Apparent Molar Volumes and Isentropic ... - ACS Publications

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Apparent Molar Volumes and Isentropic Compressibilities of Tetraalkylammonium Bromides in Aqueous Propane-1,2-diol. An Attempt to Design Hydraulic Liquids Wacław Grzybkowski and Dorota Warmińska* Department of Physical Chemistry, Chemical Faculty, Gdańsk University of Technology Narutowicza 11/12, 80-233 Gdańsk, Poland S Supporting Information *

ABSTRACT: Apparent molar volumes and apparent molar compressibilities for tetramethylammonium, tetraethylammonium, tetrapropylammonium, and tetrabutylammonium bromides in water, propane-1,2-diol, and water−propane-1,2-diol mixtures (mass fraction: 0.25, 0.50, and 0.75) have been determined from solution density measurements at T = 288.15, 293.15, 298.15, 303.15, 308.15, 313.15, and 318.15 K and sound velocity measurements at T = 298.15 K as a function of the concentration of tetraalkylammonium salt. The limiting apparent molar volumes and limiting apparent molar compressibilities have been derived using the Masson equation. The limiting expansion coefficients for tetraalkylammonium bromides in the studied solutions were also estimated. These parameters have been discussed in terms of structural factors controlling the properties of the systems.

1. INTRODUCTION The present work deals with two aspects of solution chemistry. The first is of engineering nature and is related to hydraulic liquids while the second aspect is physicochemical and is related to the structure of the solution. Hydraulic liquids, also called hydraulic fluids, are the media by which power is transferred in hydraulic systems used in power steering systems, excavators, lifts, and industrial machinery. Hydraulic systems will work most efficiently if the hydraulic fluid used has zero compressibility. Unfortunately, ideal or perfect fluids do not exist. All liquids are highly incompressible, but compressible nonetheless. Compressibility is a measure of volume reduction due to applied pressure. It increases with pressure and temperature and has significant effects on the efficiency of systems working under high pressure. Volume reduction due to compressibility affects the response time and causes loss of power in the hydraulic system.1,2 The most common hydraulic liquids are based on mineral oil or water. Fire-resistant, water-containing hydraulic fluids, which are formulated with high level water content, are a group of particular interest. One of them is Glytex HFC, a highperformance fire resistant hydraulic fluid with a water-glycol formulation, designed to meet the highest safety standards. High water content offers flame resistance, safety, and reliability. Moreover, high water content helps maintain effectiveness where evaporation is an issue or leakage occurs during high temperature operations.3,4 Hydraulic fluids contain a wide range of chemical compounds. Some of them are regular components of the systems while other ones are additives modifying the system properties.5 The present investigation was undertaken in order to explore the possibilities © XXXX American Chemical Society

of modification of the properties of binary mixtures of water and propylene glycol (propane-1,2-diol) applied as hydraulic fluids. It seems obvious that the properties of the liquids are determined by the structural factors arising from the solute− solvent interactions controlling molar volumes, compressibilities, as well as expansibilities of the solution. Structure and thermodynamic properties of tetraalkylammonium bromides in single solvent systems in water as well as in nonaqueous solvents have been extensively studied and the obtained parameters have been discussed in terms intermolecular interactions.6−13 Information concerning the respective salt solutions in mixed solvent systems is much more scarce.14−16 The properties of tetraalkylammonium bromides in water−glycol mixed solvents have only been studied for water−pentane-1,5-diol solutions.17 This is why we decided to study the effects of tetraalkylammonium bromides as additives to water−propane-1,2-diol mixtures.

2. EXPERIMENTAL SECTION Materials. All tetraalkylammonium bromides were purchased from Aldrich with purity ranging between 0.98 and 0.99. Tetraethylammonium and tetrabutylammonium bromides were used as such without purification. Tetramethylammonium bromide was recrystallized from a 50:50 (v/v) mixture of methanol and ethanol. Tetrapropylammonium bromide was recrystallized from pure acetone. All salts were dried under reduced pressure at 308 K for 48 h before use. Propane-1,2-diol (puriss.p.a., mass fraction >0.995, from Sigma-Aldrich) was used as such without Received: November 16, 2015 Accepted: July 4, 2016

A

DOI: 10.1021/acs.jced.5b00964 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

Journal of Chemical & Engineering Data

Article

Table 1. Provenance and Mass Fraction Purity of the Compounds Studied chemical name

source

initial mole fraction purity

purification method

final mole fraction purity

analysis method

propane-1,2-diol Me4NBr Et4NBr Pr4NBr Bu4NBr

Sigma-Aldrich Sigma-Aldrich Aldrich Aldrich Sigma-Aldrich

0.995 0.98 0.99 0.98 ≥0.99

none recrystallization none recrystallization none

0.995 0.99 0.99 0.99 ≥0.99

stated by supplier potentiometric titration stated by supplier potentiometric titration stated by supplier

further purification. Deionized, double distilled, and degassed water with a specific conductance of 1 × 10−6 S·cm −1 was used for the preparation of different aqueous electrolyte solutions. Table 1 briefly describes the properties of materials used. All solutions were prepared by weight dilution of the stock solution of the respective tetraalkylammonium bromide using a Radwag balance with a precision of ±0.0001 g. Apparatus and Procedure. Mixture densities were measured at different temperatures with a digital vibration-tube analyzer DMA 5000 (Anton Paar, Austria) with proportional temperature control that kept the samples at working temperature with an accuracy of 0.01 K. The apparatus was calibrated with double distilled, deionized, and degassed water and with dry air at atmospheric pressure (0.1 MPa) according to the apparatus catalog. The experimental uncertainty of density measurement was better than 50.0 × 10−3 kg·m−3. Sound velocity was determined using the sound analyzer OPTIME 1.0 from OPTEL (Poland) with an uncertainty of 0.15 m·s −1 by measuring the time it takes for a pulse of ultrasound to travel from one transducer to another (pitch-catch) or to return to the same transducer (pulse-echo). The cell was thermostated at 298.15 ± 0.01 K and calibrated with double distilled water with the value 1496.69 m·s −1 used as the sound velocity in pure water at 298.15 K.

Figure 1. Compressiblities of the propane-1,2-diol−water system against mass fraction of propane-1,2-diol at 298.15 K: (●) present study, (□) values reported by Tsiekezos and Palaiologou.

