where F represents parameters Bv1, Bv2, and θ2,3, and p is the pressure in MPa. The parameters and correlations needed for the resulting equation (eq 4) for estimation of the mean apparent molar

Figure 2. The temperature-dependence of Vϕmean for selected sample solutions at a pressure of 10 MPa and various concentration of NaCl: (a) at mNaCl = 0.1 mol·kg−1; (b) at mNaCl = 1 mol·kg−1; (c) at mNaCl = 3.58 mol·kg−1. Symbols represent experimental measurements: □, mKCl = 0.1 mol·kg−1; △, mKCl = 1 mol·kg−1, ◇, mKCl = 2.24 mol·kg−1, ○, mKCl = 3.58 mol·kg−1. Lines are provided for eye guidance only.

To provide a consistent fit of the data that allows the derivation of partial molar volumes of the individual components, we fitted the Vϕmean data with a Pitzer-type equation,37 analogous to that used by Corti and Svaro38 in the case of the mixture of 1:1 electrolytes with common ion: ϕ V mean = V0 +

Av ln(1 + bm1/2) b

+ 2RT {yB2v + (1 − y)B3v + m[yC2v + (1 − y)C3v ]} + 2RTy(1 − y)mθ2,3 + RTy(1 − y)m2ψ2,3

(4)

where V = + (1 − y is the mole fraction of NaCl in the mixture, Vi0 is the apparent molar volume of pure components at infinite dilution and Av is the Debye−Hückel limiting slope for the apparent molar volume39 both calculated from the equation provided by Mao and Duan,23 b = 1.2 for 1:1 0

yV01

y)V02;

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this study (eq 4, Table 3); Vi is the molar volume of a pure single-electrolyte aqueous solution (NaCl−H2O or KCl−H2O) calculated from the correlation of Mao and Duan.23 The effects of P, T, and ionic strength on the resulting molar volumes of mixing are presented in Figure 4. The molar volume of mixing

volume of KCl−NaCl aqueous mixtures at temperatures from (298.15 to 523.15) K and pressures from (0.1 to 40) MPa are listed in Table 3. Table 3. The Pressure-Dependent Parameters of eq 4 (B1v, B2v, θ2,3) Obtained by Fitting of Experimental Data from This Study and Literature11,26−29 to Linear Equation F = a1 + a2p (p/MPa) and Their Respective Correlated Parameters (Cv1, Cv2, ψ2,3) T/K

par

298.15

a1·10 a2·106 a1·104 a2·106 a1·104 a2·106 a1·104 a2·106 a1·104 a2·106 4

373.15 423.15 473.15 523.15

Bv1

Bv2

θ2,3

1.6405 −2.1629 −1.2013 −1.3630 −1.5355 −2.8542 −1.9190 −2.9843 −4.6769 2.9447

1.4421 0.46243 1.2727 −14.131 0.98407 −11.706 −0.98969 1.5722 −3.8714 9.9078

−1.2522 6.9899 1.1270 8.6898 1.6898 8.9567 2.1779 4.0347 8.0488 −10.162

C1v = 79.361(B1v )2 − 0.16727B1v + 0.0000114 C2v = − 0.19006B2v + 0.0000151

ψ2,3 = − 0.63883θ2,3 − 0.0000208

The performance of the obtained model equation was tested on the independent data set14 covering a broad P-T range. Since a density in this data set was measured only at one fixed mole fraction of KCl in the aqueous mixture, these data were not used for fitting of the parameters. A relative deviation of the density of KCl−NaCl aqueous mixtures calculated from the modeled mean apparent molar volume (eq 4) from the experimental data14 is 0.02, 0.08, 0.12, 0.20 % at temperatures of (298.15, 373.15, 423.15, and 473.15) K, respectively, with an average (total 76 measurements) of less than 0.1 %. Using eq 4 with derived parameters, the partial molar volume and the limiting partial molar volume of a component in ionic medium, V̅ i and V̅ 0i , were calculated from the following equations:40 ⎛ ∂V ϕ ⎞ ϕ Vi̅ = (mi + mj)⎜⎜ mean ⎟⎟ + V mean ⎝ ∂mi ⎠ ⎛ ∂V ϕ ⎞ + V jϕ Vi̅ 0 = mj ≠ i⎜⎜ mean ⎟⎟ ⎝ ∂mi ⎠m = 0 i

(5) Figure 4. Composition dependence of the molar volume of mixing in the system KCl−NaCl−H2O calculated as the difference between the molar volume of a solution and the molar volume of ideal mixture of nonideal (real) end-member aqueous solutions of NaCl and KCl. Molar volume of mixing presented as at (a) constant p = 10 MPa, ionic strength of 4 mol·kg−1, and various temperature; (b) constant T = 523.15 K, ionic strength of 4 mol·kg−1, and various pressure; (c) constant p = 10 MPa, T = 523.15 K, and various ionic strength of a solution. Composition of a solution x(KCl) is a mole fraction of KCl in electrolyte mixture.

