Article pubs.acs.org/jced
Correlations for Densities of Aqueous Electrolyte Solutions Nguyen H. Nguyen,† Fazle Hussain,‡ and Chau-Chyun Chen*,† †
Department of Chemical Engineering, and ‡Department of Mechanical Engineering, Texas Tech University, Lubbock, Texas 79409, United States ABSTRACT: We present simple %-level accuracy universal correlations for densities of aqueous electrolyte solutions at 298.15 K and 0.1 MPa. The developed expressions and parameters are based on 1032 experimental density data points for 56 aqueous single electrolyte solutions including chlorides, bromides, iodides, bicarbonates, carbonates, sulfates, nitrates, nitrites, phosphates, hydrogen phosphates, and dihydrogen phosphates. The correlations relate the solution density with “excess” mass fraction of electrolytes in solution. With molar mass and concentrations of electrolytes as input, the correlation yields density results for all 56 electrolytes with the average error of 0.97% and the maximum error of 8.05%. When grouping the electrolytes as either structure making, structure breaking, or structure superbreaking, the correlations yield the average error of 0.59% and the maximum error of 3.45%. The correlations should be very useful in estimating the density of aqueous single and multicomponent electrolyte solutions including high-salinity produced water from oil and gas production.
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INTRODUCTION The density of aqueous electrolyte solutions is an essential physical property required in many scientific and engineering calculations such as design and simulation of chemical processes.1 A specific application of interest is the development of water treatment technologies for flowback water from hydraulic fracturing and high salinity produced water from oil and gas production. Produced water has a complex composition. Its constituents cover both organic and inorganic compounds, including dissolved and dispersed oils, grease, heavy metals, radionuclides, treating chemicals, formation solids, salts, dissolved gases, scale products, waxes, and dissolved oxygen, etc.2−4 Playing a significant role in the properties of produced water are cations and anions such as Na+, K+, Ca2+, Mg2+, Fe2+, Ba2+, Sr2+, Cl−, SO42−, CO32− and HCO3−.4 Globally, 250 million barrels of saline water are produced daily from both oil and gas fields, and more than 40% of this is discharged into the environment.4 A recent survey of oil and gas produced water management practices in the United States found that more than 98% of produced water from onshore oil and gas wells is injected underground.5 These numbers illustrate how critical produced water treatment technologies are in this age, in which petroleum remains the major source of energy. Developing simple and accurate engineering correlations for density of aqueous electrolyte solutions such as produced water should help advance water treatment technologies and thus reduce injecting saline water underground. Simple and accurate engineering correlations for the density of aqueous electrolyte solutions are lacking. Existing density © XXXX American Chemical Society
correlations require empirical unary ion-specific parameters, binary ion−ion interaction parameters, or even tertiary and higher order interaction parameters that must be regressed from extensive experimental data sets. Those correlations that involve a large number of higher order interaction parameters generally find little use in engineering calculations simply because available experimental data could never be sufficient to fully quantify these empirical adjustable parameters. This is particularly true in dealing with aqueous multicomponent electrolyte solutions. The aim of this study is to develop simple %-level accuracy engineering correlations predicting the density of aqueous electrolyte solutions at room temperature and atmospheric pressure. Without the use of any unary ion-specific parameters nor binary ion−ion interaction parameters, we present universal correlations that relate the density of aqueous electrolyte solutions with molar mass of electrolytes and their concentrations.
