Investigation of Surface Properties for Electrolyte Solutions

Article pubs.acs.org/jced

Investigation of Surface Properties for Electrolyte Solutions: Measurement and Prediction of Surface Tension for Aqueous Concentrated Electrolyte Solutions Hailong Chen,† Zhaomin Li,*,† Fei Wang,† Zhuangzhuang Wang,† and Haifeng Li† †

College of Petroleum Engineering, China University of Petroleum, Qingdao, 266580, China ABSTRACT: Surface tensions for aqueous NaCl, NaBr, NaI, KCl, KBr, and KI solutions have been measured at different temperatures and different concentrations. The liquid densities and activity coefficients for electrolyte solutions are modeled accurately with the ion-based statistical associating fluid theory (SAFT2). Besides, a new surface tension prediction model on the basis of the Gibbs thermodynamic method, coupled with ion-based SAFT2 is established, which is applied to predict the surface tension of aqueous concentrated salt solutions at different concentrations and temperatures. In this model, we derived the relationship between the activity coefficient and surface tension, and the activity coefficient can be calculated by ion-based SAFT2. The model is found to give accurate prediction for the surface tension of aqueous concentrated electrolyte solutions at different concentrations and temperatures with the parameter obtained at one fixed temperature.

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INTRODUCTION Electrolyte solutions are regularly encountered in many chemical processes such as seawater treatment and extractive distillation.1 They also have a great influence in chemical industries and enhanced oil recovery. For example, in enhanced oil recovery, the variation of electrolyte solution surface tensions with pressure, temperature, and composition strongly influence the transport of fluids in reservoirs and thus the oil recovery. Moreover, salts also can increase oil recovery by reducing the solubility of CO2 in water.2 Despite their importance, the experimental data surface tensions over a large range of temperature and concentration are often unavailable. To meet the requirements, we proposed an accurate estimation method in this paper. The surface/interfacial tension of nonelectrolyte solutions have been studied by some researchers,3−27 and the interfacial properties of nonelectrolyte solutions can be well calculated under the framework of density functional theory (DFT) or density gradient theory (DGT), for example, Vinš et al.6 and Lu et al.18 The bulk properties can be determined by using SAFT EOS, and then the interfacial properties can be obtained by numerically minimizing the grand potential. However, for electrolyte solutions, it is difficult to calculate the surface tension under the framework of DFT or DGT, because the vapor−liquid equilibrium cannot be determined. What is more, for electrolyte solutions, most of the studies focused on low concentrations. Ariyama28,29 created a surface tension theory for dilute solutions. Nakamura et al.30 gained the ion distribution near the solution surface and calculated the electrolyte surface tensions. Bhuiyan et al.31 investigated the electrolyte solution surface tensions in the modified Poisson−Boltzmann approximation. Furthermore, an electrolyte solution surface tension model based on the Pitzer equation32 was established by Li et al.,33 © XXXX American Chemical Society

which showed accurate results as compared with the experimental values, but the surface tensions were still unacceptable in the high concentration region. The concentration dependence of the surface tension for an electrolyte solution was presented by Yu et al.34 based on modified mean spherical approximation (MSA),35 but the deviation was still a little bigger. Hu and Lee36 predicted the electrolyte surface tensions on the basis of Patwardhan and Kumar equations and the fundamental Butler equations. In this work, we measure the aqueous electrolyte solution surface tensions first, and then try to explore if the Gibbs thermodynamic method, coupled with a single equation of state, can be used for predicting the surface tensions of concentrated electrolyte solutions at different temperature and different concentrations. The Gibbs thermodynamic method is an attractive method due to its simplicity and has been used previously to describe the surface tensions of nonelectrolyte solutions;24−26 in calculating surface tensions, the activity coefficients of components in the bulk and hypothetical surface phases need to be calculated. This can be done by using an appropriate activity coefficient model, in the current work, a version of SAFT; that is, ion-based SAFT2, was used to well model the properties of electrolyte solutions including their densities and activity coefficients.

