Article pubs.acs.org/jced
Densities, Viscosities, and Conductivities of Aqueous Solutions of Tetrabutylphosphonium Bromide and Ethyltributylphosphonium Bromide at Different Temperatures Zhen-Yu Yang, Yu-Feng Hu,* Zhe-Yu Li,* Yu Sun, Chen-Chen Jiang, and Ji-Guang Li State Key Laboratory of Heavy Oil Processing and High Pressure Fluid Phase Behavior & Property Research Laboratory, China University of Petroleum, Beijing 102249, China ABSTRACT: The simple equations developed for prediction of physical properties of multicomponent aqueous solutions of traditional salts were investigated to see if they still work when ionic liquids were used (as solutes) in place of traditional salts. The densities, conductivities, and viscosities of the ternary system [P4,4,4,4]Br (tetrabutylphosphonium bromide) + [P2,4,4,4]Br (ethyltributylphosphonium bromide) + H2O and its binary subsystems [P4,4,4,4]Br + H2O and [P2,4,4,4]Br + H2O were measured at 298.15 K, 303.15 K, and 308.15 K, respectively. The measured values were compared with the values predicted by the above-mentioned equations. The comparison results indicate that with the use of these equations the densities, conductivities, and viscosities of [P4,4,4,4]Br + [P2,4,4,4]Br + H2O can be predicted from the corresponding data of [P4,4,4,4]Br + H2O and [P2,4,4,4]Br + H2O under the condition of identical ionic strength.
1. INTRODUCTION Both transport and thermodynamic properties of solutions of more than one salt in H2O are essential for many practical processes, including separation processes, oil recovery, wastewater treatment, and chemical engineering. Extensive data are available in literature for solutions of one salt in H2O. For example, the viscosities of the binary solution quaternary phosphonium bromide (butyl4−nphenylnPBr with n = 0−4) + H2O as well as the densities and viscosities of the binary systems CaCl2 + H2O and MgCl2 + H2O have been reported.1−3 Laliberté4 developed a new model for calculating the viscosity of aqueous solutions, critically reviewed the data available in the literature for aqueous solutions of one solute, and established the model parameters for 74 solutes. The examined solutes included electrolytes and nonelectrolytes (did not include ionic liquids, which are generally defined5 as salts that contain organic cations and melt at or below 373 K), while the examined solutions contained binary aqueous solutions and multicomponent aqueous solutions of electrolytes and of (electrolyte + nonelectrolyte).4 The agreements between experimental and calculated values were very impressive.4 Therefore, many theorists (Young and Smith,6 Patwardhan and Kumar,7,8 Hu et al.,9−12 Laliberté,4 etc.) have made great efforts to establish simple equations so as to predict the aforementioned properties for aqueous solutions of salt mixtures in terms of the widely reported data for aqueous solutions of a single salt. It is notable that the theory of Hu et al.10,11 is applicable to aqueous solutions of salt mixtures, of nonelectrolyte mixtures, and of the mixtures of salts and organic solutes.13 The Patwardhan−Kumar’s equation7,8 has been used along with the Eyring’s absolute rate theory to successfully predict the © 2014 American Chemical Society
