**3. Theory**

When two liquid chemical species mixed with each other, the total weight of the mixture is equal to the sum of masses of the individual chemical species. But it is not true in case of volume. When two miscible liquids are mixed with each other, volume of the mixtures may not equal to the sum of the volume of the individual chemical species [9]. Ideal binary liquid mixture does not have volume changes. Hence, the binary liquid mixture has deviation from ideality due to the molecular interactions between solute-solvent or two components in the mixtures. In addition, the binary liquid mixture volume either increase or decrease as the function of composition of component i in the mixture. This difference in the volume of the mixture can be taken as a criterion and measure of molecular interactions at molecular level by means of isobaric expansivity, excess molar volume, partial molar volume, excess partial molar volume and apparent molar volume (**Figure 1**).

*Isobaric expansivity* is inversely proportional to the volume of component "i" in the mixture and its product with the rate of change of volume with respect to temperature at constant pressure. Hence the isobaric expansivity is defined as;

**Figure 1.** Illustrating the density measurement of binary mixtures using Anton Paar DMA 4100 M.

$$\alpha = \frac{1}{V} \left[ \frac{\partial V}{\partial T} \right]\_P = -\frac{1}{\rho} \left[ \frac{\partial \rho}{\partial T} \right]\_P = -\left[ \frac{\partial \ln \rho}{\partial T} \right]\_P \tag{2}$$

mixtures. Hence, the partial molar volume is not necessarily the same as the molar volume of the pure component as it depends on how the molecules interact, structural rearrangement,

/mole) can be

http://dx.doi.org/10.5772/intechopen.77016

<sup>0</sup> (8)

<sup>0</sup> (9)

], [BMIM][OAc] and [BMIM][NtF<sup>2</sup>

(6)

127

(7)

(10)

(11)

] ionic liq-

]

] < [EMIM][HSO<sup>4</sup>

and the geometrical fitting of the molecules [13]. The partial molar volume (cm<sup>3</sup>

*<sup>E</sup>* + *V*<sup>1</sup>

*<sup>E</sup>* + *V*<sup>2</sup>

<sup>0</sup> + *x*<sup>2</sup> (

<sup>0</sup> − *x*<sup>1</sup> (

are the partial molar volume of component 1 and 2, respectively.

/mole). It can be defined as;

are the excess partial molar volume of component 1 and 2, respectively.

/mole) is defined as;

0 − *Vm E* \_\_\_ *x*1

0 − *Vm E* \_\_\_ *x*1

], [EMIM][HSO<sup>4</sup>

uid at the temperature range from 293.15 to 343.15 K are presented in **Table 1**. Densities of IL's used in this work and commonly used ILs are given in **Figure 2**. Density of all IL's decreases

] (this work) < [EMIM][TOS] < [BMIM][PF<sup>6</sup>

are the apparent molar volume of component 1 and 2, respectively.

*Excess partial molar volume* is the property of binary mixtures which is useful to characterize the non-ideal behavior of real mixtures. Excess partial molar volume is the different between the partial molar volume of a component "i" in a real mixture and the molar volume of the

> <sup>−</sup>*<sup>E</sup>* <sup>=</sup> *<sup>V</sup>* \_ <sup>1</sup> − *V*<sup>1</sup>

> <sup>−</sup>*<sup>E</sup>* <sup>=</sup> *<sup>V</sup>* \_ <sup>2</sup> − *V*<sup>2</sup>

*Apparent molar volume* is one of the solution thermodynamic properties which can measure the amount of solute is required to bring the solvent volume up to the solution volume.

∂ *Vm E* \_\_\_\_<sup>∂</sup> *<sup>x</sup>*<sup>1</sup> )*<sup>P</sup>*,*<sup>T</sup>*

Evaluation of Solution Thermodynamic Properties of Mixed Ionic Liquids at Different…

∂ *Vm E* \_\_\_\_<sup>∂</sup> *<sup>x</sup>*<sup>1</sup> )*<sup>P</sup>*,*<sup>T</sup>*

\_ <sup>1</sup> = *Vm*

\_ <sup>2</sup> = *Vm*

evaluated using the following equations;

*V*

*V*

component in an ideal mixture (cm3

*V*<sup>1</sup>

*V*<sup>2</sup>

Hence, the apparent molar volume (cm<sup>3</sup>

*Vφ*,1 = *V*<sup>1</sup>

*Vφ*,2 = *V*<sup>1</sup>

and *v*¯<sup>2</sup>

where; *v*¯*<sup>i</sup>*

where; *v*¯<sup>1</sup> *E* and *v*¯<sup>2</sup> *E*

where; *Vφ*·1

and *Vφ*·2

**4. Results and discussion**

**4.1. Density of pure ionic liquids**

The density of pure [EMIM][ESO<sup>4</sup>

as in the order of; [BMIM][NTF<sup>2</sup>

where; α is the isobaric expansivity, v is the volume of the fluid, ρ is the density of the fluid, T is the temperature, P is the pressure.