3. RESULTS AND DISCUSSION 3.1. Compressibility of the Binary System Propane-1,2diol−Water. As mentioned above, the most important parameter of a hydraulic liquid is its isentropic compressibility coefficient, defined as κS = −

1 ⎛⎜ ∂V ⎞⎟ V ⎝ ∂P ⎠S

Figure 1 shows compressiblities of the system propane-1,2diol−water obtained at 298.15 K, plotted against the composition of the mixture, together with respective values reported by Tsiekezos and Palaiologou.18 The lines in the figures are guide lines. As is seen, the isentropic compressibility exhibits a distinct minimum when the mass fraction of propane-1,2-diol in the mixture amounts to 0.50. Its presence indicates that the mixture propylene glycol−water may be considered as a potential hydraulic liquid. It should be noted that the experimental value of sound velocity for propane-1,2-diol at 298.15 K equal to 1508.80 m·s−1 is in the range of literature values which are rather scatter and change in the range from 1492 to 1510.6 m·s−1.19−22 A comparison of the density of propane-1,2-diol as a function of temperature is presented as the relative deviation 100*(dexp − dlit)/dexp) between values of this work and the literature values in the Supporting Information as Figure S1. As is seen, the measured densities agree well with the data from literature, showing a relative deviation smaller than 0.0004. It seems to be obvious that the observed deviations are related to different measuring methods used, the calibration procedure, and preparation of liquids and its purity.19−21,23−25 Figures S2 and S3 in the Supporting Information show the values of density and sound velocity for the binary system propane-1,2-diol−water compared with respective literature values for 298.15 K.20,22,23,26,27 Inspection of the data shows that the experimental values of densities agree satisfactorily with literature.20 Higher differences are observed for sound velocities, especially in the middle range of composition of mixture.20

(1)

Using the data obtained in the present work and presented in Table 2, one can calculate the isentropic compressibility coefficient given by the Laplace equation 1 κS = 2 νρ (2) where ν and ρ are the sound velocity and density of solution. Table 2. Experimental Density, Sound Velocity, and Isentropic Compressibility Coefficient Data for Binary System Propane-1,2-diol−Water at T = 298.15 K and the Pressure p = 0.1 MPaa mass fraction of propane-1,2-diol

ν/(m·s−1)

ρ/(kg·m−3)

1010 κS/(Pa−1)

0 0.25 0.50 0.75 1

1496.69 1639.91 1700.04 1640.25 1508.80

997.04 1017.02 1034.79 1040.37 1032.49

4.48 3.66 3.34 3.57 4.25

Standard uncertainties u are u(T) = 0.01 K, u(ρ) = 0.05 kg·m−3, u(ν) = 0.15 m·s−1, and u(p) = 10 kPa. a

B



Article

Table 3. Densities of Me4NBr in Aqueous and Aqueous Propane-1,2-diol Solutions at Temperatures between 288.15 and 318.15 K and the Pressure p = 0.1 MPaa ρ/(kg·m−3) −1

m/(mol·kg )

288.15 K

0.01656 0.02243 0.02892 0.03698 0.04656 0.05827 0.07480 0.09027 0.1058 0.1246 0.1407 water

999.77 1000.01 1000.28 1000.60 1000.99 1001.47 1002.14 1002.76 1003.38 1004.14 1004.79 999.09

0.01633 0.02216 0.02836 0.03633 0.04544 0.05760 0.07391 0.08984 0.1044 0.1253 0.1409 solvent

1021.65 1021.89 1022.14 1022.46 1.022.83 1023.31 1023.96 1024.59 1025.16 1025.96 1026.56 1020.98

0.01440 0.01958 0.02529 0.03248 0.04025 0.05065 0.0650 0.07985 0.09314 0.1099 0.1251 solvent

1041.74 1041.94 1042.17 1042.45 1042.75 1043.15 1043.70 1044.26 1044.76 1045.40 1045.98 1041.16

0.01485 0.01981 0.02565 0.03235 0.04084 0.05164 0.06663 0.08051 0.09417 0.1108 0.1261 solvent

1048.28 1048.48 1048.71 1048.98 1049.31 1049.74 1050.33 1050.87 1051.39 1052.03 1052.61 1047.67

0.01890 0.02403 0.03096 0.03759 0.04799

1040.60 1040.83 1041.13 1041.41 1041.85

293.15 K

298.15 K

303.15 K

Water 998.88 997.71 996.30 999.11 997.94 996.53 999.37 998.20 996.79 999.70 998.52 997.11 1000.08 998.90 997.48 1000.55 999.36 997.94 1001.21 1000.01 998.59 1001.83 1000.62 999.19 1002.45 1001.23 999.80 1003.19 1001.97 1000.53 1003.83 1002.60 1001.16 998.20 997.04 995.64 0.25 Mass Fraction of Propane-1,2-diol 1019.75 1017.67 1015.44 1019.98 1017.91 1015.67 1020.23 1018.15 1015.91 1020.55 1018.47 1016.23 1020.92 1018.83 1016.58 1021.40 1019.31 1017.06 1022.04 1019.95 1017.69 1022.66 1020.56 1018.30 1023.23 1021.12 1018.86 1024.01 1021.91 1019.63 1024.61 1022.50 1020.22 1019.08 1017.01 1014.78 0.50 Mass Fraction of Propane-1,2-diol 1038.60 1035.37 1032.07 1038.80 1035.57 1032.27 1039.03 1035.80 1032.50 1039.31 1036.08 1032.78 1039.61 1036.38 1033.08 1040.01 1036.78 1033.48 1040.56 1037.33 1034.03 1041.12 1037.89 1034.59 1041.62 1038.39 1035.09 1042.25 1039.04 1035.72 1042.83 1039.60 1036.30 1038.02 1034.79 1031.49 0.75 Mass Fraction of Propane-1,2-diol 1044.65 1040.98 1037.25 1044.85 1041.18 1037.45 1045.08 1041.42 1037.69 1045.35 1041.69 1037.96 1045.69 1042.03 1038.3 1046.12 1042.45 1038.73 1046.70 1043.04 1039.31 1047.24 1043.58 1039.86 1047.77 1044.11 1040.39 1048.41 1044.75 1041.03 1048.99 1045.33 1041.62 1044.04 1040.37 1036.64 Propane-1,2-diol 1036.98 1033.33 1029.62 1037.21 1033.55 1029.84 1037.51 1033.84 1030.14 1037.79 1034.12 1030.42 1038.23 1034.56 1030.86 C

308.15 K

313.15 K

318.15 K

994.68 994.91 995.16 995.48 995.85 996.31 996.95 997.55 998.15 998.88 999.51 994.02

992.86 993.09 993.34 993.66 994.03 994.48 995.12 995.72 996.31 997.04 997.65 992.21

990.86 991.08 991.33 991.65 992.01 992.46 993.10 993.69 994.29 995.01 995.62 990.21

1013.03 1013.26 1013.51 1013.82 1014.18 1014.65 1015.28 1015.89 1016.44 1017.22 1017.80 1012.38

1010.49 1010.72 1010.96 1011.27 1011.63 1012.10 1012.72 1013.32 1013.87 1014.65 1015.23 1009.84

1007.80 1008.02 1008.27 1008.58 1008.93 1009.40 1010.02 1010.62 1011.17 1011.95 1012.53 1007.15

1028.69 1028.89 1029.12 1029.40 1029.70 1030.10 1030.65 1031.21 1031.71 1032.34 1032.92 1028.11

1025.24 1025.44 1025.67 1025.95 1026.25 1026.65 1027.20 1027.76 1028.26 1028.89 1029.47 1024.66

