Vapor Pressures and Activity Coefficients of Methanol in Binary

Article pubs.acs.org/jced

Vapor Pressures and Activity Coefficients of Methanol in Binary Mixtures with 1‑Hexyl-3-methylimidazolium Bis(trifluoromethylsulfonyl)imide Javid Safarov,*,†,‡ Ismail Kul,§ Misirkhan Talibov,‡ Astan Shahverdiyev,‡ and Egon Hassel† †

Institute of Technical Thermodynamics, University of Rostock, Albert-Einstein-Straße 2, D-18059 Rostock, Germany Department of Heat and Refrigeration Techniques, Azerbaijan Technical University, H. Javid Avenue 25, AZ1073 Baku, Azerbaijan § Department of Chemistry and Biochemistry, Widener University, One University Place, Chester, Pennsylvania 19013, United States ‡

ABSTRACT: The vapor pressures of binary mixtures containing methanol and ionic liquid 1hexyl-3-methylimidazolium bis(trifluoromethylsulfonyl)imide [HMIM][NTf2] were investigated at temperatures ranging from 274.15 K to 413.15 K using the two different setups with static method. The activity coefficients γi of methanol in the [HMIM][NTf2] and osmotic coefficients ϕi of the [HMIM][NTf2] have been determined from the vapor−liquid equilibria data and are described using the Clasius−Clapeyron and NRTL equation.

1. INTRODUCTION Typical ionic liquids (ILs) have a stable liquid range of over 300 K and have a very low vapor pressure at room temperature. As is well-known, the ILs have been suggested as potentially “green” replacements for conventional organic solvents since they are nonvolatile (negligible vapor pressure), nonflammable, thermally stable, and recyclable. Binary mixtures of ILs and other fluids have been used for electrochemical applications (solar cells) and have considerably improved the performance of the devices.1,2 The thermophysical properties of ILs make them very suitable as heat transfer fluids and for short-term heat storage in power plants;3 therefore, the thermodynamic and structural properties of ILs and their mixtures are necessary for the design of many technological processes.4−7 Previous studies8,9 have shown that the addition of alcohols into ILs plays a dramatic role in their phase behavior. Vapor pressure data indicate that the volatility of solvents can be changed dramatically by the addition of an ionic liquid, while the variation extent is different depending on the nature of both the solvent and the ionic liquid involved. There is some literature with the activity coefficient information of ILs.10−13 The activity coefficients at infinite dilution γ∞ (x = 0) were measured for the various organic compounds with various ionic liquids. The experiments were carried out mostly at T = (298.15 to 333.15) K.10−12 There are some experimental activity coefficients at infinite dilution γ∞ (x = 0) values up to T = 396.15 K in ref 13. The vapor pressure measurements P of {xCH3OH + (1 − x)[HMIM][NTf2] at T = 353.11 K were presented in ref 10. In this work, we have measured the vapor pressure P of {xCH3OH + (1 − © 2015 American Chemical Society

x)[HMIM][NTf2] at the temperature range T = (274.15 to 413.15) K for the first time. This work is a continuation of our previous publications in this field.14−17 From the vapor pressure data, the activity of methanol, osmotic coefficient ϕ of IL in solution, and the activity coefficients γi at different temperatures and concentrations have been obtained.

2. EXPERIMENTAL SECTION Materials. Methanol for analysis EMSURE (> 99.9 mass %) was supplied from Merck KGaA company of Germany. The water content of the purchased solutes was less than 0.05 % per specification. Methanol was used without further purification and was carefully degassed. The ionic liquid [HMIM][NTf2] was also purchased from Merck KGaA (C12H19N5F6O4S2, CAS No. 382150-50-7, high purity product, > 99 %). To reduce the water content and volatile impurities the IL is dehydrated by applying a low-pressure vacuum of 1 to 10 Pa at a temperature of 423.15 K for 48 h with magnetic stirring. The water content of the dried IL is determined by Karl Fischer titration and is less than a mass fraction of 150 ppm. Experimental Procedure. The vapor−liquid equilibria (VLE) measurements of binary solutions of [HMIM][NTf2] with CH3OH were measured using the two high-accuracy static experimental set ups (Figures 1 and 2). The glass cells (3, 4, 27) are used for vapor pressures lower than ambient pressure at Received: November 14, 2014 Accepted: May 20, 2015 Published: June 2, 2015 1648

DOI: 10.1021/je501033z J. Chem. Eng. Data 2015, 60, 1648−1663

Journal of Chemical & Engineering Data

Article

Figure 1. Experimental installation for the vapor pressures at T = (274.15 to 323.15) K: (1), (28), (30) magnetic stirrer; (2), (36) magnet, (3) cell for water of the difference method; (4) cell for measuring sample of the difference method; (5), (37) valves for closing of cell for measuring sample of the difference method and (26) of the static cell; (6), (35), (39), (40) platinum resistance thermometers with temperature signal conditioner Omega PT-104A (19); (7), (20), (38) injection ports of measuring sample; (8), (25) electric heating; (9), (24) water heat exchange system; (10) pressure sensor head of the difference method and (23) of 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), (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 coldfinger; (33) vacuum pump; (34) PC.

Figure 2. Experimental installation: (1) thermostat; (2) platinum resistance thermometers PT-100 for the control of the measuring cell temperature by the thermostat; (3) platinum resistance thermometer PT-100 for the control of 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 measuring of temperature; (6) PC; (7) manual pressure signal conditioner; (8) flask for the sample; (9), (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 coldfinger; (18) vacuum pump.

the cell is measured by a platinum resistance thermometer PT100 (35), connected to a signal conditioner Omega PT-104A (19), with an accuracy of T = ± 0.001 K. If the vapor pressure of the solution is smaller than 30 Pa (uncertainty of measurements), the measurements are carried out using another cell in the differential part of the system. In this part, two cells are contained in one external reservoir. Both glass cells of the differential method (3, 4) are kept at constant temperature (± 0.01 K) using a thermostat Lauda Gold R-415, Germany (21). The temperature inside the cells is measured by a platinum resistance thermometer PT-100 (6), connected to a signal conditioner Omega PT-104A (19), with an accuracy of T = ± 0.001 K. The measuring cells are equipped with injection ports. The vapor pressure is measured using a calibrated high accuracy sensor head (10) [Type 616A connected (12) to the signal conditioner Type 670A (13), MKS Baratron, USA] attached to the top of the cell. The experimental uncertainty of the vapor pressure in the differential part is ΔP = ± (1 to 3) Pa (MKS Baratron pressure sensor). Both sensor heads of the static and differential parts (10, 23) are placed inside of the air reservoirs (11, 22) with an internal temperature of 333.15 ± 0.01 K. Thermostated (16) hot water is circulated between the internal and external walls. The pressure signal received from signal conditioners (13, 14) and temperature signals from the Omega PT-104A (19) are

temperatures ranging from 274.15 K to 323.15 K (Figure 1) and the metal cell for vapor pressures at the temperatures between 323.15 K and 413.15 K (Figure 2). The glass cell method consists of absolute and differential parts. They have internal and external volumes, between them flowing distilled water pumped from Lauda Gold R-415, Germany (21). Figure 1 shows the water connections of the stabilization of measuring cells and pressure head sensors in blue, electric heaters in red, and temperature measurements in green. The internal volume of the glass cell is approximately 78.56 cm3, and the volume of steel tube cells is 1 cm3. The glass cell static method consists of a bolted-top cell (27) in a water bath kept at constant temperature (± 0.01 K) using a thermostat (21). The measuring cell is equipped with an injection port. The vapor pressure is measured using a calibrated high accuracy sensor head (23) [Type 615A connected (15) to the signal conditioner Type 670A (14), MKS Baratron, USA] attached to the top of the cell. The experimental uncertainty of the pressure in the absolute vapor pressure measurement using the glass cell is ΔP = ± (10 to 30) Pa (MKS Baratron pressure sensor). The temperature inside 1649