*The excess molar volume* is the good estimator of unlike interaction in the binary mixture as a function of concentration of component "i" at constant temperature and pressure. The excess molar volume (cm3 /mole) is defined as [1, 13];

$$V\_m^E = \left. V\_m^{real} - \sum\_{l \in \mathbb{Z}, 2} V\_m^{dual} \right| \tag{3}$$

$$\mathbf{u} = \mathbf{V}\_m^{val} - \mathbf{x}\_1 \mathbf{V}\_1^n - \mathbf{x}\_2 \mathbf{V}\_2^n \tag{4}$$

$$=\frac{\mathbf{x}\_1 M\_1 + \mathbf{x}\_2 M\_2}{\rho\_{\rm mix}} - \left[\frac{\mathbf{x}\_1 M\_1}{\rho\_1} + \frac{\mathbf{x}\_2 M\_2}{\rho\_2}\right] \tag{5}$$

where; *Vm E* is the excess molar volume, *Vm real* is the molar volume of real fluid, *Vm ideal* is the molar volume of ideal, *<sup>V</sup>*<sup>1</sup> 0 and *V*<sup>2</sup> 0 are the molar volume of component 1 and 2, respectively. x1 and x2 are the mole fraction of component 1 and 2 in the binary mixture. M<sup>1</sup> and M<sup>2</sup> are the molecular weight of component 1 & 2. ρmix, ρ<sup>1</sup> & ρ<sup>2</sup> are the densities of binary mixture, component 1 and component 2, respectively.

*Partial molar volume* is the thermodynamic quantity and it is used to measure the change s in extensive properties of the binary mixture as the function of composition at constant temperature and pressure. In addition, the partial molar volume is a potential tool to estimate the solute-solvent interaction in the binary mixture at molecular level. The partial molar volume is used to measure the incremental volume by addition of co-solvent in the binary mixtures. Hence, the partial molar volume is not necessarily the same as the molar volume of the pure component as it depends on how the molecules interact, structural rearrangement, and the geometrical fitting of the molecules [13]. The partial molar volume (cm<sup>3</sup> /mole) can be evaluated using the following equations;

$$\overline{V}\_1 = \; V\_m^\mathbb{E} + V\_1^0 + \mathbf{x}\_2 \left( \frac{\partial \; V\_m^\mathbb{E}}{\partial \mathbf{x}\_1} \right)\_{p,T} \tag{6}$$

$$\nabla\_2 = \mathbf{V}\_m^\varepsilon + \mathbf{V}\_2^0 - \mathbf{x}\_1 \left(\frac{\partial \mathbf{V}\_m^t}{\partial \mathbf{x}\_i}\right)\_{p,T} \tag{7}$$

where; *v*¯*<sup>i</sup>* and *v*¯<sup>2</sup> are the partial molar volume of component 1 and 2, respectively.

*Excess partial molar volume* is the property of binary mixtures which is useful to characterize the non-ideal behavior of real mixtures. Excess partial molar volume is the different between the partial molar volume of a component "i" in a real mixture and the molar volume of the component in an ideal mixture (cm3 /mole). It can be defined as;

$$V\_1^{\overline{\varepsilon}} = \,^t\nabla\_1 - V\_1^0 \tag{8}$$

$$V\_2^{\overline{\varepsilon}} = \overline{V}\_2 - V\_2^0 \tag{9}$$

where; *v*¯<sup>1</sup> *E* and *v*¯<sup>2</sup> *E* are the excess partial molar volume of component 1 and 2, respectively.

*Apparent molar volume* is one of the solution thermodynamic properties which can measure the amount of solute is required to bring the solvent volume up to the solution volume. Hence, the apparent molar volume (cm<sup>3</sup> /mole) is defined as;

$$V\_{\mathbf{q},1} = V\_1^0 - \frac{V\_n^2}{\mathbf{x}\_1} \tag{10}$$

$$V\_{\rho,2} = V\_1^0 - \frac{V\_w^0}{\chi\_1} \tag{11}$$

where; *Vφ*·1 and *Vφ*·2 are the apparent molar volume of component 1 and 2, respectively.

#### **4. Results and discussion**

*α* = \_\_1

T is the temperature, P is the pressure.

*Vm*

= *Vm*

0 and *V*<sup>2</sup> 0

weight of component 1 & 2. ρmix, ρ<sup>1</sup>

component 2, respectively.