1. EXPERIMENTAL SECTION The chemicals used in this study are listed in Table 1. NaCl, NaBr, NaI, KCl, KBr, and KI are supplied by Sigma (USA) and are measured by a balance (model PL2002 of Mettler Toledo, Received: June 5, 2017 Accepted: September 15, 2017

A

DOI: 10.1021/acs.jced.7b00503 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

Journal of Chemical & Engineering Data

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respectively, μBO and μSO w w are the standard state chemical potentials of water, T, R, σsolu, and A̅ w are the absolute temperature, the universal gas constant, the surface tension of solution, and the partial molar surface area of water, respectively. When a system achieves equilibrium, the chemical potentials of water in these two phases are equal, and yield the expression below from eq 1 and eq 2:

Table 1. Chemicals Purity and Supplier chemical name

source

initial mass fraction purity

CASRN

sodium chloride sodium bromide sodium iodide potassium chloride potassium bromide potassium iodide

Sigma (USA) Sigma (USA) Sigma (USA) Sigma (USA) Sigma (USA) Sigma (USA)

≥99.5% ≥99.5% ≥99.5% ≥99.5% ≥99.5% ≥99.5%

7647-14-5 7647-15-6 7681-82-5 7447-40-7 7758-02-3 7681-11-0

σsolu =

Switzerland, with a full scale of 2100 g and accuracy of 0.01 g), and distilled water was used as the solvent. The surface tensions of electrolyte solutions under different temperatures and ambient pressure are measured with a commercial pendant drop tensiometer (Tracker, Teclis, see Figure 1) with an accuracy of 0.01 mN/m. The temperature during the measurements is maintained by a heating system with accuracy less than 0.1 K. The application principle of this apparatus and operation steps have been stated concretely by Lin et al.37 and Chiquet et al.38 The apparatus primarily consists of a high pressure cell in which two sapphire windows are positioned face to face. The cell permits measured pressures ranging from 0.1 to 50 MPa and measured temperatures ranging from room temperature to 400 K; the volume used is 10 cm3. Tables 2−7 show the experimental surface tensions in this work and in Abramzon’s work.39,40

(1)

μwS = μwSO + RT ln a wS − A̅ w σsolu

(2)

(3)

where σw is the pure water surface tension at the same T and P and the partial molar surface area of water in the mixture is equal to that of pure water (Aw).24,25 Equation 3 can be shown to reduce to18 σsolu = σw +

S RT ⎛ a w ⎞ ln⎜ B ⎟ A w ⎝ aw ⎠

(4)

Although there are several approaches that can be used to calculate Aw, Aw is better treated as an empirical parameter that is fitted to the experimental surface tension data.25 Since the two phases have the same pressure at equilibrium, eq 4 reduces further to σsolu − σw =

2. SURFACE TENSION PREDICTION MODEL Although the Gibbs thermodynamic method41,42 is an empirical method, it can easily extend to complex systems. For example, as for the aqueous electrolyte solutions in Figure 2, we made the following assumptions: First, a surface phase exists between the bulk liquid and the vapor phase. Second, the surface phase has a constant and uniform electrolyte concentration. Third, the surface phase is electrically neutral.In single electrolyte aqueous solution MX, the chemical potentials for water in the bulk and surface phase are shown in eq 1 and eq 2, respectively:32,43 μwB = μwBO + RT ln a wB

S Aw RT ⎛ a w ⎞ ln⎜ B ⎟ σw + A̅ w A̅ w ⎝ a w ⎠

S S RT ⎛⎜ x wγw ⎞⎟ ln⎜ B B ⎟ A w ⎝ x wγw ⎠

(5)

⎛ S S⎞ RT ⎜ x wf w ⎟ ln⎜ B B ⎟ A w ⎝ x wf w ⎠

(6)

S S RT ⎛⎜ x wφw ⎞⎟ ln⎜ B B ⎟ A w ⎝ x wφw ⎠

(7)

and σsolu − σw =

Namely, σsolu − σw =

where xw, γw, f w, and Φw are the mole fraction, the activity coefficient, the fugacity, and the fugacity coefficient of water, respectively. The reason for the unavailability of the surface tension of the system is because the xw in the surface phase and Φw in the surface and bulk phase are unknown. The Φw can be calculated directly by using ion-based SAFT2 when xw in the surface phase

where μw and aw are the chemical potential and the activity of water, superscripts S and B denote the surface and bulk phases,

