# Densities, Apparent Molar Volume, Expansivities, Hepler’s Constant, and Isobaric Thermal Expansion Coefficients of the Binary Mixtures of Piperazine with Water, Methanol, and Acetone atT = 293.15 to 328.15 K

Authors: Qazi Mohammed Omar; Jean-Noël Jaubert; Javeed A. Awan
Journal: International Journal of Chemical Engineering
 (2018)

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## Abstract

The properties of 3 binary mixtures containing piperazine were investigated in this work. In a first step, the densities for the two binary mixtures (piperazine + methanol) and (piperazine + acetone) were measured in the temperature range of 293.15 to 328.15 K and 293.15 to 323.15 K, respectively, at atmospheric pressure by using a Rudolph research analytical density meter (DDM 2911). The concentration of piperazine in the (piperazine + methanol) mixture was varied from 0.6978 to 14.007 mol/kg, and the concentration of piperazine in the (piperazine + acetone) mixture was varied from 0.3478 to 1.8834 mol/kg. On the other hand, the density data for the (piperazine + water) mixture were taken from the literature in the temperature range of 298.15 to 328.15 K. In a second step, for the 3 investigated systems, the apparent molar volume (Vϕ) and the limiting apparent molar volume (Vϕ0) at infinite dilution were calculated using the Redlich–Mayer equation. The limiting apparent molar volumes (Vϕ0) were used to study the influence of the solute-solvent and solute-solute interactions. The temperature dependency of the apparent molar volumes was used to estimate the apparent molar expansibility, Hepler’s constant ∂2Vϕ0/∂T2P, and isobaric thermal expansion coefficients αP.


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## Body

## 1. Introduction

Information about the physical properties of solutions in the vast range of solute concentrations at different temperatures is greatly important for physicochemical processes (separation process, crystallization, vaporization, desalination, waste aqua treatment, environment protection, oil retrieval, etc.) and the natural environment [1, 2].The apparent molar volumes are particularly relevant to determine the molecular interactions (solute to solute, solute to solvent, and solvent to solvent) happening in solutions [3]. Also, the apparent molar volumes of solutions at infinite dilution are useful to obtain information regarding solute to solvent and solvent to solvent interactions. However, the apparent molal volumes depend on strength of solution that can be used for the determination of solute to solute interactions [4–6].The thermophysical properties of piperazine + water is important for the design of gas processing technology [7] like in the treatment of natural gas having significant amount of H2S and in processing of refinery waste gases as well as synthesis gas for manufacturing of NH3, where solution of piperazine + water is used as a solvent for the removal of acidic gases (carbon dioxide and hydrogen sulfide). The highly effective removal of CO2 from industrial gases can also be performed by mixing piperazine with an alcohol such as the 2-amino-2-methyl-1-propanol [7, 8], which suggests that the alcoholic solutions of piperazine are also important in many separation processes. As another example, the separation of o- and p-chlorobenzoic acids from their eutectic blend usually uses a mixture of (piperazine + methanol) [9] as the solvent. In chemical processes, piperazine is present with crude products and has to be separated. In such a case, acetone is classically used due to its stronger molecular interaction with piperazine as compared to the higher molecular weight ketone [10].In conclusion, the thermophysical properties of the 3 binary systems (piperazine + water), (piperazine + acetone), and (piperazine + methanol) are involved in many separation processes and thus need to be known. Consequently, it was decided to measure the densities of the (piperazine + acetone) and (piperazine + methanol) systems in the temperature range of 293.15 to 328.1 K and 293.15 to 323.15 K, respectively, since they are not available in the open literature. The concentration of piperazine was varied from 0.6978 to 14.007 mol/kg and from 0.3478 to 1.8834 mol/kg for methanol and acetone, respectively. The density data for (piperazine + water) were taken from literature in the temperature range of 298.15 to 328.15 K. [11]. For the 3 investigated binary systems, the density data were used for the calculation of the apparent molar volume, limiting apparent molar volume, apparent molar expansivities, Hepler’s constant, and isobaric thermal expansion coefficient.


