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. 2024 Apr 22;9(17):19363–19377. doi: 10.1021/acsomega.4c00520

Estimation of Ultrasonic Velocity, Density, Internal Pressure, and Thermophysical Parameters of Ionic Liquid Mixtures: Application of Flory’s Statistical Theory

Archana Sirohi †, Arun Upmanyu †,*, Pankaj Kumar †, Monika Dhiman †, Kailash Chandra Juglan ‡, Devinder Pal Singh §, Kuldeep K Saxena ∥, Alok Bhadauria ⊥,*, Md Irfanul Haque Siddiqui #
PMCID: PMC11064050  PMID: 38708244

Abstract

graphic file with name ao4c00520_0004.jpg

Flory’s statistical theory (FST) has been employed to estimate the ultrasonic velocity, density, internal pressure, and several important thermophysical parameters such as the energy of vaporization, the heat of vaporization, cohesive energy density, polarity index, and solubility for eight binary mixtures of ionic liquids and water within the temperature range of 288.15 to 308.15 K. The ionic liquids chosen for this investigation are [BMim][dca], [BMim][TfO], [BMpy][TfO], [BMpyr][dca], [BMpyr][TfO], [EEPy][ESO4], [HMim][dca], and [MPy][MSO4]. The predicted values of ultrasonic velocity and density show good agreement with the data reported in the literature. It endorses the applicability of FST to these binary mixtures. A comparative analysis of the internal pressure values (Pi) determined by using FST and the standard thermodynamic approach is also presented. The results obtained for Pi using both approaches show good agreement. Besides, for the mixtures under study, the correlation between ultrasonic velocity, density, and surface tension has also been examined. The variation of thermophysical parameters with concentration and temperature changes has been utilized to explore the nature and strength of the solute–solvent interactions prevalent in these mixtures. It is pointed out that A–A-type interactions dominate over A-B-type interactions in water-rich regions of the mixtures.

1. Introduction

Ionic liquids (ILs) have received the attention of many researchers and industrialists due to their exceptional properties, such as low vapor pressure, a wide range of viscosity, adjustable miscibility, and good thermal conductivity.1,2 Another promising feature of ILs is their tunable physical and chemical properties. ILs are often termed designer solvents, which makes them extremely useful for special applications in industry. Ultrasonic velocity is one of the prime properties of ILs. It is used in the formulation of equations of state and to derive many thermophysical properties. Recently, some researchers3,4 calculated heat capacity, isothermal and adiabatic compressibility, molecular radius, and apparent isentropic compressibility for ILs and their mixtures using the speed of sound in conjunction with other thermophysical parameters. It is a matter of fact that for the industrial design processes of ILs, it is customary to determine their density and refractive index. Nowadays, density calculation is being used to solve the material or energy balance equations of chemical processes in industry.5

The study of molecular interactions is important in almost all fields of the physical and chemical sciences. These interactions provide valuable information about the molecular packing, orientation, and conformation of the molecules. Many researchers6−9 have investigated the molecular interactions in ILs and some binary liquid mixtures. Fumino et al.10 investigated the hydrogen bonding, Coulomb interactions, and dispersion forces in some ILs. Dhumal et al.11 reported the molecular interactions of a Cu-based metal–organic framework with a confined imidazolium-based IL using experimental and computational techniques. Recently, Wei et al.12 reported changes in molecular interactions in ILs with charged SiO2 surfaces. It is reported13−15 that the computational and experimental techniques are complementary for determining the structure, design, and thermophysical properties of liquids and their mixtures. Some researchers16−18 employed density functional theory (DFT), molecular dynamics (MD), COSMO-R, and Flory’s statistical theory (FST) to estimate these properties. Though all these theoretical formulations are found suitable to compute the thermophysical properties, FST is a valuable and powerful tool as a result of the limited input parameters and ease of calculations using a simple analytic expression. FST is a good candidate in the theoretical framework of industrial design to predict the thermodynamic properties.19 Several researchers20−22 successfully employed FST to predict the ultrasonic velocity and density with reasonable accuracy for pure liquids. Pandey et al.23 modified FST for ternary liquid mixtures to discuss their thermodynamic behavior. Oswal et al.24 tested the validity of the FST, ERAS, and Rao theories for the alkyl amines. Gepert et al.25 have compared FST and the Prigogine–Flory–Patterson (PFP) model for binary mixtures of hydrocarbons. Recently, Shrivastava et al.26 estimated various thermodynamic parameters using FST for pure ILs at elevated pressure. However, despite the high demand for ILs and their mixtures in various fields, their physicochemical properties have not yet been systematically studied, particularly for the mixtures of ILs with molecular liquids.27 Thus, there is a need to compute thermophysical properties like the speed of sound, density, adiabatic compressibility, thermal expansion, internal pressure, etc., for these liquids. Recently, binary mixtures of ILs and water have gained a lot of impetus.28−30 In their review article, Isosaari et al.,31 have summarized the use of ILs for wastewater treatment. These findings motivated us to conduct in-depth investigations of the physical properties of water-based IL mixtures.

In this investigation, FST is employed to estimate ultrasonic velocity, density, and internal pressure for eight binary mixtures of ILs and water at various temperatures. The obtained results are compared to the literature values, and a reasonable agreement is found between them. The correlation of density, ultrasonic velocity, and surface tension was also investigated. Several researchers have reported the importance of such correlations.8,32 Besides, some important thermophysical parameters were determined to understand the molecular interactions prevalent in these binary mixtures. The concentration and temperature dependence of solubility parameters and several other thermophysical parameters were also been investigated. The data required for the present study has been taken from the literature.33

2. Theoretical Formulation

FST formulations have been discussed at length by many workers.34−37 They have successfully employed it to compute the density (d), ultrasonic velocity (U), surface tension, and molar volume for organic liquids, polymers, and ILs. We extended the same formulation to IL mixtures. Herein, only those relations are reported that have been directly utilized in the present study.

Using a reduced equation of state,38 reduced volume (Ṽ), reduced temperature (T̃), characteristic pressure (P*), characteristic temperature (T*), and characteristic volume (V*) for pure ILs can be deduced as per the equations given below. Herein, the characteristic volume (V*) and characteristic temperature (T*) are the molar volume and temperature at the zero pressure limit (P = 0)39

2. 1

where Inline graphic and Inline graphic are the reduced volume and reduced temperature, respectively.

