# Study of Transport Properties of Tris (hydroxymethyl)aminomethane Hydrochloride in 20% (v/v) Acetone-Water System at303.15°K

Authors: Ajita Dixit
Journal: Journal of Applied Chemistry
 (2013)

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## Abstract

Viscometric properties of Tris-(hydroxymethyl)amino methane hydrochloride are measured in 20% (v/v) acetone-water system 303.15°K. The related parameters are the experimental values of viscosity (η) allow to determine relative viscosity (ηr), viscosity B-coefficient of the Jones-Dole equation, free energies of activation of viscous flow Δμ10≠ and Δμ20≠ per mole solvent, and solute, respectively. The excess molar volume, excess viscosity, excess Gibb’s free energy, and interaction parameter of Grunberg and Nissan have also been calculated. These studies are of great help in characterizing the structure and properties of solutions. The addition of an organic solvent to water brings about a sharp change in the solvation of ions.


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## Body

## 1. Introduction

The density is one of the key thermodynamic properties of electrolyte solutions and belongs with an equilibrium property, while the viscosity is one of the key transport properties of electrolyte solutions and belongs with a dynamic state property. Both of them rein dispensable basic data to engineering design and process optimization. Knowledge of viscometric properties studied in binary solvent system is useful for engineering design of new applications. Viscosities are important physico-chemical parameters widely studied in aqueous, aqueous-organic, and others [1]. The density and viscosity are important basic data used in chemical engineering designs, solution theory, and molecular thermodynamics [2]. Physicochemical processes of electrolyte solutions are of considerable interest due to their importance in numerous industrial processes.  Extensive experimental viscosity data are available for mixed-solvent system. In mixed-solvent electrolyte solutions, viscosity is affected by the concentration of electrolytes but also by the composition of the solvent. Even the viscosity of solvent mixtures may show a complex behavior and change significantly with composition. The knowledge of physico-chemical properties of liquid mixtures of two or more components are of theoretical and industrial importance due to their wide range of applicability as solvent media in various physico-chemical processes. In the present investigation following parameters are measured by Viscosity data of tris (hydroxymethyl)aminomethane hydrochloride is measured in 20% (v/v) acetone-water system 303.15°K is used to determine B-coefficient (B) and constant characteristic of ion-ion interactions (A) excess viscosity (VE), and excess molar free energy of activation of flow (GE). The interaction parameters Gruenberg and Nissan (d) were also calculated and reported. The parameters are analyzed to be evaluated to understand solute-solvent interaction.


## 2. Experiment

A stock solution of 0.100 M tris (hydroxymethyl)aminomethane hydrochloride is prepared in 20% (v/v) acetone-water solvent by direct weighing. Mass dilution technique used for preparation of other concentrations. The concentration of the solutions involved in the experiment was taken in range from 0.010 M to 0.100 M. Mass dilution technique was applied to prepare the solution of different concentration. Viscosities were measured by capillary viscometer of ostwald-Sprengel type (MaHaRaNa, Instruments MFG-Company (I am not related to MFG company commercially.), Ajmer India) with accuracy of 0.1 K. The Viscometer was calibrated with triple distilled water. Viscosity values were determined using the relation,(1)η=ρ(Kt-Lt),
where η  is a viscosity,  ρ  is  the  density of the liquid, t  is the flow time, and  K and L  are constants for given viscometer. The flow time was measured with digital stop watch with accuracy of  ± 0.01 sec. The K and L were obtained by measuring the flow time of triple distilled water at temperature 303.15°K. All measurements were carried out in triplicate.


## 3. Result and Discussion

### 3.1. Viscosities and Densities

The values of viscosities and densities are reported in Table1. Viscosities of the solution are increasing with the increase in concentration.Table 1
Viscosities and densities of tris (hydroxymethyl)aminomethane hydrochloride in 20% (v/v) acetone-water system at 303.15°K.
Concentration (mol dm−3)
Density (ρ) gm cm−3
Viscosity (η)  mPa s
0.0100
0.9436
0.9307
0.0200
0.9446
0.9678
0.0300
0.9458
1.0142
0.0400
0.9465
1.0344
0.0500
0.9475
1.1196
0.0600
0.9493
1.1671
0.0700
0.9506
1.2337
0.0800
0.9528
1.3015
0.0900
0.9541
1.3686
0.1000
0.9551
1.5004