## 2. Experimental Work

### 2.1. Materials

The chemicals used in this work are piperazine (purity ≥ 99%), methanol (≥99.4%), and acetone (≥99.8%). They were provided by Sigma-Aldrich (Germany) and were used without any further purification or treatment. The purity of these chemicals used along with their source and CAS number are tabulated in Table1. The deionized water has been prepared in lab through alfa-pore machine (WAP-4).Table 1
List of chemicals used in this work.
Chemicals
Purity
Source
CAS number
Piperazine
≥99%
Merck
110-85-0
Methanol
≥99.4%
Merck
67-56-1
Acetone
≥99.8%
Merck
67-64-1


### 2.2. Measurement of the Density

An analytical digital vibrating glass U-tube densitometer (DDM-2911, Rudolph) with an accuracy of 0.05 kg/m3 was used to measure the density of the 2 mixtures: piperazine + methanol and piperazine + acetone. A schematic diagram of the used densitometer is illustrated in Figure 1. The binary mixtures were prepared by weight using a Sartorius analytical weight balance with an uncertainty of ±0.00029 g (the corresponding uncertainty in molality was ±0.0004 mol/kg). The densities of the pure solvents and their blends with piperazine were measured in a temperature range varying from 298.15 to 333.15 K. The calibration of the apparatus was conducted by comparing the density of air and water at 293.15 K and the barometric pressure. Air was provided through a suction tube filled with silica balls to ensure a provision of dry air, and double-distilled water was injected through a syringe into the density meter. Silica balls were regularly heated to remove the moisture content absorbed from the atmospheric air. Once calibrated, the U-tube densitometer was washed with distilled water and dried with acetone and air. The density data reported in this study are an average of at least three runs. To remove the air bubbles from the samples, all the solutions were sonicated by using a universal ultrasonic cleaner for 30 min. Later, the samples were stored in vials and placed into a desiccator for 10 minutes for proper mixing and settling. For each measurement, the tube was washed with water and dried with acetone. During the measurements, the air pump was always turned off to avoid irregularities due to vibrations.Figure 1
Schematic diagram of the experimental setup (analytical density meter (DDM 2911)).Table2 shows the densities of the pure solvents (methanol and acetone) measured in this study in the temperature range of 293.1–328.15 K along with values reported in the literature. An average deviation of approximately 0.03% is observed between both sets of data, which suggests that our data are consistent with previously measured densities and that our equipment is reliable.Table 2
Comparison of the densities of the pure solvents measured in this study with those reported previously at various temperatures and at atmospheric pressure with standard uncertainties:u (T) = ±0.01 K u (ρ) = ±0.1 kg/m3, u (m) = ±0.0004 mol/kg, and u (P) = ±0.002 atm.
Density (ρ0) kg/m3
Methanol
Acetone
T/K
This work
Lit. value
(Reference)
T/K
This work
Lit. value
(Reference)
293.15
791.6
791.9
(Papanastasiou and Ziogas [12])
293.15
789.9
790.02
(Kinart et al. [13])
791.65
(Gonfa et al. [14])
790.355
(Janz and Tomkins [15])
298.15
786.9
786.884
(Anwar and Yasmeen [16])
298.15
784.2
784.45
(Kinart et al. [13])
786.68
(Tu et al. [17])
784.638
(Janz and Tomkins [15])
303.15
782.2
782.158
(Anwar and Yasmeen [16])
303.15
778.5
778.7
(Fan et al. [18])
781.9
(Tu et al. [19])
778.57
(Enders et al. [20])
308.15
777.2
777.2
(Tu et al. [17])
308.15
773.0
773.0
(Hafez and Hartland [21])
777.414
(Anwar and Yasmeen [16])
773.065
(Janz and Tomkins [15])
313.15
772.4
772.3
(Tu et al. [19])
313.15
767.3
767.03
(Fan et al. [18])
772.64
(Anwar and Yasmeen [16])
767.21
(Estrada-Baltazar et al [22])
318.15
767.5
767.6
(Tu et al. [17])
318.15
761.6
761.288
(Janz and Tomkins [15])
767.844
(Anwar and Yasmeen [16])
761.3
(Hafez and Hartland [21])
323.15
762.7
762.7
(Bhuiyan and Uddin [23])
323.15
755.7
755.14
(Fan et al. [18])
763.028
(Anwar and Yasmeen [16])
755.31
(Estrada-Baltazar et al [22])
328.15
757.7
759.2
(Cai et al. [24])
755.54
(Wu et al. [25])