1021.71 1021.91 1022.14 1022.42 1022.72 1023.12 1023.67 1024.24 1024.74 1025.37 1025.95 1021.13

1033.49 1033.69 1033.93 1034.20 1034.54 1034.97 1035.56 1036.11 1036.64 1037.29 1037.88 1032.88

1029.67 1029.88 1030.12 1030.39 1030.73 1031.16 1031.76 1032.30 1032.84 1033.49 1034.08 1029.06

1025.81 1026.01 1026.25 1026.52 1026.86 1027.30 1027.90 1028.45 1028.99 1029.64 1030.23 1025.19

1025.87 1026.09 1026.40 1026.68 1027.12

1022.09 1022.31 1022.62 1022.90 1023.35

1018.27 1018.50 1018.80 1019.08 1019.53



Article

Table 3. continued ρ/(kg·m−3) −1

m/(mol·kg ) 0.05960 0.07011 0.08244 0.09346 solvent

288.15 K 1042.33 1042.76 1043.27 1043.71 1039.77

293.15 K

298.15 K

303.15 K

308.15 K

313.15 K

318.15 K

1038.71 1039.14 1039.64 1040.09 1036.15

Propane-1,2-diol 1035.04 1035.48 1035.98 1036.43 1032.49

1031.34 1031.77 1032.28 1032.74 1028.78

1027.61 1028.04 1028.55 1029.01 1025.03

1023.83 1024.27 1024.78 1025.24 1021.25

1020.02 1020.46 1020.98 1021.44 1017.43

Standard uncertainties u are u(T) = 0.01 K, u(ρ) = 0.05 kg·m−3, standard uncertainty of molality u(m) = 0.001 mol·kg−1, and standard uncertainty of experimental pressure u(p) = 10 kPa.

a

Table 4. Densities of Et4NBr in Aqueous and Aqueous Propane-1,2-diol Solutions at Temperatures between 288.15 and 318.15 K and the Pressure p = 0.1 MPaa ρ/(kg·m−3) −1

m/(mol·kg )

288.15 K

293.15 K

0.01661 0.02227 0.02929 0.03728 0.04698 0.05948 0.07690 0.09286 0.1087 0.1292 0.1462 water

999.72 999.94 1000.20 1000.50 1000.86 1001.33 1001.97 1002.55 1003.12 1003.86 1004.47 999.09

998.82 999.03 999.30 999.59 999.95 1000.41 1001.04 1001.61 1002.17 1002.90 1003.50 998.20

0.01469 0.02048 0.02668 0.03467 0.04306 0.05380 0.06956 0.08443 0.09834 0.1174 0.1329 solvent

1021.57 1021.80 1022.04 1022.34 1022.67 1023.08 1023.68 1024.24 1024.77 1025.48 1026.05 1020.99

1019.67 1019.89 1020.13 1020.43 1020.75 1021.16 1021.75 1022.30 1022.82 1023.51 1024.08 1019.10

0.01492 0.02060 0.02742 0.03489 0.04277 0.05482 0.07059 0.08628 0.1006 0.1187 0.1352 solvent

1041.71 1041.92 1042.17 1042.44 1042.73 1043.16 1043.71 1044.265 1044.77 1045.40 1045.96 1041.16

1038.57 1038.78 1039.02 1039.29 1039.575 1040.00 1040.56 1041.10 1041.595 1042.23 1042.78 1038.02

0.01474 0.02101 0.02703 0.03472 0.04443

1048.21 1048.43 1048.65 1048.92 1049.26

1044.58 1044.80 1045.02 1045.29 1045.63

298.15 K

303.15 K

Water 997.66 996.25 997.86 996.46 998.12 996.71 998.41 997.00 998.76 997.35 999.21 997.79 999.83 998.41 1000.40 998.97 1000.96 999.52 1001.68 1000.23 1002.27 1000.82 997.04 995.64 0.25 Mass Fraction of Propane-1,2-diol 1017.58 1015.34 1017.80 1015.56 1018.04 1015.79 1018.34 1016.09 1018.66 1016.40 1019.06 1016.79 1019.64 1017.36 1020.18 1017.90 1020.69 1018.40 1021.37 1019.08 1021.93 1019.63 1017.02 1014.79 0.50 Mass Fraction of Propane-1,2-diol 1035.34 1032.03 1035.54 1032.24 1035.79 1032.48 1036.06 1032.75 1036.34 1033.03 1036.76 1033.45 1037.31 1034.00 1037.85 1034.53 1038.34 1035.02 1038.97 1035.64 1039.53 1036.20 1034.79 1031.49 0.75 Mass Fraction of Propane-1,2-diol 1040.91 1037.18 1041.13 1037.41 1041.35 1037.62 1041.62 1037.89 1041.96 1038.24 D

308.15 K

313.15 K

318.15 K

994.62 994.83 995.09 995.37 995.72 996.16 996.77 997.32 997.87 998.57 999.15 994.02

992.81 993.01 993.26 993.54 993.88 994.32 994.93 995.48 996.02 996.72 997.29 992.21

990.79 991.00 991.24 991.52 991.86 992.30 992.90 993.45 993.99 994.68 995.23 990.21

1012.94 1013.15 1013.38 1013.67 1013.98 1014.37 1014.94 1015.47 1015.96 1016.63 1017.18 1012.39

1010.39 1010.60 1010.83 1011.12 1011.42 1011.81 1012.37 1012.89 1013.38 1014.04 1014.58 1009.85

1007.69 1007.90 1008.12 1008.41 1008.71 1009.10 1009.66 1010.18 1010.66 1011.32 1011.85 1007.15

1028.65 1028.86 1029.10 1029.36 1029.64 1030.06 1030.61 1031.14 1031.63 1032.24 1032.80 1028.11

1025.20 1025.40 1025.65 1025.91 1026.18 1026.60 1027.14 1027.68 1028.16 1028.78 1029.33 1024.66

1021.67 1021.87 1022.11 1022.37 1022.65 1023.07 1023.61 1024.14 1024.62 1025.24 1025.79 1021.13

1033.42 1033.64 1033.86 1034.13 1034.48

1029.6 1029.82 1030.04 1030.31 1030.66

1025.73 1025.96 1026.18 1026.45 1026.79



Article


m/(mol·kg )

288.15 K

293.15 K

0.05539 0.07129 0.08692 0.1018 0.1203 0.1365 solvent

1049.64 1050.18 1050.72 1051.22 1051.84 1052.37 1047.67

1046.01 1046.55 1047.09 1047.59 1048.21 1048.74 1044.04

0.01687 0.02230 0.02829 0.03708 0.04876 0.06124 0.07768 0.09596 0.1109 0.1310 0.1484 solvent

1040.42 1040.63 1040.85 1041.18 1041.61 1042.07 1042.65 1043.29 1043.81 1044.50 1045.09 1039.78

