Density, Viscosity, and Vapor Pressure Measurements of Water +

Article pubs.acs.org/jced

Density, Viscosity, and Vapor Pressure Measurements of Water + Lithium Bis(trifluoromethylsulfonyl)imide Solutions William J. R. Gilbert,† Javid Safarov,‡,§ David L. Minnick,† M. Alejandra Rocha,† Egon P. Hassel,‡ and Mark B. Shiflett*,† †

Department of Chemical and Petroleum Engineering, University of Kansas, 1530 W. 15th, Lawrence, Kansas 66045, United States Institute of Technical Thermodynamics, University of Rostock, Albert-Einstein-Straße 2, D-18059 Rostock, Germany § Department of Heat Energy, Azerbaijan Technical University, AZ-1073 Baku, Azerbaijan ‡

ABSTRACT: The solubility, density (ρ), viscosity (η), and vapor pressure (P) of lithium bis(trifluoromethylsulfonyl)imide (LiTf2N) in water are evaluated. The maximum salt solublity for LiTf2N in water was determined to be between mass fractions (ws) of 0.8065 and 0.8217 at 295.15 K. The density (ρ) and viscosity (η) were evaluated at temperatures ranging from 298.15 to 373.15 K and mass fractions of up to 0.8024. Least-squares regression is used to correlate the viscosity and density data over the entire range of temperatures and concentrations. The vapor pressure of LiTf2N in water is determined for temperatures of 274.15 to 471.15 K and mass fractions of up to 0.8065. In addition, this work describes the solvent activity (as), osmotic coefficient (Φ), molal activity (γ±), and enthalpy of vaporization (ΔHv). The osmotic coefficients were calculated using the second virial coefficient of water, and Pitzer−Mayorga and Clausius−Clapeyron models are used to evaluate the vapor pressure data.

1. INTRODUCTION A thermoplastic, poly(vinyl fluoride) (PVF), is used as a protective coating because of its excellent chemical and environmental stability. DuPont Tedlar PVF film is utilized as a protective barrier back sheet on photovoltaic panels.1 Polymerization of vinyl fluoride to produce PVF is traditionally performed in a water emulsion at high pressures to overcome limited monomer solubility in the aqueous reaction phase.2,3 To reduce the elevated operating pressures of these polymerization processes, recent studies have investigated conducting the polymerization reaction in ionic liquids (ILs) and ionic solutions that exhibit higher vinyl fluoride monomer solubility. Specifically, the solubility of vinyl fluoride has been measured in a variety of room-temperature ILs including: 1-ethyl-3methylimidazolium bis(trifluoromethylsulfonyl)imide [C2C1im][Tf2N], 1-butyl-3-methylimidazolium dicyanamide [C4C1im][N(CN)2], 1-butyl-4-methylpyridinium tetrafluoroborate [C 4 m γ py][BF 4 ], 1-butyl-3-methylimidazolium 1,1,2,3,3,3-hexafluoropropanesulfonate [C4C1im][HFPS], and 1-octyl-3-methylimidazolium 1,1,2,2-tetrafluoroethanesulfonate [C8mim][TFES]. The results demonstrated increased monomer solubility at pressures below 5 MPa (50 bar), but polymerization reactions were not effective in the investigated ILs.4 In contrast, the same study identified lithium bis(trifluoromethylsulfonyl)imide (LiTf2N) salt + water as an ideal solvent and reaction medium for the polymerization of vinyl fluoride.5 Further investigation showed a maximum vinyl fluoride solubility of 0.0629 mass fraction in a solution composed of 0.80 mass fraction LiTf2N in water on a binary solute (VF) free basis at 1.781 MPa and 282.98 K.6 On the basis of promising thermodynamic and © 2017 American Chemical Society

kinetic results, we seek to advance this area by characterizing the physical properties of LiTf2N solutions.

2. EXPERIMENTAL SECTION 2.1. Materials. As shown in Table 1, high-purity lithium bis(trifluoromethylsulfonyl)imide ([Li+][Tf2N−]) salt was Table 1. Description of Chemical Components chemical name LiTf2N HPLC-grade water a

source IoLoTec Ionic Liquid Technologies Fisher Scientific

purification method

final mole fraction purity

N/A

0.99

evaporation minimum 0.999

analysis method ICa LC−MSb

Ion chromatography. bLiquid chromatography−mass spectrometry.

purchased from IoLoTec Ionic Liquid Technologies GmbH, Germany (99% purity, K1-0001-HP-25, Lot No. J00520.4, CAS no. 90076-65-6). Salt solutions were made using HPLC-grade water (99.9% purity, Fisher Scientific). 2.2. Experimental Measurements. The solubility of LiTf2N in water was measured visually by the incremental addition of salt to a fixed volume of water. The solubility results were used to determine the maximum LiTf2N salt concentration. For all studies, the concentration of the solution was determined Received: February 5, 2017 Accepted: May 5, 2017 Published: June 5, 2017 2056

DOI: 10.1021/acs.jced.7b00135 J. Chem. Eng. Data 2017, 62, 2056−2066

Journal of Chemical & Engineering Data

Article

by mass using an electronic scale (Sartorius ED224S, Germany) with 0.0001 g uncertainty. The density and viscosity of LiTf2N + water solutions were measured at 298.15, 323.15, 348.15, and 373.2 K and mass fractions (ws) of 0.2739, 0.4871, 0.6633, and 0.8024 at a pressure of 101 325 ± 1000 Pa. Densities were measured using an oscillating u-tube density meter (Microdensity meter, model 102B) and verified at T = 298.15 K using a helium pycnometer (Micromeritics AccuPyc 1330 with a 1 cm3 measuring cup). The microdensity meter was factory calibrated to determine the fundamental vibrational frequency using a number of fluids with known densities. The uncertainties in both density methods are 1.0 kg·m−3. The viscosity of LiTf2N + water solutions was measured using a capillary viscometer (Cannon-Manning semimicro viscometer) with an uncertainty of ±5%. Viscometer calibration was performed using Standard Test ASTM D 445 and viscosity standards 2807 and 2808 at 313.15 K. The vapor pressure (P/Pa) of LiTf2N + water solutions was measured using the two highly accurate, static experimental instruments depicted in Figures 1 and 2. A detailed description of the experimental setup and procedure is described in a

Figure 2. Experimental apparatus: (1) thermostat; (2) PT-100 platinum resistance thermometers for control of the measuring cell temperature by the thermostat; (3) platinum resistance thermometer PT-100 for control of the temperature of the measuring cell; (4) pressure transmitter 35 X HTC (Omega GmbH and Co.); (5) Omega PT-104A channel RTD input data acquisition module for the measurment of temperature; (6) PC; (7) manual pressure signal conditioner; (8) flask for the sample; (9 and 10) valves; (11) insulation of measuring cell; (12) heat-transfer reservoir; (13) measuring cell; (14) magnet; (15) magnetic stirrer; (16) vacuum indicator; (17) liquid nitrogen trap with a coldfinger; and (18) vacuum pump.

similar study.7 To demonstrate the accuracy, reference solutions of water, methanol, acetone, toluene, and 1-butanol have been measured and compared to literature values. For example, experimental and calculated values8 for water are shown in Table 2 and demonstrate combined expanded uncertainties Uc of Uc(P) = 30 Pa for P < 0.1 MPa, Uc(P) = 1500 Pa for P < 3 MPa, and Uc(P) = 8000 Pa for P < 16 MPa (level of confidence = 0.95). In the current work, vapor pressures were measured for LiTf2N + water solutions of varying salt concentrations (up to ws = 0.8065) and temperatures ranging from 274.15 to 471.15 K. For vapor pressures below ambient pressure, the apparatus containing glass cells was applied for temperatures from 274.15 to 323.15 K (Figure 1). For vapor pressures higher and lower than ambient pressure, metals cells (Figure 2) were used to test samples at temperatures ranging from 325.15 to 471.15 K. Before conducting experiments, the measuring cells were washed with water and acetone and then dried under vacuum for 3 to 5 h. Before injection, LiTf2N + water solutions were degassed while being mixed. Using the apparatus in Figure 1, the cell pressure equilibrated within 15 min and the subsequent vapor pressure readings were measured in triplicate in 10 to 20 min intervals. For the apparatus in Figure 2, equilibrium was reached in 50 to 70 min. Vapor pressure measurements were first observed using an increasing temperature ramp and were confirmed by repeating the measurements using a decreasing temperature ramp.