viscosities of a series of mixed salt solutions from the data of the single-salt solutions.12 The rule of Young and Smith6 and the theory of Hu et al.10,11 have been invoked to provide accurate predictions for conductivities of ternary systems using only the information on their constituent binary subsystems.13,14 Ionic liquids are comprised entirely of ions.5 This type of liquids is thermally very stable and their (1) conductivities are notably high, (2) vapor-pressures are extremely low, and (3) catalytic capacities are outstanding. Consequently, they have potential applicability to various fields.5 It is well-known that designing an industrial process will require investigating the physical properties of the involved key materials. As a natural consequence of their widely differing properties, ionic liquids can be mixed to achieve an optimum property for a desired application.15 Therefore, the mixtures of ionic liquids have received a growing attention and the corresponding studies have focused on their electrochemical and spectroscopic properties16,17 as well as their effects on gas solubility properties.15,18−20 On the other hand, water-contamination can significantly change their physicochemical properties. In addition, the demand of ionic liquids in the fields of colloid and surfactant has stimulated more and more studies on the properties of aqueous solutions of ionic liquids.21−26 Such properties are important not only to technical and industrial applications of ionic liquids, but also to the test of electrolyte theories. Recently, Laliberté4 and Yang13 have completed Received: November 29, 2012 Accepted: February 6, 2014 Published: February 14, 2014 554
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Table 1. Densities of the Binary Systems [P4,4,4,4]Br + H2O and [P2,4,4,4]Br + H2O at 298.15 K, 303.15 K, and 308.15 K and at the Pressure p = 0.1 MPaa b o m[P 4,4,4,4]Br
ρo298.15b
mol·kg−1 0.4996 0.7513 0.9998 1.9986 2.9989 4.0037 4.9938 6.0016 6.5026 7.0063 7.9998 8.9962
ρo303.15b
ρo308.15b
b o m[P 2,4,4,4]Br
g·cm−3 1.00850 1.01367 1.01795 1.03009 1.03703 1.04140 1.04428 1.04666 1.04729 1.04818 1.04941 1.05043
1.00658 1.01140 1.01541 1.02684 1.03351 1.03776 1.04058 1.04292 1.04396 1.04443 1.04566 1.04670
ρo298.15b
mol·kg−1 1.00444 1.00898 1.01275 1.02352 1.02996 1.03407 1.03687 1.03915 1.03991 1.04068 1.04187 1.04293
0.5002 0.7497 1.0005 1.9954 3.0008 4.0004 4.9974 5.9982 6.5009 6.9843 8.0013 8.9943
ρo303.15b
ρo308.15b
g·cm−3 1.01054 1.01607 1.02134 1.03807 1.04855 1.05526 1.06040 1.06415 1.06549 1.06691 1.06918 1.07097
1.00866 1.01398 1.01899 1.03494 1.04508 1.05166 1.05671 1.06043 1.06217 1.06318 1.06546 1.06725
1.00660 1.01169 1.01649 1.03174 1.04159 1.04801 1.05300 1.05666 1.05822 1.05941 1.06169 1.06349