(6)

Vjϕ,

where the apparent molar volume of the second component, was calculated from the correlations of Mao and Duan.23 The resulting values of V̅ i and V i0 are presented in Table 1S (Supporting Information). The effect of mixing can further be evaluated by calculation of the molar volume of mixing Vmix, which is the difference between the molar volume of a solution and an ideal molar volume, the latter calculated as a volume of ideal mixture of nonideal (real) end-member aqueous solutions of NaCl and KCl: V mix = Vsoln − {yVNaCl + (1 − y)VKCl}

is positive in all cases, increases with pressure, and the total concentration of salts (Figure 4b,c), and decreases with temperature (Figure 4a). The deviations from ideal mixing are nearly symmetric with respect to mole fraction of electrolyte components. The observed increase of Vmix of the mixtures is probably related to an increase of the proportion of repulsive forces between the molecules in the solution,

(7)

where Vsoln is calculated from the correlation for the mean apparent molar volume with adjusted parameters obtained from 746



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Figure 5. Mean apparent molar volume of KCl−NaCl aqueous mixtures as a function of the concentration of KCl in a solution. Experimental data (symbols) compared to the results of modeling using a Pitzer-type equation (eq 4), full lines, and Young’s mixing rule,41 dotted lines, at temperatures of 298.15 K (a), 373.15 K (b), 423.15 K (c), 473.15 K (d) and 523.15 K (e) and p = 10 MPa. Symbols represent experimental measurements at □, 0.1 mol·kg−1 NaCl; △, 1 mol·kg−1 NaCl; ○, 3.58 mol·kg−1 NaCl.

with three adjustable pressure-dependent parameters (eq 4). The standard deviation for the mean apparent molar volume of these mixing models from the experimental data is listed in Table 4. The results of modeling indicate that eq 4 provides a better representation of the data. However, Young’s rule used without any parameters provides broadly satisfactory results

decreasing the influence of attractive solute−solvent interactions on the solution’s volumetric properties. The results of the experiments and modeling based on the Pitzer-type equation were compared to Young’s mixing model41 formulated for the apparent molar volume of solutes. This model presents a simple solution for the calculation of the apparent molar volumes of the mixture of electrolytes from the known properties of pure binary electrolyte solutions: ϕ V mean =

∑ j

Table 4. The Standard Deviation for the Mean Apparent Molar Volume of KCl−NaCl−H2O Mixtures Calculated Using eqs 4 and 8 from the Experimental Data Obtained in This Study

mjV jϕ ∑j mj

(8)

where Vϕj is the apparent molar volume of an end-member electrolyte in the binary solution (KCl−H2O or NaCl−H2O) at the same total molality as that of a mixture calculated using the equation of Mao and Duan,23 and mj is the molality of component j in a mixture in mol·kg−1. Figure 5 panels a−e show Vϕmean values calculated from Young’s rule41 and compare those to the Pitzer-type equation 747