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The measuring glass cell and metal tube connection of the signal conditioner MKS Baratron (measuring cell−signal conditioner connection) are impossible to connect directly. In this case, the special “glass-metal” adapter was connected to the measuring glass cell. The flange connections DN 10 short (VAT Deutschland GmbH, Germany) were set up to the end of metal side of the “glass−metal” adapter and to the metal tube connection site of the signal conditioner MKS Baratron. The clamping ring and centering ring were used to connect both sides of the flange connection. The cells and signal conditioners were located approximately 40 cm from one another. The connections between them are the “glass−metal” adapters followed by a metal tube with an internal inside diameter of 3.5 mm. The metal tube part of the measuring cell−signal conditioner connection was stabilized using the water heat exchanger (9, 24), with flowing water from the reservoirs (11, 22) of a constant temperature of (333.15 ± 0.01) K. However, on the side of this connection, containing the clamping ring and centering ring, it was impossible to make the same temperature control using water flow within connected tubes. In this case, electric heating (8, 25) with insulation was used. Heating was under constant control during all experimental procedures, using electric regulators (17,18). In both cases (static and difference methods), the vapor pressures of references (water, methanol, acetone, ethanol, toluene, butanol-1, etc.) were tested many times to regulate the electric heating power for each of the measured temperatures, and this information was sent to the LabVIEW control program. In this case, the PC regulated the electric heaters during the measurements. Equilibration of the cells is a rapid process and a constant pressure in the stationary regime is reached within 15 min. Equilibrium pressure readings are performed in triplicate at approximately 10 min to 20 min intervals. The PC received vapor pressure signals every minute and tracked pressure stability inside the cell. After these readings were obtained, the next temperature regime was changed automatically using the LabVIEW program. The measurements were carried out from the low temperature (T = 274.15 K) to high temperature (T = 323.15 K) with the preprogrammed temperature steps. After reaching the maximum temperature, the thermostat was stopped automatically. The repeat of measurements from the high temperature (T = 323.15 K) to low temperature (T = 274.15 K) were continued in the same way. The measurements could be done manually in the event of problems with automated system. The experiments to determine the vapor pressure of liquids at temperatures of T = (323.15 to 473.15) K are performed in a metal cell using the static method (Figure 2). In Figure 2, the connections for heat transfer fluid between the thermostat (1) and measuring cell (13) are shown in blue. The connections for the temperature measurements are shown in green and those for the pressure measurements are shown in black. The installation consists of a stainless steel DIN 1.4571 (V4A) measuring cell (13) in a stainless steel KORASILON oil M50 (Kurt Obermeier GmbH & Co. KG, Germany) reservoir. The internal volume of the measuring cell is approximately 140 cm3 with the connected tube, hole of the pressure transmitter, and 1/2 volume of the valve (10). The volume of the platinum resistance thermometers PT-100 (2, 3) inside the measuring cell is calculated as negative volume. The temperature of the measuring cell and heat transfer reservoir (12) with KORASILON oil M50 is controlled using a thermostat (1) (LAUDA ECO RE 415 G, Germany) with an

sent to a PC (34). All systems are controlled using the LabVIEW program. Before the experiments, the measuring cells were washed with water, methanol, and acetone. All residual fluids were removed from the cells using a vacuum system (31, 32), the TRIVAC (Germany) rotary vane vacuum pump (33). This procedure requires approximately 2 h to 3 h or more to reach the desired minimal pressure. At this point, all measuring cells are sufficiently dried and are ready for the experimentation. Specific quantities of IL and methanol were evacuated, degassed in two separate flasks, and connected using an adapter (Figure 3). Methanol flowed into another flask and the

Figure 3. Flask system for the preparation of the {xCH3OH + (1 − x)[HMIM][NTf2] mixture.

concentration of the solution was defined using the weight of the flask with the solution on an electronic scale (Sartorius ED224S, Germany) with 0.0001 g uncertainty. A quantity of the solution was injected into the equilibrium cells (4, 27) from the connections (7, 20), approximately 50 % of the volume, and then the valves (7, 26) were closed. Some of the pure methanol that is separated from the measured solution moved into the vapor phase under vacuum conditions inside the cell, and the vapor−liquid phase equilibrium between the vapor (CH3OH) and liquid {[HMIM][NTf2] + CH3OH} solution was reached by stirring the two phases using magnetic stirrers (1,28) and Teflon-coated magnets (2, 36) inside the cells. 1650



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Table 1. Experimental and Calculated Literature Values18 of Vapor Pressure P of Watera T/K

Pexp/Pa

Plit/Pa

(Pexp − Plit)/Pa

T/K

Pexp/Pa

Plit/Pa

(Pexp − Plit)/Pa

279.48 286.16 291.39 293.14 296.32 296.31 298.81 301.37 303.57 307.73 308.26

953 1508 2094 2337 2834 2839 3288 3827 4360 5507 5666

961 1502 2096 2338 2840 2838 3297 3832 4351 5500 5664

−8 6 −2 −1 −6 1 −9 −5 9 7 2

312.87 313.07 314.62 318.13 318.13 322.99 323.10 323.17 328.14 328.14 328.88

7275 7345 7977 9585 9578 12260 12320 12362 15748 15746 16312

7276 7354 7984 9585 9585 12254 12321 12364 15754 15754 16321

−1 −9 −7 0 −7 6 −1 −2 −6 −8 −9

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

accuracy of ΔT = ± 0.01 K. Temperatures are measured using two different platinum resistance thermometers, PT-100 (1/10 DIN Class B, Temperatur Messelemente Hettstedt GmbH, Germany) (2, 3). One of them is directly connected to the thermostat via PT-100 Libus Modul. This thermometer transfers information from the measuring cell. Using this thermometer, the thermostat sets the desired temperature directly inside of the measuring cell, but not within the thermostat itself. This is a very important point, because it is possible to set, stabilize, and measure the experimental temperature with high accuracy directly in the measured medium. The second platinum resistance thermometer, PT-100, transfers the measured temperature into the computer via an Omega PT-104A Channel RTD Input Data Acquisition Module (Omega Engineering, inc., USA) for the measuring of temperature (5), with an accuracy of ΔT = ± 0.001 K. The vapor pressure is measured using two various Keller pressure transmitters (4) (model: SERIE 35 X HTC, Omega GmbH & Co., Germany) ranging from a maximum pressure of 300000 Pa with uncertainty ΔP = ± (400 to 1500) Pa to a pressure of 1600000 Pa with uncertainty ΔP = ± (2000 to 8000) Pa. This high temperature transmitter is suited for media temperatures up to T = 573.15 K. The pressure, acting onto the flush diaphragm, is transferred over an oil-filled capillary onto the silicon measuring cell. The capillary acts as a cooling spiral, allowing for media temperatures of up to T = 573.15 K. The temperature of the electronics, which can be monitored with the PROG30 software, may not exceed T = 393.15 K. For this purpose two air propellers are constructed in the pressure transmitter area to keep the electronics cool. Before starting the experiments, the measuring cell was washed. All fluid was removed from the measuring cells using the TRIVAC rotary vane vacuum pump (18) and using the vacuum system (16, 17). The measuring cell was dried to a minimal vacuum pressure of P = (20 to 30) Pa in preparation for the experiments. The valve (9) is closed. An exact quantity of sample (approximately 1/2 of the volume of the measuring cell) is injected into the measuring cell using the flask of sample (8) after the valve (10) is closed. Phase equilibrium is reached by stirring the two phases using a magnetic stirrer (15) and a Teflon-coated magnet (14) inside the measuring cell. Equilibration in the measuring cell is a rapid process with a constant pressure reached within approximately 50 min to 70 min. Equilibrium pressure readings are performed in 1 min

intervals and data transfer to the computer system is controlled using the LabView program. Experiments were carried out starting from low temperature (T = 333.15 K) to high temperature T = 413.15 K at ΔT = 10 K intervals. After stabilization of the system pressure, the PC (6) with LabView program increases the temperature at the predetermined intervals to measure the vapor pressure at the selected temperature. The vapor pressure of the sample increases. This procedure continues until the final temperature T = 413.15 K. The total time required for collecting measurements from T = (333.15 to 413.15) K takes approximately 10 h. After reaching maximum temperature set, the measurements were continued from high T = 413.15 K to low T = 333.15 K using the cooling of the thermostat for the comparison of total measurements. The vapor pressures of the water, methanol, acetone, toluene, 1-butanol, etc. were measured as reference substances for testing both setups. The experimental vapor pressure P/Pa results are assessed to be reliable to within ΔP = ± 0.05 % average uncertainty according to test measurements. The experimental vapor pressure results of pure water and their comparison with literature values18 are given in Table 1 to demonstrate this.

3. RESULTS AND DISCUSSION First, the vapor pressure values of pure methanol were measured as a reference at temperatures ranging from 274.15 K to 413.15 K and were compared with the available literature values.19−23 The measured experimental vapor pressures P of {xCH3OH + (1 − x)[HMIM][NTf2] at T = (274.15 to 413.15) K are listed in Table 2, and are also shown in Figure 4. The experimental vapor pressure, P, results of investigated solutions were fit to the Antoine equation: ln(P /Pa) = A − B /{(T /K) + C)}

(1)

The evaluated constants, A, B, and C, for the investigated solutions are tabulated in Table 3, the standard mean deviation is n

δP /P = 100/n·∑ [(Pexp − Pcal)/Pexp] i=1

(2)

From Table 3, it can be seen that coefficients, A, B and C, have dependency for the mole fraction of the solvent, and fitting these coefficients for the mole fraction was challenging task. Thus, we also used the Clausius−Clapeyron type equation 1651



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Table 2. Experimental Mole Fraction x of Methanol, Molality m/mol·kg−1 of ionic liquid [HMIM][NTf2], Vapor Pressure p/Pa of Solution, Calculated Corrections Due to Fugacity Coefficients φ1/φ10, Activity of Methanol as, Osmotic Coefficient ϕ, Activity Coefficients γ of {xCH3OH + (1 − x)[HMIM][NTf2] Solutiona x

m

P

1.0000 0.9728 0.9700 0.9521 0.9245 0.8803 0.8703 0.8445 0.7996 0.7502 0.7367 0.6845 0.6246 0.5500 0.4785 0.4394 0.3938 0.3733 0.3342 0.2684 0.1823 0.1175 0.0812 0.0342 0.0000