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PRIOR WORK Back in 1929, Masson6 presented an empirical generalization of the change of apparent molar volume of an electrolyte in solution, v, with the square root of molar concentration c: v = v∞ + Sv* c
(1)
∞
where v is the apparent molar volume at infinite dilution, and Sv* is the slope that is electrolyte specific. Received: June 14, 2015 Accepted: January 19, 2016
A
DOI: 10.1021/acs.jced.5b00491 J. Chem. Eng. Data XXXX, XXX, XXX−XXX
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Table 1. Fit of Data for Single Electrolytes with Universal Correlation and Refined Correlation electrolyte
number of data points
max wt % concentration
average abs % error
max abs % error
Universal Correlation 1.40 3.46 0.32 0.94 0.87 2.64
average abs % error
max abs % error
Refined Correlation 0.55 1.97 0.37 1.33 0.31 0.92
LiCl NaCl KCl
14 30 34
42.6 25.9 24
MgCl2 CaCl2 MnCl2 FeCl2 FeCl3 SrCl2 BaCl2 LaCl3 CsCl LiBr NaBr KBr MgBr2 SrBr2 BaBr2 LiI NaI KI MgI2 CaI2 BaI2 NaNO2 KNO2 Ca(NO2)2 Ba(NO2)2 LiNO3 NaNO3 KNO3
17 20 19 23 12 24 20 8 33 30 15 29 15 15 25 34 20 26 24 23 15 12 26 13 10 19 32 28
32.2 40 40 33.1 24 34 26 42.4 64 60 46.3 32.3 30 30 50 60 60 40 58 46 60 24 48 26 20 50.3 41.9 23.3
0.35 0.29 0.61 1.41 0.17 0.66 0.47 1.88 0.60 1.23 0.66 0.95 0.45 1.27 1.12 0.50 0.80 1.37 0.80 1.80 1.84 0.82 1.26 0.61 0.44 3.10 1.95 2.10
0.77 0.85 0.87 3.42 0.28 1.02 0.99 4.24 1.02 2.56 2.28 2.27 0.67 2.09 1.46 1.21 1.23 2.48 1.22 2.79 2.20 1.63 2.18 1.46 0.66 6.27 4.78 4.17
0.44 0.73 0.52 0.48 1.77 0.40 0.51 0.95 0.40 0.39 0.69 0.34 0.61 0.22 0.07 1.21 0.65 0.47 0.27 0.63 0.75 0.32 0.51 0.63 0.41 0.78 0.21 0.99
1.43 2.38 1.00 1.91 1.44 1.23 1.03 2.92 0.77 1.36 1.16 0.80 1.20 1.11 0.14 2.78 2.23 1.68 0.49 1.46 1.71 0.52 1.90 0.99 0.75 1.56 0.72 2.42
Mg(NO3)2
16
40
2.63
6.22
0.43
1.73
Ca(NO3)2
14
56
3.61
8.05
0.66
2.11
Mn(NO3)2 Fe(NO3)3 Sr(NO3)2
15 6 27
60 42 40
1.89 3.11 1.14
4.83 4.24 2.90
1.58 1.84 0.77
2.10 2.76 2.22
Ba(NO3)2 AgNO3 Li2SO4 Na2SO4 K2SO4 MgSO4 MnSO4 FeSO4 ZnSO4 Na2CO3 K2CO3 NaHCO3 KHCO3 Na3PO4 Na2HPO4 K2HPO4 NaH2PO4 KH2PO4 Na2S2O3
7 26 3 23 5 14 18 11 14 14 25 9 13 16 11 13 30 10 40
8.4 40 6 18.2 10 24.4 36 22 16 22 50 9 26 8 5.5 8 40 12 18
0.45 0.75 0.13 0.42 0.39 1.49 2.83 1.74 1.33 2.00 0.37 0.26 1.33 1.32 0.39 0.06 1.35 0.60 0.54
0.60 2.89 0.23 0.67 0.50 4.00 4.92 3.04 3.12 4.00 0.82 0.65 2.70 2.61 0.79 0.16 4.13 1.22 3.20
0.25 0.51 0.19 0.36 0.36 0.92 1.76 0.89 0.82 1.30 1.31 0.22 0.32 1.04 0.23 0.30 0.67 0.13 0.71
0.43 1.46 0.21 0.82 0.66 2.59 3.45 1.66 1.97 2.67 2.18 0.74 0.99 1.98 0.38 0.65 3.16 0.39 2.39
B
data source Zaytsev and Aseyev11 Simard and Fortier12 Jones and Talley,13 Korolev,14 Palma and Morel15 Zaytsev and Aseyev,11 Isono16 Palma and Morel,15 Isono16 Rard and Miller17 Karapet’yants et al.18 Zaytsev and Aseyev11 Zaytsev and Aseyev11 Zaytsev and Aseyev11 Isono16 Haynes19 Zaytsev and Aseyev11 Isono,16 Gucker et al.20 Palma and Morel,15 Isono16 Zaytsev and Aseyev11 Zaytsev and Aseyev11 Zaytsev and Aseyev11 Abdulagatov and Azizov21 Palma and Morel15 Palma and Morel15 Zaytsev and Aseyev11 Zaytsev and Aseyev11 Zaytsev and Aseyev11 Zaytsev and Aseyev11 Daniel and Albright22 Zaytsev and Aseyev11 Zaytsev and Aseyev11 Campbell et al.23 Abdulagatov and Azizov21 Zaytsev and Aseyev,11 Doan and Sangster24 Zaytsev and Aseyev,11 Doan and Sangster24 Zaytsev and Aseyev,11 Doan and Sangster24 Zaytsev and Aseyev11 Doan and Sangster24 Zaytsev and Aseyev,11 Doan and Sangster24 Doan and Sangster24 Haynes19 Zaytsev and Aseyev11 Liu and Ren,25 Koda and Nomura26 Zaytsev and Aseyev11 Zhuo et al.27 Zaytsev and Aseyev11 Zaytsev and Aseyev11 Haynes19 Rard and Miller,17 Apelblat et al.28 Zaytsev and Aseyev11 Zaytsev and Aseyev11 Zaytsev and Aseyev11 Haynes19 Haynes19 Haynes19 Haynes19 Haynes19 Haynes19 DOI: 10.1021/acs.jced.5b00491 J. Chem. Eng. Data XXXX, XXX, XXX−XXX