## 2.1. Materials

The chemicals used in this work are piperazine (purity ≥ 99%), methanol (≥99.4%), and acetone (≥99.8%). They were provided by Sigma-Aldrich (Germany) and were used without any further purification or treatment. The purity of these chemicals used along with their source and CAS number are tabulated in Table1. The deionized water has been prepared in lab through alfa-pore machine (WAP-4).Table 1
List of chemicals used in this work.
Chemicals
Purity
Source
CAS number
Piperazine
≥99%
Merck
110-85-0
Methanol
≥99.4%
Merck
67-56-1
Acetone
≥99.8%
Merck
67-64-1


## 2.2. Measurement of the Density

An analytical digital vibrating glass U-tube densitometer (DDM-2911, Rudolph) with an accuracy of 0.05 kg/m3 was used to measure the density of the 2 mixtures: piperazine + methanol and piperazine + acetone. A schematic diagram of the used densitometer is illustrated in Figure 1. The binary mixtures were prepared by weight using a Sartorius analytical weight balance with an uncertainty of ±0.00029 g (the corresponding uncertainty in molality was ±0.0004 mol/kg). The densities of the pure solvents and their blends with piperazine were measured in a temperature range varying from 298.15 to 333.15 K. The calibration of the apparatus was conducted by comparing the density of air and water at 293.15 K and the barometric pressure. Air was provided through a suction tube filled with silica balls to ensure a provision of dry air, and double-distilled water was injected through a syringe into the density meter. Silica balls were regularly heated to remove the moisture content absorbed from the atmospheric air. Once calibrated, the U-tube densitometer was washed with distilled water and dried with acetone and air. The density data reported in this study are an average of at least three runs. To remove the air bubbles from the samples, all the solutions were sonicated by using a universal ultrasonic cleaner for 30 min. Later, the samples were stored in vials and placed into a desiccator for 10 minutes for proper mixing and settling. For each measurement, the tube was washed with water and dried with acetone. During the measurements, the air pump was always turned off to avoid irregularities due to vibrations.Figure 1
Schematic diagram of the experimental setup (analytical density meter (DDM 2911)).Table2 shows the densities of the pure solvents (methanol and acetone) measured in this study in the temperature range of 293.1–328.15 K along with values reported in the literature. An average deviation of approximately 0.03% is observed between both sets of data, which suggests that our data are consistent with previously measured densities and that our equipment is reliable.Table 2
Comparison of the densities of the pure solvents measured in this study with those reported previously at various temperatures and at atmospheric pressure with standard uncertainties:u (T) = ±0.01 K u (ρ) = ±0.1 kg/m3, u (m) = ±0.0004 mol/kg, and u (P) = ±0.002 atm.
Density (ρ0) kg/m3
Methanol
Acetone
T/K
This work
Lit. value
(Reference)
T/K
This work
Lit. value
(Reference)
293.15
791.6
791.9
(Papanastasiou and Ziogas [12])
293.15
789.9
790.02
(Kinart et al. [13])
791.65
(Gonfa et al. [14])
790.355
(Janz and Tomkins [15])
298.15
786.9
786.884
(Anwar and Yasmeen [16])
298.15
784.2
784.45
(Kinart et al. [13])
786.68
(Tu et al. [17])
784.638
(Janz and Tomkins [15])
303.15
782.2
782.158
(Anwar and Yasmeen [16])
303.15
778.5
778.7
(Fan et al. [18])
781.9
(Tu et al. [19])
778.57
(Enders et al. [20])
308.15
777.2
777.2
(Tu et al. [17])
308.15
773.0
773.0
(Hafez and Hartland [21])
777.414
(Anwar and Yasmeen [16])
773.065
(Janz and Tomkins [15])
313.15
772.4
772.3
(Tu et al. [19])
313.15
767.3
767.03
(Fan et al. [18])
772.64
(Anwar and Yasmeen [16])
767.21
(Estrada-Baltazar et al [22])
318.15
767.5
767.6
(Tu et al. [17])
318.15
761.6
761.288
(Janz and Tomkins [15])
767.844
(Anwar and Yasmeen [16])
761.3
(Hafez and Hartland [21])
323.15
762.7
762.7
(Bhuiyan and Uddin [23])
323.15
755.7
755.14
(Fan et al. [18])
763.028
(Anwar and Yasmeen [16])
755.31
(Estrada-Baltazar et al [22])
328.15
757.7
759.2
(Cai et al. [24])
755.54
(Wu et al. [25])