1036.81 1037.01 1037.24 1037.56 1037.99 1038.45 1039.04 1039.68 1040.20 1040.89 1041.49 1036.16

298.15 K

303.15 K

0.75 Mass Fraction of Propane-1,2-diol 1042.34 1038.62 1042.89 1039.17 1043.42 1039.71 1043.92 1040.21 1044.54 1040.83 1045.07 1041.36 1040.37 1036.64 Propane-1,2-diol 1033.14 1029.44 1033.35 1029.64 1033.57 1029.86 1033.90 1030.19 1034.33 1030.63 1034.80 1031.09 1035.38 1031.69 1036.01 1032.32 1036.53 1032.84 1037.23 1033.55 1037.83 1034.14 1032.49 1028.78

308.15 K

313.15 K

318.15 K

1034.86 1035.41 1035.95 1036.45 1037.07 1037.60 1032.88

1031.04 1031.59 1032.13 1032.64 1033.26 1033.79 1029.06

1027.18 1027.74 1028.28 1028.79 1029.41 1029.95 1025.19

1025.69 1025.90 1026.12 1026.45 1026.89 1027.35 1027.95 1028.59 1029.11 1029.82 1030.42 1025.03

1021.90 1022.11 1022.34 1022.67 1023.11 1023.58 1024.18 1024.82 1025.35 1026.06 1026.66 1021.24

1018.09 1018.30 1018.53 1018.86 1019.30 1019.76 1020.37 1021.02 1021.55 1022.26 1022.87 1017.42


a

Table 5. Densities of Pr4NBr in Aqueous and Aqueous Propane-1,2-diol Solutions at Temperatures between 288.15 and 318.15 K and the Pressure p = 0.1 MPaa ρ/(kg·m−3) −1

m/(mol·kg )

288.15 K

293.15 K

298.15 K

303.15 K

308.15 K

313.15 K

318.15 K

994.46 994.61 994.79 995.01 995.26 995.56 996.02 996.43 996.85 997.38 997.83 994.03

992.63 992.78 992.96 993.18 993.42 993.72 994.17 994.57 994.98 995.49 995.93 992.21

990.62 990.77 990.94 991.15 991.39 991.68 992.12 992.53 992.92 993.4 993.84 990.21

1012.87 1013.03 1013.22 1013.46 1013.71 1014.06 1014.55 1014.99 1015.43 1016.00 1016.47 1012.39

1010.31 1010.46 1010.65 1010.89 1011.13 1011.47 1011.94 1012.37 1012.80 1013.36 1013.81 1009.85

1007.60 1007.76 1007.94 1008.17 1008.4 1008.74 1009.20 1009.61 1010.03 1010.58 1011.02 1007.15

1028.53 1028.67 1028.86

1025.07 1025.22 1025.40

1021.54 1021.68 1021.86

Water 0.01618 0.02208 0.02870 0.0370 0.04631 0.05791 0.07524 0.0912 0.1071 0.1272 0.1446 water

999.56 999.73 999.92 1000.16 1000.43 1000.76 1001.25 1001.69 1002.15 1002.73 1003.22 999.10

998.66 998.83 999.01 999.25 999.51 999.83 1000.31 1000.75 1001.19 1001.76 1002.24 998.21

0.01734 0.02323 0.03053 0.03915 0.04851 0.06184 0.08013 0.09668 0.1135 0.1351 0.1531 solvent

1021.53 1021.71 1021.93 1022.20 1022.48 1022.89 1023.45 1023.95 1024.46 1025.11 1025.65 1020.98

1019.62 1019.80 1020.02 1020.28 1020.55 1020.94 1021.48 1021.96 1022.45 1023.07 1023.60 1019.09

0.01833 0.02479 0.03320

1041.62 1041.78 1041.98

1038.46 1038.62 1038.82

997.48 996.08 997.65 996.24 997.83 996.42 998.06 996.65 998.32 996.90 998.64 997.21 999.11 997.68 999.54 998.09 999.97 998.52 1000.52 999.06 1000.99 999.52 997.04 995.65 0.25 Mass Fraction of Propane-1,2-diol 1017.53 1015.28 1017.70 1015.44 1017.91 1015.64 1018.16 1015.89 1018.43 1016.15 1018.80 1016.51 1019.32 1017.01 1019.79 1017.46 1020.26 1017.92 1020.87 1018.51 1021.37 1019.00 1017.02 1014.79 0.50 Mass Fraction of Propane-1,2-diol 1035.23 1031.92 1035.38 1032.07 1035.58 1032.26 E



Article


m/(mol·kg )

288.15 K

293.15 K

0.04218 0.05199 0.06588 0.08536 0.1038 0.1211 0.1442 0.1643 solvent

1042.19 1042.43 1042.75 1043.21 1043.63 1044.025 1044.56 1045.00 1041.16

1039.03 1039.25 1039.57 1040.02 1040.43 1040.81 1041.33 1041.77 1038.02

0.01678 0.02256 0.02941 0.03776 0.04738 0.06013 0.07772 0.09460 0.1106 0.1307 0.1487 solvent

1048.01 1048.13 1048.26 1048.42 1048.61 1048.85 1049.18 1049.50 1049.79 1050.17 1050.49 1047.67

1044.38 1044.50 1044.63 1044.79 1044.98 1045.22 1045.55 1045.86 1046.15 1046.52 1046.84 1044.04

0.01681 0.02280 0.02985 0.03823 0.0504 0.06162 0.08083 0.09848 0.1152 0.1350 0.1532 solvent

1040.13 1040.25 1040.40 1040.57 1040.81 1041.04 1041.41 1041.74 1042.05 1042.42 1042.73 1039.77

1036.52 1036.65 1036.79 1036.96 1037.20 1037.42 1037.80 1038.13 1038.44 1038.81 1039.13 1036.16

298.15 K

303.15 K

0.50 Mass Fraction of Propane-1,2-diol 1035.78 1032.45 1036.00 1032.67 1036.31 1032.98 1036.75 1033.41 1037.15 1033.80 1037.53 1034.16 1038.03 1034.66 1038.46 1035.08 1034.79 1031.49 0.75 Mass Fraction of Propane-1,2-diol 1040.70 1036.98 1040.82 1037.09 1040.95 1037.23 1041.11 1037.39 1041.30 1037.58 1041.54 1037.82 1041.88 1038.15 1042.19 1038.46 1042.48 1038.75 1042.84 1039.11 1043.15 1039.43 1040.36 1036.64 Propane-1,2-diol 1032.85 1029.14 1032.98 1029.27 1033.12 1029.42 1033.29 1029.59 1033.53 1029.84 1033.76 1030.06 1034.14 1030.44 1034.47 1030.79 1034.78 1031.09 1035.15 1031.46 1035.47 1031.79 1032.49 1028.78