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Table 1. continued number of data points
electrolyte
max wt % concentration
8 1032
KMnO4 Total
6
average abs % error
max abs % error
Universal Correlation 0.55 1.01 0.98 8.05
⎛ T − T0 ⎞ 1 Cjk = C jk0 + ⎜ ⎟Cjk ⎝ T0 ⎠
(2)
(3)
where d0 is the density of pure solvent and B1 and B2 are electrolyte-specific empirical constants. Note that B1 and B2 are “additive”. In 1986, Horsak and Slama9 applied the principle of the additivity of ionic properties to the apparent molar volume of electrolytes, separating the molar volumes into specific cationic and anionic contributions. It further introduces a parameter accounting for deviation from the additivity principle. The model satisfactorily represents density data for 24 aqueous electrolyte solutions with ion-specific parameters and ion−ion correction parameters for six cations and four anions. In 2004, Laliberte and Copper proposed an empirical equation for the density of aqueous electrolyte solutions by fitting experimental data for 59 electrolytes over wide ranges of temperature and concentration.1 vi̅ =
−6
·(T + c4)2 )
where v ̅ i is mass specific volume and wi is the weight fraction of electrolyte i, c0 to c4 are electrolyte-specific empirical constants, and T is temperature in °C. Separately, the equations of Masson and Redlich and Rosenfeld have been rewritten by Mathias10 as (5)
∞ velec = velec + c1 xelec + c 2xelec
(6)
v∞ elec
where is the apparent molar volume of electrolyte at infinite dilution, xelec is electrolyte mole fraction, and c1 and c2 are correlation parameters. Mathias further presented a very flexible correlation model with the use of unary ion-specific parameters and binary ion−ion correction parameters: ∞ ∞ 0 velec = velec + (velec − velec )xelec ∞ velec =
j
k
⎛ T − T0 ⎞ 1 Bjk = Bjk0 + ⎜ ⎟Bjk ⎝ T0 ⎠ 0 velec =
(7)
∑ xjionv∞j + ∑ ∑ xjionxkionBjk j
(8)
(9)
∑ xjionvj0 + ∑ ∑ xjionxkionCjk j
j
k
(11)
UNIVERSAL CORRELATIONS Unlike the prior studies that correlate the density of aqueous electrolyte solutions with either ion-specific parameters or electrolyte-specific parameters, we show that the density correlates with “excess” mass fraction of electrolytes in aqueous solutions, and present universal correlations for the density of solutions with molar mass and concentrations of electrolytes. We first examine density data from the literature. With hydraulic fracturing applications in mind, we focus on 14 cations (Li+, Na+, K+, Cs+, Ag+, Ca2+, Mg2+, Sr2+, Ba2+, Mn2+, Zn2+, Fe2+, Fe3+ and La3+) and 13 anions (Cl−, Br−, I−, NO2−, NO3−, HCO3−, CO32−, SO42−, S2O32−, PO43−, HPO42−, H2PO4− and MnO4−). In total, 56 electrolytes are studied. Table 1 summarizes the data and the data sources11−28 with these 56 electrolytes. Figure 1 shows the densities of 12 aqueous chloride solutions as functions of electrolyte concentrations in mole fraction up to the saturation point. Qualitatively, the densities increase linearly