### 3.2. Excess Molar Volume and Excess Viscosity

#### 3.2.1.     Excess Molar Volume

It is calculated from following expression:(2)VE=V-(X1V1+X2V2),
where V = Molar volume of Tris-(hydroxymethyl)amino methane hydrochloride solution, V1  =  Molar volume of mixed solvent, V2 =  Molar volume of solute, X1  =  Mole fraction of solvent, and X2  =  Mole fraction solute.The data are shown in Table2.Table 2
Excess molar volume and excess viscosity of tris (hydroxymethyl)aminomethane hydrochloride in 20% (v/v) acetone-water system at 303.15°K.
Concentration (mol dm−3)
Excess molar volume (VE)
Excess viscosity (ηE)
0.0100
1.2691
−0.0257
0.0200
0.2639
0.0113
0.0300
0.2360
0.0577
0.0400
0.2169
0.0780
0.0500
0.1935
0.1632
0.0600
0.1526
0.2107
0.0700
0.1206
0.2773
0.0800
0.0713
0.3452
0.0900
0.0396
0.4122
0.1000
0.0165
0.5441


#### 3.2.2. Excess Viscosity

The mixing of different compounds gives rise to solutions that generally do not behave ideally. The deviation from ideality is expressed by many thermodynamic properties, particularly by excess or residual extensive properties. Excess thermodynamic properties of mixtures correspond with the difference among the actual property and the property if the system behaves ideally and thus are useful in the study of molecular interactions and arrangements. In particular, they reflect the interactions that take place among solute-solute, solute-solvent, and solvent-solvent species. The excess viscosity (ηE) has been evaluated from the observed viscosity of the solution and that of its pure components using the relation [3]
(3)ηE=η-(X1η1+X2η2),
where η2 =  viscosity of solute.The data presented in Table2 show that the ηE values are positive in the entire concentration range at both the temperatures. This shows the presence of specific solute-solvent interactions such as hydrogen bond formation in these systems [4].


### 3.3.B-Coefficients

The Jones-Dole equation was used to analyze the viscosities following the equation [5]
(4)ηr=ηη1=1+Ac1/2+Bc,
where A = constant characteristic of ion-ion interactions, B = constant characteristic of ion-solvent interactions, and c =  molar concentrations.The values of relative viscosities are presented in Table3. The Falkenhagan coefficient A is also given for electrolytes. The B-coefficients obtained as slope of straight line have been recorded in Table 3.Table 3
B-coefficient, A, B of tris (hydroxymethyl)amino methane hydrochloride in 20% (v/v) acetone-water system at 303.15°K.
Concentration (mol dm−3)
B
c
A
B
0.0100
−0.0057
0.1031
−6.5591
0.0200
−0.0458
0.0300
−0.0959
0.0400
−0.1178
0.0500
−0.2099
0.0600
−0.2612
0.0700
−0.3331
0.0800
−0.4065
0.0900
−0.4789
0.1000
−0.6214Einstein [6] proposed an equation
(5)η=η1(1+2.5ν),
where ν  =  aggregate volume of the particles in a unit volume of solution.The previous equation describes the concentration dependence of the relative viscosity of solution of electrolyte. The coefficient ofν is 2.5ν. The term 2.5ν is taken to be valid for electrolyte and it is equivalent to the product in BC in the Jone-Doles equation. The data are presented in Table 3.


### 3.4. Activation Parameter

The viscosity data have also been analyzed on the basis of a transition state theory of relative viscosity as suggested by Rama Rao et al. [7]. The viscosity B-coefficient is expressed by equation
(6)B=(V-10-V-20)1000+[(V-10/1000)Δμ20≠-Δμ10≠]RT,
whereV-10   =  partial molar volume of solvent, V-20 =  partial molar volume of solute, Δμ10≠ =  free energy of activation per mole of solvent,   Δμ20≠ =  free energy of activation per mole of solute, B =  viscosity B-coefficient. R =  universal Gas constant (8.314 JK−1 mol−1), and T =  temperature (303.15°K).