<sup>=</sup> *<sup>x</sup>*<sup>1</sup> *<sup>M</sup>*<sup>1</sup> <sup>+</sup> *<sup>x</sup>* \_\_\_\_\_\_\_\_\_ <sup>2</sup> *<sup>M</sup>*<sup>2</sup>

is the excess molar volume, *Vm*

molar volume (cm3

where; *Vm E*

volume of ideal, *<sup>V</sup>*<sup>1</sup>

*V* [ \_\_\_ ∂*V* <sup>∂</sup>*T*]*<sup>P</sup>*

126 Laboratory Unit Operations and Experimental Methods in Chemical Engineering

**Figure 1.** Illustrating the density measurement of binary mixtures using Anton Paar DMA 4100 M.

/mole) is defined as [1, 13];

= −\_\_1 *ρ* [ ∂*ρ*\_\_\_ <sup>∂</sup>*T*]*<sup>P</sup>*

where; α is the isobaric expansivity, v is the volume of the fluid, ρ is the density of the fluid,

*The excess molar volume* is the good estimator of unlike interaction in the binary mixture as a function of concentration of component "i" at constant temperature and pressure. The excess

> *real* − ∑ *i*=1,2 *Vm*

> > <sup>0</sup> − *x*<sup>2</sup> *V*<sup>2</sup>

*real* is the molar volume of real fluid, *Vm*

are the molar volume of component 1 and 2, respectively. x1

*<sup>E</sup>* = *Vm*

*ρmix*

are the mole fraction of component 1 and 2 in the binary mixture. M<sup>1</sup>

& ρ<sup>2</sup>

*real* − *x*<sup>1</sup> *V*<sup>1</sup>

− [ *x* \_\_\_\_ <sup>1</sup> *<sup>M</sup>*<sup>1</sup> *ρ*1 + *x* \_\_\_\_ <sup>2</sup> *<sup>M</sup>*<sup>2</sup>

*Partial molar volume* is the thermodynamic quantity and it is used to measure the change s in extensive properties of the binary mixture as the function of composition at constant temperature and pressure. In addition, the partial molar volume is a potential tool to estimate the solute-solvent interaction in the binary mixture at molecular level. The partial molar volume is used to measure the incremental volume by addition of co-solvent in the binary

= −[

∂ ln*ρ* \_\_\_\_\_ <sup>∂</sup>*<sup>T</sup>* ]*<sup>P</sup>*

*ideal* (3)

<sup>0</sup> (4)

*<sup>ρ</sup>*<sup>2</sup> ] (5)

and M<sup>2</sup>

are the densities of binary mixture, component 1 and

*ideal* is the molar

are the molecular

and x2

(2)

#### **4.1. Density of pure ionic liquids**

The density of pure [EMIM][ESO<sup>4</sup> ], [EMIM][HSO<sup>4</sup> ], [BMIM][OAc] and [BMIM][NtF<sup>2</sup> ] ionic liquid at the temperature range from 293.15 to 343.15 K are presented in **Table 1**. Densities of IL's used in this work and commonly used ILs are given in **Figure 2**. Density of all IL's decreases as in the order of; [BMIM][NTF<sup>2</sup> ] (this work) < [EMIM][TOS] < [BMIM][PF<sup>6</sup> ] < [EMIM][HSO<sup>4</sup> ]


anion has great impact on density of IL's. Generally, density of pure IL's decreases due to the following reasons; (i) increasing length of the alkyl chain and (ii) increasing volume of the

The study of temperature and pressure dependence of isobaric expansivity of [EMIM][ESO<sup>4</sup>

appreciably at the temperature range from 293.15 to 343.15 K. Isothermal expansivity of all

tion at T = 293.15–343.15 K were used to estimate excess molar volume. Excess molar volumes

Generally, VE can be considered arising from three types of interactions between two components in the mixtures: (i) physical interaction mainly consisting of dispersion forces or weak dipole-dipole interactions and making a positive contribution. (ii) Chemical or specific interactions which include charge transfer, formation of hydrogen bonds and other complex forming interactions resulting in negative contribution, and (iii) the structural contributions arising from geometrical fitting of one component into another due to difference in molar

] and 2.95 × 10−4 for [EMIM][HSO<sup>4</sup>

] + [BMIM][HSO<sup>4</sup>

Evaluation of Solution Thermodynamic Properties of Mixed Ionic Liquids at Different…

http://dx.doi.org/10.5772/intechopen.77016

] from 293.15 to 343.15 K versus the mole fraction of [EMIM]

] + [BMIM][OAc], [EMIM][ESO<sup>4</sup>

studied ILs are presented in **Table 2**. [BMIM][OAc] gave 5.77 × 10−4, 4.94 × 10−

Experimental densities for different binary mixtures of [EMIM][ESO<sup>4</sup>

] and [EMIM][ESO<sup>4</sup>

], [BMIM][OAc] and [BMIM][NtF<sup>2</sup>

**Figure 2.** Density of investigated ionic liquids in this work at different temperature.

],

129

] and

4 for [BMIM]

] + [BMIM][OAc],

] as a function of composi-

] + [BMIM][NtF<sup>2</sup>

] ionic liquids. The ILs do not expanded

].

anions [1].