with mole fractions of electrolytes. Also, at any electrolyte mole fraction, the densities increase with molar mass of the electrolytes. In other words, heavier electrolytes yield higher densities−not surprisingly. Similar trends are found with nonchloride electrolytes as well. The observed relationships between the densities and the electrolyte molar concentrations and between the densities and the electrolyte molar mass suggest better correlations of the densities with the mass concentrations of electrolytes. Figure 2 shows the densities plotted against the electrolyte mass fraction. Indeed, the density data fall into a much narrower band for the 12 electrolytes. Figure 2 reveals that, at the same electrolyte mass fraction, heavier electrolytes yield higher densities. If the densities at a constant electrolyte mass fraction were independent of the electrolyte molar mass, then the electrolytes would have the same apparent volume per unit mass regardless of their
(4)
∞ velec = velec + c1 xelec
Haynes19
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wi + c 2 + c3T (c0wi + c1) e(1 × 10
data source
where v0elec is the apparent molar volume of electrolyte at pure fused state, v∞ j is a unary ion-specific parameter representing the partial molar volume of ion j at infinite dilution at 298.15 K, B0jk and B1jk are the coefficients of the symmetric binary ion−ion correction parameters to the partial molar volume at infinite dilution for the j-k ion pair, v0j is another unary ion-specific parameter representing the “pure” molar volume of ion j at 298.15 K, C0jk and C1jk are the coefficients of the symmetric binary ion−ion correction parameters to the pure molar volume for the j-k ion pair, and T0 is the reference temperature fixed at 298.15 K. Given the unary ion-specific parameters, the model calculates the density of aqueous single electrolyte solutions with an average error of ∼1% and maximum error of ∼5%. The average error is greatly reduced if the binary ion−ion correction parameters are used to correlate data.10
where bv is an empirical constant. In 1933, Root8 suggested an expression for the density of aqueous electrolyte solutions: d = d 0 + B1c + B2 c 3/2
max abs % error
Refined Correlation 0.32 0.41 0.58 3.45
In 1931, Redlich and Rosenfeld7 further expanded the concentration dependence of the apparent molal volume. v = v∞ + Sv* c + bvc
average abs % error
(10) C
DOI: 10.1021/acs.jced.5b00491 J. Chem. Eng. Data XXXX, XXX, XXX−XXX
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increase linearly with the scale of “excess” mass fraction of electrolytes. Here the “excess” mass fraction is the mass fraction of electrolytes in solution accounting only the molecular mass that is in excess of water molar mass: mex, i =
xi(Mi − M H2O) xiMi + (1 − xi)M H2O
ΔMi = Mi − M H2O
=
xiΔMi xiΔMi + M H2O
(12) (13)
where mex,i, xi, and Mi are “excess” mass fraction, mole fraction, and molar mass of electrolyte i, respectively; MH2O is molar mass of water. Figure 3 shows the densities of the 12 aqueous chloride electrolyte solutions plotted against the “excess” mass fractions
Figure 1. Density vs mole fraction for aqueous chloride electrolyte solutions at 298.15 K and 0.1 MPa: (blue ◇) LiCl, (orange □) NaCl, (gray △) KCl, (yellow ×) MgCl2, (blue ∗) CaCl2, (green ○) MnCl2, (blue +) FeCl2, (brown -) FeCl3, (gray −) SrCl2, (brown ◇) BaCl2, (blue □) LaCl3, (green △) CsCl.