The standard uncertainties (u) are u(T) = 0.01 K, u(m) = 1.0·10−4 mol·kg−1, and u(p) = 1.0 kPa, respectively. The combined expanded uncertainty (Uc) is Uc(ρ) = 5.0·10−5 g·cm−3 (0.95 level of confidence). bmo and ρo are the molality and the density of the binary solution. a
Table 2. Conductivities of the Binary Systems [P4,4,4,4]Br + H2O and [P2,4,4,4]Br + H2O at 298.15 K, 303.15 K, and 308.15 K and at the Pressure p = 0.1 MPaa b o m[P 4,4,4,4]Br
mol·kg
σo298.15b
−1
0.4996 0.7513 0.9998 1.9986 2.9989 4.0037 4.9938 6.0016 6.5026 7.0063
σo303.15b mS·cm
16.11 18.10 19.25 19.71 18.41 16.93 15.42 14.30 14.00 13.31
σo308.15b
b o m[P 2,4,4,4]Br
−1
16.52 18.93 20.30 20.80 19.47 18.08 16.56 15.44 15.10 14.40
σo298.15b
−1
0.5002 0.7497 1.0005 1.9954 3.0008 4.0004 4.9974 5.9982 6.5009 6.9843
σo308.15b
−1
mol·kg 17.19 19.90 21.50 22.51 21.30 19.98 18.53 17.26 16.80 16.09
σo303.15b mS·cm
17.74 20.40 22.10 23.50 22.00 20.30 18.72 17.22 16.54 15.77
18.34 21.40 23.30 24.90 23.60 22.10 20.50 19.00 18.46 17.85
18.87 22.10 24.10 26.30 25.50 24.20 22.50 21.10 20.60 19.77
The standard uncertainties (u) are u(T) = 0.01 K, u(m) = 1.0·10−4 mol·kg−1, and u(p) = 1.0 kPa, respectively. The combined expanded uncertainty (Uc) is Uc(σ) = 0.20 mS·cm−1 (0.95 level of confidence). bmo and σo are the molality and the conductivity of the binary solution. a
excellent reviews on the existing models for viscosity. In addition, Laliberté4 proposed a viscosity model and a mixing rule that work for multicomponent solutions at arbitrary concentrations. The agreements between model predictions and measured viscosities are very impressive.4,13 Therefore, it is important to investigate whether these predictive equations still hold when ionic liquids are used in place of traditional electrolyte solutes. As a continuation of our previous study,27 here we measured the densities, conductivities, and viscosities for the ternary system [P4,4,4,4]Br + [P2,4,4,4]Br + H2O and its binary subsystems [P4,4,4,4]Br + H2O and [P2,4,4,4]Br + H2O at different temperatures. Then, we test the simple predictive approaches using the measured data.
The experimental process according to our previous works is summarized as follows.27 The ternary solutions and its binary subsystems were prepared using a Sartorius CT225D balance with an uncertainty ± 5·10−5 mol·kg−1. The solutions were stirred for 2 h in the stoppered bottles and subsequently placed one week to ensure full dissolution. Then the measurements were made. 2.2. Property Measurements. Conductivities of solutions were measured using A Metler Toledo SevenEasy conductivity meter. The temperature was measured using a calibrated calorimeter thermometer (± 0.005 K). The calibration was according to the well established method.14 Density measurements were made using a KEM oscillatingtube digital densimeter (DA-505). The thermostatted stability was ± 0.01 K,28,29 and the uncertainty in density measurements was 5·10−5g·cm−3. Dry air and double-distilled water were used to calibrate the densimeter,28,29 and the densities thereof as a function of temperature were available in refs 30 and 31. A modified Cannon-Ubbelohde suspended level capillary viscometer that has been calibrated by the company was used to measure viscosities. The corresponding glass-sided water thermostat was controlled to 0.01 K. The stated precision of the capillary viscometers was ± 0.1 %.32 In our preliminary measurements, the capillary viscometers were also calibrated