## 3. Results and Discussion

The densities of all three binary mixtures (piperazine + water), (piperazine + methanol), and (piperazine + acetone) as a function of the molality of piperazine and temperature are presented in Table3 and plotted in Figures 2–4. The experiments cover the commercially significant concentration range of piperazine with water, methanol, and acetone, that is, concentrations that are important for industrial applications like the design of gas processing technology, liquid-liquid extraction, and leaching. More specifically, the mixtures of piperazine + methanol were prepared in a concentration range of 2.187 wt.% to 30.978 wt.% (0.6978 mol/kg to 14.007 mol/kg). Similarly, mixtures of piperazine + acetone were prepared in concentration range from 1.98 wt.% to 9.86 wt.% (0.3478 mol/kg to 1.8834 mol/kg). It is observed that the density of the mixture increases with an increase in the concentration of piperazine. However, the density decreases with an increase in the temperature.Table 3
Densities (kg/m3) of the binary mixtures (piperazine + water), (piperazine + methanol), and (piperazine + acetone) as a function of the molality and temperature at atmospheric pressure. A global uncertainty calculation was performed on each point and the corresponding values are given in parentheses.
Temperature (K)
293.15
298.15
303.15
308.15
313.15
318.15
323.15
328.15
Molality (mol/kg) of piperazine
Binary system densities (kg/m3) with global uncertainty (kg/m3) in parentheses
System (piperazine + water) (Muhammad et al. [11])
0.9838
—
998.3
996.9
995.2
993.4
991.4
989.2
986.8
3.0226
—
999.4
997.9
996.3
994.4
992.4
990.1
987.8
6.4138
—
1001.3
999.8
998.0
996.1
994.0
991.7
989.3
System (piperazine + methanol) (this work)
0.6978
805.8 (0.02)
801.2 (0.01)
796.4 (0.02)
791.3 (0.007)
786.5 (0.02)
781.7 (0.01)
776.6 (0.01)
771.3 (0.01)
1.4000
817.4 (0.04)
812.9 (0.02)
808.2 (0.03)
803.5 (0.01)
798.6 (0.02)
793.6 (0.01)
788.4 (0.02)
783.2 (0.01)
2.2148
829.6 (0.03)
825.2 (0.02)
820.5 (0.03)
815.7 (0.02)
810.9 (0.02)
805.9 (0.02)
800.8 (0.02)
795.6 (0.02)
3.0544
840.7 (0.04)
836.3 (0.02)
831.7 (0.04)
827.0 (0.04)
822.1 (0.03)
817.2 (0.03)
812.1 (0.03)
806.9 (0.02)
3.7151
849.0 (0.04)
844.6 (0.02)
840.0 (0.04)
835.3 (0.04)
830.5 (0.04)
825.6 (0.03)
820.5 (0.04)
815.4 (0.02)
5.1007
862.6 (0.05)
858.2 (0.03)
853.7 (0.04)
849.0 (0.05)
844.5 (0.04)
839.6 (0.04)
834.6 (0.04)
829.5 (0.03)
5.9003
870.3 (0.05)
866.0 (0.03)
861.5 (0.05)
856.9 (0.05)
852.1 (0.05)
847.2 (0.04)
842.2 (0.05)
837.1 (0.04)
7.4725
881.4 (0.06)
877.1 (0.03)
872.6 (0.05)
868.0 (0.06)
863.2 (0.06)
858.4 (0.05)
853.4 (0.06)
848.3 (0.04)
9.2198
893.9 (0.06)
889.6 (0.04)
885.2 (0.05)
880.6 (0.06)
875.8 (0.06)
871.0 (0.05)
866.1 (0.07)
861.1 (0.05)
14.007
912.6 (0.06)
908.4 (0.05)
903.9 (0.06)
899.3 (0.06)
894.6 (0.07)
889.6 (0.05)
884.2 (0.07)
879.3 (0.06)
System (piperazine + acetone) (this work)
0.3478
792.4 (0.01)
786.5 (0.005)
780.8 (0.01)
774.9 (0.006)
768.8 (0.002)
762.7 (0.002)
756.3 (0.002)
—
0.8416
796.7 (0.02)
791.0 (0.02)
785.2 (0.02)
779.3 (0.02)
773.3 (0.008)
767.2 (0.01)
760.9 (0.01)
—
1.0951
799.3 (0.03)
793.5 (0.02)
787.7 (0.03)
781.6 (0.02)
775.5 (0.01)
769.1 (0.02)
762.7 (0.02)
—
1.3359
802.3 (0.03)
797.0 (0.03)
790.7 (0.03)
784.6 (0.03)
778.4 (0.02)
772.1 (0.02)
765.6 (0.02)
—
1.8834
807.5 (0.03)
802.0 (0.04)
795.9 (0.03)
789.9 (0.03)
784.1 (0.02)
778.2 (0.03)
772.1 (0.03)
—Figure 2