Figure 3. Density vs “excess” mass fraction for aqueous chloride electrolyte solutions at 298.15 K and 0.1 MPa: (blue ◇) LiCl, (orange □) NaCl, (gray △) KCl, (yellow ×) MgCl2, (blue ∗) CaCl2, (green ○) MnCl2, (blue +) FeCl2, (brown -) FeCl3, (gray −) SrCl2, (brown ◇) BaCl2, (blue □) LaCl3, (green △) CsCl.
Figure 2. Density vs mass fraction for aqueous chloride electrolyte solutions at 298.15 K and 0.1 MPa: (blue ◇) LiCl, (orange □) NaCl, (gray △) KCl, (yellow ×) MgCl2, (blue ∗) CaCl2, (green ○) MnCl2, (blue +) FeCl2, (brown -) FeCl3, (gray −) SrCl2, (brown ◇) BaCl2, (blue □) LaCl3, (green △) CsCl.
of electrolytes. The narrowed band in Figure 2 collapses further and a largely linear relationship between the densities and the “excess” mass fractions emerges. The slope of this linear relationship is around 1000 kg/m3. To test this assumption further, Figure 4 shows the densities of the 56 aqueous electrolyte solutions plotted against the electrolyte “excess” mass fractions. The excellent correlation can be denoted by a nearly linear, simple quadratic expression:
individual molar mass. In other words, Figure 2 shows that the electrolytes do not have the same apparent volume per unit mass in the solutions. In fact it suggests that a heavier chloride electrolyte involves a smaller apparent volume per unit mass. In terms of the density, it suggests heavier electrolytes contribute more to the densities per unit mass of the electrolytes. Water is a highly structured liquid.29 As electrolytes dissociate to ions and form a hydration shell with neighboring water molecules, the hydrogen-bond network of the aqueous solutions should remain intact. Here we make a simplifying assumption that each electrolyte, regardless of the electrolyte molar mass, takes up the same volume as a water molecule does in the hydrogen-bond network of aqueous solutions. Following the assumption, the density should remain unchanged with increasing electrolyte concentration if the electrolytes molar mass were the same as that of water. Since electrolytes and water do not have the same molar mass, the density should
di = d 0 + C1·mex, i + C2·mex, i 2
(14)
where di is the density of aqueous electrolyte i, d0 is the density of pure water or that of aqueous solution at infinite dilution electrolyte concentration, and C1 and C2 are the universal constants. di, d0, C1, and C2 have the unit of kg/m3. The optimized values against the 1032 data points for the 56 electrolytes are summarized in Table 2 under “universal correlations.” Figure 5 shows the parity plot comparing the calculated densities against the experimental densities. The average error of predictions is 0.97%, with the maximum error being 8.05%. The top three outliers are all nitrates, that is, Mg(NO3)2 (6.22%), LiNO3 (6.27%), and Ca(NO3)2 (8.05%). D
DOI: 10.1021/acs.jced.5b00491 J. Chem. Eng. Data XXXX, XXX, XXX−XXX
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Figure 4. Density vs “excess” mass fraction for 56 aqueous electrolyte solutions at 298.15 K and 0.1 MPa. Figure 6. Parity plot for density (kg/m3) predictions with the Mathias correlation; upper and lower bars present ±5% error band.
Table 2. Coefficients for Universal and Refined Correlations (eq 14) refined correlation coefficients
( ) m3
universal correlation
structure making
structure breaking
structure superbreaking
C1 C2 d0
914.29 880.11 1000.13
705.18 1019.4 998.28
1406.6 666.62 1002.8
841.89 728.34 1002.2
Kg
comparable or better than those of the Mathias correlation with use of unary ion-specific parameters.