0.00000 0.87262 0.96522 1.57011 2.54869 4.24367 4.65102 5.74657 7.82173 10.39185 11.15419 14.38479 18.75728 25.53451 34.01340 39.81720 48.04165 52.39374 62.17489 85.06852 139.98613 234.39833 353.13652 881.33044

4252 4204 4197 4148 4051 3855 3803 3670 3459 3258 3202 3014 2794 2515 2261 2115 1936 1859 1705 1374 876 512 327 162 0

1.0000 0.9728 0.9700 0.9521 0.9245 0.8803 0.8703 0.8445 0.7996 0.7502 0.7367 0.6845 0.6246 0.5500 0.4785 0.4394 0.3938 0.3733 0.3342 0.2684 0.1823 0.1175 0.0812 0.0342

0.00000 0.87262 0.96522 1.57011 2.54869 4.24367 4.65102 5.74657 7.82173 10.39185 11.15419 14.38479 18.75728 25.53451 34.01340 39.81720 48.04165 52.39374 62.17489 85.06852 139.98613 234.39833 353.13652 881.33044

5501 5431 5422 5350 5207 4923 4856 4673 4370 4071 3991 3722 3420 3046 2691 2489 2262 2151 1949 1602 1056 615 381 191

1.0000 0.9728 0.9700 0.9521 0.9245 0.8803 0.8703

0.00000 0.87262 0.96522 1.57011 2.54869 4.24367 4.65102

7411 7308 7293 7191 6983 6583 6483

φ/φ* T = 274.15 K 1.00000 1.00006 1.00007 1.00013 1.00025 1.00050 1.00057 1.00074 1.00101 1.00126 1.00133 1.00157 1.00185 1.00220 1.00253 1.00271 1.00294 1.00304 1.00323 1.00365 1.00429 1.00475 1.00499 1.00520 1.00540 T = 278.15 K 1.00000 1.00008 1.00009 1.00017 1.00033 1.00066 1.00073 1.00094 1.00129 1.00163 1.00172 1.00202 1.00237 1.00279 1.00320 1.00343 1.00369 1.00381 1.00405 1.00444 1.00506 1.00557 1.00584 1.00605 T = 283.15 K 1.00000 1.00010 1.00012 1.00022 1.00043 1.00083 1.00092 1652

as

ϕ

γ

1.0000 0.9888 0.9871 0.9757 0.9530 0.9071 0.8949 0.8638 0.8143 0.7672 0.7541 0.7100 0.6583 0.5928 0.5331 0.4988 0.4567 0.4385 0.4023 0.3243 0.2069 0.1210 0.0773 0.0383

1.000 0.202 0.209 0.245 0.295 0.359 0.373 0.398 0.410 0.398 0.395 0.372 0.348 0.320 0.289 0.273 0.255 0.246 0.229 0.207 0.176 0.141 0.113 0.058

1.000 1.016 1.018 1.025 1.031 1.030 1.028 1.023 1.018 1.023 1.024 1.037 1.054 1.078 1.114 1.135 1.160 1.175 1.204 1.208 1.135 1.030 0.952 1.120

1.0000 0.9874 0.9857 0.9727 0.9469 0.8955 0.8834 0.8503 0.7954 0.7413 0.7268 0.6780 0.6232 0.5553 0.4907 0.4540 0.4127 0.3925 0.3557 0.2925 0.1929 0.1124 0.0697 0.0349

1.000 0.228 0.232 0.275 0.334 0.406 0.416 0.440 0.457 0.450 0.447 0.422 0.393 0.360 0.327 0.309 0.287 0.279 0.259 0.225 0.183 0.145 0.118 0.059

1.000 1.015 1.016 1.022 1.024 1.017 1.015 1.007 0.995 0.988 0.986 0.990 0.998 1.010 1.026 1.033 1.048 1.051 1.064 1.090 1.058 0.957 0.858 1.021

1.0000 0.9862 0.9842 0.9705 0.9427 0.8890 0.8756

1.000 0.248 0.258 0.297 0.362 0.433 0.446

1.000 1.014 1.015 1.019 1.020 1.010 1.006



Article

Table 2. continued x

m

P

0.8445 0.7996 0.7502 0.7367 0.6845 0.6246 0.5500 0.4785 0.4394 0.3938 0.3733 0.3342 0.2684 0.1823 0.1175 0.0812 0.0342

5.74657 7.82173 10.39185 11.15419 14.38479 18.75728 25.53451 34.01340 39.81720 48.04165 52.39374 62.17489 85.06852 139.98613 234.39833 353.13652 881.33044

6222 5769 5285 5167 4742 4273 3754 3285 3049 2777 2637 2365 1924 1265 736 460 234

1.0000 0.9728 0.9700 0.9521 0.9245 0.8803 0.8703 0.8445 0.7996 0.7502 0.7367 0.6845 0.6246 0.5500 0.4785 0.4394 0.3938 0.3733 0.3342 0.2684 0.1823 0.1175 0.0812 0.0342

0.00000 0.87262 0.96522 1.57011 2.54869 4.24367 4.65102 5.74657 7.82173 10.39185 11.15419 14.38479 18.75728 25.53451 34.01340 39.81720 48.04165 52.39374 62.17489 85.06852 139.98613 234.39833 353.13652 881.33044

12996 12802 12775 12578 12183 11418 11233 10738 9853 8937 8696 7807 6886 5898 5065 4648 4177 3952 3542 2811 1799 1041 654 342

1.0000 0.9728 0.9700 0.9521 0.9245 0.8803 0.8703 0.8445 0.7996 0.7502 0.7367 0.6845 0.6246 0.5500 0.4785 0.4394 0.3938

0.00000 0.87262 0.96522 1.57011 2.54869 4.24367 4.65102 5.74657 7.82173 10.39185 11.15419 14.38479 18.75728 25.53451 34.01340 39.81720 48.04165

21861 21514 21462 21097 20388 19066 18744 17851 16277 14560 14123 12506 10818 9014 7536 6808 6005

φ/φ* T = 283.15 K 1.00118 1.00164 1.00212 1.00224 1.00266 1.00313 1.00365 1.00412 1.00435 1.00463 1.00477 1.00504 1.00548 1.00614 1.00667 1.00695 1.00717 T = 293.15 K 1.00000 1.00015 1.00017 1.00032 1.00063 1.00123 1.00137 1.00175 1.00244 1.00316 1.00334 1.00404 1.00475 1.00553 1.00618 1.00650 1.00687 1.00705 1.00737 1.00794 1.00873 1.00932 1.00963 1.00987 T = 303.15 K 1.00000 1.00021 1.00025 1.00047 1.00091 1.00173 1.00193 1.00248 1.00346 1.00452 1.00479 1.00580 1.00685 1.00797 1.00889 1.00934 1.00984 1653

as

ϕ

γ

0.8406 0.7797 0.7146 0.6988 0.6416 0.5784 0.5084 0.4451 0.4132 0.3764 0.3575 0.3207 0.2610 0.1717 0.1000 0.0625 0.0318

0.472 0.496 0.505 0.501 0.481 0.455 0.413 0.371 0.346 0.317 0.306 0.285 0.246 0.196 0.153 0.123 0.061

0.995 0.975 0.953 0.949 0.937 0.926 0.924 0.930 0.940 0.956 0.958 0.960 0.973 0.942 0.851 0.770 0.930

1.0000 0.9852 0.9832 0.9682 0.9380 0.8797 0.8655 0.8277 0.7600 0.6898 0.6714 0.6031 0.5324 0.4563 0.3921 0.3600 0.3236 0.3062 0.2746 0.2180 0.1396 0.0808 0.0508 0.0266

1.000 0.266 0.275 0.322 0.392 0.471 0.485 0.513 0.547 0.558 0.557 0.548 0.524 0.479 0.429 0.400 0.366 0.352 0.324 0.279 0.219 0.167 0.132 0.064

1.000 1.013 1.014 1.017 1.015 0.999 0.995 0.980 0.950 0.920 0.911 0.881 0.852 0.830 0.820 0.819 0.822 0.820 0.822 0.812 0.766 0.688 0.626 0.777

1.0000 0.9843 0.9820 0.9655 0.9335 0.8737 0.8591 0.8186 0.7471 0.6690 0.6491 0.5754 0.4982 0.4156 0.3478 0.3143 0.2774

1.000 0.282 0.294 0.349 0.422 0.497 0.510 0.544 0.582 0.604 0.605 0.600 0.580 0.537 0.485 0.454 0.417

1.000 1.012 1.012 1.014 1.010 0.992 0.987 0.969 0.934 0.892 0.881 0.841 0.798 0.756 0.727 0.715 0.704