308.15 K

313.15 K

318.15 K

1029.06 1029.28 1029.58 1030.00 1030.38 1030.74 1031.22 1031.63 1028.11

1025.59 1025.80 1026.09 1026.51 1026.89 1027.24 1027.71 1028.12 1024.66

1022.04 1022.25 1022.54 1022.94 1023.32 1023.67 1024.13 1024.54 1021.13

1033.21 1033.32 1033.46 1033.62 1033.81 1034.05 1034.38 1034.68 1034.97 1035.33 1035.65 1032.87

1029.39 1029.50 1029.64 1029.80 1029.99 1030.23 1030.56 1030.86 1031.15 1031.51 1031.83 1029.05

1025.53 1025.64 1025.78 1025.94 1026.13 1026.37 1026.70 1027.00 1027.29 1027.65 1027.96 1025.19

1025.39 1025.53 1025.68 1025.85 1026.10 1026.33 1026.71 1027.06 1027.36 1027.73 1028.07 1025.03

1021.62 1021.75 1021.90 1022.08 1022.33 1022.56 1022.94 1023.30 1023.60 1023.98 1024.32 1021.25

1017.80 1017.94 1018.09 1018.27 1018.53 1018.75 1019.13 1019.50 1019.8 1020.19 1020.53 1017.43


a

The density data obtained for the solutions of tetramethylammonium, tetraethylammonium, tetrapropylammonium, and tetrabutylammonium bromide in water, propane-1,2-diol, and 0.25, 0.50, and 0.75 mass fraction aqueous propane-1,2-diol, as a function of molality of salt at temperatures between 288.15 and 318.15 K, are collected in Tables 3−6. For all investigated systems, the apparent molar volumes are found to be in linear function of the square root of concentration over both the concentration and the temperature range studied. Therefore, Masson’s equation

The differences between our data and the data obtained by George and Sastry can be explained in terms of different measuring method. 3.2. Density and Apparent Molar Volume of Tetraalkylammonium Bromides in the Mixture Propane-1,2-diol− Water. The properties of a hydraulic liquid can be modified by additives such as antiwear agents, rust inhibitors, antifoaming agents, and oxidation inhibitors. However, such substances may also affect in unintended ways the properties and structure of the modified solutions. In our work we investigated the effects of the tetraalkylammonium bromides addition on compressibility and structure of propane-1,2-diol−water systems. The apparent molar volume, VΦ, was calculated from density measurements using the equation VΦ =

(ρ0 − ρ) (mρρ0 )

+

M2 ρ

VΦ = V Φ0 + S V c

(4)

may be used to determine the limiting apparent molar volumes V0Φ. Calculated parameters and their standard deviations σ are collected in Tables S1−S4 of the Supporting Information along with the data for single solvent solutions reported by other authors.6,7,10,14,15 As is seen, our data are in good agreement with literature values. Inspection of the data shows that the experimental slope of Masson’s equation depends on solvent composition as well as on

(3)

where m denotes the molality of the solution, ρ and ρ0 are the densities of the solution and solvent, respectively, and M2 is the molar mass of the solute. F



Article

Table 6. Densities of Bu4NBr in Aqueous and Aqueous Propane-1,2-diol Solutions at Temperatures between 288.15 and 318.15 K and the Pressure p = 0.1 MPaa ρ/(kg·m−3) −1

m/(mol·kg )

288.15 K

293.15 K

298.15 K

303.15 K

308.15 K

313.15 K

318.15 K

994.35 994.48 994.61 994.78 994.97 995.21 995.55 995.88 996.20 996.62 996.96 994.03

992.52 992.64 992.77 992.93 993.12 993.35 993.68 993.99 994.29 994.69 995.02 992.21

990.50 990.62 990.74 990.89 991.07 991.29 991.6 991.9 992.19 992.57 992.89 990.21

1012.67 1012.77 1012.89 1013.03 1013.20 1013.41 1013.67 1013.94 1014.20 1014.54 1014.82 1012.38

1010.10 1010.20 1010.31 1010.44 1010.60 1010.79 1011.04 1011.29 1011.53 1011.85 1012.10 1009.84

1007.40 1007.49 1007.59 1007.71 1007.86 1008.04 1008.26 1008.49 1008.71 1009.02 1009.25 1007.15

1028.25 1028.31 1028.36 1028.43 1028.50 1028.60 1028.74 1028.86 1028.98 1029.13 1029.24 1028.11

1024.79 1024.84 1024.89 1024.95 1025.01 1025.11 1025.24 1025.34 1025.46 1025.60 1025.70 1024.65

1021.25 1021.29 1021.34 1021.40 1021.46 1021.54 1021.66 1021.76 1021.87 1022.00 1022.09 1021.12

1032.93 1032.95 1032.97 1032.99 1033.02 1033.05 1033.09 1033.12 1033.15 1033.19 1033.23 1032.88

1029.11 1029.14 1029.15 1029.18 1029.21 1029.24 1029.27 1029.31 1029.34 1029.38 1029.41 1029.06

1025.25 1025.27 1025.29 1025.32 1025.35 1025.38 1025.43 1025.46 1025.49 1025.52 1025.54 1025.19

1025.14 1025.15 1025.18 1025.23 1025.28

1021.36 1021.37 1021.40 1021.45 1021.50

1017.54 1017.56 1017.58 1017.63 1017.69

Water 0.01572 0.02172 0.02808 0.03597 0.04541 0.05713 0.07361 0.08955 0.1051 0.1248 0.1416 water

999.49 999.64 999.79 999.99 1000.22 1000.51 1000.91 1001.31 1001.69 1002.19 1002.60 999.10

998.58 998.72 998.87 999.06 999.28 999.55 999.93 1000.32 1000.68 1001.16 1001.55 998.21

0.01428 0.01985 0.02606 0.03327 0.04258 0.05362 0.06796 0.08315 0.0975 0.1166 0.1323 solvent

1021.36 1021.50 1021.66 1021.84 1022.08 1022.36 1022.71 1023.08 1023.43 1023.89 1024.27 1020.98

1019.44 1019.57 1019.72 1019.89 1020.11 1020.37 1020.70 1021.03 1021.35 1021.80 1022.15 1019.09

0.01594 0.02216 0.02841 0.03683 0.04533 0.05773 0.07547 0.09038 0.1066 0.1265 0.1447 solvent

1041.36 1041.44 1041.51 1041.61 1041.70 1041.84 1042.03 1042.19 1042.36 1042.57 1042.73 1041.16

1038.20 1038.27 1038.34 1038.43 1038.52 1038.64 1038.82 1038.97 1039.13 1039.32 1039.46 1038.01

0.01580 0.02183 0.02764 0.03625 0.04644 0.05849 0.07464 0.09041 0.1064 0.1271 0.1446 solvent

1047.74 1047.76 1047.78 1047.81 1047.84 1047.87 1047.91 1047.95 1047.99 1048.04 1048.08 1047.67

1044.11 1044.13 1044.14 1044.17 1044.20 1044.23 1044.27 1044.31 1044.35 1044.39 1044.43 1044.04