The reduced volume Ṽ in terms of the coefficient of thermal expansion (α) can be computed using the relation given below:

2. 2

where α can be calculated in terms of ultrasonic velocity (U) and density (d) at various temperatures and concentrations using a well-known relation available in the literature:

2. 3

P* can be evaluated from the knowledge of α and KT:

2. 4

where γP is the thermal pressure coefficient at the zero pressure limit and KT is the isothermal compressibility. KT was determined using a formula taken from the literature.40,41 The above relations have been employed to compute P*, V*, and T* for mixture components. Thereafter, these parameters were used to determine the segment fractions (ψ), site fraction (θ), and interaction parameter (χ12) for the binary mixtures. The segment fractions are calculated as follows:

2. 5

and

2. 6

where ψ1 and ψ2 are the segment fractions, Vi* (i = 1, 2) is the characteristic volume, and Xi (i = 1, 2) is the mole fraction of solute (water) and solvent (ILs), respectively. The site fraction is given by

2. 7

The interaction parameter is calculated as

2. 8

The segment fractions (ψ1 and ψ2), site fraction (θ2), and interaction parameter (χ12) are used to determine the values of characteristic pressure (P*) and characteristic temperature (T*) of mixtures based on the following relations:

2. 9
2. 10

2.1. Surface Tension for the Binary Ionic Liquid’s Mixture and Flory Theory

Patterson and Rastogi42 derived the characteristic surface tension (σ*) and reduced surface tension [σ(Ṽ)] for pure liquids based upon the principle of corresponding states. They further used these parameters to calculate the surface tension; σ = σ* × σ(Ṽ). Some researchers43 extended the same formulation to compute surface tension for IL. In this study, we extended the same approach to a binary mixture of ILs and water.

The characteristic surface tension (σ*) for binary mixtures can be calculated as

2.1. 11

where P* and T* are calculated using eqs 9 and 10 and k is the Boltzmann constant.

The reduced surface tension [σ(Ṽ)] is deduced as a function of the reduced volume (Ṽm) for binary mixtures as

2.1. 12

where M is the fractional change in the neighborhood cell count in the surface phase. Its value generally exists between 0.26 and 0.29. The surface tension of an IL mixture is computed using the following equation:

2.1. 13

2.2. Estimation of Ultrasonic Velocity and Their Correlation with Density and Surface Tension

Ultrasonic velocity plays a vital role in chemical ultrasonics. Simply, in conjunction with density, it can provide valuable information about liquid systems. In the present study, the density (d) and a diagnostic parameter, the surface tension (σ), are utilized to calculate the ultrasonic velocity of these systems using the standard correlation available in the literature:44,45

Auerbach relation:
2.2. 14

Alternberg relation:
2.2. 15

Singh–Pandey–Sanguri relation:
2.2. 16

modified Auerbach relation:
2.2. 17

2.3. FST and Estimation of Density

The ideal reduced volume Ṽ0 of the binary mixture can be obtained as

2.3. 18

Ṽ0 is further used to calculate the ideal reduced temperature, T̃0:

2.3. 19

The excess reduced volume is given by

2.3. 20

The reduced volume is then obtained as

2.3. 21

Finally, the molar volume (Vm) in terms of the characteristic volume of the mixture (V*) and the reduced volume (calculated using eq 21) can be obtained as

2.3. 22

V* can be calculated using the additive properties of the mixture:

2.3. 23

The density of the mixture (d) is then given by

2.3. 24

where Meff is the effective mass of the mixture and Vm is calculated using eq 22.

2.4. Estimation of Internal Pressure and FST

Internal pressure is a very useful thermophysical parameter, and its importance in the field of thermodynamics was first highlighted by Hildebrand and later by various workers.46−50 Due to the complex procedure of its experimental measurements, many empirical/semiempirical relations have been proposed to compute the internal pressure based on ultrasonic velocity, molecular radius, and thermal expansion at different temperatures for pure as well as mixtures. The thermodynamic method is the most prominent approach to computing the internal pressure (Pi), which is rewritten below in its usual form:

2.4. 25

where α and KT are the thermal expansivity and isothermal compressibility of the given mixtures, which can be deduced using the following standard relations:51

2.4. 26
2.4. 27

Pandey and co-workers computed the internal pressure (PFST) for liquid mixtures at 303.15 K using FST. Later, the same approach was opted by many workers to compute the internal pressure for different liquid mixtures. The mathematical formulation to compute the PFST is reproduced below:

2.4. 28

In the above relation, αFST and (KT)FST are the thermal expansivity and isothermal compressibility calculated using Flory’s parameters as

2.4. 29
2.4. 30

In the above relations, Ṽm and P* are the reduced volume and characteristic pressure of mixtures; their values have been computed using eqs 2 and 9. Herein, we have also employed eq 28 for the first time to compute the Pi values for the binary mixtures of water and ILs. The obtained results are then compared with the Pi values obtained by using the thermodynamic method.

2.5. Application of FST to Compute the Thermophysical Parameters of IL Mixtures

In this work, FST has been employed for the first time to compute some important thermodynamic parameters,32 viz., energy of vaporization (ΔEV), heat of vaporization (ΔH), cohesive energy density (ced), solubility parameter (δ), and polarity index (n) for binary mixtures of water and ILs, using the following relations:

2.5. 31
2.5. 32

The cohesive energy density basically depends upon ΔEV, n, and the molar volume (Vm) of the mixture. The general form of the relation is given below:

2.5. 33

where here the polarity index is n = 1. The solubility parameter is given by

2.5. 34

Hildebrand originally developed the solubility parameter relations for organic liquids. Here, we are investigating its application to binary mixtures of water and ILs.

3. Results and Discussion

3.1. Estimation of Ultrasonic Velocity Using FST

In the present study, ultrasonic velocity (U) is computed for eight binary mixtures of water and ILs using four empirical relations, viz., Auerbach relation (UA), Alternberg relation (UAR), Singh–Pandey–Sanguri relation (USR), and modified Auerbach relation (UMR) (eqs 14–17). The following ILs were used in the present investigation.

  • I.

    1-Butyl-3-methylimidazolium dicyanamide [BMim][dca]

  • II.

    1-Butyl-3-methylimidazolium trifluoromethanesulfonate [BMim][TfO]

  • III.

    1-Butyl-3-methylpyridinium trifluoromethanesulfonate [BMpy][TfO]

  • IV.

    1-Butyl-1-methylpyrrolidinium dicyanamide [BMpyr][dca]

  • V.

    1-Butyl-1-methylpyrrolidinium trifluoromethanesulfonate [BMpyr][TfO]

  • VI.

    1,2-Diethylpyridinium ethylsulfate [EEPy][ESO4]

  • VII.

    1-Hexyl-3-methylimidazolium dicyanamide [HMim][dca]

  • VIII.

    1-Methylpyridinium methylsulfate [MPy][MSO4]

Theoretically obtained values of the ultrasonic velocity are reported in Table S1 (Supporting Information) as well as plotted against the mole fraction (X1) of water at different temperatures and depicted in Figure 1a–h. The close look of Figure 1a indicates that for water + [BMim][dca] binary mixture, the U values obtained using Auerbach relation (UA), Singh–Pandey–Sanguri relation (USP), and modified Auerbach relation (UMA) are in reasonable agreement with ultrasonic velocity (U*) data reported in the literature.33 However, the Alternberg relation (UAR) reports a strong deviation with the increase in the mole fraction of water. This deviation is much more pronounced for the higher mole fractions of water. Figure 1b–h also indicates similar results, which confirm that except for UAR, the other three relations; UA, UMA, and USP, can be employed to compute the ultrasonic velocity for water + [BMim][TfO], water + [BMpy][TfO], water + [BMpyr][dca], water + [EEpy][ESO4], water + [HMim][dca], and water + [MMpy][MSO4] mixtures. In the case of water+[BMpyr][TfO] [Figure 1e], the deviation of UA, UMA, and USP with respect to U* increased for X1 > 0.7. It is also noticed for the same system that the Alternberg relation (UAR) shows reasonable agreement until X1 = 0.7.