Density of the (piperazine + water) system as a function of piperazine molality at various temperatures.Figure 3
Density of the (piperazine + methanol) system as a function of piperazine molality at various temperatures.Figure 4
Density of the (piperazine + acetone) system as a function of piperazine molality at various temperatures.The apparent molar volumes [26] (Vϕ) (in m3/mol) of piperazine were calculated from the densities of the solutions by using the equation given below:(1)Vϕ=Mρ+ρ0−ρm⋅ρ⋅ρ0,where m is the molality of piperazine (mol/kg), ρ and ρ0 are densities (in kg/m3) of the solution and pure solvent, respectively, and M is the molar mass of piperazine (in kg/mol). The apparent molar volume (Vϕ) of all three binary mixtures (piperazine + water), (piperazine + methanol), and (piperazine + acetone) calculated from Equation (1) as a function of molality of piperazine and temperature is tabulated in Table 4 and plotted in Figures 5–7 (denoted by markers). Figures 5–7 show that Vϕ values rise with rise in temperature for each binary mixture, highlighting that the overall order of the structure is improved or increased in solution with rising temperature [27]. The influence of the molality depends on the studied system, that is, the apparent molar volumes may rise, decrease, or progress through a maximum. Our data were correlated with the Redlich–Mayer equation [28]:(2)Vϕ=Vϕ0+Svm+Bv⋅m,where Vϕ0 is the limiting apparent molar volume of the piperazine mixtures and Sv and Bv are two regression parameters. Figures 6 and 7 highlight that our data are accurately correlated with such a simple model. The corresponding values of Vϕ0, Sv, and Bv are tabulated in Table 5. From this table, notably, the Vϕ0 values rise with rise in temperature for each binary mixture. As highlighted by [29], this behavior characterizes the presence of strong solute to solvent interactions that are strengthened with the rise in temperature. It is worth noting that this behavior was also observed for many systems. We can cite the (methanol + methyl acetate) system reviewed by [30], the (methanol + ethyl acetate), the (ethanol + methyl acetate) and (ethanol + ethyl acetate) systems studied by [29], the (methanol + isopropyl alcohol), the (methyl salicylate + DMSO) and (hydroxamic acid + DMSO) examined by [31]. The Vϕ0 values of the mixtures rise in the following order: (piperazine + methanol) < (piperazine + water) < (piperazine + acetone), which could be due—as explained by [29]—to an enhancement in the strengths of the solute to solvent interactions. This enhancement results in an increase of contraction in the volume.Table 4
Apparent molar volume (m3/mol) of the binary mixtures (piperazine + water), (piperazine + methanol), and (piperazine + acetone) as a function of the molality and temperature at atmospheric pressure with the standard uncertainty: u (Vϕ) = ±0.35 × 10−6 m3/mol.
Temperature (K)
293.15
298.15
303.15
308.15
313.15
318.15
323.15
328.15
Molality (mol/kg) of piperazine
Binary system apparent molar volumes 106 × Vϕ (m3/mol)
System (piperazine + water)
0.9838
—
85.02
85.16
85.32
85.49
85.67
85.88
86.13
3.0226
—
85.43
85.57
85.72
85.89
86.08
86.28
86.50
6.4138
—
85.37
85.52
85.68
85.87
86.06
86.27
86.50
System (piperazine + methanol)
0.6978
75.02
75.24
75.50
75.84
76.07
76.38
77.32
78.39
1.4000
76.96
77.05
77.18
77.15
77.48
77.97
78.69
79.32
2.2148
77.69
77.84
78.02
78.13
78.44
78.83
79.39
79.88
3.0544
78.29
78.46