[EMIM][HSO<sup>4</sup>

[EMIM][ESO<sup>4</sup>

[EMIM][ESO<sup>4</sup>

[ESO<sup>4</sup>

[NtF<sup>2</sup>

**4.2. Isobaric expansivity**

**4.3. Excess molar volume**

], 4.09 × 10−4 for [EMIM][ESO<sup>4</sup>

] + [BMIM][NtF<sup>2</sup>

] + [BMIM][HSO<sup>4</sup>

volumes resulting in negative excess molar volume [16].

for the binary mixtures of [EMIM][ESO<sup>4</sup>

] are shown in **Figures 3**–**5**.

**Table 1.** Density as function of temperature for pure ionic liquids.

(this work) < [MMIM][MSO<sup>4</sup> ] < [BMIM][TOS] < [HMIM][PF<sup>6</sup> ] < [OMIM][PF<sup>6</sup> ] < [EMIM][ESO<sup>4</sup> ] (this work) < [BMIM][BF<sup>4</sup> ] < [HMIM][BF<sup>4</sup> ] < [EMIM][SCN] < [BMIM][OAc] (this work) < Water at 298.15 K. Densities of all the studied ionic liquids slightly decreases with increasing temperatures from 293.15 to 343.15 K. It is observed that temperature effect on densities of studied ionic liquids are very small and it may be neglected. The density of ILs' decrease as in the order of; [BMIM][NtF<sup>2</sup> ] < [EMIM][HSO<sup>4</sup> ] < [EMIM][ESO<sup>4</sup> ] < [BMIM][OAc] (**Figure 1**). Since the densities of pure ionic liquids play an important role to estimate the volumetric behavior of individual IL's with other IL's in the binary mixtures for the whole composition at different temperatures. It is noted that the length of alkyl-chain in cation as well as the variety of Evaluation of Solution Thermodynamic Properties of Mixed Ionic Liquids at Different… http://dx.doi.org/10.5772/intechopen.77016 129

**Figure 2.** Density of investigated ionic liquids in this work at different temperature.

anion has great impact on density of IL's. Generally, density of pure IL's decreases due to the following reasons; (i) increasing length of the alkyl chain and (ii) increasing volume of the anions [1].

#### **4.2. Isobaric expansivity**

The study of temperature and pressure dependence of isobaric expansivity of [EMIM][ESO<sup>4</sup> ], [EMIM][HSO<sup>4</sup> ], [BMIM][OAc] and [BMIM][NtF<sup>2</sup> ] ionic liquids. The ILs do not expanded appreciably at the temperature range from 293.15 to 343.15 K. Isothermal expansivity of all studied ILs are presented in **Table 2**. [BMIM][OAc] gave 5.77 × 10−4, 4.94 × 10− 4 for [BMIM] [NtF<sup>2</sup> ], 4.09 × 10−4 for [EMIM][ESO<sup>4</sup> ] and 2.95 × 10−4 for [EMIM][HSO<sup>4</sup> ].

#### **4.3. Excess molar volume**

(this work) < [MMIM][MSO<sup>4</sup>

(this work) < [BMIM][BF<sup>4</sup>

**S. No**

1 [EMIM] [SCN] [10]

2 [BMIM] [BF<sup>4</sup> ] [5]

3 [HMIM] [BF<sup>4</sup> ] [5, 10]

4 [OMIM] [BF<sup>4</sup> ] [11]

5 [BMIM] [PF<sup>6</sup> ] [12]

6 [EMIM] [TOS] [13]

7 [BMIM] [TOS] [13]

8 [MMIM] [MSO<sup>4</sup> ] [14]

9 [EMIM] [EtSO<sup>4</sup> ] [15]

10 [BMIM] [MSO<sup>4</sup> ]

[5]

11 [EMIM] [HSO<sup>4</sup> ]\*

12 [EMIM] [OAc]\*

13 [BMIM] [NtF2]\*

the order of; [BMIM][NtF<sup>2</sup>

] < [BMIM][TOS] < [HMIM][PF<sup>6</sup>

at 298.15 K. Densities of all the studied ionic liquids slightly decreases with increasing temperatures from 293.15 to 343.15 K. It is observed that temperature effect on densities of studied ionic liquids are very small and it may be neglected. The density of ILs' decrease as in