#### 3.4.1.  Solvent Activation Parameter:Δμ10≠

Δ
μ
1
0
≠ is calculated from equation proposed by Eying et al. 										(7)Δμ10≠=RTIn(η1V-10HN),
where N = Avogadro’s number (6.023 × 1023 gm·atom), H =  Planck’s constant (6.626 × 10−34 J·sec), and η1 =  viscosity of solvent.


#### 3.4.2. Solvent Activation Parameter:Δμ20≠

Solvent activation parameter,Δμ20≠, is derived from following expression:
(8)Δμ20≠=Δμ10≠+(RTV-10)[1000B-V-10-V-20).The values of solventΔμ10≠ and solute  Δμ20≠ and activation free energies are given in Table 4.Table 4
Activation parameters of tris (hydroxymethyl)aminomethane hydrochloride in 20% (v/v) acetone-water system at 303.15°K.
Concentration (mol dm−3)
Δ
μ
1
0
≠  (in kJ mol−1) 105
Δ
μ
2
0
≠  (in kJ mol−1) 105
0.0100
2.6244
−6.4836
0.0200
2.6283
−6.4798
0.0300
2.6329
−6.4752
0.0400
2.6348
−6.4732
0.0500
2.6426
−6.4654
0.0600
2.6467
−6.4613
0.0700
2.6522
−6.4558
0.0800
2.6575
−6.4505
0.0900
2.6624
−6.4456
0.1000
2.6714
−6.4365According to Feakins model, the greater the value ofΔμ20≠ is, the greater the structure ability of the solute is. The values of Δμ20≠ are very large as compared to those of Δμ10≠, which suggests that the formation of transition state is accompanied with breaking and distortion of intermolecular bonds.


### 3.5. Excess Free Energy of Activation for Viscous FlowGE and Interaction Parameter d

#### 3.5.1. Excess Free Energy of Activation for Viscous FlowGE

The extra-thermodynamic property, excess Gibb’s free energy of activation of flow (GE) for the solution has been computed from the Eyring equation [8]
(9)GE=RT[InηV-(X1Inη1V1+X2Inη2V2)].The values are listed in Table5. The value of GE  increases with the increase in concentration of solute and also increases with the increase in temperature suggesting the interactions became stronger.Table 5
Excess molar free energy of activation of flow (GE) and Grunberg and Nissan       constant tris (hydroxymethyl)amino methane hydrochloride in 20% (v/v) acetone-water system at 303.15°K.
Concentration  (mol dm−3)
Excess molar free energy of activation of flow (GE)
Grunberg and Nissan (d)
0.0100
16.9678
0.0001
0.0200
56.1698
0.0004
0.0300
103.0463
−0.0012
0.0400
122.8588
−0.0007
0.0500
202.7112
−0.0003
0.0600
243.5637
−0.0002
0.0700
299.0243
−0.0002
0.0800
351.6797
−0.0003
0.0900
401.7946
−0.0001
0.1000
494.6975
−0.0001


#### 3.5.2. Interaction Parameterd

The impact of solute on viscosity is understood in terms of parameterd, which is regarded as a measure of the strength of interaction between components of solution. It has been estimated using relationship proposed by Gruenberg and Nissan [9]
(10)Inη=X1Inη1+X2Inη2+X1X2d,
where d  =  Grunberg and Nissan parameter:
(11)D∝WRT,
where W =  interaction energy.The values ofd are reported in Table 5.


## 3.1. Viscosities and Densities

The values of viscosities and densities are reported in Table1. Viscosities of the solution are increasing with the increase in concentration.Table 1
Viscosities and densities of tris (hydroxymethyl)aminomethane hydrochloride in 20% (v/v) acetone-water system at 303.15°K.
Concentration (mol dm−3)
Density (ρ) gm cm−3
Viscosity (η)  mPa s
0.0100
0.9436
0.9307
0.0200
0.9446
0.9678
0.0300
0.9458
1.0142
0.0400
0.9465
1.0344
0.0500
0.9475
1.1196
0.0600
0.9493
1.1671
0.0700
0.9506
1.2337
0.0800
0.9528
1.3015
0.0900
0.9541
1.3686
0.1000
0.9551
1.5004