2. EXPERIMENTAL SECTION 2.1. Chemicals and Procedures. The chemicals used in this work are reagent grade and their purity is >99%. Ethyltributylphosphonium bromide (its molar mass is 311.2816 g·mol−1) and tetrabutylphosphonium bromide (its molar mass is 339.3348 g·mol−1) were supplied by Lanzhou Greenchem ILS, LICP. CAS. China. These ionic liquids were dried for 48 h under the conditions of vacuum and 343.15 K immediately prior to their use. 555
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Table 3. Viscosities of the Binary Systems [P4,4,4,4]Br + H2O and [P2,4,4,4]Br + H2O at 298.15 K, 303.15 K, and 308.15 K and at the Pressure p = 0.1 MPaa b o m[P 4,4,4,4]Br
ηo298.15b
mol·kg−1 0.4996 0.7513 0.9998 1.9986 2.9989 4.0037 4.9938 6.0016 6.5026 7.0063 0.4996 0.7513
ηo303.15b
ηo308.15b
1.2823 1.6769 1.9153 3.1001 4.5893 6.0593 7.4031 8.7096 9.3332 9.9459 1.2823 1.6769
ηo303.15b
mol·kg−1
mPa·s 1.4825 1.8715 2.2455 3.8748 5.6411 7.3736 9.0301 10.6521 11.4629 12.2937 1.4825 1.8715
ηo298.15b
b o m[P 2,4,4,4]Br
1.1419 1.4693 1.6601 2.6103 3.8392 5.0365 6.0849 7.1006 7.6179 8.1702 1.1419 1.4693
ηo308.15b
mPa·s
0.5002 0.7497 1.0005 1.9954 3.0008 4.0004 4.9974 5.9982 6.5009 6.9843 0.5002 0.7497
1.4036 1.8007 2.0057 3.1768 4.8056 6.3912 7.9763 9.6812 10.6201 11.5790 1.4036 1.8007
1.2252 1.5892 1.7419 2.6330 3.9778 5.2912 6.5399 7.8519 8.5791 9.3298 1.2252 1.5892
1.0836 1.4264 1.5243 2.1901 3.3312 4.4474 5.4413 6.4586 7.0046 7.5612 1.0836 1.4264
The standard uncertainties (u) are u(T) = 0.01 K, u(m) = 1.0·10−4 mol·kg−1, and u(p) = 1.0 kPa, respectively. The combined expanded uncertainty (Uc) is Uc(η) = 1% (0.95 level of confidence). bmo and ηo are the molality and the viscosity of the binary solution. a
Table 4. The Parameters for the Binary Systems [P4,4,4,4]Br + H2O and [P2,4,4,4]Br + H2O at 298.15 K, 303.15 K, and 308.15 K and at the Pressure p = 0.1 MPa T
parameter
298.15
303.15
308.15
o ρ[P 2,4,4,4]Br+H2O
298.15
303.15
308.15
0.99813 −0.1722 0.714 −0.4499 0.1181 −0.1160 4.1 × 10−4
0.999649 −0.1409 0.6320 −0.3937 0.1020 −0.0985 9.0 × 10−5 T
0.99386 −0.0898 0.5329 −0.3304 0.0844 −0.0804 6.8 × 10−5
A0 10A1 A2 10A3 10A4 102A5 δoρ parameter
1.02242 −0.9651 0.16814 −0.9405 0.2367 −0.2280 2.8 × 10−4
1.01805 −0.8505 0.15112 −0.8412 0.2106 −0.2020 1.9 × 10−4 T
1.01425 −0.7632 0.131763 −0.7616 0.1895 −0.1810 2.2 × 10−4
298.15
303.15
308.15
o σ[P 2,4,4,4]Br+H2O
298.15
303.15
308.15
B0 10−1B1 10−1B2 B3 B4 B5 103B6 δoσ parameter
8.33702 2.234941 −1.619706 5.77063 −1.12677 0.11361 −4.60 1.0 × 10−2
6.83928 2.810602 −2.092208 7.6327 −1.50547 0.15195 −6.13 8.8 × 10−3 T