78.65
78.78
79.11
79.48
79.98
80.41
3.7151
78.48
78.66
78.86
79.03
79.31
79.67
80.11
80.49
5.1007
79.49
79.70
79.93
80.13
80.30
80.66
81.07
81.45
5.9003
79.61
79.82
80.04
80.24
80.54
80.90
81.29
81.68
7.4725
80.52
80.75
81.00
81.23
81.55
81.89
82.29
82.68
9.2198
80.69
80.92
81.18
81.43
81.77
82.11
82.47
82.84
14.007
82.43
82.71
83.01
83.31
83.66
84.07
84.55
84.93
System (piperazine + acetone)
0.3478
97.37
98.38
99.39
102.11
104.76
107.33
110.96
—
0.8416
95.20
95.88
96.72
98.09
99.43
100.86
102.50
—
1.0951
94.14
94.91
95.75
97.22
98.65
100.24
101.94
—
1.3359
92.75
92.69
94.15
95.49
96.78
98.16
99.71
—
1.8834
92.02
92.32
93.37
94.36
95.06
95.77
96.69
—Figure 5
Apparent molar volume (Vϕ) of the binary mixture (piperazine + water) as a function of piperazine molality at different temperatures.Figure 6
Apparent molar volume (Vϕ) of the binary mixture (piperazine + methanol) as a function of piperazine molality at different temperatures. The correlations performed with the Redlich–Mayer equation are plotted as solid/dashed lines.Figure 7
Apparent molar volume (Vϕ) of the binary mixture (piperazine + acetone) as a function of piperazine molality at different temperatures. The correlations performed with the Redlich–Mayer equation are plotted as solid/dashed lines.Table 5
Values of the limiting apparent molar volume (Vϕ0) along with the Sv and Bv parameters to be used in the Redlich–Mayer equation for each of the 3 binary systems as a function of temperature.
Temperature (K)
293.15
298.15
303.15
308.15
313.15
318.15
323.15
328.15
System (piperazine + water)
106 ×  Vϕ0 (m3·mol−1)
—
83.78
83.94
84.11
84.30
84.49
84.71
85.07
106 × Sv (m3·kg1/2·mol−3/2)
—
1.65
1.61
1.60
1.57
1.56
1.53
1.39
106 × Bv (m3·kg·mol−2)
—
−0.40
−0.39
−0.39
−0.38
−0.37
−0.36
−0.33
System (piperazine + methanol)
106 × Vϕ0 (m3·mol−1)
72.57
72.75
72.99
73.27
73.57
74.01
75.48
77.05
106 × Sv (m3·kg1/2·mol−3/2)
3.72
3.69
3.63
3.47
3.45
3.38
2.58
1.67
106 × Bv (m3·kg·mol−2)
−0.31
−0.29
−0.27
−0.22
−0.21
−0.20
−0.05
0.11
System (piperazine + acetone)
106 × Vϕ0 (m3·mol−1)
102.68
104.72
105.89
111.82
117.01
121.20
129.50
—
106 × Sv (m3·kg1/2·mol−3/2)
−9.60
−11.54
−12.17
−19.19
−24.51
−27.62
−37.74
—
106 × Bv (m3·kg·mol−2)
1.26
1.68
2.14
4.66
6.21
6.67
10.19
—The values ofSV and BV are also tabulated in Table 5. The SV values are negative for (piperazine + acetone) and positive for the (piperazine + water) and (piperazine + methanol) systems at each temperature. The SV value decreases with rise in temperature for each binary system. The strength of the solute to solute interactions of each system increases in the following order: (piperazine + methanol) > (piperazine + water) > (piperazine + acetone). The solute to solute interaction decreases with an increase in temperature for each binary system. The BV values are negative for the (piperazine + methanol) and (piperazine + water) mixtures and positive for the (piperazine + acetone) mixture at each temperature. The BV values rise with rise in temperature for each binary system. The negative BV values show rise in solute to solute interactions for mixtures that is, (piperazine + water) and (piperazine + methanol). The positive BV values indicate strong solute to solute interactions for the (piperazine + acetone) system.The temperature dependence of the limiting apparent molar volume (Vϕ0) can be expressed in terms of the following equation [26]:(3)Vϕ0=A+BT+CT2,where A, B, and C are empirical parameters and T is the temperature. The limiting apparent molar expansibility (Eϕ0) can be obtained by differentiating Eq. (3) with respect to the temperature:(4)Eϕ0=∂Vϕ0∂T=B+2CT,The (Eϕ0) values for each binary system are tabulated in Table 6 which gives important information related to the solute to solvent interactions [32]. Table 6 depicts that, at each temperature, the (Eϕ0) values are positive for all three binary systems and decrease with rise in temperature.Table 6