Figure 1.

Figure 1

Figure 1

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Comparison of ultrasonic velocity estimated using the Auerbach relation (UA), Alternberg relation (UAR), Singh–Pandey–Sanguri relation (USP), and modified Auerbach relation (UMA) along with the literature values (U*) for binary mixtures. Solid line is a guide for eye.

The reasonable agreement of UA, UMA, and USP with U* also affirms the U–d–σ correlation and the ability of FST to compute the ultrasonic velocity for the given water + IL mixtures. The higher deviation of UAR values from the literature data is due to the noncompliance of the assumptions made for the derivation of this relation. The general agreement of UA, UMA, and USP with U* is further confirmed from the absolute percentage deviation (Table 1). It is pertinent to mention here that, however, the general agreement is reached between theoretical models (UA, UMA, and USP) with U*, but the deviation is still toward the higher side. It is attributed to the fact that these relations were originally derived for organic mixtures having component size is almost similar, but in the present systems, the size and structure of ILs and water molecules are different, which leads to a higher deviation. It further suggests that these relations also need modification, considering the complex structure of IL to estimate the ultrasonic velocity for given mixtures.

Table 1. Absolute Percentage Deviation of Computed Ultrasonic Velocity from Experimental Values for Eight Ionic Liquid Mixtures.

T/K UA UAT USP UMA T/K UA UAT USP UMA
  Water + [BMim][dca]   Water + [BMpyr][TfO]
288.15 4.63 17.83 7.59 1.95 288.15 5.47 14.57 8.4 1.05
298.15 3 19.86 6.72 3.7 298.15 5.47 14.57 8.4 1.05
308.15 1.45 21.87 5.83 5.46 308.15 2.14 18.36 6.58 4.61
  Water + [BMim][TfO]   Water + [EEpy][ESO4]
288.15 4.95 17.43 7.9 1.6 288.15 2.14 18.36 6.58 4.61
298.15 3.31 19.48 7.02 3.36 298.15 7.09 20.2 9.97 1.19
308.15 1.65 21.48 6.11 5.13 308.15 3.79 24.32 8.16 2.85
  Water + [BMpy][TfO]   Water + [HMim][dca]
288.15 5.13 15.93 8.07 1.42 288.15 1.45 21.87 5.83 5.46
298.15 3.31 16.33 7.02 3.36 298.15 2.55 14.85 5.95 4.55
308.15 1.65 18.02 6.11 5.14 308.15 1.5 15.43 5.09 6.28
  Water + [BMpyr][dca]   Water + [Mpy][MSO4]
288.15 4.74 20.62 7.69 1.83 288.15 6.31 33.4 9.21 2.49
298.15 4.74 20.62 7.69 1.83 298.15 6.31 33.4 9.21 2.49
308.15 1.54 24.7 5.99 5.28 308.15 3.69 38.06 7.63 3.43
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3.2. Estimation of Density Using FST

Density is an important thermodynamic parameter. It is presently used to characterize liquid mixtures in industry.19,38,52 It is also used in conjunction with ultrasonic velocity and temperature to compute important physical parameters, such as the coefficient of thermal expansion. In the present study, the density (dFST) of eight binary IL mixtures is computed using FST, and the obtained results are compared with the literature values (d*). Density data, computed by using FST, and their percentage deviation from the literature values at various concentrations and temperatures are reported in Table 2. A perusal of Table 2 reveals good agreement between the computed and literature values of density for all the systems under study. The mean percentage deviation (MPD) for each system at different temperatures is reported in Table 3. It is obvious from Table 3 that MPD is less than 1.5% for all the binary mixtures of ILs at all temperatures. It confirms the validity of FST to predict density in the given concentration and temperature range.

Table 2. Computed Density (dFST) and Literature (d*)33 Density along with Percentage Deviations for Eight Binary Mixtures of Water and Ionic Liquids at Different Temperaturesa.