**Name 293.15 298.15 303.15 308.15 313.15 318.15 323.15 328.15 333.15 338.15 343.15**

128 Laboratory Unit Operations and Experimental Methods in Chemical Engineering

NA 1.1168 NA 1.1107 NA 1.1047 NA 1.0927 NA NA NA

NA 1.2076 1.2041 1.2005 1.1970 1.1934 1.1899 NA 1.1754 NA NA

NA 1.1488 1.1453 1.1418 1.1384 1.1350 1.1316 NA NA NA NA

NA 1.1018 NA NA NA NA NA NA NA NA NA

NA 1.3697 1.3635 1.3592 1.3555 1.3520 1.3474 NA NA NA NA

NA 1.3895 1.3853 1.3811 1.3769 1.3727 1.3686 NA NA NA NA

NA 1.3415 1.3341 1.3248 1.3206 NA NA NA NA NA NA

1.2424 1.2394 1.2363 1.2333 1.2302 1.2272 1.2241 1.2211 1.2181 1.2151 1.2120 1.2402\* 1.2368\* 1.2334\* 1.2300\* 1.2266\* 1.2232\* 1.2199\* 1.2165\* 1.2132\* 1.2099\* 1.2066\*

NA 1.2107 1.2074 1.2041 1.2008 1.1975 1.1942 NA NA NA NA

1.3691 1.3660 1.3629 1.3599 1.3567 1.3537 1.3508 1.3477 1.3448 1.3418 1.3388

1.0555 1.0525 1.0495 1.0465 1.0435 1.0405 1.0375 1.0346 1.0316 1.0287 1.0257

1.4406 1.4358 1.4310 1.4262 1.4215 1.4167 1.4120 1.4073 1.4026 1.3979 1.3933

NA 1.3016 1.2976 1.2937 1.2897 1.2858 1.2819 NA 1.14997 1.14667 1.14347

the densities of pure ionic liquids play an important role to estimate the volumetric behavior of individual IL's with other IL's in the binary mixtures for the whole composition at different temperatures. It is noted that the length of alkyl-chain in cation as well as the variety of

] < [EMIM][ESO<sup>4</sup>

] < [HMIM][BF<sup>4</sup>

**Table 1.** Density as function of temperature for pure ionic liquids.

] < [EMIM][HSO<sup>4</sup>

] < [OMIM][PF<sup>6</sup>

] < [EMIM][SCN] < [BMIM][OAc] (this work) < Water

] < [EMIM][ESO<sup>4</sup>

] < [BMIM][OAc] (**Figure 1**). Since

]

Experimental densities for different binary mixtures of [EMIM][ESO<sup>4</sup> ] + [BMIM][OAc], [EMIM][ESO<sup>4</sup> ] + [BMIM][NtF<sup>2</sup> ] and [EMIM][ESO<sup>4</sup> ] + [BMIM][HSO<sup>4</sup> ] as a function of composition at T = 293.15–343.15 K were used to estimate excess molar volume. Excess molar volumes for the binary mixtures of [EMIM][ESO<sup>4</sup> ] + [BMIM][OAc], [EMIM][ESO<sup>4</sup> ] + [BMIM][NtF<sup>2</sup> ] and [EMIM][ESO<sup>4</sup> ] + [BMIM][HSO<sup>4</sup> ] from 293.15 to 343.15 K versus the mole fraction of [EMIM] [ESO<sup>4</sup> ] are shown in **Figures 3**–**5**.

Generally, VE can be considered arising from three types of interactions between two components in the mixtures: (i) physical interaction mainly consisting of dispersion forces or weak dipole-dipole interactions and making a positive contribution. (ii) Chemical or specific interactions which include charge transfer, formation of hydrogen bonds and other complex forming interactions resulting in negative contribution, and (iii) the structural contributions arising from geometrical fitting of one component into another due to difference in molar volumes resulting in negative excess molar volume [16].


**Table 2.** Observed and literature values of isobaric thermal expansivities.

**Figure 3.** Excess molar volume of binary mixture of [EMIM][ESO<sup>4</sup> ] + [BMIM][OAc] at different temperature.

Excess molar volumes are positive over the whole composition range for [EMIM][ESO<sup>4</sup> ] + [BMIM][OAc] and [EMIM][ESO<sup>4</sup> ] + [BMIM][NtF<sup>2</sup> ]. [EMIM][ESO<sup>4</sup> ] + [BMIM][HSO<sup>4</sup> ] also has positive values at temperature from 293.15 to 343.15 K. But, [EMIM][ESO<sup>4</sup> ] + [BMIM][HSO<sup>4</sup> ] has a negative values at 308.15 and 313.15 K which is indicated that alkyl group substitution at anions has a significant role in the formation of hydrogen bond with other IL's at different temperature. The rise in temperature does not show any considerable effect on the excess molar volume of all the studied mixed IL's systems. But [EMIM][ESO<sup>4</sup> ] + [EMIM][HOS<sup>4</sup> ] system has shown negative deviation from 0 to 3.5 at 308.15 K and 0 to 6.5 mole fraction of [EMIM][ESO<sup>4</sup> ] in [EMIM][HSO<sup>4</sup>

of ion's in IL's.