## 3.2. Excess Molar Volume and Excess Viscosity

### 3.2.1.     Excess Molar Volume

It is calculated from following expression:(2)VE=V-(X1V1+X2V2),
where V = Molar volume of Tris-(hydroxymethyl)amino methane hydrochloride solution, V1  =  Molar volume of mixed solvent, V2 =  Molar volume of solute, X1  =  Mole fraction of solvent, and X2  =  Mole fraction solute.The data are shown in Table2.Table 2
Excess molar volume and excess viscosity of tris (hydroxymethyl)aminomethane hydrochloride in 20% (v/v) acetone-water system at 303.15°K.
Concentration (mol dm−3)
Excess molar volume (VE)
Excess viscosity (ηE)
0.0100
1.2691
−0.0257
0.0200
0.2639
0.0113
0.0300
0.2360
0.0577
0.0400
0.2169
0.0780
0.0500
0.1935
0.1632
0.0600
0.1526
0.2107
0.0700
0.1206
0.2773
0.0800
0.0713
0.3452
0.0900
0.0396
0.4122
0.1000
0.0165
0.5441


### 3.2.2. Excess Viscosity

The mixing of different compounds gives rise to solutions that generally do not behave ideally. The deviation from ideality is expressed by many thermodynamic properties, particularly by excess or residual extensive properties. Excess thermodynamic properties of mixtures correspond with the difference among the actual property and the property if the system behaves ideally and thus are useful in the study of molecular interactions and arrangements. In particular, they reflect the interactions that take place among solute-solute, solute-solvent, and solvent-solvent species. The excess viscosity (ηE) has been evaluated from the observed viscosity of the solution and that of its pure components using the relation [3]
(3)ηE=η-(X1η1+X2η2),
where η2 =  viscosity of solute.The data presented in Table2 show that the ηE values are positive in the entire concentration range at both the temperatures. This shows the presence of specific solute-solvent interactions such as hydrogen bond formation in these systems [4].


## 3.2.1.     Excess Molar Volume

It is calculated from following expression:(2)VE=V-(X1V1+X2V2),
where V = Molar volume of Tris-(hydroxymethyl)amino methane hydrochloride solution, V1  =  Molar volume of mixed solvent, V2 =  Molar volume of solute, X1  =  Mole fraction of solvent, and X2  =  Mole fraction solute.The data are shown in Table2.Table 2
Excess molar volume and excess viscosity of tris (hydroxymethyl)aminomethane hydrochloride in 20% (v/v) acetone-water system at 303.15°K.
Concentration (mol dm−3)
Excess molar volume (VE)
Excess viscosity (ηE)
0.0100
1.2691
−0.0257
0.0200
0.2639
0.0113
0.0300
0.2360
0.0577
0.0400
0.2169
0.0780
0.0500
0.1935
0.1632
0.0600
0.1526
0.2107
0.0700
0.1206
0.2773
0.0800
0.0713
0.3452
0.0900
0.0396
0.4122
0.1000
0.0165
0.5441


## 3.2.2. Excess Viscosity

The mixing of different compounds gives rise to solutions that generally do not behave ideally. The deviation from ideality is expressed by many thermodynamic properties, particularly by excess or residual extensive properties. Excess thermodynamic properties of mixtures correspond with the difference among the actual property and the property if the system behaves ideally and thus are useful in the study of molecular interactions and arrangements. In particular, they reflect the interactions that take place among solute-solute, solute-solvent, and solvent-solvent species. The excess viscosity (ηE) has been evaluated from the observed viscosity of the solution and that of its pure components using the relation [3]
(3)ηE=η-(X1η1+X2η2),
where η2 =  viscosity of solute.The data presented in Table2 show that the ηE values are positive in the entire concentration range at both the temperatures. This shows the presence of specific solute-solvent interactions such as hydrogen bond formation in these systems [4].