Figure 1. Pendant drop tensiometry apparatus and video-image digitization equipment. B



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Table 2. Experimental Values of Surface Tension σ for Aqueous NaCl Solutions as a Function of Salt Mass Fraction w and Temperature T at Pressure P = (100 ± 5) kPaa σ/(mN/m) at t/°C 20

25

30

40

50

60

mass %

b

c

b

c

b

c

b

c

b

c

b

c

0 2.5 5 7.5 10 12.5 15 17.5 20 22.5 25

72.75 73.42 74.09 74.85 75.60 76.54 77.52 78.70 79.82 81.03 81.95

72.75

71.97 72.63 73.32 74.15 74.90 75.80 76.70 77.82 78.85 80.32 81.41

71.97

71.15 71.83 72.56 73.35 74.17 75.09 76.11 77.20 78.26 79.77 80.80

71.18

69.55 70.33 71.12 71.95 72.81 73.86 74.90 75.98 76.99 78.54 79.70

69.54

67.90 68.93 69.91 70.62 71.32 72.46 73.55 74.68 75.71 77.32 78.45

67.90

66.17 67.21 68.24 69.21 70.14 71.18 72.22 73.43 74.52 76.01 77.14

66.17

74.10 75.60 77.50 79.85

73.35 74.90 76.70 78.85

72.55 74.15 76.10 78.26

71.10 72.80 74.90 76.95

69.95 71.30 73.55 75.70

a

Standard uncertainties u are u(P) = 5 kPa, u(T) = 0.1 K, u(w) = 0.005, and u(σ) = 0.3 mN/m. bThe measured surface tensions in this work. cFrom Abramzon et al.39

Table 3. Experimental Values of Surface Tension σ for Aqueous NaI Solutions as a Function of Salt Mass Fraction w and Temperature T at Pressure P = (100 ± 5) kPaa σ/(mN/m) at t/°C 20

25

30

40

50

60

mass %

b

c

b

c

b

c

b

c

b

c

b

c

0 5 10 15 20 25 30 35 40 45 50 55

72.75 73.15 73.60 74.17 74.70 75.15 75.50 76.29 77.10 78.25 79.35 80.66

72.75 73.15 73.60

71.97 72.40 73.00 73.48 73.96 74.40 74.90 75.71 76.50 77.63 78.85 80.14

71.97 72.40 73.00

71.15 71.66 72.22 72.79 73.34 73.80 74.26 75.08 75.85 77.03 78.34 79.68

71.18 71.65 72.25

69.55 70.23 70.81 71.36 71.85 72.45 72.92 73.76 74.60 75.96 77.30 78.66

69.54 70.25 70.80

67.90 68.78 69.34 69.81 70.35 70.95 71.56 72.50 73.35 74.77 76.17 77.68

67.90 68.75 69.30

66.17 67.40 67.93 68.42 68.86 69.43 69.96 71.19 72.24 73.77 75.04 77.15

66.17 67.39 67.93

74.70 75.50

78.26 79.35

73.95 74.90

77.63 78.80

73.35 74.25

77.05 78.30

71.85 72.90

75.96 77.30

70.35 71.55

74.76 76.15

68.88 69.99

73.74 75.04

a Standard uncertainties u are u(P) = 5 kPa, u(T) = 0.1 K, u(w) = 0.005, and u(σ) = 0.3 mN/m. bThe measured surface tensions in this work. cFrom Abramzon et al.39

where λk is a parameter of salt k fitted from the experimental surface tension data of binary systems at 313.15 K. So the molality of salt k in the surface phase can be expressed as follows:

is known, which will be discussed later. To obtain the xw in the surface phase, an assumption is proposed that the molality of an electrolyte in the surface phase is proportional to that in the bulk phase, that is,

mkS

=

gk mkB

mkS = (1 − λk (xwB)2 )mkB

(8)