**4.4. Partial molar volume**

[OAc] and [BMIM][NtF<sup>2</sup>

temperatures, except [EMIM][ESO<sup>4</sup>

excess molar volume as a function of [EMIM][ESO<sup>4</sup>

**Figure 5.** Excess molar volume of binary mixture of [EMIM][ESO<sup>4</sup>

**Figure 4.** Excess molar volume of binary mixture of [EMIM][ESO<sup>4</sup>

**Figures 6**–**8** shows the partial molar volume of [EMIM][ESO<sup>4</sup>

studied system shows negative deviation for the mole fractions of [EMIM][ESO<sup>4</sup>

] + [EMIM][HSO<sup>4</sup>

]. It may be due to the formation of hydrogen bond and also because of inter-

] + [BMIM][NtF<sup>2</sup>

] + [EMIM][HSO<sup>4</sup>

Evaluation of Solution Thermodynamic Properties of Mixed Ionic Liquids at Different…

] at T (293.15–343.15) K. The values of partial molar volume of all

] system. [EMIM][ESO<sup>4</sup>

] is mainly depends on nature and changes

] at different temperature.

] at different temperature.

http://dx.doi.org/10.5772/intechopen.77016

131

] in [EMIM][HSO<sup>4</sup>

], [BMIM]

] at different

]

] + [EMIM][HSO<sup>4</sup>

actions. It is also observed that the sign of the excess molar volume and shape of the curve of

Evaluation of Solution Thermodynamic Properties of Mixed Ionic Liquids at Different… http://dx.doi.org/10.5772/intechopen.77016 131

**Figure 4.** Excess molar volume of binary mixture of [EMIM][ESO<sup>4</sup> ] + [EMIM][HSO<sup>4</sup> ] at different temperature.

**Figure 5.** Excess molar volume of binary mixture of [EMIM][ESO<sup>4</sup> ] + [BMIM][NtF<sup>2</sup> ] at different temperature.

in [EMIM][HSO<sup>4</sup> ]. It may be due to the formation of hydrogen bond and also because of interactions. It is also observed that the sign of the excess molar volume and shape of the curve of excess molar volume as a function of [EMIM][ESO<sup>4</sup> ] is mainly depends on nature and changes of ion's in IL's.

#### **4.4. Partial molar volume**

] +

]

]

] also has

] system has

] + [BMIM][HSO<sup>4</sup>

Excess molar volumes are positive over the whole composition range for [EMIM][ESO<sup>4</sup>

has a negative values at 308.15 and 313.15 K which is indicated that alkyl group substitution at anions has a significant role in the formation of hydrogen bond with other IL's at different temperature. The rise in temperature does not show any considerable effect on the excess molar

shown negative deviation from 0 to 3.5 at 308.15 K and 0 to 6.5 mole fraction of [EMIM][ESO<sup>4</sup>

]. [EMIM][ESO<sup>4</sup>

] + [BMIM][HSO<sup>4</sup>

] + [BMIM][OAc] at different temperature.

**This work Literature**

] + [EMIM][HOS<sup>4</sup>

] + [BMIM][NtF<sup>2</sup>

positive values at temperature from 293.15 to 343.15 K. But, [EMIM][ESO<sup>4</sup>