Article


m

P

0.3733 0.3342 0.2684 0.1823 0.1175 0.0812 0.0342

52.39374 62.17489 85.06852 139.98613 234.39833 353.13652 881.33044

5659 5002 3935 2497 1456 908 485

1.0000 0.9728 0.9700 0.9521 0.9245 0.8803 0.8703 0.8445 0.7996 0.7502 0.7367 0.6845 0.6246 0.5500 0.4785 0.4394 0.3938 0.3733 0.3342 0.2684 0.1823 0.1175 0.0812 0.0342

0.00000 0.87262 0.96522 1.57011 2.54869 4.24367 4.65102 5.74657 7.82173 10.39185 11.15419 14.38479 18.75728 25.53451 34.01340 39.81720 48.04165 52.39374 62.17489 85.06852 139.98613 234.39833 353.13652 881.33044

35430 34836 34739 34114 32895 30603 30058 28606 25951 23043 22217 19400 16484 13352 10865 9700 8439 7906 6911 5361 3365 1930 1233 669

1.0000 0.9728 0.9700 0.9521 0.9245 0.8803 0.8703 0.8445 0.7996 0.7502 0.7367 0.6845 0.6246 0.5500 0.4785 0.4394 0.3938 0.3733 0.3342 0.2684 0.1823 0.1175 0.0812 0.0342

0.00000 0.87262 0.96522 1.57011 2.54869 4.24367 4.65102 5.74657 7.82173 10.39185 11.15419 14.38479 18.75728 25.53451 34.01340 39.81720 48.04165 52.39374 62.17489 85.06852 139.98613 234.39833 353.13652 881.33044

55540 54526 54378 53366 51382 47697 46806 44392 40063 35303 34030 29330 24450 19362 15367 13523 11634 10813 9408 7250 4498 2582 1642 901

1.0000 0.9728

0.00000 0.87262

84932 83314

φ/φ* T = 303.15 K 1.01006 1.01047 1.01114 1.01204 1.01269 1.01303 1.01329 T = 313.15 K 1.00000 1.00030 1.00035 1.00066 1.00127 1.00243 1.00270 1.00343 1.00477 1.00624 1.00665 1.00808 1.00956 1.01114 1.01241 1.01300 1.01364 1.01391 1.01442 1.01521 1.01622 1.01696 1.01731 1.01760 T = 323.15 K 1.00000 1.00042 1.00048 1.00090 1.00173 1.00326 1.00363 1.00464 1.00645 1.00844 1.00897 1.01095 1.01300 1.01514 1.01682 1.01760 1.01840 1.01875 1.01934 1.02026 1.02143 1.02224 1.02264 1.02295 T = 333.15 K 1.00000 1.00056 1654

as

ϕ

γ

0.2615 0.2312 0.1820 0.1156 0.0674 0.0421 0.0225

0.400 0.368 0.313 0.241 0.180 0.140 0.067

0.700 0.692 0.678 0.634 0.574 0.518 0.657

1.0000 0.9835 0.9808 0.9635 0.9296 0.8659 0.8507 0.8102 0.7360 0.6544 0.6312 0.5520 0.4697 0.3811 0.3105 0.2773 0.2414 0.2262 0.1979 0.1536 0.0965 0.0554 0.0354 0.0192

1.000 0.297 0.313 0.370 0.447 0.530 0.543 0.572 0.612 0.637 0.644 0.645 0.629 0.590 0.537 0.503 0.462 0.443 0.407 0.344 0.261 0.193 0.148 0.070

1.000 1.011 1.011 1.012 1.006 0.984 0.977 0.959 0.920 0.872 0.857 0.806 0.752 0.693 0.649 0.631 0.613 0.606 0.592 0.572 0.529 0.471 0.436 0.562

1.0000 0.9822 0.9796 0.9617 0.9267 0.8616 0.8458 0.8030 0.7260 0.6410 0.6182 0.5339 0.4459 0.3539 0.2813 0.2478 0.2133 0.1983 0.1727 0.1332 0.0827 0.0475 0.0302 0.0166

1.000 0.322 0.334 0.388 0.466 0.548 0.562 0.596 0.639 0.668 0.673 0.681 0.672 0.635 0.582 0.547 0.502 0.482 0.441 0.370 0.278 0.203 0.155 0.073

1.000 1.010 1.010 1.010 1.002 0.979 0.972 0.951 0.908 0.854 0.839 0.780 0.714 0.643 0.588 0.564 0.542 0.531 0.517 0.496 0.454 0.404 0.372 0.485

1.0000 0.9815

1.000 0.334

1.000 1.009



Article


m

P

0.9700 0.9521 0.9245 0.8803 0.8703 0.9245 0.8803 0.8703 0.8445 0.7996 0.7502 0.7367 0.6845 0.6246 0.5500 0.4785 0.4394 0.3938 0.3733 0.3342 0.2684 0.1823 0.1175 0.0812 0.0342

0.96522 1.57011 2.54869 4.24367 4.65102 2.54869 4.24367 4.65102 5.74657 7.82173 10.39185 11.15419 14.38479 18.75728 25.53451 34.01340 39.81720 48.04165 52.39374 62.17489 85.06852 139.98613 234.39833 353.13652 881.33044

83075 81451 78350 72484 70978 166379 153247 149852 141250 126047 108672 104080 86763 69439 51922 38412 32290 26532 24397 20521 14897 9173 5330 3501 1187

1.0000 0.9728 0.9700 0.9521 0.9245 0.8803 0.8703 0.8445 0.7996 0.7502 0.7367 0.6845 0.6246 0.5500 0.4785 0.4394 0.3938 0.3733 0.3342 0.2684 0.1823 0.1175 0.0812 0.0342

0.00000 0.87262 0.96522 1.57011 2.54869 4.24367 4.65102 5.74657 7.82173 10.39185 11.15419 14.38479 18.75728 25.53451 34.01340 39.81720 48.04165 52.39374 62.17489 85.06852 139.98613 234.39833 353.13652 881.33044

125739 123217 122834 120357 115608 106673 104363 98394 88034 76311 73210 61631 49915 37967 28805 24583 20507 18777 16087 11860 7331 4263 2763 1534

1.0000 0.9728 0.9700 0.9521 0.9245 0.8803 0.8703 0.8445 0.7996

0.00000 0.87262 0.96522 1.57011 2.54869 4.24367 4.65102 5.74657 7.82173

181556 177725 177186 173479 166379 153247 149852 141250 126047

φ/φ* T = 333.15 K 1.00065 1.00121 1.00230 1.00435 1.00488 1.00386 1.00721 1.00807 1.01028 1.01418 1.01866 1.01984 1.02433 1.02884 1.03343 1.03697 1.03858 1.04010 1.04067 1.04169 1.04318 1.04469 1.04571 1.04620 1.02964 T = 343.15 K 1.00000 1.00075 1.00086 1.00160 1.00300 1.00566 1.00635 1.00813 1.01123 1.01475 1.01568 1.01917 1.02271 1.02633 1.02912 1.03041 1.03165 1.03218 1.03301 1.03430 1.03569 1.03663 1.03709 1.03747 T = 353.15 K 1.00000 1.00097 1.00111 1.00205 1.00386 1.00721 1.00807 1.01028 1.01418 1655

as

ϕ

γ

0.9788 0.9602 0.9246 0.8571 0.8398 0.9199 0.8502 0.8320 0.7860 0.7041 0.6097 0.5846 0.4895 0.3935 0.2955 0.2194 0.1847 0.1520 0.1398 0.1177 0.0856 0.0528 0.0307 0.0202 0.0144

0.347 0.404 0.480 0.567 0.586 0.511 0.597 0.617 0.654 0.700 0.743 0.751 0.775 0.776 0.745 0.696 0.662 0.612 0.586 0.537 0.451 0.328 0.232 0.172 0.075

1.009 1.008 1.000 0.974 0.965 0.995 0.966 0.956 0.931 0.881 0.813 0.794 0.715 0.630 0.537 0.459 0.420 0.386 0.375 0.352 0.319 0.290 0.261 0.248 0.421

1.0000 0.9807 0.9777 0.9587 0.9222 0.8532 0.8353 0.7889 0.7080 0.6158 0.5914 0.4995 0.4060 0.3099 0.2358 0.2015 0.1683 0.1541 0.1322 0.0976 0.0604 0.0351 0.0228 0.0127

1.000 0.349 0.364 0.419 0.496 0.584 0.604 0.644 0.689 0.728 0.735 0.753 0.750 0.716 0.663 0.628 0.579 0.557 0.508 0.427 0.313 0.223 0.167 0.077

1.000 1.008 1.008 1.007 0.998 0.969 0.960 0.934 0.885 0.821 0.803 0.730 0.650 0.563 0.493 0.458 0.427 0.413 0.395 0.363 0.331 0.299 0.281 0.370