X1 d* dFST % Dev d* dFST % Dev d* dFST % Dev
  T = 288.15 K T = 298.15 K T = 308.15 K
Water + [BMim][dca]
0 1066.58 1066.58 0.00 1060.17 1060.17 0.00 1053.83 1053.83 0.00
0.1088 1065.59 1067.14 0.15 1059.16 1060.71 0.15 1054.35 1052.79 0.15
0.1227 1065.44 1067.21 0.17 1059.01 1060.78 0.17 1054.42 1052.64 0.17
0.2017 1064.62 1067.68 0.29 1058.16 1061.23 0.29 1054.85 1051.77 0.29
0.2943 1063.46 1068.27 0.45 1056.98 1061.8 0.46 1055.39 1050.55 0.46
0.3952 1061.88 1068.97 0.67 1055.35 1062.45 0.67 1056.02 1048.88 0.68
0.503 1059.83 1069.7 0.93 1053.24 1063.14 0.94 1056.66 1046.7 0.95
0.5985 1057.37 1070.18 1.21 1050.71 1063.58 1.22 1057.06 1044.09 1.24
0.7032 1053.63 1070.06 1.56 1046.89 1063.42 1.58 1056.87 1040.15 1.61
0.805 1047.26 1067.76 1.96 1040.5 1061.18 1.99 1054.65 1033.69 2.03
0.9006 1035.92 1058.19 2.15 1029.6 1052 2.18 1045.77 1023.11 2.21
0.9503 1024.07 1043 1.85 1018.75 1037.62 1.85 1032.01 1013.06 1.87
1 999.1 999.1 0.00 997.04 997.04 0.00 994.02 994.02 0.00
Water + [BMim][TfO]
0 1307.5 1307.5 0.00 1299.55 1299.55 0.00 1291.62 1291.62 0.00
0.1348 1305.34 1303.64 0.13 1297.37 1295.68 0.13 1289.44 1287.74 0.13
0.2028 1303.95 1301.3 0.20 1295.98 1293.3 0.21 1288.04 1285.33 0.21
0.2056 1303.89 1301.2 0.21 1295.92 1293.22 0.21 1287.97 1285.23 0.21
0.3083 1301.23 1296.7 0.35 1293.25 1288.66 0.36 1285.29 1280.65 0.36
0.4985 1285.26 1273.42 0.68 1277.25 1265.25 0.69 1269.28 1257.08 0.71
0.6062 1273.53 1258.59 0.93 1265.56 1250.44 0.95 1257.63 1242.22 0.97
0.7015 1249.11 1231.3 1.19 1241.35 1223.33 1.21 1233.61 1215.23 1.24
0.8064 1198.93 1180.1 1.45 1191.87 1172.98 1.47 1184.71 1165.56 1.51
0.8998 1166.61 1149.84 1.60 1160.13 1143.39 1.61 1153.47 1136.56 1.64
0.9309 1130.07 1116.26 1.46 1124.36 1110.62 1.46 1118.34 1104.51 1.49
0.9548 999.1 999.1 1.24 997.04 997.04 1.24 994.02 994.02 1.25
1 1285.26 1273.42 0.00 1277.25 1265.25 0.00 1269.28 1257.08 0.00
Water + [BMpy][TfO]
0 1287.07 1287.07 0.00 1279.41 1279.41 0.00 1271.8 1271.8 0.00
0.0794 1286.06 1285.23 0.06 1278.62 1277.62 0.08 1271 1269.98 0.08
0.1517 1284.96 1283.28 0.13 1277.76 1275.63 0.17 1270.13 1267.96 0.17
0.2502 1283.1 1279.99 0.24 1276.28 1272.28 0.31 1268.64 1264.58 0.32
0.3515 1280.54 1275.76 0.38 1274.23 1268 0.49 1266.57 1260.24 0.50
0.4528 1276.96 1270.21 0.53 1271.33 1262.4 0.71 1263.65 1254.58 0.72
0.5628 1271.08 1261.9 0.73 1266.49 1254.01 1.00 1258.79 1246.08 1.02
0.6561 1263.08 1251.55 0.92 1259.79 1243.59 1.30 1252.08 1235.57 1.34
0.7494 1249.41 1235.48 1.13 1248.09 1227.52 1.68 1240.41 1219.46 1.72
0.8383 1224.23 1208.29 1.32 1225.8 1200.56 2.10 1218.28 1192.69 2.15
0.9201 1171.21 1155.76 1.34 1176.4 1149.07 2.38 1169.47 1142.04 2.40
0.9603 1114.93 1103.57 1.03 1120.78 1098.18 2.06 1114.78 1092.3 2.06
1 999.1 999.1 0.00 997.04 997.04 0.00 994.02 994.02 0.00
Water + [BMpyr][dca]
0 1019.17 1019.17 0.00 1019.17 1019.17 0.00 1007.93 1007.93 0.00
0.096 1020.09 1018.92 0.11 1020.09 1018.92 0.11 1008.81 1007.63 0.12
0.1277 1020.42 1018.84 0.16 1020.42 1018.84 0.16 1009.13 1007.52 0.16
0.2116 1021.41 1018.6 0.28 1021.41 1018.6 0.28 1010.06 1007.23 0.28
0.3077 1022.73 1018.31 0.43 1022.73 1018.31 0.43 1011.31 1006.85 0.44
0.3942 1024.14 1018.08 0.60 1024.14 1018.08 0.60 1012.63 1006.5 0.61
0.4952 1026.08 1017.78 0.82 1026.08 1017.78 0.82 1014.45 1006.03 0.84
0.5023 1026.23 1017.76 0.83 1026.23 1017.76 0.83 1014.59 1005.99 0.86
0.6047 1028.62 1017.45 1.10 1028.62 1017.45 1.10 1016.84 1005.42 1.14
0.6137 1028.85 1017.41 1.12 1028.85 1017.41 1.12 1017.05 1005.35 1.16
0.7061 1031.35 1016.91 1.42 1031.35 1016.91 1.42 1019.41 1004.54 1.48
0.7177 1031.68 1016.81 1.46 1031.68 1016.81 1.46 1019.71 1004.4 1.52
0.7571 1032.76 1016.39 1.61 1032.76 1016.39 1.61 1020.75 1003.86 1.68
0.8208 1034.21 1015.22 1.87 1034.21 1015.22 1.87 1022.17 1002.57 1.95
0.8468 1034.51 1014.46 1.98 1034.51 1014.46 1.98 1022.5 1001.84 2.06
0.9034 1033.48 1011.96 2.13 1033.48 1011.96 2.13 1021.76 999.84 2.19
0.904 1033.44 1011.92 2.13 1033.44 1011.92 2.13 1021.73 999.81 2.19
0.9492 1027.84 1008.27 1.94 1027.84 1008.27 1.94 1017.1 997.62 1.95
0.9507 1027.5 1008.1 1.92 1027.5 1008.1 1.92 1016.81 997.53 1.93
0.9517 1027.26 1007.98 1.91 1027.26 1007.98 1.91 1016.62 997.47 1.92
1 999.1 999.1 0.00 999.1 999.1 0.00 994.02 994.02 0.00
Water + [BMpyr][TfO]
0 1260.33 1260.33 0.00 1260.33 1260.33 0.00 1245.78 1245.78 0.00
0.0559 1259.79 1259.04 0.06 1259.79 1259.04 0.06 1245.23 1244.55 0.05
0.1084 1259.22 1257.8 0.11 1259.22 1257.8 0.11 1244.64 1243.3 0.11
0.2076 1257.91 1255.12 0.22 1257.91 1255.12 0.22 1243.3 1240.51 0.22
0.2997 1256.32 1252.05 0.34 1256.32 1252.05 0.34 1241.66 1237.3 0.35
0.408 1253.73 1247.41 0.51 1253.73 1247.41 0.51 1239.01 1232.47 0.53
0.5038 1250.37 1241.91 0.68 1250.37 1241.91 0.68 1235.59 1226.79 0.72
0.6003 1245.2 1234.21 0.89 1245.2 1234.21 0.89 1230.37 1218.89 0.94
0.7052 1235.58 1221.39 1.16 1235.58 1221.39 1.16 1220.74 1205.88 1.23
0.8095 1216.25 1198.77 1.46 1216.25 1198.77 1.46 1201.62 1183.37 1.54
0.9018 1174.84 1155.9 1.64 1174.84 1155.9 1.64 1161.16 1141.73 1.70
0.9533 1119.91 1104.38 1.41 1119.91 1104.38 1.41 1108.18 1092.63 1.42
1 999.1 999.1 0.00 999.1 999.1 0.00 994.02 994.02 0.00
Water + [EEpy][ESO4]
0 1245.78 1245.78 0.00 1225.93 1225.93 0.00 1212.65 1212.65 0.00
0.0559 1245.23 1244.55 0.05 1225.38 1224.31 0.09 1212.07 1211.14 0.08
0.1084 1244.64 1243.3 0.11 1225.32 1224.06 0.10 1212.01 1210.87 0.09
0.2076 1243.3 1240.51 0.22 1224.62 1222.4 0.18 1211.26 1209.22 0.17
0.2997 1241.66 1237.3 0.35 1223.65 1219.81 0.31 1210.22 1206.65 0.30
0.408 1239.01 1232.47 0.53 1222.32 1216.82 0.45 1208.8 1203.43 0.45
0.5038 1235.59 1226.79 0.72 1220.31 1212.76 0.62 1206.68 1199.29 0.62
0.6003 1230.37 1218.89 0.94 1216.37 1205.78 0.88 1202.6 1192.05 0.89
0.7052 1220.74 1205.88 1.23 1209.02 1194.96 1.18 1195.12 1180.85 1.21
0.8095 1201.62 1183.37 1.54 1195.41 1177.39 1.53 1181.48 1163.05 1.58
0.9018 1161.16 1141.73 1.70 1161.14 1138.4 2.00 1147.67 1124.48 2.06
0.9533 1108.18 1092.63 1.42 1116.26 1092.23 2.20 1104.07 1080.72 2.16
1 994.02 994.02 0.00 999.1 999.1 0.00 994.02 994.02 0.00
Water + [HMim][dca]
0 1053.83 1053.83 0.00 1028.56 1028.56 0.00 1022.4 1022.4 0.00
0.1088 1054.35 1052.79 0.15 1029.11 1028.25 0.08 1022.95 1022.07 0.09
0.1227 1054.42 1052.64 0.17 1029.43 1028.07 0.13 1023.26 1021.88 0.13
0.2017 1054.85 1051.77 0.29 1030.26 1027.61 0.26 1024.07 1021.38 0.26
0.2943 1055.39 1050.55 0.46 1031.25 1027.08 0.41 1025.04 1020.81 0.41
0.3952 1056.02 1048.88 0.68 1032.49 1026.41 0.59 1026.26 1020.08 0.61
0.503 1056.66 1046.7 0.95 1034.24 1025.46 0.86 1027.97 1019.04 0.88
0.5985 1057.06 1044.09 1.24 1036.25 1024.31 1.17 1029.93 1017.78 1.19
0.7032 1056.87 1040.15 1.61 1039 1022.4 1.62 1032.63 1015.71 1.67
0.805 1054.65 1033.69 2.03 1041.88 1019.6 2.19 1035.45 1012.81 2.24
0.9006 1045.77 1023.11 2.21 1043.09 1014.13 2.86 1036.72 1007.62 2.89
0.9503 1032.01 1013.06 1.87 1038.1 1009.12 2.87 1032.04 1003.34 2.86
1 994.02 994.02 0.00 997.04 997.04 0.00 994.02 994.02 0.00
Water + [Mpy][MSO4]
0 1352.86 1352.86 0.00 1352.86 1352.86 0.00 1339.37 1339.37 0.00
0.0574 1351.6 1350.36 0.09 1351.6 1350.36 0.09 1338.1 1336.86 0.09
0.073 1351.23 1349.61 0.12 1351.23 1349.61 0.12 1337.74 1336.11 0.12
0.1111 1350.29 1347.74 0.19 1350.29 1347.74 0.19 1336.78 1334.23 0.19
0.1927 1347.99 1343.32 0.35 1347.99 1343.32 0.35 1334.45 1329.82 0.35
0.2941 1344.39 1336.61 0.58 1344.39 1336.61 0.58 1330.81 1323.12 0.58
0.4005 1339.29 1327.54 0.88 1339.29 1327.54 0.88 1325.63 1314.09 0.88
0.4996 1332.52 1316.5 1.22 1332.52 1316.5 1.22 1318.79 1303.09 1.20
0.6077 1321.25 1299.41 1.68 1321.25 1299.41 1.68 1307.43 1286.07 1.66
0.7064 1304.22 1276.09 2.20 1304.22 1276.09 2.20 1290.36 1262.91 2.17
0.8058 1273.04 1237.51 2.87 1273.04 1237.51 2.87 1259.29 1224.76 2.82
0.901 1209.25 1168.89 3.45 1209.25 1168.89 3.45 1196.21 1157.51 3.34
0.9497 1142.44 1107.24 3.18 1142.44 1107.24 3.18 1130.82 1097.68 3.02
0.9645 1112.06 1081.91 2.79 1112.06 1081.91 2.79 1101.35 1073.27 2.62
1 999.1 999.1 0.00 999.1 999.1 0.00 994.02 994.02 0.00
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a