0.01582 0.01829 0.02164 0.02961 0.03804

1039.87 1039.88 1039.90 1039.95 1040.00

1036.26 1036.27 1036.29 1036.34 1036.39

997.39 995.98 997.53 996.11 997.68 996.25 997.86 996.42 998.07 996.63 998.34 996.88 998.70 997.23 999.07 997.58 999.41 997.91 999.87 998.35 1000.24 998.71 997.04 995.65 0.25 Mass Fraction of Propane-1,2-diol 1017.34 1015.08 1017.47 1015.20 1017.61 1015.33 1017.77 1015.48 1017.97 1015.67 1018.21 1015.89 1018.51 1016.17 1018.83 1016.46 1019.13 1016.74 1019.53 1017.11 1019.85 1017.41 1017.02 1014.78 0.50 Mass Fraction of Propane-1,2-diol 1034.95 1031.64 1035.02 1031.70 1035.08 1031.75 1035.17 1031.83 1035.25 1031.91 1035.36 1032.02 1035.53 1032.17 1035.67 1032.297 1035.81 1032.43 1035.99 1032.59 1036.11 1032.71 1034.78 1031.48 0.75 Mass Fraction of Propane-1,2-diol 1040.43 1036.70 1040.45 1036.72 1040.47 1036.74 1040.49 1036.76 1040.52 1036.79 1040.55 1036.82 1040.60 1036.86 1040.63 1036.90 1040.66 1036.93 1040.70 1036.98 1040.74 1037.01 1040.36 1036.64 Propane-1,2-diol 1032.58 1028.88 1032.59 1028.89 1032.62 1028.92 1032.67 1028.97 1032.72 1029.02 G



Article


m/(mol·kg ) 0.04728 0.05314 0.05937 0.07842 0.09719 0.1142 0.13404 0.1528 solvent

288.15 K 1040.06 1040.09 1040.10 1040.20 1040.28 1040.34 1040.43 1040.49 1039.77

293.15 K

298.15 K

1036.45 1036.46 1036.50 1036.59 1036.66 1036.73 1036.82 1036.90 1036.16

Propane-1,2-diol 1032.77 1029.07 1032.79 1029.08 1032.83 1029.13 1032.92 1029.22 1033.00 1029.30 1033.06 1029.37 1033.15 1029.46 1033.23 1029.54 1032.48 1028.77

303.15 K

308.15 K

313.15 K

318.15 K

1025.33 1025.35 1025.39 1025.49 1025.57 1025.64 1027.40 1025.81 1025.03

1021.55 1021.58 1021.62 1021.72 1021.80 1021.88 1021.98 1022.06 1021.24

1017.75 1017.76 1017.81 1017.91 1018.00 1018.08 1018.18 1018.27 1017.42


a

Figure 2. Dependence of limiting apparent molar volume of tetraalkylammonium bromides on the solvent composition at 298.15 K: (■) Me4NBr, (●) Et4NBr, (▲) Pr4NBr, and (⧫) Bu4NBr.

tetraalkylammonium bromides in pure propane-1,2-diol suggesting strong ion−ion interaction for this system. It might be caused by low value of dielectric constant of propane-1,2-diol if compare to water. Figure 2 presents the dependence of limiting apparent molar volume of tetraalkylammonium bromides on the solvent composition at 298.15 K. It is not surprising the values of V0Φ increase with the length of alkyl chain, i.e. from tetramethylammonium bromide to tetrabutylammonium bromide. However, some apparent irregularities may be seen. Limiting apparent molar volumes of tetraethylammonium and tetramethylammonium

alkyl chain length of the tetraalkylammonium cation. Furthermore, the slope changes in decreasing order from tetramethylammonium bromide to tetrabutylammonium bromide irrespective of solvent composition. It should be noted that the values of the slope are negative for tetrapropylammonium and tetrabutylammonium bromides in water solution. The latter observation may be considered as an indication of hydrophobic interactions. The values of the slope depend on solvent composition. Increase of propane-1,2-diol content brings about a marked increase of the slope. The highest values of SV are observed for H



Article

It consists in a marked increase of the limiting molar expansibility coefficient. This seems to be due to the fact that the water structure is destroyed and the alkyl chains of the tetraalkylammonium cations are unsolvated, at least partially. Further addition of propane-1,2-diol to the system results in decrease of the limiting molar expansibility coefficient. An analogous effect is not observed for tetramethylammonium and tetraethylammonium bromides, for which the values of the limiting molar expansibility coefficient decrease slightly over the whole concentration range. 3.3. Sound Velocity and Apparent Molar Compressibility of Tetraalkylammonium Bromides in Propane-1,2diol−Water Mixture at 298.15 K. The obtained values of sound velocity for tetraalkylammonium bromides in water, propane-1,2-diol, as well as in propane-1,2-diol−Water mixtures are presented in Table 8. It is clear that sound velocity depends on the nature of the electrolyte, that is, the size of the cation, its concentration, as well as on solvent composition. Detailed inspection of collected data shows that irrespectively of the nature and concentration of the salt, the dependence on solvent composition follows a similar pattern. There is a marked increase in velocity caused by initial addition of propylene glycol, and the function reaches a maximum value at mass fraction amounting to 0.50. For aqueous, water rich solutions and for propane-1,2-diol solutions, the sound velocity increases with rising concentration of the solute. The effect is connected with the size of the cation whereby an increase of the number carbon atoms in the tetraalkylammonium cation brings about an increase in sound velocity. However, in low water content solutions the increase is observed for tetramethylammonium, tetraethylammonium, and tetrapropylammonium bromides only. In the case of tetrabutylammonium bromide solutions, the studied relationship is distinctly different. Sound velocity is practically independent of salt concentration for 0.50 mass fraction of propane-1,2-diol and even decreases with increasing concentration for 0.75 mass fraction of propane-1,2-diol solution. It seems to be evident that the effects are due to the changes in mixed solvent structure and solvation. Apparent molar compressibility KS,Φ, defined as the difference between the compressibility of the solution and the compressibility of the pure solvent per mole of solute, is given by the following equation

bromides decrease monotonically with increasing contribution of propane-1,2-diol in the mixture. The same is observed in for high water content solutions of tetrapropylammonium and tetrabutylammonium bromides, while further addition of propane-1,2-diol causes an increase of limiting molar volumes, particularly notable for tetrabutylammonium bromide. This is obviously related to an essential change in nature of the solute−solvent interactions, that is an increase in hydrophobic interactions due to elongation of the alkyl chain of the cation. Thus, the effect is particularly marked for the limiting molar volume of tetrabutylammonium bromide. Inspection of the data presented in Tables S1−S4 shows that the limiting molar volumes of the studied salts increase linearly with temperature irrespectively of the nature of the cation or the composition of the solvent. In order to further explore the effect of temperature on limiting molar volume, the values of limiting molar expansibility coefficients