Figure 1. Experimental apparatus for measuring vapor pressures at T = (274.15 to 323.15) K: (1, 28, and 30) magnetic stirrer; (2 and 36) magnet, (3) cell for water in the difference method; (4) cell for measuring sample in the difference method; (5 and 37) valves for closing the cell for the measuring sample of the difference method and (26) of the static cell; (6, 35, 39, and 40) platinum resistance thermometers with an Omega PT-104A temperature signal conditioner (19); (7, 20, and 38) injection ports of the measuring sample; (8 and 25) electric heating; (9 and 24) water heat exchange system; (10) pressure sensor head of the difference method and (23) of the static cell; (11) pressure sensor reservoir of the difference method and (22) of the static method cell; (12) pressure signal connection of the difference method cell and (15) of the static method cell; (13) pressure signal conditioner of the difference method and (14) of the static method cell; (16) thermostat HAAKE F5; (17 and 18) electric heater control systems; (21) thermostat Lauda Gold R-415; (27) static cell; (29) injection cell; (31) vacuum indicator; (32) liquid nitrogen trap with a coldfinger; (33) vacuum pump; and (34) PC. 2057



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Table 2. Experimental and Literature Values8 for the Vapor Pressure of Watera T/K

Pexp/Pa

Plit/Pa

Pexp − Plit/Pa

T/K

Pexp/Pa

Plit/Pa

Pexp − Plit/Pa

274.15 279.48 286.16 291.39 293.14 296.32 296.31 298.81 301.37 303.57 307.73 308.26 312.87 313.07 314.62 318.13 318.13 322.99 323.10 323.17

661 953 1508 2094 2337 2834 2839 3288 3827 4360 5507 5666 7275 7345 7977 9585 9578 12 260 12 320 12 362

657 961 1502 2096 2339 2840 2838 3297 3832 4351 5500 5664 7276 7354 7984 9585 9585 12 254 12 321 12 364

4 −8 6 −2 −2 −6 1 −9 −5 9 7 2 −1 −9 −7 0 −7 6 −1 −2

328.14 328.14 328.88 333.15 343.15 353.15 363.15 373.15 383.15 393.15 403.15 413.15 423.15 433.15 443.15 453.15 463.15 468.15 470.15 471.15

15 748 15 746 16 312 20 056 31 279 47 450 70 210 101 425 143 287 198 752 270 216 361 642 476 334 618 336 792 154 1 002 713 1 255 226 1 398 871 1 459 748 1 490 952

15 754 15 754 16 321 19 946 31 201 47 414 70 182 101 418 143 379 198 674 270 280 361 539 476 165 618 235 792 187 1 002 811 1 255 236 1 398 820 1 459 719 1 490 935

−6 −8 −9 110 78 36 28 7 −92 78 −64 103 169 101 −33 −98 −10 51 29 17

a Standard uncertainties u are u(T) = 0.01 K, and combined expanded uncertainties Uc are Uc(P) = 30 Pa for P < 0.1 MPa, Uc(P) = 1500 Pa for P < 3 MPa, and Uc(P) = 8000 Pa for P < 16 MPa (level of confidence = 0.95).

Figure 3. Solubility of LiTf2N in water at 295.15 K, with 80.65, 82.17, and 84.49 wt % (ws = 0.8065, 0.8217, and 0.8449) salt in water from left to right, respectively.

3. RESULTS AND DISCUSSION 3.1. Salt Solubility. The solubility of LiTf2N in water was observed at room temperature and mass fractions of 0.8065, 0.8217, 0.8449, and 0.8705 salt. Figure 3 displays the experimental solubility measurements for three salt concentrations and indicates that the solubility limit of LiTf2N in water is between mass fractions of 0.8065 and 0.8217 salt at 295.15 K. To ensure solubility, all subsequent studies were conducted using a maximum salt mass fraction at or slightly below 0.8065. 3.2. Density and Viscosity Studies. The density (ρ/kg·m−3) and viscosity (η/mPa·s) of LiTf2N + water solutions were investigated at various salt concentrations in water. Table 3 displays the data for the density and viscosity of LiTf2N + water solutions with respect to the temperature and salt concentration. Correlations were constructed by applying least-squares analysis for the density (eq 1) and viscosity (eq 2) where T = T/K − 273.15 and ws = LiTf2N mass fraction in water. The density fit resulted in a standard deviation of 2.55 kg·m−3 and an absolute average deviation of 2.20 kg·m−3.

The viscosity correlation had a standard deviation of 6.26% and an absolute average deviation of 3.63%. Table 4 lists the coefficients for both correlations. Equations 1 and 2 were used to predict the variation of LiTf2N + water solution properties at incremental concentrations, as shown in Figures 4 and 5. In the figures, dotted lines represent theoretical values based on mass fractions above the solubility limit (ws ≈ 0.81). ρ/kg· m−3 = [a0 + a1T + a 2ws + a3T 2 + a4ws 2 + a5Tws] × 1000 (1)

ln(η)/mPa·s = a0 + a1T + a 2ws + a3T 2 + a4ws 2 + a5Tws + a6T 3 + a 7ws 3 + a8Tws 2 + a 9T 2ws

(2)

3.3. Vapor Pressure. The experimental vapor pressures (P/Pa), solvent activities (as), osmotic coefficients (Φ), and molal activity coefficients (γ±) are listed in Table 5. Vapor pressures were measured for LiTf2N concentrations ranging from 0.0608 to 14.518 mol·kg−1 (ws = 0.0171 to 0.8065) and 2058



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Table 3. Experimental Mass Fraction of Salt (ws) in Water and the Corresponding Density (ρ/kg·m−3) and Viscosity (η/mPa·s) of LiTf2N Solutions Measured at 101 325 Paa ρ/kg·m−3

ws 0.2739 0.4871 0.6633 0.8024 0.2739 0.4871 0.6633 0.8024 0.2739 0.4871 0.6633 0.8024 0.2739 0.4871 0.6633 0.8024

T = 298.15 1160 1325 1493 1654 T = 323.15 1148 1304 1467 1624 T = 348.15 1131 1282 1440 1598 T = 373.15 1109 1258 1401 1557

η/mPa·s K 1.54 2.74 5.34 18.23 K 0.88 1.50 2.83 8.75 K 0.59 1.00 1.82 5.20

Figure 4. Correlated densities for LiTf2N + water solutions using leastsquares analysis described by eq 1. Lines represent the LiTf2N mass fraction in water, and dotted lines represent mass fractions above the saturated solubility.

K 0.48 0.68 1.54 3.42

a

Standard uncertainties u are u(P) = 1000 Pa, u(ω) = 0.0001, u(T) = 0.01 K, and combined expanded uncertainties Uc are Uc(ρ) = 1.0 kg·m3 and Uc(η) = 0.05 (level of confidence = 95%). The uncertainty in mass fractions does not include sample purities.