Standard uncertainty: X1 is ±0.0001, d is ±0.00003 g·cm–3, and U is ±0.3 m·s–1.33

Table 3. Mean Percentage Deviation of the Computed Value of Density for Eight Binary Mixtures of Water and ILs.

T (K) water + [BMim][dca] water + [BMpy][TfO] water + [BMpyr][TfO] water + [HMim][dca]
288.15 0.88 0.60 0.65 0.90
298.15 0.88 0.94 0.65 1.00
308.15 0.90 0.96 0.68 1.02
T (K) water + [BMim][tfo] water + [BMpyr][dca] water + [EEpy][ESO4] water + [Mpy][MSO4]
288.15 0.72 1.13 0.68 1.50
298.15 0.73 1.13 0.73 1.50
308.15 0.75 1.17 0.74 1.45
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3.3. Estimation of Internal Pressure Using FST

Internal pressure has been computed using the thermodynamic method (Pi) and FST (PFST) for eight binary mixtures of water and ILs at various temperatures. The results obtained are reported in Table 4. Additionally, thermal expansivity and isothermal compressibility using the thermodynamic method (α, KT) and FST [αFST, (KT)FST] are computed and tabulated in Table S2 [Supporting file]. Due to the nonavailability of the experimental data of Pi for these mixtures, the Pi values obtained by using the thermodynamic method are considered standard to check the validity of FST in predicting the internal pressure. The ratio of PFST/Pi is plotted against the mole fraction (X1) for eight IL mixtures at different temperatures in Figure 2. As is obvious from Figure 2, the PFST/Pi ratio is closer to unity for all of the mixtures under study. It confirms the applicability of FST to predict the Pi values for these mixtures. To generalize the validity of FST, this approach can be applied to these and similar ILs that are mixed with other suitable organic solvents.

Table 4. Internal Pressure Computed Using the Thermodynamic Approach (Pi) and Flory’s Theory (PFST) at Different Temperatures for Eight IL Mixtures.