α=

0 1 ⎛ ∂V Φ ⎞ ⎟ ⎜ V Φ0 ⎝ ∂T ⎠

(5)

were calculated. Table 7 and Figure 3 present the obtained values of limiting molar expansibility coefficient at 298.15 K plotted against the solvent composition. Table 7. Limiting Molar Expansibility Coefficients at 298.15 K in 103 K−1 for Tetraalkylammonium Bromides in Aqueous and Aqueous 1,2-Propanodiol Solutions

electrolyte

water

0.25 mass fraction of propylene1,2-diol

Me4NBr Et4NBr Pr4NBr Bu4NBr

0.870 0.682 0.714 0.917

0.807 0.681 1.174 1.426



propylene1,2-diol

0.425 0.696 0.960 1.161

0.347 0.579 0.672 0.800

0.414 0.241 0.523 0.531

KS, Φ =

(VκS − n1V10κS0) n2

(6)

where κS and κS0 denote the adiabatic compressibilities of the solution and the solvent, respectively; n1 and n2 are the numbers of solvent and solute moles; V denotes the solution volume, and V01 is the molar volume of the solvent. In the present study, the values of apparent molar isentropic compressibility of the electrolyte solutions were calculated using the equation KS, Φ = Figure 3. Limiting molar expansibility coefficient against the solvent composition at 298.15 K: (■) Me4NBr, (●) Et4NBr, (▲) Pr4NBr, and (⧫) Bu4NBr.

(κSρ0 − κS0ρ) (mρρ0 )

+

M 2κS ρ

(7)

It has been found that apparent molar isentropic compressibility follows a linear function of the square root of concentration and the respective limiting values were determined using linear extrapolation based on the equation

Inspection of the plots shows that the most characteristic feature of the dependence on solvent composition is the initial change caused by propylene-1,2-diol addition to water, observed for tetrapropylammonium and tetrabutylammonium bromides.

KS, Φ = KS,0 Φ + bK c I

(8) DOI: 10.1021/acs.jced.5b00964 J. Chem. Eng. Data XXXX, XXX, XXX−XXX


Article

Table 8. Sound Velocity for Tetraalkylammonium Bromides in Aqueous and Aqueous Propane-1,2-diol Solutions at 298.15 K and the Pressure p = 0.1 MPaa 0.25 mass fraction of propane1,2-diol

water m/(mol·kg−1)

ν/(m·s−1)

m/(mol·kg−1)

ν/(m·s−1)

0.0000 0.01656 0.02243 0.02892 0.03698 0.04656 0.05827 0.07480 0.09027 0.1058 0.1246 0.1407

1496.69 1497.70 1498.05 1498.44 1498.95 1499.50 1500.20 1501.13 1502.02 1502.87 1503.99 1504.84

0.0000 0.01633 0.02216 0.02836 0.03633 0.04544 0.05760 0.07391 0.08984 0.1044 0.1253 0.1409

1639.91 1640.75 1641.02 1641.32 1641.69 1642.10 1642.60 1643.27 1643.94 1644.52 1645.29 1645.87

0.01661 0.02227 0.02929 0.03728 0.04698 0.05948 0.07690 0.09286 0.1087 0.1292 0.1462

1498.53 1499.15 1499.92 1500.76 1501.80 1503.15 1504.98 1506.54 1508.24 1510.22 1511.93

0.01469 0.02048 0.02668 0.03467 0.04306 0.05380 0.06956 0.08443 0.09834 0.1174 0.1329

1641.25 1641.75 1642.26 1642.93 1643.62 1644.38 1645.61 1646.64 1647.66 1649.01 1650.03

0.01618 0.02208 0.02870 0.0370 0.04631 0.05791 0.07524 0.0912 0.1071 0.1272 0.1446

1499.49 1500.49 1501.60 1503.01 1504.56 1506.50 1509.37 1511.93 1514.50 1517.74 1520.53

0.01734 0.02323 0.03053 0.03915 0.04851 0.06184 0.08013 0.09668 0.1135 0.1351 0.1531

1642.04 1642.76 1643.61 1644.62 1645.73 1647.32 1649.35 1651.22 1653.09 1655.48 1657.43

0.01572 0.02172 0.02808 0.03597 0.04541 0.05713 0.07361 0.08955 0.1051 0.1248 0.1416

1500.44 1501.84 1503.30 1505.12 1507.29 1509.94 1513.64 1517.08 1520.53 1524.56 1529.34

0.01428 0.01985 0.02606 0.03327 0.04258 0.05362 0.06796 0.08315 0.0975 0.1166 0.1323

1641.98 1642.75 1643.61 1644.62 1645.83 1647.32 1649.06 1651.05 1652.75 1655.14 1657.09

0.50 mass fraction of propane1,2-diol m/(mol·kg−1) Me4NBr 0.0000 0.01958 0.02529 0.03248 0.04025 0.05065 0.0650 0.07985 0.09314 0.1099 0.1251

0.75 mass fraction of propane1,2-diol

propane-1,2-diol

ν/(m·s−1)

m/(mol·kg−1)

ν/(m·s−1)

m/(mol·kg−1)

ν/(m·s−1)

1700.04 1700.98 1701.22 1701.48 1701.75 1702.11 1702.57 1702.93 1703.29 1703.65 1704.02

0.0000 0.01981 0.02565 0.03235 0.04084 0.05164 0.06663 0.08051 0.09417 0.1108 0.1261

1640.25 1641.10 1641.30 1641.59 1641.92 1642.25 1642.61 1642.90 1643.27 1643.61 1643.94

0.0000 0.01890 0.02403 0.03096 0.03759 0.04799 0.05960 0.07011 0.08244 0.09346

1508.80 1509.94 1510.22 1510.61 1511.00 1511.60 1512.22 1512.75 1513.36 1513.93

0.02101 0.02703 0.03472 0.04443 0.05539 0.07129 0.08692 0.1018 0.1203 0.1365

1641.35 1641.59 1641.99 1642.43 1642.94 1643.61 1644.28 1644.96 1645.63 1646.32

0.01687 0.02230 0.02829 0.03708 0.04876 0.06124 0.07768 0.09596 0.1109 0.1310 0.1484

1510.05 1510.39 1510.76 1511.36 1512.18 1512.95 1513.93 1515.07 1515.93 1517.08 1517.94

0.02256 0.02941 0.03776 0.04738 0.06013 0.07772 0.09460 0.1106 0.1307 0.1487

1640.92 1641.12 1641.35 1641.59 1641.88 1642.27 1642.60 1642.90 1643.27 1643.61

0.02279 0.02985 0.03823 0.05044 0.06162 0.08083 0.09847 0.1152 0.1350 0.1532

1509.85 1510.20 1510.51 1511.08 1511.48 1512.22 1512.90 1513.54 1514.22 1514.79

Et4NBr 0.01492 1701.12 0.02060 1701.49 0.02742 1701.85 0.03489 1702.41 0.04277 1702.93 0.05482 1703.65 0.07059 1704.38 0.08628 1705.1 0.1006 1705.83 0.1187 1706.55 0.1352 1707.28 Pr4NBr 0.01833 1701.12 0.02479 1701.49 0.03320 1701.85 0.04218 1702.21 0.05199 1702.57 0.06588 1703.29 0.08536 1704.02 0.1038 1704.74 0.1211 1705.20 0.1442 1705.83 0.1643 1706.55 Bu4NBr 0.01594 1700.05 0.02216 1700.03 0.02841 1700.03 0.03683 1700.05 0.04533 1700.03 0.05773 1700.00 0.07547 1700.03 0.09038 1700.08 0.1066 1700.01 0.1265 1700.06 0.1447 1700.09