1.0000 0.9799 0.9770 0.9575 0.9199 0.8502 0.8320 0.7860 0.7041

1.000 0.364 0.376 0.432 0.511 0.597 0.617 0.654 0.700

1.000 1.007 1.007 1.006 0.995 0.966 0.956 0.931 0.881



Article


m

P

0.7502 0.7367 0.6845 0.6246 0.5500 0.4785 0.4394 0.3938 0.3733 0.3342 0.2684 0.1823 0.1175 0.0812 0.0342

10.39185 11.15419 14.38479 18.75728 25.53451 34.01340 39.81720 48.04165 52.39374 62.17489 85.06852 139.98613 234.39833 353.13652 881.33044

108672 104080 86763 69439 51922 38412 32290 26532 24397 20521 14897 9173 5330 3501 1948

1.0000 0.9728 0.9700 0.9521 0.9245 0.8803 0.8703 0.8445 0.7996 0.7502 0.7367 0.6845 0.6246 0.5500 0.4785 0.4394 0.3938 0.3733 0.3342 0.2684 0.1823 0.1175 0.0812 0.0342

0.00000 0.87262 0.96522 1.57011 2.54869 4.24367 4.65102 5.74657 7.82173 10.39185 11.15419 14.38479 18.75728 25.53451 34.01340 39.81720 48.04165 52.39374 62.17489 85.06852 139.98613 234.39833 353.13652 881.33044

256274 250648 249813 244289 234078 215037 210146 197846 175879 151290 144546 119980 94801 69680 50345 41623 33724 30843 25660 18268 11307 6606 4377 2434

1.0000 0.9728 0.9700 0.9521 0.9245 0.8803 0.8703 0.8445 0.7996 0.7502 0.7367 0.6845 0.6246 0.5500 0.4785 0.4394 0.3938 0.3733 0.3342

0.00000 0.87262 0.96522 1.57011 2.54869 4.24367 4.65102 5.74657 7.82173 10.39185 11.15419 14.38479 18.75728 25.53451 34.01340 39.81720 48.04165 52.39374 62.17489

354351 346292 345037 337152 322420 295133 288661 271544 241008 206448 197068 162988 127577 92250 65120 52891 42191 38143 31638

φ/φ* T = 353.15 K 1.01866 1.01984 1.02433 1.02884 1.03343 1.03697 1.03858 1.04010 1.04067 1.04169 1.04318 1.04469 1.04571 1.04620 1.04661 T = 363.15 K 1.00000 1.00123 1.00142 1.00263 1.00487 1.00907 1.01015 1.01287 1.01776 1.02325 1.02476 1.03029 1.03598 1.04169 1.04611 1.04811 1.04992 1.05059 1.05178 1.05348 1.05509 1.05618 1.05669 1.05714 T = 373.15 K 1.00000 1.00154 1.00178 1.00328 1.00610 1.01135 1.01260 1.01590 1.02183 1.02858 1.03042 1.03714 1.04416 1.05121 1.05666 1.05912 1.06128 1.06210 1.06342 1656

as

ϕ

γ

0.6097 0.5846 0.4895 0.3935 0.2955 0.2194 0.1847 0.1520 0.1398 0.1177 0.0856 0.0528 0.0307 0.0202 0.0112

0.743 0.751 0.775 0.776 0.745 0.696 0.662 0.612 0.586 0.537 0.451 0.328 0.232 0.172 0.079

0.813 0.794 0.715 0.630 0.537 0.459 0.420 0.386 0.375 0.352 0.319 0.290 0.261 0.248 0.328

1.0000 0.9793 0.9762 0.9557 0.9178 0.8467 0.8283 0.7819 0.6985 0.6041 0.5780 0.4824 0.3832 0.2832 0.2055 0.1702 0.1382 0.1264 0.1053 0.0751 0.0466 0.0272 0.0180 0.0100

1.000 0.375 0.390 0.450 0.525 0.612 0.632 0.668 0.716 0.757 0.767 0.791 0.798 0.771 0.726 0.694 0.643 0.616 0.565 0.475 0.342 0.240 0.177 0.081

1.000 1.007 1.006 1.004 0.993 0.962 0.952 0.926 0.874 0.805 0.785 0.705 0.614 0.515 0.429 0.387 0.351 0.339 0.315 0.280 0.255 0.232 0.222 0.294

1.0000 0.9788 0.9754 0.9546 0.9154 0.8423 0.8249 0.7785 0.6950 0.5993 0.5731 0.4770 0.3759 0.2737 0.1942 0.1581 0.1264 0.1143 0.0949

1.000 0.384 0.402 0.462 0.541 0.631 0.646 0.680 0.726 0.769 0.779 0.803 0.814 0.792 0.752 0.723 0.672 0.646 0.591

1.000 1.006 1.006 1.003 0.990 0.957 0.948 0.922 0.869 0.799 0.778 0.697 0.602 0.498 0.406 0.360 0.321 0.306 0.284



Article


m

P

0.2684 0.1823 0.1175 0.0812 0.0342

85.06852 139.98613 234.39833 353.13652 881.33044

22155 13757 8129 5404 3000

1.0000 0.9728 0.9700 0.9521 0.9245 0.8803 0.8703 0.8445 0.7996 0.7502 0.7367 0.6845 0.6246 0.5500 0.4785 0.4394 0.3938 0.3733 0.3342 0.2684 0.1823 0.1175 0.0812 0.0342

0.00000 0.87262 0.96522 1.57011 2.54869 4.24367 4.65102 5.74657 7.82173 10.39185 11.15419 14.38479 18.75728 25.53451 34.01340 39.81720 48.04165 52.39374 62.17489 85.06852 139.98613 234.39833 353.13652 881.33044

480818 469361 467661 456570 435324 397673 388560 365108 323006 276017 263412 217248 169309 120276 83077 66361 52197 46526 38526 26615 16548 9802 6596 3648

1.0000 0.9728 0.9700 0.9521 0.9245 0.8803 0.8703 0.8445 0.7996 0.7502 0.7367 0.6845 0.6246 0.5500 0.4785 0.4394 0.3938 0.3733 0.3342 0.2684 0.1823 0.1175 0.0812 0.0342

0.00000 0.87262 0.96522 1.57011 2.54869 4.24367 4.65102 5.74657 7.82173 10.39185 11.15419 14.38479 18.75728 25.53451 34.01340 39.81720 48.04165 52.39374 62.17489 85.06852 139.98613 234.39833 353.13652 881.33044

641267 625086 622801 607213 577523 525780 513624 481228 424435 362325 346200 284798 221622 155687 104908 82105 63549 56434 46394 31364 19703 11595 7966 4385

1.0000 0.9728 0.9700 0.9521

0.00000 0.87262 0.96522 1.57011

841830 819224 816015 794098

φ/φ* T = 373.15 K 1.06534 1.06705 1.06819 1.06875 1.06924 T = 383.15 K 1.00000 1.00192 1.00221 1.00407 1.00765 1.01403 1.01558 1.01957 1.02679 1.03491 1.03709 1.04515 1.05357 1.06226 1.06890 1.07190 1.07445 1.07547 1.07691 1.07906 1.08089 1.08211 1.08269 1.08322 T=393.15 K 1.00000 1.00241 1.00275 1.00508 1.00954 1.01734 1.01919 1.02412 1.03281 1.04241 1.04491 1.05451 1.06448 1.07498 1.08314 1.08682 1.08983 1.09098 1.09262 1.09506 1.09697 1.09829 1.09889 1.09947 T=403.15 K 1.00000 1.00302 1.00345 1.00638 1657

as

ϕ

γ

0.0666 0.0414 0.0245 0.0163 0.0091

0.497 0.355 0.247 0.182 0.083

0.248 0.227 0.209 0.201 0.265

1.0000 0.9780 0.9748 0.9534 0.9123 0.8387 0.8207 0.7742 0.6898 0.5941 0.5682 0.4722 0.3710 0.2657 0.1847 0.1479 0.1166 0.1041 0.0863 0.0597 0.0372 0.0221 0.0149 0.0082

1.000 0.397 0.413 0.474 0.562 0.647 0.663 0.695 0.741 0.782 0.791 0.814 0.825 0.810 0.775 0.749 0.698 0.674 0.615 0.517 0.367 0.254 0.186 0.085

1.000 1.005 1.005 1.001 0.987 0.953 0.943 0.917 0.863 0.792 0.771 0.690 0.594 0.483 0.386 0.337 0.296 0.279 0.258 0.223 0.204 0.188 0.183 0.240

1.0000 0.9771 0.9739 0.9517 0.9092 0.8341 0.8163 0.7685 0.6836 0.5890 0.5641 0.4683 0.3679 0.2610 0.1772 0.1392 0.1080 0.0960 0.0790 0.0536 0.0337 0.0199 0.0137 0.0075

1.000 0.414 0.428 0.492 0.583 0.667 0.681 0.715 0.759 0.795 0.801 0.823 0.832 0.821 0.794 0.773 0.723 0.698 0.637 0.537 0.378 0.261 0.190 0.087

1.000 1.004 1.004 1.000 0.983 0.948 0.938 0.910 0.855 0.785 0.766 0.684 0.589 0.475 0.370 0.317 0.274 0.257 0.237 0.200 0.185 0.169 0.168 0.220