In the current study, we adopted eq 10 for the calculation of the molar fraction of water in the surface phase and Gibbs thermodynamic method analysis. The fugacity coefficient of water in eq 7 can be calculated by ion-based SAFT2 shown in eq 11 after obtaining the mole fraction of water in the surface phase with the Gibbs thermodynamic method, that is,

where mk and gk are the molality and the proportionality parameter of salt k, respectively. With the molar surface area of pure water taken from Suarez et al.25 and the activity of water obtained using the Pitzer activity coefficient model, Li et al.32 considered the proportionality parameter gk as a constant, which was obtained from the experimental surface tension data of aqueous single-salt solutions. However, the assumption is unsatisfactory at high concentration by using this proportionality constant, which is because when the mole fraction of water is very close to 0, the surface and bulk phase both move to a pure electrolyte, and g tends to unity. A modified assumption that gk is a function of the bulk water mole fraction xBw has been proposed: gk = 1 −

λk (x wB)2

(10)

⎛ ∂a ̃res ⎞ ln φi = a ̃res + ⎜ ⎟ − ⎝ ∂xi ⎠T , P

N

⎛

∑ xj⎜⎜ ∂a ̃ j=1

res ⎞

⎟⎟ ⎝ ∂xj ⎠T , P

⎛ ∂a ̃ ⎛ ∂a ̃res ⎞ + ρ⎜ − ln(1 + ρ⎜ ⎟ ⎟ ⎝ ∂ρ ⎠T , X ⎝ ∂ρ ⎠T , X res ⎞

(11)

res

where a is the dimensionless residual Helmholtz free energy, N is the number of components, P and subscript X is the pressure and composition of system. ρ is liquid densities of the aqueous

(9) C



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Table 4. Experimental Values of Surface Tension σ for Aqueous KI Solutions as a Function of Salt Mass Fraction w and Temperature T at Pressure P = (100 ± 5) kPaa σ/(mN/m) at t/°C 20

25

30

40

50

60

mass %

b

c

b

c

b

c

b

c

b

c

b

c

0 1 2 3 4 5 6 7 8 9 10 11 12

72.75 73.24 73.65 74.15 75.05 75.44 76.12 76.76 77.23 78.32 79.11 80.21 81.04

72.75

71.97 72.53 73.00 73.57 74.45 74.79 75.4 76.04 77.03 77.68 78.6 79.5 80.2

71.97

71.15 71.81 72.35 72.85 73.70 74.00 74.75 75.39 76.15 77.09 78.00 78.84 79.51

71.18

69.55 70.45 71.05 71.62 72.40 72.70 73.39 74.09 74.96 75.86 76.83 77.67 78.40

69.54

67.90 68.95 69.69 70.32 71.20 71.47 72.15 72.60 73.86 74.62 75.66 76.43 77.16

67.90

66.17 67.52 68.36 68.95 69.75 69.98 70.53 70.97 72.70 73.19 74.36 75.26 75.86

66.17

77.20

77.28

76.10

75.02

73.95

72.75


Table 5. Experimental Values of Surface Tension σ for Aqueous NaBr Solutions as a Function of Salt Mass Fraction w and Temperature T at Pressure P = (100 ± 5) kPaa σ/(mN/m) at t/°C 20

30

40

50

60

70

80

mass %

b

c

b

c

b

c

b

c

b

c

b

c

b

c

0 5 10 15 20 25 30 35 40

72.75 74.11 75.50 76.51 77.40 78.93 80.32 82.00 83.50

72.75

71.15 72.43 73.50 74.83 75.40 77.25 78.62 80.31 81.93

71.18

69.55 70.75 72.00 73.14 74.10 75.68 77.05 78.73 80.36

69.54

67.90 69.07 70.00 71.36 72.60 74.00 75.26 77.05 78.56

67.90

66.17 67.28 68.40 69.67 70.80 72.31 73.60 75.37 76.87

66.17

64.39 65.49 66.40 67.85 69.50 70.52 71.87 73.90 75.73

64.41

62.61 63.71 64.73 65.99 67.34 68.60 70.06 71.81 73.32

62.60

75.6 77.4 80.30 83.50

73.8 75.8 78.60 81.90

72.0 74.2 77.00 80.30

70.2 72.5 75.30 78.60

68.4 70.8 73.60 76.90

66.6 69.0 71.90 75.70

64.8 67.1 70.02 73.40

a

Standard uncertainties u are u(P) = 5 kPa, u(T) = 0.1 K, u(w) = 0.005, and u(σ) = 0.3 mN/m. bThe measured surface tensions in this work. cFrom Abramzon et al.39

electrolyte solutions and can be calculated in terms of the equation below:

The calculation of hard sphere term in ion-based SAFT2 is the same as that in SAFT1.47 The dispersion term is calculated from Ji’s work.48 The association term49 is applied to water molecules in this work, and the RPM44 used in ion-based SAFT2 is to illustrate long-range Coulombic interactions:

⎡ ⎛ ∂ 2a ̃res ⎞ ⎤ ⎛ ∂P ⎞ ⎛ ∂a ̃res ⎞ ⎥ = RT ⎢1 + 2ρ⎜ + ρ2 ⎜ ⎜ ⎟ ⎟ 2 ⎟ ⎥ ⎢ ∂ ρ ⎝ ∂ρ ⎠T , X ⎝ ⎠ ∂ ρ ⎠ ⎝ ⎣ T ,X T ,X ⎦ (12)

a ̃ion = −

Ion-based SAFT2 is defined based on the dimensionless residual Helmholtz free energy ares consisting of the following terms that represent interactions between segments: a ̃res = a ̃hs + a disp + a ̃ion ̃ + a assoc ̃

3X2 − 2(1 + 2X )3/2 + 6X + 2 12πNAvρd3

(14)

where NAv is the Avogadro number, X is the dimensionless quantity given by

(13)

(15)

X = κd

the superscripts refer to hard-sphere, dispersion, association, and ionic interactions, respectively. The association term in eq 13 refers to the hydrogen-bond interactions existing in water−water pairs in the aqueous electrolyte solutions, and the ionic term in eq 13 is only used for electrolyte solutions and given by the restricted primitive model (RPM)44 in the MSA formalism. Each ion-based SAFT2 salt molecule consists of two segments: cation and anion. Moreover, the temperature-independent ion-based SAFT2 parameters of water, cation, and anion are taken from Ji’s work.45,46

and d is the effective diameter defined by d=

∑ xi′di

(16)

i

where xi′ is the mole fraction of ion i on a solvent-free basis, κ is the Debye inverse screening length defined by κ2 =

D

4π εw kT

∑ ρn,j qj 2 = j

4πe 2 εw kT

∑ ρn, j zj 2 j

(17)



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Table 6. Experimental Values of Surface Tension σ for Aqueous KCl Solutions as a Function of Salt Mass Fraction w and Temperature T at Pressure P = (100 ± 5) kPaa σ/(mN/m) at t/°C 20

30

40

50

60

70

80

mass %

b

c

b

c

b

c

b

c

b

c

b

c

b

c

0 2.5 5 7.5 10 12.5 15 17.5 20

72.75 73.32 73.89 74.52 75.13 75.61 76.15 77.10 77.99

72.75

71.15 71.83 72.44 73.09 73.68 74.44 75.18 75.74 76.32

71.18

69.55 70.27 71.05 71.66 72.24 72.88 73.56 74.18 74.82

69.54

67.90 68.58 69.17 69.84 70.49 71.12 71.74 72.36 73.00

67.90

66.17 66.95 67.70 68.21 68.76 69.37 69.83 70.47 71.10

66.17

64.39 65.00 65.55 66.46 67.35 67.94 68.47 69.17 69.81

64.41

62.61 63.25 63.91 64.64 65.37 66.05 66.73 67.35 68.12

62.60

73.92 75.10 76.10

72.47 73.66 75.11

71.01 72.22 73.52

69.21 70.49 71.70

67.71 68.75 69.88

65.59 67.34 68.47

63.92 65.38 66.71


Table 7. Experimental Values of Surface Tension σ for Aqueous KBr Solutions as a Function of Salt Mass Fraction w and Temperature T at Pressure P = (100 ± 5) kPaa σ/(mN/m) at t/°C 20