Table 4. Coefficients from Least-Squares Regression Analysis Applied to Equations 1 and 2a coefficients a0 a1 a2 a3 a4 a5 a6 a7 a8 a9

density, ρ/kg·m−3 9.9944 −1.0600 4.9372 −3.5741 4.3029 −1.0078

× × × × × ×

ln[viscosity, η/mPa·s]

10−1 10−5 10−1 10−6 10−1 10−3

5.6748 −3.1075 2.9031 1.7121 −4.7282 −7.0442 −4.3961 7.7172 −1.2194 7.7699

× 10−1 × 10−2 × 10−4 × 10−3 × 10−7 × 10−2 × 10−5

Figure 5. Correlated viscosity for LiTf2N + water solutions using the least-squares analysis described by eq 2. Lines represent LiTf2N mass fractions in water, and dotted lines represent mass fractions above the saturated solubility.

Regression results in absolute deviations of 2.20 kg·m−3 and 3.36% for the density and viscosity, respectively. a

temperatures from 274.15 to 471.15 K. The vapor pressure data listed in Table 5 is plotted in Figure 6. 3.4. Solvent Activity Coefficients. The activity coefficients (as) were calculated using eq 3 and experimental vapor pressures. In addition, the equation is a function of the temperature (T/K), gas constant (R/m3·Pa·K−1·mol−1), vapor pressure of pure water (P*/Pa), second virial coefficient of water vapor (Bs/m3·mol−1), and molar volume of pure water vapor (V*s/m3·mol−1). Vapor pressure phase solvent nonideality is corrected using the virial equation. The virial coefficients, volumes of water vapor, and vapor pressures of pure water are listed in Table 6. Figure 7 depicts the calculated results of solvent activity with respect to temperature and LiTf2N salt concentration. (B − V s*)(P − P*) ⎛ P ⎞ ln(as) = ln⎜ ⎟ + s ⎝ P* ⎠ RT

3.5. Osmotic Coefficients. Osmotic coefficients of the various solutions were calculated using eq 4, which utilizes the sum of stoichiometric numbers of anions and cations (v = v‑ + v+), the molality of the salt solution (m/mol·kg−1), and the molecular weight of water (Ms/kg·mol−1). The osmotic coefficient results are illustrated in Figure 8.

Φ=−

ln(as) vmMs

(4)

The osmotic coefficients are modeled using the Pitzer and Mayorga correlation represented by eq 5.9 The term f Φ is represented by eqs 6−8, where AΦ (eq 7) is the Debye−Hückel limiting law slope for the osmotic coefficient (Φ) on a molal basis. Equation 8 is used to calculate the ionic strength in molarity where mj is the molarity of the jth ion and zj is the

(3) 2059



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Table 5. Experimental Mass Fraction of Salt (ws) in Water, Corresponding Molality (m/mol·kg−1), Vapor Pressure (P/Pa), Solvent Activity (as), Osmotic Coefficient (Φ), and Activity Coefficients (γ±) of LiTf2N Solutionsa ws

ms/mol·kg−1

0.0000 0.0171 0.0212 0.0291 0.0525 0.0780 0.1118 0.2090 0.3086 0.3945 0.4946 0.6036 0.6682 0.7210 0.7600 0.7824 0.8065

0.0000 0.0608 0.0753 0.1043 0.1931 0.2945 0.4387 0.9202 1.5550 2.2698 3.4095 5.3500 7.0153 9.0029 11.0284 12.5209 14.5190

0.0000 0.0171 0.0212 0.0291 0.0525 0.0780 0.1118 0.2090 0.3086 0.3945 0.4946 0.6036 0.6682 0.7210 0.7600 0.7824 0.8065

0.0000 0.0608 0.0753 0.1043 0.1931 0.2945 0.4387 0.9202 1.5550 2.2698 3.4095 5.3500 7.0153 9.0029 11.0284 12.5209 14.5190

0.0000 0.0171 0.0212 0.0291 0.0525 0.0780 0.1118 0.2090 0.3086 0.3945 0.4946 0.6036 0.6682 0.7210 0.7600 0.7824 0.8065

0.0000 0.0608 0.0753 0.1043 0.1931 0.2945 0.4387 0.9202 1.5550 2.2698 3.4095 5.3500 7.0153 9.0029 11.0284 12.5209 14.5190

0.0000 0.0171

0.0000 0.0608

P/Pa T = 274.15 657 656 655 654 653 651 647 634 613 585 534 444 364 275 196 145 94 T = 278.15 873 872 871 870 869 866 861 846 818 781 716 602 501 385 278 212 140 T = 283.15 1228 1226 1225 1224 1221 1217 1211 1187 1150 1099 1011 854 716 557 411 317 217 T = 293.15 2339 2336

as

Φ

γ±

1.0000 0.9985 0.9970 0.9954 0.9939 0.9909 0.9848 0.9650 0.9331 0.8905 0.8129 0.6759 0.5542 0.4187 0.2985 0.2208 0.1432

1.000 0.714 0.674 0.664 0.704 0.794 0.897 1.074 1.237 1.418 1.687 2.050 2.335 2.684 3.043 3.348 3.716

1.000 0.358 0.332 0.301 0.269 0.267 0.278 0.334 0.424 0.557 0.871 1.840 3.567 7.534 15.830 27.127 55.476

1.0000 0.9989 0.9977 0.9966 0.9954 0.9920 0.9863 0.9691 0.9370 0.8947 0.8203 0.6897 0.5741 0.4412 0.3186 0.2430 0.1605

1.000 0.671 0.628 0.615 0.654 0.734 0.840 1.043 1.209 1.392 1.613 1.944 2.196 2.523 2.879 3.136 3.498

1.000 0.317 0.290 0.257 0.222 0.216 0.222 0.263 0.329 0.421 0.624 1.209 2.209 4.441 8.940 14.752 28.069

1.0000 0.9984 0.9976 0.9968 0.9943 0.9911 0.9862 0.9666 0.9365 0.8950 0.8234 0.6956 0.5833 0.4538 0.3349 0.2583 0.1768

1.000 0.635 0.595 0.571 0.615 0.691 0.794 1.013 1.183 1.356 1.582 1.899 2.133 2.436 2.753 3.000 3.312

1.000 0.285 0.258 0.226 0.190 0.182 0.184 0.213 0.261 0.330 0.482 0.909 1.612 3.102 5.918 9.338 16.633

1.0000 0.9987

1.000 0.585

1.000 0.242

Table 5. continued

K

K

K

K

2060

ws

ms/mol·kg−1

0.0212 0.0291 0.0525 0.0780 0.1118 0.2090 0.3086 0.3945 0.4946 0.6036 0.6682 0.7210 0.7600 0.7824 0.8065

0.0753 0.1043 0.1931 0.2945 0.4387 0.9202 1.5550 2.2698 3.4095 5.3500 7.0153 9.0029 11.0284 12.5209 14.5190

0.0000 0.0171 0.0212 0.0291 0.0525 0.0780 0.1118 0.2090 0.3086 0.3945 0.4946 0.6036 0.6682 0.7210 0.7600 0.7824 0.8065

0.0000 0.0608 0.0753 0.1043 0.1931 0.2945 0.4387 0.9202 1.5550 2.2698 3.4095 5.3500 7.0153 9.0029 11.0284 12.5209 14.5190

0.0000 0.0171 0.0212 0.0291 0.0525 0.0780 0.1118 0.2090 0.3086 0.3945 0.4946 0.6036 0.6682 0.7210 0.7600 0.7824 0.8065

0.0000 0.0608 0.0753 0.1043 0.1931 0.2945 0.4387 0.9202 1.5550 2.2698 3.4095 5.3500 7.0153 9.0029 11.0284 12.5209 14.5190

0.0000 0.0171 0.0212 0.0291 0.0525 0.0780 0.1118

0.0000 0.0608 0.0753 0.1043 0.1931 0.2945 0.4387

P/Pa T = 293.15 2335 2334 2328 2320 2310 2262 2192 2097 1936 1652 1399 1107 837 665 473 T = 303.15 4247 4242 4241 4239 4231 4220 4201 4115 3981 3811 3522 3026 2577 2070 1582 1279 934 T = 313.15 7385 7376 7375 7372 7358 7339 7307 7161 6935 6653 6173 5338 4576 3717 2881 2352 1750 T = 323.15 12 352 12 339 12 336 12 331 12 309 12 278 12 223

as

Φ

γ±

0.9983 0.9979 0.9953 0.9919 0.9876 0.9671 0.9372 0.8967 0.8279 0.7066 0.5984 0.4736 0.3582 0.2846 0.2024