1.0000 0.9761 0.9727 0.9493

1.000 0.433 0.448 0.517

1.000 1.003 1.003 0.997



Article


m

φ/φ*

P

0.9245 0.8803 0.8703 0.8445 0.7996 0.7502 0.7367 0.6845 0.6246 0.5500 0.4785 0.4394 0.3938 0.3733 0.3342 0.2684 0.1823 0.1175 0.0812 0.0342

2.54869 4.24367 4.65102 5.74657 7.82173 10.39185 11.15419 14.38479 18.75728 25.53451 34.01340 39.81720 48.04165 52.39374 62.17489 85.06852 139.98613 234.39833 353.13652 881.33044

753598 683020 667209 624090 548728 467637 446347 366315 284079 197382 130171 100589 76730 67484 55113 36716 23050 13681 9527 5214

1.0000 0.9728 0.9700 0.9521 0.9245 0.8803 0.8703 0.8445 0.7996 0.7502 0.7367 0.6845 0.6246 0.5500 0.4785 0.4394 0.3938 0.3733 0.3342 0.2684 0.1823 0.1175 0.0812 0.0342

0.00000 0.87262 0.96522 1.57011 2.54869 4.24367 4.65102 5.74657 7.82173 10.39185 11.15419 14.38479 18.75728 25.53451 34.01340 39.81720 48.04165 52.39374 62.17489 85.06852 139.98613 234.39833 353.13652 881.33044

1089155 1057733 1052896 1023816 969109 876285 854469 799642 701171 595444 567345 464618 358736 246529 160181 121721 91557 80315 64762 42580 27052 16147 11292 6138

T=403.15 K 1.01183 1.02138 1.02354 1.02944 1.03982 1.05112 1.05411 1.06541 1.07714 1.08966 1.09946 1.10380 1.10732 1.10868 1.11051 1.11324 1.11526 1.11666 1.11728 1.11792 T = 413.15 K 1.00000 1.00373 1.00431 1.00777 1.01432 1.02554 1.02820 1.03490 1.04704 1.06024 1.06377 1.07680 1.09039 1.10499 1.11635 1.12145 1.12546 1.12696 1.12904 1.13201 1.13410 1.13556 1.13622 1.13691

as

ϕ

γ

0.9058 0.8287 0.8112 0.7632 0.6778 0.5839 0.5589 0.4636 0.3635 0.2555 0.1700 0.1319 0.1009 0.0889 0.0727 0.0486 0.0305 0.0181 0.0126 0.0069

0.606 0.691 0.702 0.734 0.776 0.808 0.814 0.834 0.842 0.834 0.813 0.794 0.745 0.721 0.658 0.555 0.389 0.267 0.193 0.088

0.980 0.941 0.932 0.904 0.848 0.778 0.759 0.677 0.582 0.465 0.355 0.300 0.256 0.238 0.218 0.181 0.168 0.154 0.156 0.202

1.0000 0.9748 0.9709 0.9473 0.9025 0.8251 0.8066 0.7598 0.6741 0.5796 0.5541 0.4593 0.3591 0.2501 0.1642 0.1253 0.0946 0.0831 0.0671 0.0443 0.0282 0.0168 0.0118 0.0064

1.000 0.457 0.478 0.538 0.628 0.707 0.721 0.746 0.787 0.819 0.826 0.844 0.852 0.847 0.829 0.814 0.766 0.741 0.678 0.572 0.398 0.272 0.196 0.089

1.000 1.002 1.001 0.995 0.976 0.937 0.927 0.900 0.843 0.773 0.752 0.671 0.575 0.455 0.343 0.285 0.240 0.223 0.201 0.165 0.155 0.143 0.145 0.187

Standard uncertainties u are u(T) = 0.01 K, u(x) = 0.0001 mole fraction, u(m) = 0.00001 mol·kg−1, and the combined expanded uncertainties Uc are Uc(P) = 30 Pa for P < 0.1 MPa, Uc(P) = 1500 Pa for P < 3 MPa, Uc(P) = 8000 Pa for P < 16 MPa, (level of confidence = 0.95). a

to fit the vapor pressure results in all of the mole fraction intervals of the investigated solutions: B + C ln T T

ln P = A +

The evaluated coefficients ai, bi, and ci for the investigated {xCH3OH + (1 − x)[HMIM][NTf2] solutions are tabulated in Table 4. The uncertainty of fitting was approximately ur(ΔP/P) = 0.0549. The coefficients ai, bi, and ci are not valid only at x = 0. The activity of the solvent, as, and osmotic coefficients, ϕ, were calculated from the experimental vapor pressure values using the following equations:

(3)

where P is vapor pressure in Pa; T is the absolute temperature in K; A, B, and C are the coefficients of the equation, which depend on the mole fraction of the solvent as follows: 3

A=

3 j

∑ aix , i=0

B=

3 j

∑ bix , i=0

C=

∑ cix i=0

j

(4) 1658

ln as = ln(P /P*) + (Bs − V s*)(P ‐P*)/RT

(5)

ϕ = −ln as /(νmMs)

(6) DOI: 10.1021/je501033z J. Chem. Eng. Data 2015, 60, 1648−1663


Article

Table 4. Clausius−Clapeyron Equation Fitting Parameters ai, bi, and ci ai

bi

ci

a0 = 33.7377 a1 = 61.5118 a2 = −223.187 a3 = 185.189

b0 = −3913.16 b1 = 400.113 b2 = −175.188 b3 = −2346.69

c0 = −2.59713 c1 = −9.01695 c2 = 36.8315 c3 = −29.9868

where P and P* are the vapor pressures of the solution and pure solvent, respectively; Bs and V*s are the second virial coefficient of methanol vapor and molar volume of pure liquid methanol, respectively; ν is the sum of stoichiometric numbers of anion and cation (ν− + ν+) of [HMIM][NTf2]; m is molality of [HMIM][NTf2] and Ms is the molecular weight of methanol, respectively. The second term on the right-hand side of eq 5 takes into account the nonideality of the solvent vapor using the virial equation. The obtained values for as and ϕ are tabulated in Table 2 and are shown in Figures 5 and 6. The

Figure 4. Plot of vapor pressure P/kPa of {xCH3OH+(1-x)[HMIM][NTf2] mixture versus mole fraction x of CH3OH. ◆, 274.15 K; ■, 278.15 K; ▲, 283.15 K; ●, 293.15 K; ▼ 303.15 K; ×, 313.15 K; +, 323.15 K; ◇, 333.15 K; □, 343.15 K; △, 353.15 K; ○, 363.15 K; ▽, 373.15 K; cross-in-box, 383.15 K; ⊕, 393.15 K; ★, 403.15 K; ☆ 413.15 K, ____ equations 3 and 4

Table 3. Antoine Parameters A, B, C and Standard Deviations δP/P of the Solutions x/(mole fraction)

A

B

C

(Δp/p)/%

1.0000 0.9728 0.9700 0.9521 0.9245 0.8803 0.8703 0.8445 0.7996 0.7502 0.7367 0.6845 0.6246 0.5500 0.4785 0.4394 0.3938 0.3733 0.3342 0.2684 0.1823 0.1175 0.0812 0.0342

23.3496 23.2640 23.2528 23.1845 23.0556 22.8760 22.8517 22.7981 22.7283 22.7886 22.8185 22.9612 22.9441 22.1859 20.4287 18.9879 17.8504 17.3292 16.8122 15.4896 15.4355 15.3597 15.9209 14.3701

3551.4600 3522.5200 3519.2000 3499.9100 3464.2500 3433.0700 3437.6100 3457.2900 3520.7100 3703.3600 3767.4000 4065.3600 4342.7900 4236.7500 3489.2800 2818.3000 2371.9200 2172.4200 2038.1400 1608.4600 1843.4400 2091.0400 2619.3500 2002.8500

−37.2312 −38.0101 −38.0830 −38.4989 −39.2760 −39.3812 −38.8954 −37.2686 −32.8193 −22.4525 −18.9191 −2.4761 14.9653 20.7877 0.2146 −25.7700 −43.8068 −52.9826 −57.2725 −79.8819 −60.9473 −44.5315 −15.6108 −58.4557

0.1776 0.1997 0.2069 0.2396 0.3126 0.4250 0.4101 0.4388 0.5933 0.6763 0.6702 0.6542 0.5298 0.3941 0.3533 0.3509 0.3843 0.6022 0.6349 0.5632 0.4387 0.5445 0.0235 0.0828

Figure 5. Plot of activity of methanol as in {xCH3OH + (1 − x)[HMIM][NTf2] mixture versus mole fraction x of CH3OH: ◆, 274.15 K; ■, 278.15 K; ▲, 283.15 K; ●, 293.15 K; ▼ 303.15 K; ×, 313.15 K; +, 323.15 K; ◇, 333.15 K; □, 343.15 K; △, 353.15 K; ○, 363.15 K; ▽, 373.15 K; cross-in-box, 383.15 K; ⊕, 393.15 K; ★, 403.15 K; ☆, 413.15 K.