30

40

50

60

70

80

mass %

b

c

b

c

b

c

b

c

b

c

b

c

b

c

0 5 10 15 20 25 30 35 40

72.75 73.93 74.51 74.90 75.30 76.16 77.43 78.85 80.30

72.75 73.90 74.50

71.15 72.42 73.05 73.27 73.82 74.82 76.15 77.51 78.92

71.18 72.40 73.00

69.55 70.85 71.44 71.74 72.29 73.39 74.72 76.17 77.58

69.54 70.80 71.40

67.90 69.14 69.86 70.21 70.82 71.86 73.23 74.64 76.06

67.90 69.10 69.80

66.17 67.31 67.95 68.49 69.25 70.24 71.64 73.11 74.53

66.17 67.30 68.00

64.39 65.40 66.14 66.77 67.46 68.61 69.93 71.39 72.87

64.41 65.40 66.10

62.61 63.44 64.11 64.86 65.73 66.79 68.15 69.57 71.22

62.60 63.40 64.10

75.30 77.40 80.30

73.80 76.10 78.90

72.30 74.70 77.60

a

70.80 73.20 76.10

b

69.20 71.60 74.50

67.50 69.90 72.90

65.70 68.10 71.20 c

Standard uncertainties u are u(P) = 5 kPa, u(T) = 0.1 K, u(w) = 0.005, and u(σ) = 0.3 mN/m. The measured surface tensions in this work. From Abramzon et al.40

3. RESULTS AND DISCUSSIONS 3.1. Results for Densities of Aqueous Electrolyte Solutions Modeled by Ion-Based SAFT2. Because of the restriction of experimental data of densities of electrolyte solutions, six salts (NaCl, NaBr, NaI, KCl, KBr, KI) are selected to illustrate the calculation accuracy of this approach. Figures 3 and 4 give the relationship between the experimental points and the calculated curves for six salt solutions at 298.15 K. For NaI solution, densities are modeled up to 6.1 mol/kgH2O. Figure 5 shows a good agreement between experimental and calculated data of aqueous NaCl solutions at 293.15, 323.15, and 373.15 K. The average and maximum relative errors of densities of electrolyte solutions are shown in Table 8, from which we can easily see the maximum average relative errors from 0.19% (KCl) to 0.37% (KBr), and the maximum relative error is more close to the average relative errors compare to the results presented by Cameretti.50 From what we discussed above, we can draw the conclusion that ion-based SAFT2 can well represent the densities of electrolyte solutions at different temperatures over a large range of concentration and it is more accurate and stable than the method used by Cameretti. 3.2. Results for Activity Coefficient of Aqueous Electrolyte Solutions Modeled by Ion-Based SAFT2. Because of the restriction of experimental data of fugacity coefficient of electrolyte solutions, the activity coefficient of six

Figure 2. Surface-phase model of electrolyte solutions.

where e, ρn,j,, εw, qj, and zj are the charge of an electron, number density of ion j, dielectric constant of water, charge of ion j(=zje), and valence of the ion j, respectively. E



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Table 8. Average and Maximum Relative Errors for Salt Solution Densities Cameretti50

this work salt

Mmaxa

ARD (%)c

max (%)b

ARD (%)c

max (%)b

NaCl NaBr NaI KCl KBr KI

6.0 5.9 6.1 4.2 5.1 4.0

0.23 0.20 0.28 0.19 0.37 0.26

0.51 0.33 0.41 0.47 0.59 0.53

0.4 0.9 0.3 0.8 1.0 0.4

0.9 1.7 0.6 1.8 1.7 0.9

a

Mmax is the maximum calculated molality. bMax is the maximum deviation of the experimental and calculated data. cARD = 1/N ∑iN= 1| (ρiexp − ρical)/ρiexp|

Figure 3. Densities of aqueous NaCl, NaBr, NaI solutions at 298.15 K: experimental data (symbols);51 modeled (curves).

Figure 6. Activity coefficient of NaCl solutions at different temperatures, with shapes indicating the experimental data53 and curves showing the calculated values. Figure 4. Densities of aqueous KCl, KBr, KI solutions at 298.15 K: experimental data (symbols);51 modeled (curves).

Figure 7. Activity coefficient of NaCl, NaBr, and NaI solutions at 298.15 K in the rectangular coordinate system, with shapes indicating the experimental data54 and curves showing the calculated values.