0.548 0.538 0.575 0.635 0.734 0.980 1.157 1.334 1.537 1.818 2.031 2.304 2.584 2.786 3.053

0.216 0.185 0.151 0.143 0.143 0.161 0.192 0.238 0.340 0.619 1.049 1.887 3.324 4.931 8.102

1.0000 0.9988 0.9986 0.9981 0.9962 0.9937 0.9892 0.9690 0.9375 0.8975 0.8296 0.7129 0.6073 0.4879 0.3730 0.3016 0.2203

1.000 0.537 0.520 0.501 0.541 0.600 0.688 0.951 1.136 1.302 1.500 1.771 1.973 2.212 2.482 2.657 2.892

1.000 0.222 0.196 0.165 0.130 0.120 0.119 0.132 0.157 0.193 0.268 0.461 0.755 1.327 2.279 3.275 4.989

1.0000 0.9988 0.9987 0.9983 0.9964 0.9938 0.9895 0.9698 0.9392 0.9011 0.8363 0.7234 0.6203 0.5040 0.3908 0.3191 0.2375

1.000 0.555 0.498 0.467 0.525 0.587 0.670 0.926 1.119 1.273 1.456 1.695 1.889 2.112 2.365 2.532 2.748

1.000 0.218 0.192 0.162 0.128 0.118 0.116 0.125 0.144 0.173 0.236 0.399 0.633 1.053 1.708 2.377 3.559

1.0000 0.9990 0.9987 0.9983 0.9965 0.9940 0.9896

1.000 0.479 0.476 0.451 0.499 0.564 0.662

1.000 0.191 0.167 0.139 0.107 0.098 0.096

K

K

K

K



Article

Table 5. continued ws

ms/mol·kg−1

0.2090 0.3086 0.3945 0.4946 0.6036 0.6682 0.7210 0.7600 0.7824 0.8065

0.9202 1.5550 2.2698 3.4095 5.3500 7.0153 9.0029 11.0284 12.5209 14.5190

0.0000 0.0171 0.0212 0.0291 0.0525 0.0780 0.1118 0.2090 0.3086 0.3945 0.4946 0.6036 0.6682 0.7210 0.7600 0.7824 0.8065

0.0000 0.0608 0.0753 0.1043 0.1931 0.2945 0.4387 0.9202 1.5550 2.2698 3.4095 5.3500 7.0153 9.0029 11.0284 12.5209 14.5190

0.0000 0.0171 0.0212 0.0291 0.0525 0.0780 0.1118 0.2090 0.3086 0.3945 0.4946 0.6036 0.6682 0.7210 0.7600 0.7824 0.8065

0.0000 0.0608 0.0753 0.1043 0.1931 0.2945 0.4387 0.9202 1.5550 2.2698 3.4095 5.3500 7.0153 9.0029 11.0284 12.5209 14.5190

0.0000 0.0171 0.0212 0.0291 0.0525 0.0780 0.1118 0.2090 0.3086 0.3945 0.4946 0.6036

0.0000 0.0608 0.0753 0.1043 0.1931 0.2945 0.4387 0.9202 1.5550 2.2698 3.4095 5.3500

Table 5. continued P/Pa T = 323.15 11 986 11 620 11 173 10 392 9010 7799 6367 4992 4120 3109 T = 333.15 19 946 19 926 19 923 19 913 19 878 19 827 19 738 19 355 18 770 18 053 16 796 14 560 12 620 10 338 8154 6761 5130 T = 343.15 31 201 31 172 31 167 31 153 31 099 31 018 30 880 30 284 29 383 28 270 26 322 22 828 19 819 16 289 12 936 10 776 8227 T = 353.15 47 414 47 373 47 366 47 344 47 262 47 139 46 929 46 025 44 668 42 986 40 035 34 723

as

Φ

γ±

ws

ms/mol·kg−1

0.9705 0.9410 0.9049 0.8418 0.7302 0.6323 0.5164 0.4051 0.3344 0.2524

0.904 1.086 1.222 1.401 1.645 1.813 2.037 2.274 2.428 2.631

0.102 0.116 0.137 0.181 0.294 0.451 0.726 1.145 1.565 2.300

0.6682 0.7210 0.7600 0.7824 0.8065

7.0153 9.0029 11.0284 12.5209 14.5190

1.0000 0.9990 0.9989 0.9984 0.9966 0.9941 0.9896 0.9705 0.9413 0.9056 0.8428 0.7310 0.6340 0.5196 0.4101 0.3402 0.2582

1.000 0.456 0.423 0.438 0.488 0.561 0.660 0.902 1.079 1.213 1.392 1.639 1.803 2.018 2.243 2.390 2.588

1.000 0.179 0.156 0.128 0.098 0.089 0.087 0.094 0.107 0.127 0.166 0.265 0.402 0.644 1.011 1.371 1.971

0.0000 0.0171 0.0212 0.0291 0.0525 0.0780 0.1118 0.2090 0.3086 0.3945 0.4946 0.6036 0.6682 0.7210 0.7600 0.7824 0.8065

0.0000 0.0608 0.0753 0.1043 0.1931 0.2945 0.4387 0.9202 1.5550 2.2698 3.4095 5.3500 7.0153 9.0029 11.0284 12.5209 14.5190

1.0000 0.9991 0.9989 0.9985 0.9968 0.9942 0.9898 0.9708 0.9421 0.9067 0.8446 0.7331 0.6369 0.5239 0.4163 0.3470 0.2651

1.000 0.422 0.399 0.407 0.467 0.550 0.650 0.893 1.064 1.198 1.375 1.625 1.785 1.993 2.205 2.346 2.538

1.000 0.164 0.142 0.116 0.088 0.080 0.078 0.083 0.094 0.110 0.144 0.229 0.344 0.542 0.835 1.120 1.597

0.0000 0.0171 0.0212 0.0291 0.0525 0.0780 0.1118 0.2090 0.3086 0.3945 0.4946 0.6036 0.6682 0.7210 0.7600 0.7824 0.8065

0.0000 0.0608 0.0753 0.1043 0.1931 0.2945 0.4387 0.9202 1.5550 2.2698 3.4095 5.3500 7.0153 9.0029 11.0284 12.5209 14.5190

1.0000 0.9991 0.9990 0.9985 0.9968 0.9943 0.9899 0.9710 0.9426 0.9074 0.8456 0.7342

1.000 0.391 0.370 0.389 0.457 0.543 0.644 0.889 1.055 1.188 1.365 1.617

1.000 0.154 0.132 0.107 0.080 0.073 0.071 0.076 0.086 0.100 0.131 0.207

0.0000 0.0171 0.0212 0.0291 0.0525 0.0780 0.1118 0.2090 0.3086 0.3945 0.4946 0.6036 0.6682 0.7210 0.7600 0.7824 0.8065

0.0000 0.0608 0.0753 0.1043 0.1931 0.2945 0.4387 0.9202 1.5550 2.2698 3.4095 5.3500 7.0153 9.0029 11.0284 12.5209 14.5190