vapor pressure results P* of pure methanol were used from our measurements in this work (Table 2) after the comparison of them with the available literature values. The values of V*s required for eq 5 were calculated from the density values using the software “Thermofluid”,21 “Refprop”,22 and various literature values; for example,23−25 values of Bs were taken from software “Thermofluid”,21 “Refprop”22 using ref 23. All values used for the calculation are shown in Table 5. Binary mixtures of IL with nonelectrolyte components belong to the class of electrolyte solutions covering the entire 1659



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energy of mixing of these types of mixtures, we have tried to describe the results of the activity coefficients by using purely empirical expressions well-known in the thermodynamics of nonelectrolyte mixtures. After several attempts with the simple Margules equation, the Wilson equation, and the UNIQUAC equation, it was found that the nonrandom two-liquid (NRTL) equation gives the best empirical description of the activity coefficients. Equation 7 has been used to determine activity coefficients γ1 using the NRTLequation from experimental data of partial pressures P including the vapor pressure of the pure solutes p*: P

φ = P*x1γ1NRTL φ*

(7)

Corrections due to fugacity coefficients φ and φ* have been accounted for by φ = exp[ − (V s − Bs )(P − P*)/RT ] φ*

(8)

The literature sources of second virial coefficients Bs and molar liquid volumes Vs of methanol were already discussed above. The calculated values of activity coefficients γ1 are given in Table 2 and shown in Figure 7 and the deviation of calculated γcal and fitted γfit values are shown in Figure 8. It turned out that eq 7 is only a small correction for the values of γ1 which is within ± 1 %. The NRTL activity coefficient model, which is based on the local composition theory of Wilson26 and the two-liquid

Figure 6. Plot of osmotic coefficient ϕ of {xCH3OH + (1 − x)[HMIM][NTf2] mixture versus mole fraction x of CH3OH: ◆, 274.15 K; ■, 278.15 K; ▲, 283.15 K; ●, 293.15 K; ▼ 303.15 K; ×, 313.15 K; +, 323.15 K; ◇, 333.15 K; □, 343.15 K; △, 353.15 K; ○, 363.15 K; ▽, 373.15 K; cross-in-box, 383.15 K; ⊕, 393.15 K; ★, 403.15 K; ☆, 413.15 K.

Table 5. Vapor Pressure P*/Pa of Pure Methanol, Second Virial Coefficient Bs/(m3·mol−1) of Vapor Methanol and Molar Volume Vs*/(m3·mol−1) of Liquid Methanol at Different Temperatures T/Ka T

P* [this work]

Bs/(m3·mol−1)21−23

Vs*/(m3·mol−1)21−23

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

4252 5501 7411 12996 21861 35430 55540 84932 125739 181556 256274 354351 480818 641267 841830 1089155

−0.0028490 −0.0025888 −0.0023049 −0.0018516 −0.0015163 −0.0012654 −0.0010739 −0.0009235 −0.0008018 −0.0007010 −0.0006166 −0.0005461 −0.0004879 −0.0004401 −0.0003991 −0.0003585

3.962·10−5 3.980·10−5 4.003·10−5 4.051·10−5 4.099·10−5 4.150·10−5 4.202·10−5 4.256·10−5 4.314·10−5 4.374·10−5 4.438·10−5 4.507·10−5 4.581·10−5 4.662·10−5 4.751·10−5 4.849·10−5

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

Figure 7. Plot of activity coefficient γ of methanol in {xCH3OH + (1 − x)[HMIM][NTf2] mixture versus mole fraction x of CH3OH: ◆, 274.15 K; ■, 278.15 K; ▲, 283.15 K; ●, 293.15 K; ▼ 303.15 K; ×, 313.15 K; +, 323.15 K; ◇, 333.15 K; □, 343.15 K; △, 353.15 K; ○, 363.15 K; ▽, 373.15 K; cross-in-box, 383.15 K; ⊕, 393.15 K; ★, 403.15 K; ☆, 413.15 K.

range of composition including the pure liquid electrolyte. Since there exists no reliable theoretical models for the Gibbs 1660



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Figure 8. Deviation of calculated γcal and fitted γfit values of activity coefficient γ of methanol in {xCH3OH + (1 − x)[HMIM][NTf2] mixture versus mole fraction x at various temperatures T/K using equations 3 and 4.

solution theory of Scott27 was developed by Renon and Prausnitz in 1968.28 The model was applied to highly nonideal VLE and LLE systems. The NRTL model activity coefficient expression for components in a binary {xCH3OH + (1 − x)[HMIM][NTf2] system is given by

Table 6. Parameters of the NRTL Equation

⎡ ⎛ ⎞2 G21 ln γ1NRTL = (1 − x)2 ⎢τ21⎜ ⎟ ⎢⎣ ⎝ x + (1 − x)G21 ⎠ +

⎤ ⎥ (1 − x + xG12)2 ⎥⎦ τ12G12

(9)

where τij and Gij are defined as Gij = exp( −αijτij),

τij =

gij − gjj RT

(10)

here αij = αji = α (i, j = 1,2; i ≠ j) is the nonrandomness factor in the mixture, and gij is energy interaction between i and j component molecules. Table 6 contains the parameters αij and to the experimental VLE data. τij obtained by fitting γNRTL 1 The enthalpy of vaporization ΔHv/J·mol−1 of methanol for the three middle temperatures [for temperature interval T = (274.15 to 323.15) K in T = 298.15 K, for temperature interval T = (323.15 to 373.15) K in T = 348.15 K and for temperature interval T = (373.15 to 413.15) K in T = 398.15 K] was defined using the following equation29 and tabulated in Table 7. d ln P d

1 T

()

=−

ΔHv R

T/K

τ12

τ21

α = α12 = α21

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

0.2137 0.32628 0.31953 0.52138 0.54207 0.59427 0.58899 0.57471 0.59308 0.59993 0.55014 0.57584 0.44331 0.54446 0.51778 0.24958

−0.59252 −0.52144 −0.76358 −0.0267 −0.3461 −0.042598 −0.012217 −0.00036892 −0.018909 −0.070266 −0.077219 −0.17443 −0.0085304 −0.33512 −0.29414 −1.6499

0.8185 0.61004 0.78 −0.40834 −0.33713 −0.83577 −1.029 −1.208 −1.3343 −1.3964 −1.5317 −1.5738 −1.8493 −1.6555 −1.7744 −1.153

ΔHv = −R ·

d ln P d

( T1 )

(12)

After the integration of (12) we can find ⎛ ΔHv ⎞⎛ 1 ⎞ ⎟⎜ ⎟ + C ln P = ⎜ − ⎝ R ⎠⎝ T ⎠

(13)

ΔHv = RT (C − ln P), J·mol−1

(14)

We compared our interpolated to T = 353.11 K vapor pressure values (Table 2) with those from ref 10. The average deviation of our values from those from ref 10 is around (ΔP/P) = ± 50 % at small molalities of [HMIM][NTf2], and this deviation sharply decreases with the increasing of ionic liquid molality up to (ΔP/P) = ± 0.1 %. We cannot discuss such deviations at

(11)

If we will plot ln(P) as a function of (1/T), we can define ΔHv from the slope of the line: 1661



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Table 7. Enthalpy of Vaporization ΔHv, J·mol−1, of CH3OH in {xCH3OH + (1 − x)[HMIM][NTf2]