6.80215 2.966293 −2.112468 7.44165 −1.42305 0.13978 −5.51 8.0 × 10−3
B0 10−1B1 10−1B2 B3 B4 B5 103B6 δoσ parameter
8.17578 2.636891 −1.693039 5.32322 −0.92232 0.08365 −3.1 5.8 × 10−3
7.11082 3.137219 −2.103406 7.00515 −1.27538 0.11998 −4.55 6.8 × 10−3 T
7.16864 3.273217 −2.219955 7.75854 −1.50319 0.15087 −6.09 1.5 × 10−2
o η[P 4,4,4,4]Br+H2O
298.15
303.15
308.15
o η[P 2,4,4,4]Br+H2O
298.15
303.15
308.15
C0 C1 C2 C3 C4 C5 C6 δoη
−1.73434 9.98286 −13.64094 10.61548 −3.38006 0.40198
−16.44345 70.64397 −112.41658 91.62404 −39.39785 8.67868 −0.77292 2.5 × 10−3
−12.96654 54.89468 −84.44084 65.74522 −26.49044 5.34143 −0.423 1.9 × 10−3
C0 C1 C2 C3 C4 C5 C6 δoη
−23.33991 100.94819 −163.45665 134.55322 −58.52842 12.97899 −1.15051 2.2 × 10−3
−22.19978 93.92135 −148.45209 118.66647 −49.96206 10.67525 −0.90765 6.3 × 10−4
−24.74804 103.65787 −163.37947 129.94356 −54.63995 11.69072 −1.00031 1.8 × 10−3
parameter o ρ[P 4,4,4,4]Br+H2O
A0 10A1 10A2 10A3 10A4 102A5 δoρ parameter o σ[P 4,4,4,4]Br+H2O
2.4 × 10−3
with materials of known viscosity (η) such as water (ηT=298.15 K = 0.8903 mPa·s),33,34 ethylene glycol (ηT=298.15 K = 9.408 mPa·s), and diethylene glycol (ηT=298.15 K = 26.812 mPa·s).33,34
T
of MiXi in MiXi + H2O (i = 1 and 2) and in M1X1 + M2X2 + H2O, respectively (we used the superscript I to mean that the ionic strength (denoted by I) of each binary solution is identical to that of the corresponding ternary solution). The equation of Patwardhan and Kumar8 is given by eq 1:
3. RESULTS AND DISCUSSION 3.1. Equations for Prediction of Density and Conductivity of Aqueous Solutions of Ionic Liquids. In this study, Qo,I MiXi (Q = ρ, σ, η, etc.) and QMiXi stand for the properties
ρ=
∑ YM X /∑ (YM X /ρMo,IX ) i i
i
556
i i
i
i i
(1)
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Table 5. Comparisons of Predicted and Measured Densities for the Ternary Solution [P4,4,4,4]Br (B) + [P2,4,4,4]Br (C) + H2O at Different Temperatures and at the Pressure p = 0.1 MPaa mB
mC mol·kg
0.0999 0.5999 1.1991 1.7989 0.2498 1.4986 2.9765 4.4815 0.3997 2.3996 4.8007 7.1960
−1
0.4006 2.4086 4.8209 7.2308 0.2494 1.4871 2.9854 4.4487 0.0994 0.5865 1.1649 1.7402
ρexpt.
Table 6. Comparisons of Predicted and Measured Conductivities for the Ternary Solution [P4,4,4,4]Br (B) + [P2,4,4,4]Br (C) + H2O at Different Temperatures and at the Pressure p = 0.1 MPaa
ρeq 1 g·cm
298.15 K 1.00996 1.04638 1.05998 1.06646 1.00952 1.04286 1.05499 1.06010 1.00909 1.03951 1.04971 1.05408
−3
1.00951 1.04276 1.05489 1.05957 1.00948 1.04261 1.05475 1.05950 1.00948 1.04261 1.05476 1.05951
0.4006 2.4086 4.8209 7.2308 0.2494 1.4871 2.9854 4.4487 0.0994 0.5865 1.1649 1.7402
303.15 K 1.00809 1.04289 1.05627 1.06274 1.00762 1.03938 1.05128 1.05634 1.00715 1.03602 1.04600 1.05034
0.0999 0.5999 1.1991 1.7989 0.2498 1.4986 2.9765 4.4815 0.3997 2.3996 4.8007 7.1960
0.4006 2.4086 4.8209 7.2308 0.2494 1.4871 2.9854 4.4487 0.0994 0.5865 1.1649 1.7402
308.15 K 1.00603 1.03938 1.05251 1.05898 1.00552 1.03584 1.04753 1.05258 1.00503 1.03247 1.04224 1.04656