X1 Pi (MPa) PFST (MPa) Pi (MPa) PFST (MPa) Pi (MPa) PFST (MPa) X1 Pi (MPa) PFST (MPa) Pi (MPa) PFST (MPa) Pi (MPa) PFST (MPa)
  Water + [BMim][dca]   Water + [EEPy][ESO4]
  T = 288.15 K T = 298.15 K T = 308.15 K   T = 288.15 K T = 298.15 K T = 308.15 K
0 665.1 665.1 676.5 676.5 687.6 687.6 0 771.1 771 782.8 782.7 794.9 794.8
0.1088 663.2 659.7 675.1 671.5 686.5 682.9 0.0987 772.5 765.4 784.3 777.4 796.7 790
0.1227 663 658.9 675 670.8 686.3 682.2 0.1089 772.4 764.7 784.4 776.7 796.9 789.3
0.2017 661.9 654.3 673.9 666.5 685.3 678.2 0.2048 773.1 758.4 786.4 771 798.9 783.9
0.2943 660.6 648 672.6 660.6 684 672.7 0.3037 775.7 750 789.2 763.2 802 776.5
0.3952 658.8 639.6 671 652.7 682.5 665.4 0.3979 778.1 740.4 791.8 754.1 804.5 767.8
0.503 656.7 628.4 669.1 642.4 680.7 655.8 0.4922 781.6 728.3 795.4 742.8 808.3 757.1
0.5985 654.4 615.6 667 630.6 678.8 644.8 0.6018 786 709.4 799.9 724.9 812.5 740.3
0.7032 649.8 597.1 662.8 613.6 675 629.2 0.7084 791.3 683.5 805 700.5 817.5 717.2
0.805 638.8 571 652.8 589.9 665.7 607.7 0.8029 791.4 648.7 804.9 668.1 816.9 686.6
0.9006 607.8 534.5 625.5 557.9 641.8 579.8 0.8984 760.1 590.8 774.7 614.2 787.3 636.5
0.9503 567.4 507.7 590.6 535.5 612 561.5 0.9493 678.1 540.7 698.2 568.7 716.7 595.1
1 472.2 472.1 508.7 508.7 543.3 543.3 1 472.2 472.1 508.7 508.7 543.3 543.3
  Water + [BMim][TfO]   Water + [BmPy][TfO]
  T = 288.15 K T = 298.15 K T = 308.15 K   T = 288.15 K T = 298.15 K T = 308.15 K
0 585.2 585.1 593.9 593.9 602.1 602.1 0 589.4 589.4 597.9 598 606.2 606.2
0.1348 586.8 581.1 595.6 590.3 604 598.9 0.0794 587.1 590.4 596 599.2 604.5 607.2
0.2028 587.7 578.7 596.7 588.1 605.1 596.9 0.1517 584.8 591.5 593.9 600.3 602.6 608.4
0.2056 587.8 578.6 597.1 588.1 605.9 596.8 0.2502 581.1 593.3 590.5 602.2 599.5 610.5
0.3083 589.6 574.1 598.7 584.1 607.1 593.3 0.3515 576.4 595.3 586.4 604.6 595.8 613
0.4985 593.7 563.1 603.2 574.3 611.9 584.6 0.4528 570.6 598.1 581.2 607.5 591.2 616
0.6062 596.5 553.9 606.5 566.3 615.6 577.6 0.5628 562.5 601.9 574.1 611.5 584.9 620.2
  Water + [BMim][TfO]   Water + [BmPy][TfO]
  T = 288.15 K T = 298.15 K T = 308.15 K   T = 288.15 K T = 298.15 K T = 308.15 K
0.7015 599.2 543.2 609.9 557 619.4 569.7 0.6561 553.5 605.6 566.2 615.7 578 624.7
0.8064 599.7 527.2 612.6 543.7 623.8 558.9 0.7494 541.3 609.1 555.8 620.1 569.2 629.7
0.8998 590.7 505.6 608.1 526.9 623.4 546.6 0.8383 524.8 608.7 542.1 621.9 558.2 633.4
0.9309 580.8 497 601.1 521 619.3 543.3 0.9201 502.6 592.8 525.2 611.6 546.2 628.1
0.9548 567.6 489.3 591.1 516.2 612.2 541.3 0.9603 488.7 568.4 516.1 592.1 541.7 613.6
1 472.2 472.1 508.7 508.7 543.3 543.3 1 472.1 472.2 508.7 508.7 543.3 543.3
  Water + [BmPyr][TfO]   Water + [Hmim][dca]
  T = 288.15 K T = 298.15 K T = 308.15 K   T = 288.15 K T = 298.15 K T = 308.15 K
0 606.6 606.6 615.6 615.6 624.3 624.2 0 617.5 617.5 628 628 637.8 637.8
0.0559 607.4 604.8 616.6 614 625.6 622.8 0.0785 617.3 614.8 628 625.5 637.9 635.5
0.1084 608.2 603 617.4 612.4 626.1 621.4 0.1191 617.5 613.2 628 624 637.9 634.2
0.2076 610.2 599.2 619.6 609 628.4 618.2 0.2124 617.5 609.2 628.1 620.3 638 630.8
0.2997 612.5 595 622.1 605.2 631 614.7 0.3055 617.6 604.5 628.2 616 638.1 626.8
0.408 615.8 589 625.5 599.7 634.5 609.7 0.4019 617.6 598.5 628.3 610.5 638.2 621.8
0.5038 619.3 582.2 629.3 593.6 638.3 604.3 0.5096 617.7 590 628.5 602.8 638.6 614.7
0.6003 623.5 573.4 633.8 585.7 642.9 597.3 0.6069 617.6 580 628.6 593.7 638.5 606.5
0.7052 628.5 560.4 639.4 574.3 648.9 587.2 0.7123 616.1 565.2 627.3 580.3 637.3 594.4
0.8095 631.2 541.7 643.7 558.2 654.6 573.6 0.8067 610.3 546.1 622.5 563.5 633.3 579.6
0.9018 619.8 516.1 636.7 537.4 651.4 557.1 0.9031 587 516.9 603.5 538.8 618.3 559.3
0.9533 590.7 496 613.1 522.5 633.1 547.3 0.9499 556 497.4 578.7 523.9 599 548.6
  Water + [MPy][MSO4]   Water + [BMim][dca]
  T = 288.15 K T = 298.15 K T = 308.15 K   T = 288.15 K T = 298.15 K T = 308.15 K
0 943.6 943.5 963 963 982.6 982.6 0.3942 673.3 650.4 686.4 664.7 698.9 676.1
0.0574 941.4 936.9 961.4 956.5 980.7 976.3 0.4952 673.2 640.2 686.6 655.2 699.1 667.2
0.073 941.5 935 961.1 954.7 980.4 974.4 0.5023 673.3 639.4 686.6 654.4 699.1 666.5
0.1111 940.6 930.1 960.6 949.9 979.9 969.8 0.6047 673.4 625.8 686.9 641.7 699.5 654.8
0.1927 938.5 918.7 958.8 938.9 978.3 959.1 0.6137 673.3 624.4 686.8 640.4 699.4 653.6
0.2941 936.2 902 956.6 922.6 976 943.2 0.7061 671.4 607.3 685.1 624.6 697.8 639.1
0.4005 932.1 880.3 952.8 901.6 972.7 922.8 0.7177 670.9 604.7 684.7 622.2 697.4 636.9
0.4996 926.3 855.2 947.3 877.3 967.3 899.1 0.7571 668.0 595.1 682.1 613.3 694.9 628.9
0.6077 915 819.4 936.1 842.5 956.1 865.2 0.8208 658.3 575.6 673.1 595.6 686.6 612.9
0.7064 894 775.2 915.2 799.7 934.8 823.6 0.8468 651.1 565.9 666.6 586.8 678.6 605.1
0.8058 847.4 712.2 869.1 738.6 887.8 764.1 0.9034 623.7 540.0 642.0 563.8 658.7 585.0
0.901 740.1 621.9 764.6 651.4 786.7 679.6 0.904 623.2 539.6 641.4 563.5 658.3 584.8
0.9497 636 557.8 664.7 589.8 691.4 620.3 0.9492 579.8 512.4 603.2 540.2 624.6 565.6
0.9645 595 535 626.5 568.2 654.2 599.5 0.9507 577.8 511.4 601.5 539.4 623.2 564.9
1 472.2 472.1 508.7 508.7 543.3 543.3 0.9517 576.4 510.7 600.3 538.8 622.2 564.5
  Water + [BMim][dca] 1 472.2 472.1 508.7 508.7 543.3 543.3
  T = 288.15 K T = 298.15 K T = 308.15 K              
0 675.1 675.1 687.9 687.9 697.6 697.6              
0.096 674.5 670.6 687.4 683.6 697.7 693.6              
0.1277 674.3 668.9 687.2 682 698.1 692.2              
0.2116 673.9 664 686.9 677.5 698.3 687.9              
0.3077 673.9 657.5 686.6 671.3 698.2 682.2              
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Figure 2.