## 3.3.B-Coefficients

The Jones-Dole equation was used to analyze the viscosities following the equation [5]
(4)ηr=ηη1=1+Ac1/2+Bc,
where A = constant characteristic of ion-ion interactions, B = constant characteristic of ion-solvent interactions, and c =  molar concentrations.The values of relative viscosities are presented in Table3. The Falkenhagan coefficient A is also given for electrolytes. The B-coefficients obtained as slope of straight line have been recorded in Table 3.Table 3
B-coefficient, A, B of tris (hydroxymethyl)amino methane hydrochloride in 20% (v/v) acetone-water system at 303.15°K.
Concentration (mol dm−3)
B
c
A
B
0.0100
−0.0057
0.1031
−6.5591
0.0200
−0.0458
0.0300
−0.0959
0.0400
−0.1178
0.0500
−0.2099
0.0600
−0.2612
0.0700
−0.3331
0.0800
−0.4065
0.0900
−0.4789
0.1000
−0.6214Einstein [6] proposed an equation
(5)η=η1(1+2.5ν),
where ν  =  aggregate volume of the particles in a unit volume of solution.The previous equation describes the concentration dependence of the relative viscosity of solution of electrolyte. The coefficient ofν is 2.5ν. The term 2.5ν is taken to be valid for electrolyte and it is equivalent to the product in BC in the Jone-Doles equation. The data are presented in Table 3.


## 3.4. Activation Parameter

The viscosity data have also been analyzed on the basis of a transition state theory of relative viscosity as suggested by Rama Rao et al. [7]. The viscosity B-coefficient is expressed by equation
(6)B=(V-10-V-20)1000+[(V-10/1000)Δμ20≠-Δμ10≠]RT,
whereV-10   =  partial molar volume of solvent, V-20 =  partial molar volume of solute, Δμ10≠ =  free energy of activation per mole of solvent,   Δμ20≠ =  free energy of activation per mole of solute, B =  viscosity B-coefficient. R =  universal Gas constant (8.314 JK−1 mol−1), and T =  temperature (303.15°K).


### 3.4.1.  Solvent Activation Parameter:Δμ10≠

Δ
μ
1
0
≠ is calculated from equation proposed by Eying et al. 										(7)Δμ10≠=RTIn(η1V-10HN),
where N = Avogadro’s number (6.023 × 1023 gm·atom), H =  Planck’s constant (6.626 × 10−34 J·sec), and η1 =  viscosity of solvent.


### 3.4.2. Solvent Activation Parameter:Δμ20≠

Solvent activation parameter,Δμ20≠, is derived from following expression:
(8)Δμ20≠=Δμ10≠+(RTV-10)[1000B-V-10-V-20).The values of solventΔμ10≠ and solute  Δμ20≠ and activation free energies are given in Table 4.Table 4
Activation parameters of tris (hydroxymethyl)aminomethane hydrochloride in 20% (v/v) acetone-water system at 303.15°K.
Concentration (mol dm−3)
Δ
μ
1
0
≠  (in kJ mol−1) 105
Δ
μ
2
0
≠  (in kJ mol−1) 105
0.0100
2.6244
−6.4836
0.0200
2.6283
−6.4798
0.0300
2.6329
−6.4752
0.0400
2.6348
−6.4732
0.0500
2.6426
−6.4654
0.0600
2.6467
−6.4613
0.0700
2.6522
−6.4558
0.0800
2.6575
−6.4505
0.0900
2.6624
−6.4456
0.1000
2.6714
−6.4365According to Feakins model, the greater the value ofΔμ20≠ is, the greater the structure ability of the solute is. The values of Δμ20≠ are very large as compared to those of Δμ10≠, which suggests that the formation of transition state is accompanied with breaking and distortion of intermolecular bonds.


## 3.4.1.  Solvent Activation Parameter:Δμ10≠

Δ
μ
1
0
≠ is calculated from equation proposed by Eying et al. 										(7)Δμ10≠=RTIn(η1V-10HN),
where N = Avogadro’s number (6.023 × 1023 gm·atom), H =  Planck’s constant (6.626 × 10−34 J·sec), and η1 =  viscosity of solvent.


## 3.4.2. Solvent Activation Parameter:Δμ20≠

Solvent activation parameter,Δμ20≠, is derived from following expression:
(8)Δμ20≠=Δμ10≠+(RTV-10)[1000B-V-10-V-20).The values of solventΔμ10≠ and solute  Δμ20≠ and activation free energies are given in Table 4.Table 4
Activation parameters of tris (hydroxymethyl)aminomethane hydrochloride in 20% (v/v) acetone-water system at 303.15°K.
Concentration (mol dm−3)
Δ
μ
1
0
≠  (in kJ mol−1) 105
Δ
μ
2
0
≠  (in kJ mol−1) 105
0.0100
2.6244
−6.4836
0.0200
2.6283
−6.4798
0.0300
2.6329
−6.4752
0.0400
2.6348
−6.4732
0.0500
2.6426
−6.4654
0.0600
2.6467
−6.4613
0.0700
2.6522
−6.4558
0.0800
2.6575
−6.4505
0.0900
2.6624
−6.4456
0.1000
2.6714
−6.4365According to Feakins model, the greater the value ofΔμ20≠ is, the greater the structure ability of the solute is. The values of Δμ20≠ are very large as compared to those of Δμ10≠, which suggests that the formation of transition state is accompanied with breaking and distortion of intermolecular bonds.