0.01580 0.02183 0.02764 0.03625 0.04644 0.05849 0.07464 0.09041 0.1064 0.1271 0.1446

1639.64 1639.44 1639.24 1639.00 1638.67 1638.33 1637.90 1637.57 1637.23 1636.90 1636.57

0.02961 0.03804 0.04728 0.05314 0.05937 0.07842 0.09719 0.1142 0.1340 0.1528

1509.37 1509.52 1509.66 1509.80 1509.92 1510.22 1510.50 1510.79 1511.08 1511.36

a Standard uncertainties u are u(T) = 0.01 K, standard uncertainty of molality u(m) = 0.001 mol·kg−1, standard uncertainty of sound velocity u(ν) = 0.15 m·s−1, and standard uncertainty of experimental pressure u(p) = 10 kPa.

where K0S,Φ represents the limiting apparent molar isentropic compressibility and bK is the experimental slope. The coefficients of eq 8, their uncertainties, as well as the respective values of the residual deviations, σ, along with the data for single solvent solutions reported by other authors are collected in Table 9.7,28,29

Inspection of the slopes shows that apparent molar isentropic compressibility increases with rising concentration. This suggests that addition of the electrolytes makes the solutions less structured and tetraalkylammonium bromides may be considered as the structure-breakers. The negative values of limiting apparent molar isentropic compressibility of all the electrolytes in water J



Article

Table 9. Coefficients of Gucker Equation for Apparent Molar Isentropic Compressibility of Tetraalkylammonium Bromides in Aqueous and Aqueous Propane-1,2-diol Solutions at 298.15 K electrolyte

1015 KoS,Φ/(m5·N−1·mol−1)

Me4NBr

−5.3 ± 0.21 −7.1a, −3.1b −8.98 ± 0.20 −8.2, −4.7b −11.15 ± 0.14 −11.8, −7.7b −23.67 ± 0.34 −23.3a, −18.2b −22c

1015 bk/(m13·N−2·mol−3)1/2

1015 σ/(m5·N−1·mol−1)

Water

Et4NBr Pr4NBr Bu4NBr

a


1.67 ± 0.10 4.81 ± 0.22 19.38 ± 0.16 32.43 ± 0.34


2.02 ± 0.23 13.59 ± 0.52 45.03 ± 0.54 96.99 ± 0.20


2.51 ± 0.43 24.21 ± 0.29 62.93 ± 0.10 126.09 ± 0.17


−8.33 ± 0.31 12.51 ± 0.46 64.11 ± 0.68 115.34 ± 0.41

0.419 ± 0.025

0.21

0.556 ± 0.24

0.21

0.495 ± 0.016

0.14

1.119 ± 0.042

0.35

0.25 Mass Fraction of Propane-1,2-diol 0.610 ± 0.012 0.924 ± 0.027 0.385 ± 0.019 0.886 ± 0.042 0.50 Mass Fraction of Propane-1,2-diol 1.024 ± 0.029 0.971 ± 0.064 0.896 ± 0.061 0.092 ± 0.025 0.75 Mass Fraction of Propane-1,2-diol 1.035 ± 0.052 0.507 ± 0.035 0.490 ± 0.010 −0.489 ± 0.020 Propane-1,2-diol 0.789 ± 0.042 0.861 ± 0.054 0.603 ± 0.076 0.318 ± 0.046

0.11 0.22 0.17 0.40 0.20 0.53 0.54 0.21 0.37 0.26 0.10 0.17 0.23 0.48 0.26 0.14

Reference 18.. bReference 19. cReference 7.

solutions and of tetramethylammonium bromide in propane1,2-diol can be interpreted in terms of loss of compressibility, while the positive values of K0S,Φ observed for solutions in mixed solvents, regardless of the composition of the mixture, are an indication of an increase in compressibility of the solution compared to the pure solvent. As is seen from Table 9 and Figure 4, the values of limiting apparent molar isentropic compressibility of the tetraalkylammonium bromides increase in the following order Me4NBr < Et4NBr < Pr4NBr < Bu4NBr

for propane-1,2-diol and propane-1,2-diol-water mixtures, while the sequence Me4NBr > Et4NBr > Pr4NBr > Bu4NBr

is observed for water. The presented variations can be explained if terms of several effects. The most important of them seems to be that the intrinsic volume and compressibility of the tetraalkylammonium cation increase with the number of carbon atoms in the cation. The second contribution, resulting from ion−solvent interactions, may be either positive or negative. The first of the two factors, that is, intrinsic compressibility, determines the variation observed for tetraalkylammonium salts in propane-1,2-diol and mixtures of propane-1,2-diol and water. The negative and decreasing values of limiting apparent molar isentropic compressibility observed in the case of water solutions are induced by hydrophobic effect, which is

Figure 4. Limiting apparent molar compressibility against the solvent composition at 298.15 K: (■) Me4NBr, (●) Et4NBr, (▲) Pr4NBr, and (⧫) Bu4NBr.

especially pronounced in the case of tetrapropylammonium and tetrabutylammonium cations. K



Article

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4. CONCLUSIONS It has been established that thermodynamic properties of propane-1,2-diol−water mixtures are modified by addition of tetraalkylammonium bromides. The observed effect of the solutes on molar volumes and compressibilities is rather small in magnitude. Moreover, it is dependent on solvent composition and temperature. All the effects are easily interpreted in terms of change in hydrophobic interactions. Variations of limiting apparent molar volumes and compressibilities, as well as expansibility coefficients, with solvent composition observed for tetrapropylammonium and tetrabutylammonium bromide solutions are different than the corresponding variations induced by tetramethylammonium and tetraethylammonium bromides. The fact that Pr4NBr and Bu4NBr exhibit the lowest level of variation of limiting apparent molar volumes indicates the existence of a hydrophobic effect.

■

ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jced.5b00964. Coefficients of Masson equation for apparent molar volume of tetraalkylammonium bromides in water and in aqueous propane-1,2-diol solutions at temperatures between 288.15 and 318.15 K. Relative deviations 100*(dexp − dlit)/dexp) between experimental and literature values of the density of propane-1,2-diol as a function of temperature. Experimental values of density and sound velocity for binary system propane-1,2-diol− water together with respective literature values for 298.15 K(PDF)

■

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

■ ■

ACKNOWLEDGMENTS We are indebted to E. Gajewska for valuable technical assistance during measurements. REFERENCES

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