K

K

K

K

2061

P/Pa T = 353.15 30 177 24 865 19 830 16 569 12 693 T = 363.15 70 182 70 126 70 114 70 083 69 960 69 779 69 467 68 130 66 137 63 659 59 301 51 439 44 738 36 938 29 576 24 794 19 068 T = 373.15 101 418 101 343 101 326 101 281 101 105 100 842 100 391 98 462 95 612 92 051 85 773 74 405 64 779 53 601 43 113 36 251 27 978 T = 383.15 143 379 143 279 143 256 143 192 142 945 142 570 141 933 139 211 135 199 130 184 121 335 105 239 91 679 75 980 61 297 51 676 39 980

as

Φ

γ±

0.6386 0.5268 0.4205 0.3516 0.2696

1.774 1.976 2.180 2.317 2.506

0.309 0.481 0.733 0.976 1.383

1.0000 0.9992 0.9990 0.9986 0.9969 0.9943 0.9899 0.9711 0.9430 0.9081 0.8466 0.7353 0.6403 0.5293 0.4244 0.3561 0.2741

1.000 0.360 0.353 0.371 0.450 0.536 0.640 0.884 1.047 1.179 1.356 1.609 1.764 1.961 2.157 2.289 2.474

1.000 0.145 0.124 0.100 0.075 0.068 0.066 0.070 0.079 0.092 0.120 0.189 0.281 0.432 0.648 0.856 1.214

1.0000 0.9993 0.9991 0.9987 0.9970 0.9944 0.9900 0.9713 0.9436 0.9089 0.8477 0.7367 0.6423 0.5324 0.4289 0.3610 0.2790

1.000 0.333 0.329 0.354 0.437 0.529 0.634 0.879 1.037 1.168 1.345 1.599 1.752 1.944 2.131 2.259 2.441

1.000 0.139 0.118 0.095 0.071 0.064 0.062 0.066 0.074 0.085 0.111 0.174 0.257 0.392 0.582 0.763 1.070

1.0000 0.9993 0.9992 0.9987 0.9970 0.9945 0.9901 0.9715 0.9440 0.9096 0.8488 0.7378 0.6439 0.5347 0.4323 0.3649 0.2827

1.000 0.313 0.310 0.341 0.427 0.523 0.629 0.873 1.029 1.159 1.335 1.592 1.742 1.930 2.111 2.235 2.415

1.000 0.133 0.113 0.091 0.067 0.061 0.059 0.062 0.069 0.080 0.103 0.162 0.237 0.359 0.528 0.688 0.962

K

K

K

K



Article

Table 5. continued ws

ms/mol·kg−1

0.0000 0.0171 0.0212 0.0291 0.0525 0.0780 0.1118 0.2090 0.3086 0.3945 0.4946 0.6036 0.6682 0.7210 0.7600 0.7824 0.8065

0.0000 0.0608 0.0753 0.1043 0.1931 0.2945 0.4387 0.9202 1.5550 2.2698 3.4095 5.3500 7.0153 9.0029 11.0284 12.5209 14.5190

0.0000 0.0171 0.0212 0.0291 0.0525 0.0780 0.1118 0.2090 0.3086 0.3945 0.4946 0.6036 0.6682 0.7210 0.7600 0.7824 0.8065

0.0000 0.0608 0.0753 0.1043 0.1931 0.2945 0.4387 0.9202 1.5550 2.2698 3.4095 5.3500 7.0153 9.0029 11.0284 12.5209 14.5190

0.0000 0.0171 0.0212 0.0291 0.0525 0.0780 0.1118 0.2090 0.3086 0.3945 0.4946 0.6036 0.6682 0.7210 0.7600 0.7824 0.8065

0.0000 0.0608 0.0753 0.1043 0.1931 0.2945 0.4387 0.9202 1.5550 2.2698 3.4095 5.3500 7.0153 9.0029 11.0284 12.5209 14.5190

0.0000 0.0171 0.0212 0.0291 0.0525

0.0000 0.0608 0.0753 0.1043 0.1931

Table 5. continued P/Pa T = 393.15 198 674 198 544 198 512 198 423 198 082 197 560 196 676 192 904 187 374 180 445 168 194 145 839 127 110 105 530 85 389 72 139 55 970 T = 403.15 270 280 270 115 270 072 269 952 269 488 268 776 267 569 262 432 254 957 245 541 228 879 198 424 173 026 143 859 116 739 98 830 76 893 T = 413.15 361 539 361 334 361 277 361 117 360 496 359 538 357 918 351 036 341 077 328 477 306 210 265 396 231 523 192 762 156 865 133 132 103 816 T = 423.15 476 165 475 907 475 832 475 622 474 802

as

Φ

γ±

ws

ms/mol·kg−1

1.0000 0.9994 0.9992 0.9988 0.9971 0.9945 0.9902 0.9716 0.9444 0.9102 0.8497 0.7387 0.6453 0.5371 0.4357 0.3686 0.2866

1.000 0.292 0.293 0.328 0.419 0.517 0.624 0.868 1.021 1.150 1.326 1.585 1.733 1.916 2.091 2.212 2.389

1.000 0.127 0.108 0.086 0.063 0.057 0.056 0.058 0.065 0.074 0.096 0.150 0.219 0.328 0.478 0.619 0.862

0.0780 0.1118 0.2090 0.3086 0.3945 0.4946 0.6036 0.6682 0.7210 0.7600 0.7824 0.8065

0.2945 0.4387 0.9202 1.5550 2.2698 3.4095 5.3500 7.0153 9.0029 11.0284 12.5209 14.5190

1.0000 0.9994 0.9993 0.9988 0.9972 0.9946 0.9903 0.9718 0.9449 0.9109 0.8506 0.7398 0.6469 0.5395 0.4391 0.3724 0.2904

1.000 0.271 0.275 0.314 0.410 0.511 0.619 0.863 1.012 1.141 1.317 1.577 1.723 1.902 2.071 2.189 2.363

1.000 0.121 0.102 0.081 0.059 0.054 0.052 0.055 0.060 0.069 0.089 0.138 0.201 0.298 0.430 0.554 0.769

0.0000 0.0171 0.0212 0.0291 0.0525 0.0780 0.1118 0.2090 0.3086 0.3945 0.4946 0.6036 0.6682 0.7210 0.7600 0.7824 0.8065

0.0000 0.0608 0.0753 0.1043 0.1931 0.2945 0.4387 0.9202 1.5550 2.2698 3.4095 5.3500 7.0153 9.0029 11.0284 12.5209 14.5190

1.0000 0.9995 0.9993 0.9989 0.9972 0.9947 0.9903 0.9719 0.9453 0.9115 0.8515 0.7409 0.6485 0.5419 0.4425 0.3764 0.2944

1.000 0.250 0.258 0.300 0.401 0.505 0.615 0.859 1.005 1.134 1.309 1.569 1.714 1.889 2.052 2.166 2.338

1.000 0.115 0.097 0.076 0.056 0.050 0.049 0.051 0.056 0.064 0.082 0.128 0.185 0.272 0.388 0.497 0.689

0.0000 0.0171 0.0212 0.0291 0.0525 0.0780 0.1118 0.2090 0.3086 0.3945 0.4946 0.6036 0.6682 0.7210 0.7600 0.7824 0.8065

0.0000 0.0608 0.0753 0.1043 0.1931 0.2945 0.4387 0.9202 1.5550 2.2698 3.4095 5.3500 7.0153 9.0029 11.0284 12.5209 14.5190

1.0000 0.9995 0.9993 0.9989 0.9973

1.000 0.237 0.247 0.291 0.395

1.000 0.111 0.093 0.073 0.053

0.0000 0.0171 0.0212 0.0291 0.0525 0.0780 0.1118 0.2090 0.3086 0.3945

0.0000 0.0608 0.0753 0.1043 0.1931 0.2945 0.4387 0.9202 1.5550 2.2698

K

K

K

K

2062

P/Pa T = 423.15 473 533 471 394 462 286 449 169 432 566 403 173 349 246 304 649 253 823 206 888 175 793 137 375 T = 433.15 618 235 617 918 617 820 617 547 616 479 614 818 612 023 600 140 583 130 561 512 523 240 452 961 395 165 329 358 268 980 228 823 179 008 T = 443.15 792 187 791 803 791 676 791 326 789 958 787 806 784 210 768 910 747 052 719 296 670 167 579 645 505 569 421 605 344 824 293 661 230 070 T = 453.15 1 002 811 1 002 353 1 002 193 1 001 750 1 000 006 997 267 992 665 973 167 945 486 910 196

as

Φ

γ±

0.9947 0.9904 0.9720 0.9455 0.9119 0.8521 0.7416 0.6494 0.5435 0.4448 0.3790 0.2972