Figure 5. Densities of aqueous NaCl solutions at 293.15, 323.15, and 373.15 K: experimental data (symbols);51,52 modeled (curves).

Figure 6 gives the calculated the activity coefficients at various temperatures, where the effect of temperature on the activity coefficient is well captured. Figures 7 and 8 show the experimental points and the calculated curves for NaCl, NaBr, NaI, electrolyte solutions at 298.15 K in the rectangular coordinate system and

salts (NaCl, NaBr, NaI, KCl, KBr, KI) are selected to illustrate the calculation accuracy of the ion-based SAFT2. The activity coefficients of all electrolyte solutions are taken from Pitzer et al.53 and Hamer et al.54 F



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Figure 8. Activity coefficient of NaCl, NaBr, and NaI solutions at 298.15 K in the semilog coordinate system, with shapes indicating the experimental data54 and curves showing the calculated values.

Figure 10. Activity coefficient of KCl, KBr, and KI solutions at 298.15 K in the semilog coordinate system, with shapes indicating the experimental data54 and curves showing the calculated values.

the semilog coordinate system, respectively. For NaCl, NaBr, and NaI solutions, the activity coefficients are modeled up to 6.0 mol/kgH2O. Figures 9 and 10 show the calculated activity

Table 9. Average and Maximum Relative Errors of Activity Coefficient of Aqueous Electrolyte Solutions Calculated by (Model/expt) in This Work salt

Mmaxa

ARD(%)c

max (%)b

salt

Mmaxa

ARD (%)c

max (%)b

NaCl NaBr NaI

6.0 6.0 6.0

0.65 0.54 0.67

0.98 1.64 2.32

KCl KBr KI

4.8 5.5 4.5

0.66 0.37 0.22

1.05 1.10 0.73

Mmax is the maximum calculated molality. b“max” is the maximum deviation of the experimental and calculated data. cARD = 1/N ∑iN= 1| (γiexp − γical)/γiexp|. a

3.3. Results for Surface Tensions of Aqueous Electrolyte Solutions Predicted by This Model. The values of parameter λ and the ARDs of the calculated surface tensions for all systems are listed in Table 10, from which we can easily see the Table 10. Fitted λ Values and Average Calculated Relative Deviations of Surface Tension component

λ

ARD (%)a

component

λ

ARD (%)a

NaCl NaBr NaI

0.1219 0.1139 0.0521

0.31 0.47 0.50

KCl KBr KI

0.1199 0.0820 0.7773

0.42 0.49 0.21

Figure 9. Activity coefficient of KCl, KBr, and KI solutions at 298.15 K in the rectangular coordinate system, with shapes indicating the experimental data54 and curves showing the calculated values. a

coefficients of KCl, KBr, and KI electrolyte solutions at 298.15 K in the rectangular coordinate system and the semilog coordinate system, respectively. For KBr solution, the activity coefficient is modeled up to 5.5 mol/kgH2O. From Figures 7−10, we can see the calculated activity coefficients exhibit a good agreement with the experimental data at different temperatures. Table 9 shows the average and maximum relative deviations of activity coefficients of electrolyte solutions, from which we can easily see the maximum average relative deviations vary from 0.22% (KI) to 0.67% (NaI), and the maximum relative deviation 2.32% for NaI at temperature 298.15 K, with a molality of 6 mol/kgH2O. From what we discussed above, we can draw the conclusion that ion-based SAFT2 can well represent the activity coefficients of aqueous electrolyte solutions at different temperatures over a large range of concentrations.

ARD = 1/N ∑i N= 1|(σiexp − σical)/σiexp|.

maximum fitting deviations is 0.50% for NaI. It is clear from the results that the parameter λ was positive, which means that the concentration of ions absorbed in the surface phase was smaller than that in the bulk phase. In this wok, we use the same values of λ shown in Table 10 to predict the surface tensions of electrolyte solutions at different temperatures. As shown in Table 11 the Gibbs thermodynamic method coupled with ion-based SAFT2 can well predict the surface tensions of all salt solutions considered in this work. The results are also compared with those of others.32,34 The better representation of surface tensions of salt solutions could be attributed to the accurate representation of the densities and activity coefficients by ion-based SAFT2. G