mol·kg
−0.00045 −0.00346 −0.00480 −0.00646 0.00004 −0.00024 −0.00023 −0.00056 0.00039 0.00298 0.00481 0.00515 2.47·10−3
1.00762 1.03936 1.05158 1.05684 1.00759 1.03921 1.05144 1.05674 1.00759 1.03921 1.05145 1.05674 δρ
−0.00047 −0.00338 −0.00444 −0.00555 0.00003 −0.00016 0.00015 0.00038 0.00044 0.00308 0.00521 0.00609 2.36·10−3
1.00553 1.03579 1.04771 1.05277 1.00550 1.03564 1.04756 1.05267 1.00550 1.03564 1.04757 1.05268 δρ
−0.00050 −0.00345 −0.00456 −0.00586 0.00002 −0.00019 0.00003 0.00009 0.00046 0.00306 0.00511 0.00585 2.32·10−3
σexpt
mC
δρ
δρb 0.0999 0.5999 1.1991 1.7989 0.2498 1.4986 2.9765 4.4815 0.3997 2.3996 4.8007 7.1960
mB
σeq2
−1
δσ −1
mS·cm
0.0999 0.5999 1.1991 0.2498 1.4986 2.9765 0.3997 2.3996 4.8007
0.4006 2.4086 4.8209 0.2494 1.4871 2.9854 0.0994 0.5865 1.1649
298.15 K 17.69 20.10 15.69 16.01 18.69 14.66 15.35 17.24 13.41
0.0999 0.5999 1.1991 0.2498 1.4986 2.9765 0.3997 2.3996 4.8007
0.4006 2.4086 4.8209 0.2494 1.4871 2.9854 0.0994 0.5865 1.1649
303.15 K 18.16 21.90 17.57 16.40 20.20 16.34 15.70 18.51 15.29
0.0999 0.5999 1.1991 0.2498 1.4986 2.9765 0.3997 2.3996 4.8007
0.4006 2.4086 4.8209 0.2494 1.4871 2.9854 0.0994 0.5865 1.1649
308.15 K 18.42 23.50 19.75 17.20 22.10 17.65 16.52 20.40 17.06
17.42 21.27 16.64 16.92 20.22 15.83 16.43 19.13 14.92 δσb
−0.015 0.058 0.061 0.057 0.082 0.080 0.070 0.109 0.112 7.1·10−2
17.98 22.72 16.35 17.42 21.52 16.12 16.88 20.28 15.70 δσ
−0.010 0.038 −0.069 0.062 0.065 −0.013 0.075 0.096 0.027 5.0·10−2
18.54 24.65 19.93 18.02 23.40 19.00 17.52 22.12 17.96 δσ
0.007 0.049 0.009 0.048 0.059 0.076 0.060 0.085 0.053 4.9·10−2
The standard uncertainties (u) are u(T) = 0.01 K, u(m) = 1.0·10−4 mol·kg−1, and u(p) = 1.0 kPa. The combined expanded uncertainty (Uc) is Uc(σ) = 0.20 mS·cm−1 (0.95 level of confidence). bδσ = Σi N= 1|σMiXi(eq 2) − σMiXi(expt)|/(NσMiXi(expt)). a
σ=
∑ yM X σMo,IX i i
i
i i
(2)
with yMiXi = IMiXi/ΣiIMiXi. To predict viscosities for M1X1 + M2X2 + ··· + MnXn + H2O using only the data (ηo,I MiXi) of MiXi + H2O (i = 1, 2, ···,n) of identical ionic strength, Hu invoked12 the Eyring’s absolute rate theory and the Patwardhan and Kumar’s equation7,8 to derive eq 3:
The standard uncertainties (u) are u(T) = 0.01 K, u(m) = 1.0·10−4 mol·kg−1, and u(p) = 1.0 kPa, respectively. The combined expanded uncertainty (Uc) is Uc(ρ) = 5.0·10−5 g·cm−3 (0.95 level of confidence). b δρ = Σi N= 1|ρMiXi(eq 1) − ρMiXi(expt)|/(NρMiXi(expt)). a
ln η =
with YMiXi = yMiXi + mMiXiMMiXi, where y, ρ, m, and M denote ionic strength fraction, molality, molar mass, and density, respectively. The Young’s rule35,36 allows using the conductivities of MiXi + H2O (i = 1 and 2) to estimate the data for M1X1 + M2X2 + H2O under the condition of constant ionic strength (i.e., the ionic strength in the examined three solutions is the same):
∑ (x M X /x Mo,IX ) ln ηMo,IX i i
i
i i
i i
(3)
where xo,I MiXi stands for the mole fraction of the binary solution MiXi + H2O (i = 1, 2, ···, n). 3.2. Comparisons with Experimental Data. The procedure for test of eqs 1 to 3 can be described briefly as follows. 557