0.501 0.611 0.856 1.000 1.128 1.303 1.564 1.708 1.880 2.039 2.151 2.320

0.048 0.047 0.049 0.053 0.061 0.078 0.121 0.174 0.255 0.362 0.461 0.638

1.0000 0.9995 0.9994 0.9989 0.9973 0.9947 0.9904 0.9721 0.9459 0.9123 0.8527 0.7423 0.6506 0.5451 0.4473 0.3817 0.2998

1.000 0.223 0.235 0.282 0.389 0.497 0.608 0.853 0.994 1.122 1.297 1.559 1.701 1.871 2.025 2.135 2.303

1.000 0.107 0.090 0.070 0.051 0.046 0.045 0.047 0.051 0.058 0.074 0.114 0.164 0.239 0.336 0.427 0.590

1.0000 0.9995 0.9994 0.9990 0.9974 0.9948 0.9905 0.9723 0.9461 0.9128 0.8535 0.7430 0.6516 0.5467 0.4496 0.3843 0.3025

1.000 0.209 0.224 0.273 0.382 0.493 0.604 0.849 0.989 1.116 1.290 1.554 1.695 1.862 2.012 2.120 2.286

1.000 0.103 0.086 0.067 0.049 0.044 0.043 0.044 0.048 0.055 0.070 0.108 0.155 0.223 0.312 0.395 0.545

1.0000 0.9996 0.9994 0.9990 0.9974 0.9948 0.9906 0.9724 0.9464 0.9132

1.000 0.195 0.212 0.263 0.376 0.488 0.601 0.846 0.983 1.110

1.000 0.099 0.083 0.064 0.046 0.042 0.041 0.042 0.046 0.052

K

K

K

K



Article

Φ − 1 = f Φ + mBΦ + m2C Φ

Table 5. continued ws 0.4946 0.6036 0.6682 0.7210 0.7600 0.7824 0.8065

ms/mol·kg−1 3.4095 5.3500 7.0153 9.0029 11.0284 12.5209 14.5190

0.0000 0.0171 0.0212 0.0291 0.0525 0.0780 0.1118 0.2090 0.3086 0.3945 0.4946 0.6036 0.6682 0.7210 0.7600 0.7824 0.8065

0.0000 0.0608 0.0753 0.1043 0.1931 0.2945 0.4387 0.9202 1.5550 2.2698 3.4095 5.3500 7.0153 9.0029 11.0284 12.5209 14.5190

0.0000 0.0171 0.0212 0.0291 0.0525 0.0780 0.1118 0.2090 0.3086 0.3945 0.4946 0.6036 0.6682 0.7210 0.7600 0.7824 0.8065

0.0000 0.0608 0.0753 0.1043 0.1931 0.2945 0.4387 0.9202 1.5550 2.2698 3.4095 5.3500 7.0153 9.0029 11.0284 12.5209 14.5190

P/Pa

as

T = 453.15 K 847 739 0.8541 732 751 0.7439 638 949 0.6527 533 117 0.5484 436 494 0.4519 372 287 0.3871 291 946 0.3052 T = 463.15 K 1 255 236 1.0000 1 254 695 0.9996 1 254 495 0.9995 1 253 940 0.9991 1 251 743 0.9974 1 248 279 0.9949 1 242 485 0.9906 1 217 914 0.9725 1 183 106 0.9467 1 138 773 0.9137 1 060 204 0.8547 915 505 0.7446 797 995 0.6537 666 070 0.5501 546 304 0.4545 466 213 0.3897 366 291 0.3081 T = 471.15 K 1 490 935 1.0000 1 490 336 0.9996 1 490 100 0.9995 1 489 436 0.9991 1 486 815 0.9975 1 482 662 0.9949 1 475 724 0.9907 1 446 355 0.9726 1 405 013 0.9470 1 352 142 0.9141 1 258 451 0.8554 1 085 807 0.7453 946 442 0.6549 790 183 0.5517 649062 0.4568 554 763 0.3926 436 297 0.3108

Φ 1.284 1.548 1.688 1.852 1.999 2.104 2.269

γ±

f Φ = −A Φ

0.066 0.102 0.145 0.208 0.288 0.364 0.503

(5)

I 1+b I

(6)

⎡ ⎤2/3 ⎛1⎞ e2 1/2 ⎜ ⎟(2πN d ) ⎢ ⎥ a s ⎝3⎠ ⎣ 4πε0εrkT ⎦

AΦ =

I = 0.5∑ mjzj 2

(

(7)

)

(8)

Φ

1.000 0.182 0.201 0.254 0.370 0.484 0.597 0.842 0.978 1.104 1.278 1.543 1.682 1.843 1.985 2.089 2.251

1.000 0.096 0.079 0.062 0.044 0.040 0.039 0.040 0.043 0.049 0.062 0.096 0.137 0.194 0.267 0.336 0.463

1.000 0.168 0.189 0.245 0.364 0.480 0.594 0.839 0.972 1.098 1.272 1.538 1.675 1.834 1.972 2.073 2.234

1.000 0.092 0.076 0.059 0.042 0.038 0.037 0.039 0.041 0.047 0.059 0.091 0.129 0.183 0.250 0.313 0.430

The term B is described by eq 9 but can be modified, as shown in eq 10, to better fit both aqueous and nonaqueous solutions.9,11,12 In the case of LiTf2N + water solutions, better experimental agreement is achieved when BΦ is represented by eq 10. In eqs 9−11, the terms β(0), β(1), β(2), C(0), and C(1) are Pitzer’s ionic interaction parameters (Table 7) and α(1), α(2), and α(3) are adjustable parameters with the best-suited values being 2.0, 7.0, and 1.0, respectively.13,14 BΦ = β (0) + β (1) exp( −α(1) I )

(9)

BΦ = β (0) + β (1) exp( −α(1) I ) + β (2) exp( −α(2) I ) (10)

The third osmotic virial coefficient (CΦ) utilizes Archer’s extension and is represented by eq 11.15,16 This equation is valid only for 1:1 electrolyte ratios. C Φ = C(0) + C(1) exp( −α(3) I )

(11)

3.6. Mean Molal Activity. The mean molal activity coefficient (γ±) was calculated for LiTf2N + water solutions (Figure 9) using the Pitzer equation in conjunction with the Archer extension (eqs 12−15). ⎡ m1/2 ⎤ ⎛2⎞ 1/2 ⎜ ⎟ln(1 + bm ⎥ ln(γ±) = −A Φ⎢ + ) ⎝b⎠ ⎣ 1 + bm1/2 ⎦ 2 ⎛m ⎞ + m(2β (0) + A1 + A 2 ) + ⎜ ⎟(3C(0) + A3) ⎝ 2 ⎠ A1 =

(12)

⎛ ⎞ ⎛ α2 m⎞ 2β (1) ⎜ ⎜⎜1 + α(1)m1/2 + (1) ⎟⎟ exp(− α(1)m1/2)⎟ 1 − 2 ⎟ 2 ⎠ α(1)m ⎜⎝ ⎝ ⎠ (13)

A2 =

a

Standard uncertainties u are u(T) = 0.01 K, u(w) = 0.0001, u(m) = 0.0001 mol·kg−1. Combined expanded uncertainties Uc are Uc(P) = 30 Pa, Uc(as) = 0.0003, Uc(Φ) = 0.008, and Uc(γ±) = 0.002 for vapor pressure values of P < 0.1 MPa and Uc(P) = 1500 Pa, Uc(as) = 0.0005, Uc(Φ) = 0.009, and Uc(γ±) = 0.002 for vapor pressure values of P < 3 MPa (level of confidence = 0.95). Uncertainties in mass fractions and molalities do not include sample purities.