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Table 11. ARDs of Surface Tensions for Electrolyte Solutions at Different Temperatures ARD(%) T(K)

a b

mass (%)a

293.15 298.15 303.15 323.15 333.15

25 25 25 25 25

293.15 303.15 323.15 333.15 343.15 353.15

40 40 40 40 40 40

293.15 298.15 303.15 323.15 333.15

55 55 55 55 55

293.15 303.15 323.15 333.15 343.15 353.15

20 20 20 20 20 20

293.15 303.15 323.15 333.15 343.15 353.15

40 40 40 40 40 40

293.15 298.15 303.15 323.15 333.15

12 12 12 12 12

Mmaxb NaCl 5.70 5.70 5.70 5.70 5.70 NaBr 6.48 6.48 6.48 6.48 6.48 6.48 NaI 8.17 8.17 8.17 8.17 8.17 KCl 3.35 3.35 3.35 3.35 3.35 3.35 KBr 5.60 5.60 5.60 5.60 5.60 5.60 KI 0.82 0.82 0.82 0.82 0.82

this work

32

34

0.14 0.10 0.07 0.58 0.73

0.29 0.32 0.65

0.29 0.89 1.35

1.30 1.33 1.31 1.28 1.38

1.60 1.55 1.73 1.87 2.06

0.97 0.90 0.83 0.79 0.75 0.63 0.46 0.50 0.63 0.98 1.21

0.55

1.08

0.84 1.58

1.29 1.66

0.43 0.36 0.46 0.63 0.56 0.42

0.11 0.17 0.62 1.15 0.25 0.20

0.43 0.61 0.99 1.36 0.41 0.37

0.66 0.58 0.42 0.44 0.30 0.18

0.45 0.58 0.47 0.31 0.17

0.47 0.77 0.70 0.53 0.24

0.37 0.30 0.25 0.45 0.61

0.55

Figure 11. Surface tensions of aqueous NaCl solutions at different temperatures: experimental data (symbols); predicted (curves).

Figure 12. Surface tensions of aqueous NaBr solutions at different temperatures: experimental data (symbols); predicted (curves).

0.16 0.17 0.16 0.70 1.06

The maximum mass concentration of electrolyte solution predicted. The maximum molality of electrolyte solution predicted.

The predicted surface tensions of aqueous NaCl, KBr, and NaBr solutions at different temperatures are shown in Figures 11−13, respectively. Although the parameter λ is fitted to the experimental data at 313.15 K, the model can well predict the surface tensions at other temperatures. The value of g is increasing with the mass percentage of salt increasing in the solution, which is also true for other single salt solutions.

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CONCLUSIONS (1) The liquid densities of electrolyte solutions containing NaCl, NaBr, NaI, KCl, KBr, and KI at different temperatures and different concentrations are modeled with ion-based SAFT2, which presents more accurate and stable results than others such as Cameretti.50 Our results show that the overall average relative deviation is 0.26%.

Figure 13. Surface tensions of aqueous KCl solutions at different temperatures: experimental data (symbols); predicted (curves). H



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(2) The activity coefficients of electrolyte solutions containing six salts at different temperatures and different concentrations are modeled with ion-based SAFT2, the calculated results show a good agreement to the experimental data with the overall average relative deviation being 0.53%. (3) We make the first exploration in predicting the surface tensions of aqueous electrolyte solutions at different temperatures in terms of Gibbs thermodynamic method, coupled with ion-based SAFT2. Besides, we derived the relationship between activity coefficient and surface tension, and the activity coefficient can be calculated by Ion-based SAFT2. The model is found to give accurate prediction for the surface tension of aqueous electrolyte solutions at different temperatures and concentrations with the only fitting parameters λk obtained at one fixed temperature. Our results show that the overall average relative deviation of predicted surface tensions is 0.54%.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. ORCID

Zhaomin Li: 0000-0002-2547-5737 Funding

This work was supported by National Natural Science Foundation of China (No. 51304229), the Fundamental Research Funds for the Central Universities (R1602013A) and the Innovation Project Funds for the Central Universities (YCX2017024). Notes

The authors declare no competing financial interest.

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Investigation of Surface Properties for Electrolyte Solutions

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