The limiting apparent molar expansibility (Eϕ0) and isobaric thermal expansion coefficient αP.
Temperature (K)
293.15
298.15
303.15
308.15
313.15
318.15
323.15
328.15
Binary mixtures
106 × Eϕ0 (m3·mol−1·K−1)
Piperazine + water
—
2.64
3.24
3.84
4.44
5.04
5.64
6.24
Piperazine + methanol
−0.04
0.03
0.10
0.16
0.23
0.29
0.35
0.41
Piperazine + acetone
25.38
46.78
68.18
89.58
110.98
132.38
153.78
—
103 × αP (K−1)
Piperazine + water
—
0.31
0.39
0.46
0.53
0.60
0.67
0.73
Piperazine + methanol
−0.39
0.28
0.95
1.62
2.28
2.93
3.52
4.08
Piperazine + acetone
2.47
4.47
6.44
8.01
9.48
10.92
11.88
—According to Hepler’s theory [33] the so-called Hepler’s constant, ∂2Vϕ0/∂T2, can be used to classify a solute into two categories, whether solute can act as a builder of structure or as a breaker of structure. If the ∂2Vϕ0/∂T2 value is positive, then the solute is favorable in development or making of structure. Conversely, if the ∂2Vϕ0/∂T2 value is negative, then the solute will act as a structure breaker. The values of ∂2Vϕ0/∂T2 are −0.33, −2.89, and −12.25 for the binary mixtures, that is, (piperazine + water), (piperazine + methanol), and (piperazine + acetone), respectively. Thus, piperazine acts as a structure breaker in solution. The proof for the effect of Hepler’s constant on microscopic structure is discussed in the literature [34].The isobaric thermal expansion coefficient,αp, of the solute was calculated using the apparent molar volume and apparent molar expansibility at infinite dilution data:(5)αp=1Vϕ0∂Vϕ0∂T=Eϕ0Vϕ0.The isobaric thermal expansion coefficient,αP, is also tabulated in Table 6. A higher value of αP was obtained for acetone, and lower value of αP was obtained for water.


## 4. Conclusion

In this work, new density data for 2 binary mixtures (piperazine + methanol) and (piperazine + acetone) were measured from 293.15 K to 328.15 K. It was found that the density of both the mixtures increases with increase in temperature but decreases with increase in concentration. Similarly,Vϕ values rise with increase in concentration of piperazine in methanol but decreases in case of acetone. Also, the apparent molar volume (Vϕ), limiting apparent molar volume (Vϕ0), apparent molar expansibility (Eϕ0), Hepler’s constant, and isobaric thermal expansion coefficient (αP) were calculated and reported in this work. The limiting apparent molar volume Vϕ0 increases with temperature, which highlights the strong interactions of the solute with the solvent. The positive apparent molar expansibility (Eϕ0) decreases with temperature, which indicates that the interactions increase with a rise in the temperature of the solution. The negative values of the Helper’s constant suggest that piperazine acts as a structure breaker in the solvent. The Redlich–Mayer equation was used to correlate the apparent molar volume with the standard deviation, u(Vϕ) = ±0.35 × 10−6 mol/m3.



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