⎛ ⎞ ⎛ α2 m⎞ 2β (2) ⎜ ⎜⎜1 + α(2)m1/2 + (2) ⎟⎟ exp(− α(2)m1/2)⎟ 1 − 2 ⎟ 2 ⎠ m ⎜⎝ α(2) ⎝ ⎠ (14)

A3 = 4C

⎛ ⎛ 2 3 3/2 ⎜6 − ⎜⎜6 + 6α(3)m1/2 + 3α(3) m + α(3) m − ⎜ ⎝ (1) ⎝

⎞ exp( − α(3)m1/2)⎟⎟ ⎠ ⎠

α 4 m2 ⎞ (3) ⎟ 2 ⎟

4 2 α(3) m

(15)

absolute value for the jth ionic strength. Other terms represented in the equations are Avogadro’s number (Na/mol−1), the density of pure liquid water (ds/kg·m−3), electron charge (e/C), the permittivity of the vacuum (εo/F·m−1), the dielectric permittivity of water (εr), Boltzmann’s constant (k/J·K−1), and the absolute temperature (T) in Kelvin. The Pitzer ionic parameter (b) is an adjustable parameter with a value of 3.2 resulting in the best fit. Also, terms εr and ds are temperaturedependent variables that can be found in the literature.8,10

3.7. Enthalpy of Vaporization. The enthalpy of vaporization was computed for LiTf2N + water solutions at molal salt concentrations from 0.0000 to 14.5190 mol·kg−1 (ws = 0.0000 to 0.8065) and temperatures ranging from 289.15 to 448.15 K using the Clausius−Clapeyron relationship shown in eq 16 and experimentally acquired vapor pressure data.17 The latent heat of vaporization for the previously referenced samples is displayed in Table 8. Under isothermal conditions, the enthalpy of vaporization is directly proportional to the salt concentration. 2063



Article

Figure 6. Vapor pressures of LiTf2N + water solutions at varying concentration and temperature: ■, 471.15 K; ⧫, 463.15 K; ●, 453.15 K; ▲, 443.15 K; ◨, 433.15 K; ☆, 423.15 K; ◑, 413.15 K; ◮, 403.15 K; ◧, 393.15 K; ★, 383.15 K; ◐, 373.15 K; ◭, 363.15 K; ⬓, 353.15 K; ▼, 343.15 K; ◒, 333.15 K; ▽, 323.15 K; □, 313.15 K; ◊, 303.15 K; ○, 293.15 K; △, 283.15 K; ×, 278.15 K; +, 274.15 K.

Figure 7. Calculated solvent activity (as) for LiTf2N + water solutions with respect to temperature and salt concentration: ■, 471.15 K; ⧫, 463.15 K; ●, 453.15 K; ▲, 443.15 K; ◨, 433.15 K; ☆, 423.15 K; ◑, 413.15 K; ◮, 403.15 K; ◧, 393.15 K; ★, 383.15 K; ◐, 373.15 K; ◭, 363.15 K; ⬓, 353.15 K; ▼, 343.15 K; ◒, 333.15 K; ▽, 323.15 K; □, 313.15 K; ◊, 303.15 K; ○, 293.15 K; △, 283.15 K; ×, 278.15 K; +, 274.15 K.

Table 6. Second Virial Coefficient (Bs), Molar Volume (V*s), and Vapor Pressure (P*) of Pure Water with Respect to Temperature for LiTf2N + Water Solutionsa

a

T/K

Bs × 103/m3·mol−1

V*s × 105/m3·mol−1

P*/Pa

274.15 278.15 283.15 293.15 303.15 313.15 323.15 333.15 343.15 353.15 363.15 373.15 383.15 393.15 403.15 413.15 423.15 433.15 443.15 453.15 463.15 471.15

−1.98227 −1.82124 −1.64467 −1.35783 −1.13805 −0.96689 −0.83155 −0.72301 −0.63481 −0.56226 −0.50189 −0.45114 −0.40804 −0.37112 −0.33922 −0.31145 −0.28711 −0.26563 −0.24656 −0.22955 −0.21428 −0.20317

1.8017 1.8017 1.8022 1.8048 1.8095 1.8157 1.8234 1.8324 1.8426 1.8539 1.8663 1.8798 1.8945 1.9102 1.9271 1.9452 1.9646 1.9853 2.0074 2.031 2.0564 2.0779

657 873 1228 2339 4247 7385 12 352 19 946 31 201 47 414 70 182 101 418 143 379 198 674 270 280 361 539 476 165 618 235 792 187 1 002 811 1 255 236 1 490 935

Figure 8. Calculated osmotic coefficients for LiTf2N + water solutions with respect to temperature and salt concentration: ■, 471.15 K; ⧫, 463.15 K; ●, 453.15 K; ▲, 443.15 K; ◨, 433.15 K; ☆, 423.15 K; ◑, 413.15 K; ◮, 403.15 K; ◧, 393.15 K; ★, 383.15 K; ◐, 373.15 K; ◭, 363.15 K; ⬓, 353.15 K; ▼, 343.15 K; ◒, 333.15 K; ▽, 323.15 K; □, 313.15 K; ◊, 303.15 K; ○, 293.15 K; △, 283.15 K; ×, 278.15 K; +, 274.15 K.

Source: Wagner and Pruß.8

4. CONCLUSIONS The physical properties (density, viscosity, and vapor pressure) of LiTf2N + water solutions were measured and modeled over a wide range of temperatures (274.15 to 471.15 K) for the first time. The maximum soluble salt solubility for LiTf2N in water was determined to be between ws = 0.8065 and 0.8217 at 295.15 K. In the study, linear regression is used to describe viscosity and density trends as a function of temperature and

Elevated salt concentrations yield greater interactions between ions and water. Increased attractive bonding interactions suppress the salt solution vapor pressure and concomitantly require increased energy to vaporize the sample, thus explaining the observed trends. d ln(P) d

1 T

()

=−

ΔH v R

(16) 2064



Article

Table 7. Pitzer Ionic Coefficients Applied to Equations 9−11a

a

T/K

β(0)

β(1)

β(2)

C(0)

C(1)

274.15 278.15 283.15 293.15 303.15 313.15 323.15 333.15 343.15 353.15 363.15 373.15 383.15 393.15 403.15 413.15 423.15 433.15 443.15 453.15 463.15 471.15

0.102004 0.325333 0.308849 0.203956 0.487186 0.222298 0.206002 0.311311 0.234349 0.194343 0.080514 0.091299 0.044735 −0.005202 −0.057306 −0.106117 −0.136817 −0.188460 −0.217292 −0.275759 −0.331461 −0.341184

0.479053 −0.330411 −0.512434 −0.411110 −1.416716 −0.752560 −0.757991 −1.028437 −0.825471 −0.702906 −0.363707 −0.410297 −0.282604 −0.138221 0.019335 0.184066 0.285215 0.457225 0.559835 0.760758 0.944233 1.020766

−27.951260 −30.527490 −33.233760 −38.161670 −39.291840 −40.463010 −44.368590 −45.966040 −48.808440 −50.875030 −53.094570 −54.134720 −55.396790 −56.796240 −58.369670 −60.038570 −61.005050 −62.185100 −63.215640 −64.497530 −65.625610 −66.546480

0.002279 −0.006070 −0.006280 −0.003544 −0.014218 −0.005081 −0.004542 −0.008442 −0.005832 −0.004489 −0.000509 −0.001000 0.000592 0.002304 0.004103 0.005793 0.006838 0.008649 0.009640 0.011706 0.013650 0.013964