Figure 2

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Ratio of internal pressure ratio (PFST/Pi) obtained using the thermodynamic method and the FST method. Solid line is a guide for eye.

3.4. Thermophysical Parameters, Molecular Interactions, and FST

Some other important physical parameters, such as energy of vaporization (ΔEV), heat of vaporization (ΔH), cohesive energy density (ced), surface tension (σ), and polarity index (n), have been evaluated using FST in the given range of concentrations and temperatures. The obtained results of ΔEV, ΔH, and σ are reported in Table S3. In the current work, σ has been used in the calculation of the ultrasonic velocity using eqs 14–17. The importance of these parameters to understand the nature of molecular interactions prevalent in the various mixtures has been reported by many workers.26,32,53−55 The energy of vaporization (ΔEV) is defined as the energy utilized in the evaporation of one mol of the liquid by breaking all the associated forces, whereas the enthalpy of vaporization (ΔH) is a sum of the pressure-volume work done and the internal energy of the system. In the current study, these parameters are evaluated for given mixtures at given temperatures and concentrations, as reported in Table S1. The portrayal of Table S1 indicates that both ΔEv and ΔHv represent a similar decrease with an increase in the concentration of water in the mixtures. The decreasing trend in both of these parameters hints at a decrease in the cohesive forces with the addition of the first component.56 The ced represents both specific and nonspecific intermolecular interactions, which overall contribute to the total intermolecular interaction energies, whereas internal pressure counts only the specific interactions present in the liquid state. In the present study, ced is computed for eight IL mixtures, as reported in Table 5. The perusal of Table 5 indicates that ced decreases with a decrease in concentration of the ILs in the given mixtures at all temperatures. The decreasing values of ced suggest a decrease in the cohesion present within the liquid mixture and, hence, an increase in the molecular interactions.57 The Hildebrand solubility parameter (δ) is the square root of the ced and is important to access the intermolecular interactions in the liquid system. Several workers58,59 have calculated δ for organic liquid mixtures and polymer mixtures to analyze their solubility. Recently, Pandey and co-worker32,50 computed δ for pure ILs. In the present study, δ is calculated for given mixtures of water at various concentrations and temperatures, as reported in Table 5. The portrayal of Table 5 indicates that δ values gradually decrease in the water-rich region in these binary mixtures. This indicates that the solute–solute (A–A) interactions dominate over the solute–solvent (A–B) interactions in the water-rich region of the mixtures.

Table 5. Cohesive Energy Density (ced) and Solubility Parameters (δ) for Eight Binary Mixtures at Different Temperatures.