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STRUCTURE MAKING AND STRUCTURE BREAKING The universal correlation, eq 14, follows the argument of an unaltered hydrogen-bond network or water lattice structure upon insertion of electrolytes into aqueous solutions. It is wellknown that not all electrolytes behave the same way. Some electrolytes are known to be “structure making” as they do not distort the lattice structure in aqueous solutions while some electrolytes are known to be “structure breaking” because they create “local loosening” of the water lattice structure near ions.30,31 “Local loosening” or “structure breaking” of the water lattice structure implies a larger apparent volume for the added electrolytes. Therefore, the contributions to the densities per unit “excess” mass of “structure making” electrolytes should be the same and represent the upper limit. On the other hand, the contributions for “structure breaking” electrolytes should be lower than that for “structure making” electrolytes. Marcus proposed “structural entropies” as a unique metric of water structure making and breaking by the ions.29,31 The structural entropies, Sstr, are the “water-structural contributions” to the entropies of hydration, and their values for over 120 ions have been reported.31 According to Marcus,31 ions with Sstr greater than 20 J·K−1·mol−1 are structure breakers, and these are mainly anions. Ions with Sstr less than −20 J·K−1·mol−1 are structure makers, and these are mainly monatomic multivalent cations. Ions with Sstr within the intermediate region of ±20 J· K−1·mol−1 are expected to have little or no effect on the structure of water. Sstr values taken from Marcus,31 for some common ions are tabulated in Table 3. We determine the structure making or breaking nature of electrolytes based on the sum of Sstr values of the constituent ions. Clearly electrolytes are considered structure making if both the constituent cation and the anion are structure making. Likewise, electrolytes are considered structure breaking if both the constituent cation and the anion are structure breaking. The narrow band of Figure 4 is found to fall into two primary curves, one for structure making and the other for structure breaking. For borderline cases the decision on the electrolytes is made based on how the experimental density data fall with the
Figure 5. Parity plot for density (kg/m3) predictions with the universal correlation; upper and lower bars present ±5% error band.
% average error =
1 n
n
∑ i
exp di − calc di 100 exp di
(15)
In comparison, the Mathias correlation yields the average error of 1.17% and the maximum error of 10.4% for the 29 electrolytes with available Mathias ion-specific parameters10 that are included in Table 1. Figure 6 shows the parity plot for the Mathias correlation. It is remarkable that, without the use of any ion-specific parameters, eq 14 yields predictions that are E
DOI: 10.1021/acs.jced.5b00491 J. Chem. Eng. Data XXXX, XXX, XXX−XXX
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Table 3. Tabulated Entropy Values of Common Ions31 cation +
Li Na+ K+ Cs+ Ag+ Mg2+ Ca2+ Sr2+ Ba2+ Mn2+ Fe2+ Zn2+ La3+ Fe3+
Sstr (J·K−1·mol−1) −52 −14 47 68 −15 −113 −59 −53 −18 −87 −152 −104 −113 −97
structure effect
anion −
structure making borderline structure breaking structure breaking borderline structure making structure making structure making borderline structure making structure making structure making structure making structure making
Cl Br− I− NO2− NO3− HCO3− H2PO4− HPO42− PO43− SO42− CO32− S2O32− MnO4−
Sstr (J·K−1·mol−1)
structure effect
58 81 117 47 66 −17 −4 −57 −131 8 178 36 100
structure breaking structure breaking structure breaking structure breaking structure breaking borderline borderline structure making structure making borderline structure breaking structure breaking structure breaking
primary density curves for the two families of electrolytes. Figure 7 shows the densities and the “excess” mass fractions for
Figure 8. Density vs “excess” mass fraction for structure breaking electrolytes (green ◇) and structure superbreaking electrolytes (yellow ×).
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Figure 7. Density vs “excess” mass fraction for structure making electrolytes (blue ○) and structure breaking electrolytes (yellow ◇).
MULTICOMPONENT ELECTROLYTE SOLUTIONS Both the universal correlation and the refined correlation can be readily generalized to calculate the densities for aqueous multicomponent electrolyte solutions. mex, i d = ∑ di0· + ∑ C1, i·mex, i + ∑ C2, i·mex, i 2 ∑ m j ex, j (16) i i i
both structure making and structure breaking electrolytes. Figure 8 further shows that, among the structure breaking electrolytes, the five nitrate electrolytes exhibit exceptionally strong structure breaking behavior. These five nitrate electrolytes are considered “structure superbreaking.” Table 4 presents the classification of the 56 electrolytes examined in this study in terms of the three families of electrolytes. The universal correlation of eq 14 is therefore refined by taking into account the different nature of electrolytes in aqueous solutions. The quadratic relationship of eq 14 is applied to each of the three families of electrolytes and the corresponding correlation parameters are shown in Table 2. The parity plot comparing the experimental densities and the densities calculated with the refined correlation is shown in Figure 9. The average error and the maximum error have improved further from 0.98% to 0.59% and from 8.05% to 3.45%, respectively. Table 1 details the results for all 56 electrolytes.