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(2) Determine the values of mo,I MiXi for MiXi in MiXi + H2O (i = 1 and 2) according to the relationship mo,I MiXi = mM1X1 + mM2X2 (mMiXi (i = 1 and 2) is the molality of MiXi in M1X1 + M2X2 + H2O). o,I o,I (3) Insert the values of ρo,I MiXi, ηMiXi, and σMiXi obtained from eqs 4 to 6 into eqs 1 to 3 to predict the corresponding data for M1X1 + M2X2 + H2O. (4) Compare predicted and measured values. The average relative differences between measured and predicted densities (δρ), conductivities (δσ), and viscosities (δη) can be expressed as29
Table 7. Comparisons of Measured and Predicted Viscosities for the Ternary System [P4,4,4,4]Br (B) + [P2,4,4,4]Br (C) + H2O at Different Temperatures and at the Pressure p = 0.1 MPaa mB
ηexpt.
mC mol·kg
−1
0.0999 0.5999 1.1991 0.2498 1.4986 2.9765 0.3997 2.3996 4.8007
ηeq 3 δη
mPa·s 298.15 K 1.4107 5.0026 9.8185 1.4409 5.1081 10.3349 1.4567 5.5072 10.5893
0.4006 2.4086 4.8209 0.2494 1.4871 2.9854 0.0994 0.5865 1.1649
0.0999 0.5999 1.1991 0.2498 1.4986 2.9765 0.3997 2.3996 4.8007
0.4006 2.4086 4.8209 0.2494 1.4871 2.9854 0.0994 0.5865 1.1649
303.15 K 1.2508 4.1745 7.8606 1.2608 4.2054 8.2607 1.2710 4.5671 8.5214
0.0999 0.5999 1.1991 0.2498 1.4986 2.9765 0.3997 2.3996 4.8007
0.4006 2.4086 4.8209 0.2494 1.4871 2.9854 0.0994 0.5865 1.1649
308.15 K 1.1037 3.4738 6.4477 1.1110 3.5039 6.7773 1.1232 3.8305 6.9803
1.4200 4.9703 9.9080 1.4409 5.1797 10.0927 1.4653 5.4391 10.4004 δηb
0.0066 −0.0064 0.0091 0.0000 0.0140 −0.0234 0.0059 −0.0124 −0.0178 1.0·10−2
1.2375 4.1033 8.0443 1.2516 4.2540 8.2159 1.2691 4.4446 8.4845 δη
−0.0107 −0.0171 0.0234 −0.0073 0.0116 −0.0054 −0.0015 −0.0268 −0.0043 1.2·10−2
1.0959 3.4392 6.6018 1.1106 3.5629 6.7306 1.1286 3.7202 6.9331 δη
−0.0070 −0.0100 0.0239 −0.0004 0.0168 −0.0069 0.0047 −0.0288 −0.0068 1.1·10−2
N
δρ =
i=1
i i
l=0
σMo iX i(calc) =
∑ Bl (mMo X )l/2 i i
l=0
ηMo X (calc) = i i
∑ Cl(mMo X )l i i
l=0
(8)
N
δη =
∑ |δη,i|/N i=1
(9)
with δQ,i = (Qi(calc) − Qi(expt))/Qi(expt) (Q = ρ, σ, and η), where N is the number of measured data. 3.3. Verifications of Equations. Tables 1 to 3 show the measured values of ρoMiXi, σoMiXi, and ηoMiXi of [P4,4,4,4]Br + H2O and [P2,4,4,4]Br + H2O at the three temperatures, respectively. Table 5 compares predicted and experimental density data for the system [P4,4,4,4]Br + [P2,4,4,4]Br + H2O at the three temperatures (298.15 K, 303.15 K, and 308.15 K). The value of −3 δeq1 ρ is (2.40 ± 0.08)·10 . The predicted and measured values of σexpt. for [P4,4,4,4]Br + [P2,4,4,4]Br + H2O are compared in Table 6. The results are 2 −2 eq 2 −2 2 −2 δeq and δeq σ,298.15 = 7.1·10 , δσ,303.15 = 5.0·10 σ,308.15 = 4.9·10 , respectively. According to the results shown in Table 7, the measured viscosities of the solution [P4,4,4,4]Br + [P2,4,4,4]Br + H2O show 3 good conformity to eq 3. The δeq value is (1.1 ± 0.1)·10−2 and η 3 the change in temperature has little influence on δeq η .