volume of all the studied mixed IL's systems. But [EMIM][ESO<sup>4</sup>

[BMIM][OAc] and [EMIM][ESO<sup>4</sup>

**Figure 3.** Excess molar volume of binary mixture of [EMIM][ESO<sup>4</sup>

**S. no Name α (1/K)**

130 Laboratory Unit Operations and Experimental Methods in Chemical Engineering

2 [BMIM][BF<sup>4</sup>

3 [HMIM][BF<sup>4</sup>

4 [BMIM][PF<sup>6</sup>

7 [MMIM][MSO<sup>4</sup>

8 [BMIM][MSO<sup>4</sup>

9 [EMIM][EtSO<sup>4</sup>

11 [EMIM][NtF<sup>2</sup>

1 [EMIM][SCN] [8] NA 7.23 × 10−4

5 [EMIM][TOS] [11] NA 5.80 × 10−4 6 [BMIM][TOS] [11] NA 6.19 × 10−4

10 [BMIM][OAc] 5.77 × 10−4 NA

**Table 2.** Observed and literature values of isobaric thermal expansivities.

] [5] NA 5.84 × 10−4

] [5, 8] NA 6.14 × 10−4

] [10] NA 6.63 × 10−4

] [12] NA 10.52 × 10−4

] [13] 4.09 × 10−4 4.88 × 10−4

] 2.95 × 10−4 NA

] 4.94 × 10−4 NA

**Figures 6**–**8** shows the partial molar volume of [EMIM][ESO<sup>4</sup> ] in [EMIM][HSO<sup>4</sup> ], [BMIM] [OAc] and [BMIM][NtF<sup>2</sup> ] at T (293.15–343.15) K. The values of partial molar volume of all studied system shows negative deviation for the mole fractions of [EMIM][ESO<sup>4</sup> ] at different temperatures, except [EMIM][ESO<sup>4</sup> ] + [EMIM][HSO<sup>4</sup> ] system. [EMIM][ESO<sup>4</sup> ] + [EMIM][HSO<sup>4</sup> ]

**Figure 6.** Partial molar volume of [EMIM][ESO<sup>4</sup> ] in [BMIM][NtF<sup>2</sup> ] at different temperature.

system has positive deviation due to very strong physical interaction between these two IL's at molecular level. Usually, physical interaction is dispersion forces or weak dipole-dipole

] in [BMIM][OAc] at different temperature.

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133

] at T (293.15–343.15) K are presented in **Figures 9**–**11**. [EMIM][ESO<sup>4</sup>

] in [BMIM][NtF<sup>2</sup>

] in [EMIM][HSO<sup>4</sup>

] at different temperature.

] + [BMIM][OAc] shows negative deviation which indicates that

],[BMIM][OAc] and

] + [BMIM]

interaction.

[BMIM][NtF<sup>2</sup>

[NtF<sup>2</sup>

**4.5. Excess partial molar volume**

**Figure 8.** Partial molar volume of [EMIM][ESO<sup>4</sup>

] and [EMIM][ESO<sup>4</sup>

**Figure 9.** Excess partial molar volume of [EMIM][ESO<sup>4</sup>

The excess partial molar volume of [EMIM][ESO<sup>4</sup>

**Figure 7.** Partial molar volume of [EMIM][ESO<sup>4</sup> ] in [EMIM][HSO<sup>4</sup> ] at different temperature.

has positive deviation due to very strong physical interaction between [EMIM][ESO<sup>4</sup> ] and [BMIM][OAc]/[BMIM][NtF<sup>2</sup> ]. Physical interaction mainly consisting of dispersion forces or weak dipole-dipole interaction, and weak ion-dipole interaction make a positive deviation. The partial molar volume of [EMIM][ESO<sup>4</sup> ] with [EMIM][OAc] and [BMIM][NtF<sup>2</sup> ] mixtures are more negative than [EMIM][ESO<sup>4</sup> ] + [EMIM][HSO4] mixtures, which imply that there are stronger ion-dipole interactions. On the other hand, packing effect, charge transfer, hydrogen bond formation, other complex interaction, geometrical fitting one component into other due to difference in molar volume make a negative deviation. [EMIM][ESO<sup>4</sup> ] + [EMIM][HSO<sup>4</sup> ]

**Figure 8.** Partial molar volume of [EMIM][ESO<sup>4</sup> ] in [BMIM][OAc] at different temperature.

system has positive deviation due to very strong physical interaction between these two IL's at molecular level. Usually, physical interaction is dispersion forces or weak dipole-dipole interaction.

#### **4.5. Excess partial molar volume**

has positive deviation due to very strong physical interaction between [EMIM][ESO<sup>4</sup>

] in [EMIM][HSO<sup>4</sup>

] in [BMIM][NtF<sup>2</sup>

weak dipole-dipole interaction, and weak ion-dipole interaction make a positive deviation.

stronger ion-dipole interactions. On the other hand, packing effect, charge transfer, hydrogen bond formation, other complex interaction, geometrical fitting one component into other due

to difference in molar volume make a negative deviation. [EMIM][ESO<sup>4</sup>

]. Physical interaction mainly consisting of dispersion forces or

] at different temperature.

] at different temperature.