## 3.5. Excess Free Energy of Activation for Viscous FlowGE and Interaction Parameter d

### 3.5.1. Excess Free Energy of Activation for Viscous FlowGE

The extra-thermodynamic property, excess Gibb’s free energy of activation of flow (GE) for the solution has been computed from the Eyring equation [8]
(9)GE=RT[InηV-(X1Inη1V1+X2Inη2V2)].The values are listed in Table5. The value of GE  increases with the increase in concentration of solute and also increases with the increase in temperature suggesting the interactions became stronger.Table 5
Excess molar free energy of activation of flow (GE) and Grunberg and Nissan       constant tris (hydroxymethyl)amino methane hydrochloride in 20% (v/v) acetone-water system at 303.15°K.
Concentration  (mol dm−3)
Excess molar free energy of activation of flow (GE)
Grunberg and Nissan (d)
0.0100
16.9678
0.0001
0.0200
56.1698
0.0004
0.0300
103.0463
−0.0012
0.0400
122.8588
−0.0007
0.0500
202.7112
−0.0003
0.0600
243.5637
−0.0002
0.0700
299.0243
−0.0002
0.0800
351.6797
−0.0003
0.0900
401.7946
−0.0001
0.1000
494.6975
−0.0001


### 3.5.2. Interaction Parameterd

The impact of solute on viscosity is understood in terms of parameterd, which is regarded as a measure of the strength of interaction between components of solution. It has been estimated using relationship proposed by Gruenberg and Nissan [9]
(10)Inη=X1Inη1+X2Inη2+X1X2d,
where d  =  Grunberg and Nissan parameter:
(11)D∝WRT,
where W =  interaction energy.The values ofd are reported in Table 5.


## 3.5.1. Excess Free Energy of Activation for Viscous FlowGE

The extra-thermodynamic property, excess Gibb’s free energy of activation of flow (GE) for the solution has been computed from the Eyring equation [8]
(9)GE=RT[InηV-(X1Inη1V1+X2Inη2V2)].The values are listed in Table5. The value of GE  increases with the increase in concentration of solute and also increases with the increase in temperature suggesting the interactions became stronger.Table 5
Excess molar free energy of activation of flow (GE) and Grunberg and Nissan       constant tris (hydroxymethyl)amino methane hydrochloride in 20% (v/v) acetone-water system at 303.15°K.
Concentration  (mol dm−3)
Excess molar free energy of activation of flow (GE)
Grunberg and Nissan (d)
0.0100
16.9678
0.0001
0.0200
56.1698
0.0004
0.0300
103.0463
−0.0012
0.0400
122.8588
−0.0007
0.0500
202.7112
−0.0003
0.0600
243.5637
−0.0002
0.0700
299.0243
−0.0002
0.0800
351.6797
−0.0003
0.0900
401.7946
−0.0001
0.1000
494.6975
−0.0001


## 3.5.2. Interaction Parameterd

The impact of solute on viscosity is understood in terms of parameterd, which is regarded as a measure of the strength of interaction between components of solution. It has been estimated using relationship proposed by Gruenberg and Nissan [9]
(10)Inη=X1Inη1+X2Inη2+X1X2d,
where d  =  Grunberg and Nissan parameter:
(11)D∝WRT,
where W =  interaction energy.The values ofd are reported in Table 5.


## 4. Conclusion

Knowledge of transport properties is important in all these applications to understand the molecular interactions. Viscosity increases as a function of concentration and decreases in increase in temperatures. The values ofB-coefficient show solute-solvent interactions in the present systems. The values, Δμ20≠, are very large as compared to those of Δμ10≠ which suggests that the formation of transition state is accompanied with breaking and distortion of intermolecular bonds. Volumetric data are used to test molecular theories or models of solution to extend our understanding about molecular interactions among components.



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