efficiencies in dye-sensitized solar cells. Chem. Mater. 2004, 16, 2694− 2696. (3) Van Valkenburg, M. E. V.; Vaughn, R. L.; Williams, M.; Wilkes, J. S. Thermochemistry of ionic liquid heat-transfer fluids. Thermochim. Acta 2005, 425, 181−188. (4) Earle, M. J.; Seddon, K. R. Ionic liquids. Green solvents for the future. Pure Appl. Chem. 2001, 72, 1391−1398. (5) Marczak, W.; Verevkin, S. P.; Heintz, A. Enthalpies of solution of organic solutes in the ionic liquid 1-methyl-3-ethylimidazolium bis(trifluoromethylsulfonyl)amide. J. Solution Chem. 2001, 32, 519− 526. (6) Heintz, A.; Kulikov, D. V.; Verevkin, S. P. Thermodynamic properties of mixtures containing ionic liquids. Activity coefficients at infinite dilution of alkanes, alkenes, and alkylbenzenes in 4-methyl-nbutylpyridinium tetrafluoroborate using gas-liquid chromatography. J. Chem. Eng. Data 2001, 46, 1526−1529. (7) Domanska, U.; Marciniak, A. Solubility of ionic liquid [EMIM][PF6] in alcohols. J. Phys. Chem. B 2004, 108, 2376−2382. (8) Crosthwaite, J. M.; Aki, S. N. V. K.; Maginn, E. J.; Brennecke, J. F. Liquid phase behavior of imidazolium-based ionic liquids with alcohols. J. Phys. Chem. B 2004, 08, 5113−5119. (9) Crosthwaite, J. M.; Muldoon, M. J.; Aki, S. N. V. K.; Maginn, E. J.; Brennecke, J. F. Liquid phase behaviour of ionic liquids with alcohols: Experimental studies and modeling. J. Phys. Chem. B 2006, 110, 9354−9361. (10) Kato, R.; Gmehling, J. Systems with ionic liquids: Measurement of VLE and γ∞ data and prediction of their thermodynamic behavior using original UNIFAC, mod. UNIFAC(Do) and COSMO-RS(Ol). J. Chem. Thermodyn. 2005, 37, 603−619. (11) Letcher, T. M.; Marciniak, A.; Marciniak, M.; Domańska, U. Activity coefficients at infinite dilution measurements for organic solutes in the ionic liquid 1-hexyl-3-methyl-imidazolium bis(trifluoromethylsulfonyl)-imide using g.l.c. at T = (298.15, 313.15, and 333.15) K. J. Chem. Thermodyn. 2005, 37, 1327−1331. (12) Heintz, A.; Verevkin, S. P.; Ondo, D. Thermodynamic properties of mixtures containing ionic liquids. 8. Activity coefficients at infinite dilution of hydrocarbons, alcohols, esters, and aldehydes in 1-hexyl-3-methylimidazolium bis(trifluoromethylsulfonyl) imide using gas-liquid chromatography. J. Chem. Eng. Data 2006, 51, 434−437. (13) Heintz, A.; Verevkin, S. P.; Lehmann, J. K.; Vasiltsova, T. V.; Ondo, D. Activity coefficients at infinite dilution and enthalpies of solution of methanol, 1-butanol, and 1-hexanol in 1-hexyl-3-methylimidazolium bis(trifluoromethyl-sulfonyl) imide. J. Chem. Thermodyn. 2007, 39, 268−274. (14) Safarov, J.; Geppert − Rybczyńska, M.; Hassel, E.; Heintz, A. Vapor pressures and activity coefficients of binary mixtures of 1-ethyl3-methylimidazolium bis(trifluoromethylsulfonyl) imide with acetonitrile and tetrahydrofuran. J. Chem. Thermodyn. 2012, 47, 56−61. (15) Heintz, A.; Vasiltsova, T. V.; Safarov, J.; Bich, E.; Verevkin, S. P. Thermodynamic properties of mixtures containing ionic liquids. 9. Activity coefficients at infinite dilution of hydrocarbons, alcohols, esters and aldehydes in tri-methyl-butyl-ammonium bis-(trifluoromethylsulfonyl) imide using gas−liquid chromatography and static method. J. Chem. Eng. Data 2006, 51, 648−655. (16) Safarov, J. T.; Verevkin, S. P.; Bich, E.; Heintz, A. Vapor pressures and activity coefficients of n-alcohols and benzene in binary mixtures with 1-methyl-3-butyl-imidazolium octylsulfate and 1-methyl3-octyl-imidazolium tetrafluoroborate. J. Chem. Eng. Data 2006, 51, 518−525. (17) Verevkin, S.; Safarov, J.; Bich, E.; Hassel, E.; Heintz, A. Thermodynamic properties of mixtures containing ionic liquids: Vapor pressures and activity coefficients of n-alcohols and benzene in binary mixtures with 1-methyl-3-butyl-imidazolium bis (trifluoromethylsulfonyl)imide. Fluid Phase Equilib. 2005, 236 (1−2), 222−228. (18) 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.

ΔHv/J·mol−1 x/mol fraction of CH3OH

T = 298.15 K

T = 348.15 K

T = 398.15 K

1.0000 0.9728 0.9700 0.9521 0.9245 0.8803 0.8703 0.8445 0.7996 0.7502 0.7367 0.6845 0.6246 0.5500 0.4785 0.4394 0.3938 0.3733 0.3342 0.2684 0.1823 0.1175 0.0812 0.0342

38569.37 38474.34 38456.64 38353.90 38154.40 37807.62 37728.10 37478.74 36851.05 35885.95 35581.06 34262.01 32680.21 30740.46 28938.51 28063.92 27108.75 26698.55 25958.32 25056.10 24338.23 24085.19 24265.27 25839.48

37131.22 37037.12 37020.39 36933.85 36799.26 36533.44 36465.49 36328.79 35997.93 35448.16 35250.51 34417.47 33142.91 31326.93 28953.19 27349.58 25852.50 25400.69 24324.16 22433.58 22391.49 22984.06 23885.26 24115.20

35981.12 35781.44 35753.73 35587.26 35264.47 34850.15 34769.68 34577.01 34187.17 33931.51 33887.96 33571.26 33158.45 31565.99 28843.64 26710.81 24812.35 23862.96 22968.90 20886.09 21593.09 21870.39 23614.40 22942.45

small molalities because there is only one isotherm T = 353.11 K in ref 10, and there are no other values of this binary system in literature.

■

CONCLUSION Vapor−liquid equilibria of methanol (CH3OH) in the ionic liquid (IL) 1-hexyl-3-methylimidazolium bis(trifluoromethylsulfonyl)imide [HMIM][NTf2] over a wide range of temperatures [T = (274.15 to 468.15) K] were studied for the first time. The Antoine, Polynomial, Clausius− Clapeyron, and NRTL equations were used to fit the experimental results to obtain activity coefficients. The best fit was obtained using the Clausius−Clapeyron equation. Activity coefficients γi of methanol in the [HMIM][NTf2] and osmotic coefficients ϕi of the [HMIM][NTf2] have been determined.

■

AUTHOR INFORMATION

Corresponding Author

*Tel:+49 381 4989415: Fax: +49 381 4989402. E-mail: javid. [email protected]. Notes

The authors declare no competing financial interest.

■

REFERENCES

(1) Wang, P.; Wenger, B.; Humphry-Baker, R.; Moster, J.-E.; Teuscher, J.; Kantlehner, W.; Mezger, J.; Stoyanov, E. V.; Zakeeruddin, S. M.; Graetzel, M. Charge separation and efficient light energy conversion in sensitized mesoscopic solar cells based on binary ionic liquids. J. Am. Chem. Soc. 2005, 127, 6850−6856. (2) Wang, P.; Zakeeruddin, S. M.; Humphry-Baker, R.; Graetzel, M. A binary ionic liquid electrolyte to achieve ≥ 7 % power conversion 1662



Article

(19) Ambrose, D.; Sprake, C. H. S. Thermodynamic properties of organic oxygen compounds, XXV. Vapour pressures and normal boiling temperatures of aliphatic alcohols. J. Chem. Thermodyn. 1970, 2, 631−645. (20) Ambrose, D.; Sprake, C. H. S.; Townsend, R. Thermodynamic properties of organic oxygen compounds, XXXVII. Vapour pressures of methanol, ethanol, pentan-1-ol, and octan-1-ol from the normal boiling temperature to the critical temperature. J. Chem. Thermodyn. 1975, 7, 185−190. (21) Wagner, W., Overhoff, U. ThermoFluids: Interactive Software for the Calculation of Thermodynamic Properties for More than 60 Pure Substances; CD-ROM, Springer: Berlin, 2006. (22) Lemmon, E. W., Huber, M. L., McLinden, M. O. NIST Standard Reference Database 23: Reference Fluid Thermodynamic and Transport Properties-REFPROP, version 9.1; National Institute of Standards and Technology, Standard Reference Data Program: Gaithersburg, MD, 2013. (23) K. M. de Reuck, Craven, R.J.B., Methanol. International Thermodynamic Tables of the Fluid State-12; Blackwell Scientific: Oxford, 1993. (24) Yokoyama, O.; Uematsu, M. Thermodynamic properties of {xCH3OH + (1 − x)H2O} with x = (1.0000, 0.8005, 0.4002, and 0.3034) in the temperature range from 320 to 420 K at pressures to 200 MPa. J. Chem. Thermodyn. 2003, 35, 813−823. (25) Osada, O.; Sato, M.; Uematsu, M. Thermodynamic properties of {xCH3OH + (1 − x)H2O} with x = (1.0000 and 0.4993) in the temperature range from 320 to 420 K at pressures to 200 MPa. J. Chem. Thermodyn. 1999, 31, 451−464. (26) Wilson, G. M. Vapor−liquid equilibrium. XI. A new expression for the excess free energy of mixing. J. Am. Chem. Soc. 1964, 2, 127− 130. (27) Scatchard, G.; Wood, S. E.; Mochel, J. M. Vapor−liquid equilibrium. VII. Carbon tetrachloride−methanol mixtures. J. Am. Chem. Soc. 1946, 68, 1960−1963. (28) Renon, H.; Prausnitz, J. M. Local compositions in thermodynamic excess functions for liquid mixtures. AlChE J. 1968, 14, 135−144. (29) Smith, J. M.; Van Ness, H. C.;Abbott, M. M. Introduction to Chemical Engineering Thermodynamics, 5th ed.; McGraw-Hill: New York, 1996.

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Vapor Pressures and Activity Coefficients of Methanol in Binary

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