X1 ced (kJ/m3) δ (kJ/m3)1/2 ced (kJ/m3) δ (kJ/m3)1/2 ced (kJ/m3) δ (kJ/m3)1/2 X1 ced (kJ/m3) δ (kJ/m3)1/2 ced (kJ/m3) δ (kJ/m3)1/2 ced (kJ/m3) δ (kJ/m3)1/2
  Water + [BMim][dca]   Water + [EEPy][ESO4]
  T = 288.15 K T = 298.15 K T = 308.15 K   T = 288.15 K T = 298.15 K T = 308.15 K
0 66.51 815.52 67.65 822.49 68.76 829.2 0 62.43 790.1 77.11 878.11 79.49 891.56
0.1088 66.54 815.74 67.69 822.74 68.8 829.47 0.0987 62.48 790.44 77.23 878.8 79.63 892.36
0.1227 66.55 815.76 67.69 822.76 68.81 829.51 0.1089 62.54 790.8 77.23 878.82 79.63 892.38
0.2017 66.57 815.93 67.72 822.95 68.84 829.73 0.2048 62.65 791.53 77.4 879.75 79.81 893.38
0.2943 66.59 816.06 67.75 823.13 68.88 829.96 0.3037 62.77 792.3 77.52 880.46 79.96 894.2
0.3952 66.59 816.05 67.77 823.2 68.91 830.11 0.3979 62.94 793.35 77.65 881.2 80.09 894.91
0.503 66.55 815.81 67.75 823.1 68.91 830.15 0.4922 63.11 794.42 77.74 881.73 80.21 895.6
0.5985 66.42 814.99 67.65 822.49 68.85 829.74 0.6018 63.3 795.59 77.71 881.55 80.22 895.66
0.7032 66.03 812.6 67.33 820.58 68.6 828.25 0.7084 63.47 796.71 77.34 879.4 79.93 894.06
0.805 64.91 805.64 66.37 814.66 67.78 823.29 0.8029 63.45 796.58 76.02 871.89 78.84 887.94
0.9006 61.75 785.83 63.63 797.71 65.44 808.92 0.8984 62.51 790.63 71.35 844.69 74.86 865.2
0.9503 57.5 758.27 59.92 774.08 62.22 788.8 0.9493 60.41 777.22 64.28 801.77 68.87 829.86
1 47.22 687.14 50.87 713.26 54.33 737.07 1 54.33 737.07 47.22 687.14 54.33 737.07
  Water + [BMim][TfO]   Water + [BmPy][TfO]
  T = 288.15 K T = 298.15 K T = 308.15 K   T = 288.15 K T = 298.15 K T = 308.15 K
0 58.52 764.95 59.39 770.68 60.21 775.95 0 58.94 767.71 59.8 773.28 60.62 778.6
0.1348 58.64 765.76 59.53 771.54 60.35 776.87 0.0794 59.02 768.24 59.87 773.76 60.7 779.09
0.2028 58.71 766.24 59.6 772.03 60.43 777.4 0.1517 59.1 768.77 59.94 774.18 60.77 779.53
0.2056 58.72 766.26 59.61 772.07 60.44 777.42 0.2502 59.22 769.51 60.03 774.77 60.86 780.15
0.3083 58.82 766.95 59.72 772.81 60.57 778.24 0.3515 59.35 770.4 60.14 775.5 60.98 780.93
0.4985 59.05 768.46 59.99 774.55 60.87 780.2 0.4528 59.5 771.37 60.27 776.34 61.13 781.84
0.6062 59.16 769.13 60.14 775.49 61.06 781.42 0.5628 59.68 772.53 60.43 777.36 61.31 782.99
  Water + [BMim][TfO]   Water + [BmPy][TfO]
  T = 288.15 K T = 298.15 K T = 308.15 K   T = 288.15 K T = 298.15 K T = 308.15 K
0.7015 59.17 769.25 60.23 776.1 61.23 782.47 0.6561 59.81 773.35 60.55 778.17 61.47 784.03
0.8064 58.91 767.55 60.15 775.59 61.32 783.05 0.7494 59.82 773.43 60.61 778.53 61.6 784.88
0.8998 57.42 757.74 59.1 768.75 60.67 778.93 0.8383 59.37 770.52 60.33 776.72 61.5 784.22
0.9309 56.16 749.4 58.14 762.53 60.01 774.66 0.9201 57.37 757.46 58.86 767.23 60.49 777.73
0.9548 54.48 738.11 56.82 753.78 59.02 768.24 0.9603 54.49 738.18 56.65 752.65 58.81 766.91
1 47.22 687.14 50.87 713.26 54.33 737.07 1 47.22 687.14 50.87 713.26 54.33 737.07
  Water + [BmPyr][TfO]   Water + [Hmim][dca]
  T = 288.15 K T = 298.15 K T = 308.15 K   T = 288.15 K T = 298.15 K T = 308.15 K
0 60.66 778.86 60.66 778.86 62.43 790.1 0 68.76 829.2 62.8 792.45 63.78 798.65
0.0559 60.7 779.11 60.7 779.11 62.48 790.44 0.0785 68.8 829.47 62.87 792.89 63.85 799.09
0.1084 60.75 779.43 60.75 779.43 62.54 790.8 0.1191 68.81 829.51 62.91 793.14 63.89 799.34
0.2076 60.86 780.12 60.86 780.12 62.65 791.53 0.2124 68.84 829.73 63.01 793.78 64 799.98
0.2997 60.97 780.83 60.97 780.83 62.77 792.3 0.3055 68.88 829.96 63.13 794.55 64.12 800.75
0.408 61.12 781.76 61.12 781.76 62.94 793.35 0.4019 68.91 830.11 63.28 795.5 64.27 801.7
0.5038 61.25 782.63 61.25 782.63 63.11 794.42 0.5096 68.91 830.15 63.49 796.79 64.48 803.01
0.6003 61.37 783.42 61.37 783.42 63.3 795.59 0.6069 68.85 829.74 63.71 798.19 64.72 804.46
0.7052 61.42 783.68 61.42 783.68 63.47 796.71 0.7123 68.6 828.25 63.96 799.74 64.99 806.16
0.8095 61.06 781.43 61.06 781.43 63.45 796.58 0.8067 67.78 823.29 64.06 800.4 65.17 807.29
0.9018 59.29 770 59.29 770 62.51 790.63 0.9031 65.44 808.92 63.28 795.49 64.68 804.26
0.9533 55.99 748.27 55.99 748.27 60.41 777.22 0.9499 62.22 788.8 61.2 782.33 63.06 794.1
1 47.22 687.14 47.22 687.14 54.33 737.07 1 54.33 737.07 50.87 713.26 54.33 737.07
  Water + [MPy][MSO4]   Water + [BMim][dca]
  T = 288.15 K T = 298.15 K T = 308.15 K   T = 288.15 K T = 298.15 K T = 308.15 K
0 94.36 971.38 94.36 971.38 98.26 991.26 0.3942 67.75 67.75 823.09 836.96 70.05 836.96
0.0574 94.33 971.24 94.33 971.24 98.23 991.11 0.4952 67.78 67.78 823.27 837.34 70.11 837.34
0.073 94.32 971.17 94.32 971.17 98.22 991.04 0.5023 67.78 67.78 823.27 837.36 70.12 837.36
0.1111 94.29 971.02 94.29 971.02 98.18 990.88 0.6047 67.72 67.72 822.94 837.4 70.12 837.4
0.1927 94.21 970.63 94.21 970.63 98.11 990.5 0.6137 67.71 67.71 822.86 837.36 70.12 837.36
0.2941 94.04 969.76 94.04 969.76 97.94 989.66 0.7061 67.42 67.42 821.1 836.3 69.94 836.3
0.4005 93.72 968.08 93.72 968.08 97.63 988.08 0.7177 67.35 67.35 820.69 836.03 69.89 836.03
0.4996 93.2 965.39 93.2 965.39 97.14 985.57 0.7571 67.04 67.04 818.8 834.71 69.67 834.71
0.6077 92.11 959.72 92.11 959.72 96.09 980.27 0.8208 66.1 66.1 813.01 830.5 68.97 830.5
0.7064 90.16 949.55 90.16 949.55 94.25 970.85 0.8468 65.44 65.44 808.97 827.51 68.48 827.51
0.8058 86.02 927.48 86.02 927.48 90.35 950.51 0.9034 62.96 62.96 793.48 816 66.58 816
0.901 76.7 875.76 76.7 875.76 81.62 903.46 0.904 62.92 62.92 793.23 815.81 66.56 815.81
0.9497 66.83 817.51 66.83 817.51 72.47 851.28 0.9492 58.72 58.72 766.32 795.77 63.33 795.77
0.9645 62.46 790.34 62.46 790.34 68.43 827.21 0.9507 58.52 58.52 765.01 794.79 63.17 794.79
1 47.22 687.14 47.22 687.14 54.33 737.07 0.9517 58.39 58.39 764.11 794.12 63.06 794.12
  Water + [BMim][dca] 1 47.22 684.11 54.33 737.07 54.33 737.07
  T = 288.15 K T = 298.15 K T = 308.15 K              
0 67.51 821.67 67.51 821.67 69.76 835.25              
0.096 67.57 822.01 67.57 822.01 69.83 835.62              
0.1277 67.59 822.13 67.59 822.13 69.85 835.75              
0.2116 67.64 822.44 67.64 822.44 69.91 836.12              
0.3077 67.7 822.78 67.7 822.78 69.98 836.55              
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4. Conclusions

In the current study, density, internal pressure, ultrasonic velocity, and some important thermophysical properties of eight binary mixtures of water and ILs have been evaluated at three different temperatures using FST. The very low mean percentage deviation of computed density values (Table 3) and the PFST/Pi ratio being closer to unity (Figure 2) for all the mixtures under study confirm the applicability of FST for the evaluation of density and internal pressure of the liquid mixtures. The reasonable agreement of the Auerbach relation (UA), Singh–Pandey–Sanguri relation (USP), and modified Auerbach relation (UMA) with the literature values (U*) validates the U–d–σ correlation for the given systems. The variations of the solubility parameter (δ) in the given concentration at different temperatures indicate the dominance of A–A interactions over A–B in the water-rich region of the water + IL mixtures.

Acknowledgments

The authors are thankful to Chitkara University, Punjab, India, for providing facilities concerning data analysis and graphic tools. The authors extend their appreciation to the Researchers Supporting Project Number (RSPD2024R999), King Saud University, Riyadh, Saudi Arabia. The authors express their gratitude to Manipal Institute of Technology, MAHE Bengaluru Campus for providing them with facilities and financial assistance.

Supporting Information Available

The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/acsomega.4c00520.

  • Computed values of ultrasonic velocity using Auerbach (UA), Alternberg (UAR), Singh–Pandey–Sanguri (USP), and modified Auerbach (UMA) relations; volume expansivity (α) and isothermal compressibility (KT); and internal pressure (Pi and PFST), energy of vaporization (ΔEV), heat of vaporization (ΔH), surface tension (σ) for eight binary mixtures of water, and ILs at different temperatures (PDF)

The authors declare no competing financial interest.

Supplementary Material

ao4c00520_si_001.pdf (151.1KB, pdf)

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