0.176987 −0.187029 −0.166172 −0.018754 −0.451748 −0.071088 −0.067125 −0.227057 −0.115332 −0.057698 0.110829 0.093021 0.161238 0.234611 0.310891 0.382130 0.427620 0.503886 0.546371 0.632475 0.715246 0.729427

Source: Archer.15,16

Table 8. Enthalpy of Vaporization (ΔHv/J·mol−1) for LiTf2N + Water Solutions enthalpy of vaporization, ΔHv/J·mol−1

Figure 9. Calculated molal activity coefficients for LiTf2N + water solutions with respect to temperature and salt concentration: ■, 471.15 K; ⧫, 463.15 K; ●, 453.15 K; ▲, 443.15 K; ◨, 433.15 K; ☆, 423.15 K; ◑, 413.15 K; ◮, 403.15 K; ◧, 393.15 K; ★, 383.15 K; ◐, 373.15 K; ◭, 363.15 K; ⬓, 353.15 K; ▼, 343.15 K; ◒, 333.15 K; ▽, 323.15 K; □, 313.15 K; ◊, 303.15 K; ○, 293.15 K; △, 283.15 K; ×, 278.15 K; +, 274.15 K.

salt molality, m/mol·kg−1

T = 289.15 K

T = 348.15 K

T = 398.15 K

T = 448.15 K

0.000 0.061 0.075 0.104 0.193 0.295 0.439 0.920 1.555 2.270 3.409 5.350 7.015 9.003 11.028 12.521 14.519

44 287 44 292 44 317 44 336 44 327 44 341 44 372 44 347 44 368 44 457 44 724 45 395 46 131 47 400 48 920 50 638 53 194

42 216 42 222 42 223 42 223 42 224 42 222 42 223 42 227 42 260 42 285 42 323 42 336 42 452 42 721 43 230 43 601 44 050

40 603 40 608 40 608 40 609 40 609 40 607 40 606 40 603 40 620 40 628 40 636 40 601 40 655 40 842 41 200 41 480 41 813

39 410 39 415 39 415 39 414 39 413 39 409 39 404 39 383 39 374 39 351 39 301 39 165 39 133 39 208 39 464 39 660 39 883

ORCID

Mark B. Shiflett: 0000-0002-8934-6192 Notes

The authors declare no competing financial interest.

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mass fraction. In addition, vapor−liquid equilibria was studied and fit using the Pitzer−Mayorga and Clausius−Clapeyron models. Activity coefficients (γ±) of water in LiTf2N and the osmotic coefficients (Φ) of LiTf2N have been determined.

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ACKNOWLEDGMENTS M.B.S. thanks Dr. Akimichi Yokozeki for his analysis of the density and viscosity data and also dedicates this article to his memory. DEDICATION I am extremely thankful and blessed to have known and worked with Michi for 25 years. A verse from the Bible, Psalms 32:8,

AUTHOR INFORMATION

Corresponding Author

*Tel: 785-864-6719. E-mail: Mark.B.Shifl[email protected]. 2065



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best summarizes his relationship to me. “I will instruct you and guide you along the best pathways for your life; I will advise you and watch your progress.”

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ABBREVIATIONS LiTf2N, lithium bis(trifluoromethylsulfonyl)imide; PVF, poly(vinyl fluoride); [C2C1im][Tf2N], 1-ethyl-3-methylimidazolium bis(trifluoromethylsulfonyl)imide; [C 4 C 1 im][N(CN) 2 ], 1-butyl-3-methylimidazolium dicyanamide; [C4mγpy][BF4], 1-butyl-4-methylpyridinium tetrafluoroborate; [C 4 C 1im][HFPS], 1-butyl-3-methylimidazolium 1,1,2,3,3,3-hexafluoropropanesulfonate; [C8mim][TFES], 1-octyl-3-methylimidazolium 1,1,2,2-tetrafluoroethanesulfonate

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REFERENCES

(1) El Amrani, A.; Mahrane, A.; Moussa, F.; Boukennous, Y. Solar Module Fabrication. Int. J. Photoenergy 2007, 2007, 27610. (2) Uschold, R. E. Vinyl Fluoride Polymerization and Aqueous Dispersion of Vinyl Fluoride Polymer. U.S. Patent No. 8,735,520, 2014. (3) Uschold, R. E. Vinyl Fluoride Interpolymers. U.S Patent No. 6,403,740, 2002. (4) Shiflett, M. B.; Elliott, B. A.; Yokozeki, A. Phase Behavior of Vinyl Fluoride in Room-Temperature Ionic Liquids [emim][Tf2N], [bmim][N(CN)2], [bmpy][BF4], [bmim][HFPS] and [omim][TFES]. Fluid Phase Equilib. 2012, 316, 147−155. (5) Mather, B. D.; Reinartz, N. M.; Shiflett, M. B. Polymerization of Vinyl Fluoride in Ionic Liquid and Ionic Solutions. Polymer 2016, 82, 295−304. (6) Minnick, D. L.; Gilbert, W. J. R.; Rocha, M. A.; Shiflett, M. B. Thermodynamic Measurement and Modeling of Vinyl Fluoride Solubility in Aqueous Lithium Bis(trifluoromethylsufonyl)imide Li+Tf2N− - H2O Solutions. Fluid Phase Equilib. 2017, 444, 61. (7) Safarov, J.; Kul, I.; Talibov, M.; Shahverdiyev, A.; Hassel, E. Vapor Pressures and Activity Coefficients of Methanol in Binary Mixtures with 1-Hexyl-3-methylimidazolium Bis(trifluoromethylsulfonyl)imide. J. Chem. Eng. Data 2015, 60, 1648− 1663. (8) Wagner, W.; Pruß, A. The IAPWS Formulation 1995 for the Thermodynamic Properties of Ordinary Water Substance for General and Scientific Use. J. Phys. Chem. Ref. Data 2002, 31, 387−535. (9) Pitzer, K. S.; Mayorga, G. Thermodynamics of Electrolytes. II. Activity and Osmotic Coefficients for Strong Electrolytes with One or Both Ions univalent. J. Phys. Chem. 1973, 77, 2300−2308. (10) Archer, D. G.; Wang, P. The Dielectric Constant of Water and Debye-Hückel Limiting Law Slopes. J. Phys. Chem. Ref. Data 1990, 19, 371−411. (11) Pitzer, K. S. Thermodynamics of Electrolytes. I. Theoretical Basis and General Equations. J. Phys. Chem. 1973, 77, 268−277. (12) Pitzer, K. S. Activity Coefficients in Electrolyte Solutions. CRC Press: Boca Raton, FL, 1991; p 542. (13) Nasirzadeh, K.; Papaiconomou, N.; Neueder, R.; Kunz, W. Vapor Pressures, Osmotic and Activity Coefficients of Electrolytes in Protic Solvents at Different Temperatures. 1. Lithium Bromide in Methanol. J. Solution Chem. 2004, 33, 227−245. (14) Barthel, J.; Neueder, R. Electrolyte Data Collection; Dechema: Frankfurt, 1992; Vol. XII, part 1a. (15) Archer, D. G. Thermodynamic Properties of the NaBr+H2O System. J. Phys. Chem. Ref. Data 1991, 20, 509−555. (16) Archer, D. G. Thermodynamic Properties of the NaCl+H2O System. II. Thermodynamic Properties of NaCl (aq), NaCl·2H2 (cr), and Phase Equilibria. J. Phys. Chem. Ref. Data 1992, 21, 793−829. (17) Perry, R. H.; Green, D. W. Perry’s Chemical Engineers’ Handbook; McGraw-Hill Professional: New York, 1999; p 2640.

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Density, Viscosity, and Vapor Pressure Measurements of Water +

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