where d is the density of the aqueous solution, d0i is the density of aqueous solution of electrolyte i at infinite dilution electrolyte concentration, C1,i and C2,i are the universal constants for electrolyte i, and mex,i and mex,j are “excess” mass fraction of electrolyte i and electrolyte j, respectively. ∑jmex,j represents the total “excess” mass fraction from all electrolytes for the aqueous solution. Equation 16 suggests simple additivities of contributions to the densities from each electrolyte i. d, d0i , C1,i, and C2,i have unit of kg/m3. The values for d0i , C1,i, and C2,i depend on the choice of universal or refined correlations and the associated parameters in Table 2 for each electrolyte i. To test the performance of the universal correlations for aqueous multicomponent electrolyte solutions, density predictions are performed for aqueous NaCl and KCl mixed electrolyte solutions and Dead Sea water. Figure 10 shows the parity plot for the density predictions against the density data of Kumar32 for the aqueous NaCl−KCl F
DOI: 10.1021/acs.jced.5b00491 J. Chem. Eng. Data XXXX, XXX, XXX−XXX
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Table 4. Three Main Categories of Aqueous Electrolytes (M: structure making, B: structure breaking; sB: structure superbreaking)
mixed electrolyte solution. Also shown are the prediction results from the Mathias correlation. The average errors for the mixed electrolytes are 0.73% and 0.21% with the Mathias correlation and the refined correlation, respectively. The predicted densities from the refined correlation for the mixed electrolytes show a curved shape at high concentrations− consistent with its quadratic nature. Recently Zezin et al.33 reported extensive new data for the densities of the aqueous NaCl−KCl solution. Their data at 298 K and 0.1 MPa are consistent with the data of Kumar. The average error for the density predictions against the data of Zezin et al. is 0.29% with the refined correlation. Figure 11 shows the parity plot for the density predictions against the Dead Sea waters data34 with the Mathias correlation
Figure 9. Parity plot for density (kg/m3) predictions with the refined correlation; upper and lower bars present the ±5% error band.
Figure 11. Parity plot for density (kg/m3) predictions for Dead Sea water: (blue ◇) the refined correlation, (gray △) the Mathias correlation; upper and lower bars present ±3% error band.
and the refined correlation. For Dead Sea water, the average errors are 0.51% and 0.10% for the Mathias correlation and the refined correlation, respectively. The universal correlations are, however, limited to the inorganic electrolytes examined in this study. Future studies should expand the scope to cover aqueous organic electrolytes.
Figure 10. Parity plot for density (kg/m3) predictions for aqueous NaCl-KCl solution: (blue ◇) the refined correlation, (gray △) the Mathias correlation; upper and lower bars present ±3% error band.
G
DOI: 10.1021/acs.jced.5b00491 J. Chem. Eng. Data XXXX, XXX, XXX−XXX
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CONCLUSION Simple universal correlations are developed for the density of aqueous electrolyte solutions at 298.15 K and 0.1 MPa. On the basis of the assumption of unaltered hydrogen-bond network structure, the %-level accuracy correlation represents remarkably well the density with the “excess” mass fraction of electrolytes in aqueous solutions. The correlation is further refined when the concept of “structure making” and “structure breaking” is taken into account for the electrolytes. When plotted against the “excess” mass fraction of electrolytes, the density of structure making electrolytes should represent the upper limit for aqueous electrolyte solutions while the density of structure breaking and superbreaking electrolytes should always be less than that of structure making electrolytes. Our simple universal correlations should be very useful for estimating the density of aqueous electrolyte solutions.
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AUTHOR INFORMATION
Corresponding Author
*Tel.: +1 806.834.3098. E-mail:
[email protected]. Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS The authors gratefully acknowledge the financial support of the Jack Maddox Distinguished Engineering Chair Professorship in Sustainable Energy sponsored by the J. F Maddox Foundation. The authors thank Matt Kovalski for his valuable input.
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DOI: 10.1021/acs.jced.5b00491 J. Chem. Eng. Data XXXX, XXX, XXX−XXX