T/K

Pitzer-type eq 4

Young’s rule41 eq 8

298.15 373.15 423.15 473.15 523.15 average

0.17 0.49 0.44 0.58 0.89 0.50

0.20 0.73 0.68 0.95 1.60 0.83



Article

(6) Williams, A. E.; McKibben, M. A. A brine interface in the SaltonSea Geothermal System, California: Fluid geochemical and isotopic characteristics. Geochim. Cosmochim. Acta 1989, 53, 1905−1920. (7) Loehe, J. R.; Donohue, M. D. Recent advances in modeling thermodynamic properties of aqueous strong electrolyte systems. AIChE J. 1997, 43, 180−195. (8) Saluja, P. P. S.; LeBlanc, J. C. Apparent molar heat capacities and volumes of aqueous solutions of MgCI2, CaCI2, and SrCI2 at elevated temperatures. J. Chem. Eng. Data 1987, 32, 72−76. (9) Majer, V.; Gates, J. A.; Inglese, A.; Wood, R. H. Volumetric properties of aqueous NaCl solutions from 0.0025 to 5.0 mol kg−1, 323 to 600 K, and 0.1 to 40 MPa. J. Chem. Thermodyn. 1988, 20, 949−968. (10) Gates, J. A.; Wood, R. H. Density and apparent molar volume of aqueous CaCI2 at 323−600 K. J. Chem. Eng. Data 1989, 34, 53−56. (11) Dedick, E. A.; Hershey, J. P.; Sotolongo, S.; Stade, D. J.; Millero, F. J. The PVT properties of concentrated aqueous electrolytes IX. The volume properties of KCl and K2SO4 and their mixtures with NaCI and Na2SO4 as a function of temperature. J. Solution Chem. 1990, 19, 353−374. (12) Obsil, M.; Majer, V.; Hefter, G. T.; Hynek, V. Volumes of MgCl2(aq) at temperatures from 187 K to 512 K and pressures up to 29 MPa. J. Chem. Thermodyn. 1997, 29, 575−593. (13) Abdulagatov, I. M.; Azizov, N. D. Densities and apparent molar volumes of concentrated aqueous LiCl solutions at high temperatures and high pressures. Chem. Geol. 2006, 230, 22−41. (14) Al Ghafri, S.; Maitland, G. C.; Trusler, J. P. M. Densities of aqueous MgCl 2 (aq), CaCl2 (aq), KI(aq), NaCl(aq), KCl(aq), AlCl3(aq), and (0.964 NaCl + 0.136 KCl)(aq) at temperatures between (283 and 472) K, pressures up to 68.5 MPa, and molalities up to 6 mol·kg−1. J. Chem. Eng. Data 2012, 57, 1288−1304. (15) Rogers, P. S. Z.; Pitzer, K. S. Volumetric properties of aqueous sodium chloride solutions. J. Phys. Chem. Ref. Data 1982, 11, 15−77. (16) Pabalan, R. T.; Pitzer, K. S. Thermodynamics of concentrated electrolyte mixtures and the prediction of mineral solubilities to high temperatures for mixtures in the system Na−K−Mg−Cl−SO4−OH− H2O. Geochim. Cosmochim. Acta 1987, 51, 2429−2443. (17) Wang, P.; Pitzer, K. S.; Simonson, J. M. Thermodynamic properties of aqueous magnesium chloride solutions from 250 to 600 K and to 100 MPa. J. Phys. Chem. Ref. Data 1998, 27, 971−991. (18) Safarov, J. T.; Najafov, G. N.; Shahverdiyev, A. N.; Hassel, E. (p,ρ,T) and (ps,ρs,Ts) properties, and apparent molar volumes V of CaCl2(aq) at T=298.15 to 398.15 K and at pressures up to p=60 MPa. J. Mol. Liq. 2005, 116, 165−174. (19) 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. (20) Phutela, R. C.; Pitzer, K. S.; Saluja, P. P. S. Thermodynamics of aqueous magnesium-chloride, calcium-chloride, and strontium-chloride at elevated temperatures. J. Chem. Eng. Data 1987, 32, 76−80. (21) Rowland, D.; May, P. M. A Pitzer-based characterization of aqueous magnesium chloride, calcium chloride and potassium iodide solution densities to high temperature and pressure. Fluid Phase Equilib. 2013, 338, 54−62. (22) Archer, D. Thermodynamic properties of the NaCl+H2O system II. Thermodynamic properties of NaCI(aq), NaCI·2H20(cr), and phase equilibria. J. Phys. Chem. Ref. Data 1992, 21, 793−829. (23) Mao, S.; Duan, Z. The P,V,T,x properties of binary aqueous chloride solutions up to T = 573 K and 100 MPa. J. Chem. Thermodyn. 2008, 40, 1046−1063. (24) Kratky, O.; Leopold, H.; Stabinger, H. Determination of density of liquids and gases to an accuracy of 10−6 g/cm3, with a sample volume of only 0.6 cm3. Z. Agnew. Phys. 1969, 27, 273−276. (25) Picker, P.; Tremblay, E.; Jolicoeur, C. A high-precision digital readout flow densimeter for liquids. J. Solution Chem. 1974, 3, 377− 384. (26) Majer, V.; Crovetto, R.; Wood, R. H. A new version of vibratingtube flow densitometer for measurements at temperatures up to 730 K. J. Chem. Thermodyn. 1991, 23, 333−344.

and can be suitable for rough estimations of density and mean apparent molar volume of mixed KCl−NaCl aqueous solutions for many applications.

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CONCLUSIONS The experimental results of this study provide the comprehensive data set for the volumetric properties of mixed aqueous KCl−NaCl solutions over broad temperature, pressure, and composition ranges relevant to fluid processes in sedimentary basins, natural and engineered geothermal systems, and some engineering applications. We demonstrate that for simple applications the volumetric properties of KCl−NaCl mixtures can be calculated from the properties of pure end-member aqueous solutions with reasonably high accuracy at temperatures of up to 523.15 K. However, a higher accuracy can be achieved with an empirical correlation based on a Pitzer-type equation with three adjustable pressure-dependent parameters. From the latter fit, accurate values of the mean apparent molar volume, the partial molar volume of dissolved components, and limiting partial molar volume of these solutes can be computed. The experimental data and the correlation will be used directly for the parametrization of thermodynamic models describing the properties of aqueous mixtures of electrolytes.

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ASSOCIATED CONTENT

S Supporting Information *

Table containing the mean apparent molar volume of aqueous KCl−NaCl mixtures, partial molar volumes of components, and limiting partial molar volumes of solutes in ionic media calculated from the obtained experimental data. 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

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REFERENCES

The authors are sincerely thankful to Dr. Hans Stabinger for providing the densimeter and encouragement for the project. Ferdinand Hingerl assisted with calculation routine and contributed by the discussion on fluid properties. Peter Tremaine provided valuable comments on the experimental details and interpretation of results. An earlier version of the manuscript was improved significantly by two anonymous JCED referees.

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Volumetric Properties of Mixed Electrolyte Aqueous Solutions at

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