4. CONCLUSIONS The densities, conductivities, and viscosities of the ternary system [P4,4,4,4]Br + [P2,4,4,4]Br + H2O and its binary subsystems [P4,4,4,4]Br + H2O and [P2,4,4,4]Br + H2O were measured at three temperatures. The results were used to test whether the predictive equations established for traditional salt solutions are applicable to aqueous solutions of ionic liquid mixtures. The comparison results confirm that the examined approaches allow us to well predict the densities, viscosities, and conductivities of [P4,4,4,4]Br + [P2,4,4,4]Br + H2O from the corresponding data of its binary subsystems [P4,4,4,4]Br + H2O and [P2,4,4,4]Br + H2O if the ionic strength of the three solutions is identical.
(1) Fit the measured data of ρoMiXi (density, cf. Table 1), σoMiXi (conductivity, cf. Table 2), and ηoMiXi (viscosity, cf. Table 3) of MiXi + H2O (i = 1 and 2) to eqs 4 to 6
∑ Al (mMo X )l/2
∑ |δσ ,i|/N i=1
The standard uncertainties (u) are u(T) = 0.01 K, u(m) = 1.0·10−4 mol·kg−1, and u(p) = 1.0 kPa, respectively. The combined expanded uncertainty (Uc) is Uc(η) = 1% (0.95 level of confidence). bδη = Σi N= 1|ηMiXi(eq 3) − ηMiXi(expt)|/(NηMiXi(expt)).
i i
(7)
N
δσ =
a
ρMo X (calc) =
∑ |δρ,i|/N
(4)
(5)
■
(6)
AUTHOR INFORMATION
Corresponding Author
moMiXi
where denotes the molality of MiXi in MiXi + H2O (i = 1 and 2). The values of l were increased until the values of δoQ,MiXi = ΣjN= 1(|QoMiXi(calc) − QoMiXi(expt)|/QoMiXi(expt))/N (Q = ρ, σ, and η) are less than a few parts in 10−3. The thus-obtained values of Al, Bl, Cl, δoρ,MiXi, δoσ,MiXi, and δoη,MiXi are shown in Table 4.
*E-mail:
[email protected];
[email protected]. Tel.: 8610-89733846. Funding
The authors thank the National Natural Science Foundation of China (21276271, 20976189, and 21076224) and Science 558
dx.doi.org/10.1021/je400101s | J. Chem. Eng. Data 2014, 59, 554−559
Journal of Chemical & Engineering Data
Article
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Foundation of China University of Petroleum, Beijing (qzdx2011-01) for financial support. Notes
The authors declare no competing financial interest.
■
ACKNOWLEDGMENTS
■
REFERENCES
The authors thank the Lanzhou Greenchem ILS, LICP, CAS, China, for supplying the ILs used herein.
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dx.doi.org/10.1021/je400101s | J. Chem. Eng. Data 2014, 59, 554−559