] with [EMIM][OAc] and [BMIM][NtF<sup>2</sup>

] + [EMIM][HSO4] mixtures, which imply that there are

[BMIM][OAc]/[BMIM][NtF<sup>2</sup>

The partial molar volume of [EMIM][ESO<sup>4</sup>

are more negative than [EMIM][ESO<sup>4</sup>

**Figure 7.** Partial molar volume of [EMIM][ESO<sup>4</sup>

**Figure 6.** Partial molar volume of [EMIM][ESO<sup>4</sup>

132 Laboratory Unit Operations and Experimental Methods in Chemical Engineering

] and

]

] mixtures

] + [EMIM][HSO<sup>4</sup>

The excess partial molar volume of [EMIM][ESO<sup>4</sup> ] in [EMIM][HSO<sup>4</sup> ],[BMIM][OAc] and [BMIM][NtF<sup>2</sup> ] at T (293.15–343.15) K are presented in **Figures 9**–**11**. [EMIM][ESO<sup>4</sup> ] + [BMIM] [NtF<sup>2</sup> ] and [EMIM][ESO<sup>4</sup> ] + [BMIM][OAc] shows negative deviation which indicates that

**Figure 9.** Excess partial molar volume of [EMIM][ESO<sup>4</sup> ] in [BMIM][NtF<sup>2</sup> ] at different temperature.

molar volume of [EMIM][ESO<sup>4</sup>

**Figure 12.** Apparent molar volume of [EMIM][ESO<sup>4</sup>

**Figure 13.** Apparent molar volume of [EMIM][ESO<sup>4</sup>

(**Figure 14**).

] in [EMIM][HSO<sup>4</sup>

of the composition from 293.15 to 333.15 K which implies that there is strong packing effect due to similar size of cation in both IL's (**Figure 13**). [EMIM][ESO4] + [BMIM][OAc] gave negative apparent molar volume which means that there is very strong hydrogen bond formation and charge-charge interaction between one and another at molecular level

Evaluation of Solution Thermodynamic Properties of Mixed Ionic Liquids at Different…

] in [BMIM][NtF<sup>2</sup>

] in [EMIM][HSO<sup>4</sup>

] at different temperature.

] at different temperature.

] shows positive deviation as function

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135

**Figure 10.** Excess partial molar volume of [EMIM][ESO<sup>4</sup> ] in [EMIM][HSO<sup>4</sup> ] at different temperature.

**Figure 11.** Excess partial molar volume of [EMIM][ESO<sup>4</sup> ] in [EMIM][OAc] at different temperature.

there is very strong packing effect. The packing effect caused by a large difference in molecular size and configuration between two IL's, charge transfer, hydrogen bond formation and the ion-dipole attractions are even more dominant in IL's mixtures as function of compositions at T (293.15–343.15) K.

#### **4.6. Apparent molar volume**

[EMIM][ESO<sup>4</sup> ] in [BMIM][NtF<sup>2</sup> ] has positive deviation up to 0.7 mole fraction of [EMIM] [ESO<sup>4</sup> ] due to strong dipole-dipole interaction, dispersion, induction and dipolar forces acting in between these two IL's for entire temperature range (**Figure 12**). The apparent molar volume of [EMIM][ESO<sup>4</sup> ] in [EMIM][HSO<sup>4</sup> ] shows positive deviation as function of the composition from 293.15 to 333.15 K which implies that there is strong packing effect due to similar size of cation in both IL's (**Figure 13**). [EMIM][ESO4] + [BMIM][OAc] gave negative apparent molar volume which means that there is very strong hydrogen bond formation and charge-charge interaction between one and another at molecular level (**Figure 14**).

**Figure 12.** Apparent molar volume of [EMIM][ESO<sup>4</sup> ] in [BMIM][NtF<sup>2</sup> ] at different temperature.

**Figure 13.** Apparent molar volume of [EMIM][ESO<sup>4</sup> ] in [EMIM][HSO<sup>4</sup> ] at different temperature.

there is very strong packing effect. The packing effect caused by a large difference in molecular size and configuration between two IL's, charge transfer, hydrogen bond formation and the ion-dipole attractions are even more dominant in IL's mixtures as function of composi-

] in [EMIM][HSO<sup>4</sup>

] at different temperature.

] due to strong dipole-dipole interaction, dispersion, induction and dipolar forces acting in between these two IL's for entire temperature range (**Figure 12**). The apparent

] has positive deviation up to 0.7 mole fraction of [EMIM]

] in [EMIM][OAc] at different temperature.

tions at T (293.15–343.15) K.

**4.6. Apparent molar volume**

] in [BMIM][NtF<sup>2</sup>

**Figure 11.** Excess partial molar volume of [EMIM][ESO<sup>4</sup>

**Figure 10.** Excess partial molar volume of [EMIM][ESO<sup>4</sup>

134 Laboratory Unit Operations and Experimental Methods in Chemical Engineering

[EMIM][ESO<sup>4</sup>

[ESO<sup>4</sup>

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**Figure 14.** Apparent molar volume of [EMIM][ESO<sup>4</sup> ] in [EMIM][OAc] at different temperature.
