Henry‘s constant

5.4 T HERMODYNAMIC PARAMETERS

5.4.1 Henry‘s constant

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strong Lewis acid−base interactions between the ILs and the dissolved CO2 is not the only effect on the solubility of CO₂‖.

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considered to be the pure gas solute [4, 165]. The fugacity coefficient is assumed equal to unity and Henry‘s law constant (kH) is determined using the following equation [9, 61, 143, 223]:



 



 

 x

k P^CO

H x

2

lim0 5-1

where P is the partial pressure of the gas and k_H (T) will have units of pressure and is inversely proportional to the mole fraction of gas in the liquid (x). For gases that behave nearly ideally, the solubility is linearly related to the pressure. Therefore, the Henry‘s law constant can be found by calculating the linear slope of the data.

The CO2 gas exhibits a nonlinear trend as the CO2 pressure is increased for all the studied RTILs as shown in Fig 5-21 to Fig 5-24 (the curves begin to flatten out, indicating that the IL is beginning to approach its maximum, pressure-independent capacity for CO₂ [39]) so the Henry‘s law constant can be found by fitting a second- order polynomial to the data and calculating the limiting slope as the solubility approaches zero [61, 81]. Accordingly, equation 5-2 was used to model the experimental values [224] with a correlation coefficient (R²) greater than 0.996.

c bx ax

k_H  ²  5-2

The Henry‘s law constant at infinite dilution (kH) was calculated from equation 5-1 as follows:

x b k P^CO

H x 

 



 



2

lim0 5-3

The Henry‘s law constants for all the studied ILs and the correlation coefficients of the polynomial equation (equation 5-2) are presented in Table 5-5. The Henry‘s law constant value is an indication of the gas solubility in the solvent; the decrease of the value is an indication of the increases of gas solubility in the solvent. In addidtion, Henry‘s law constants can be used to classify whether the absorption is of physical or chemical type. Usually, a small value of Henry‘s law constants less than 3 MPa at 298 K would be the case of a chemical absorption for CO2 into ILs [181].

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Fig 5-21 Solubility of CO2 in [C2CNHim]-based ILs as a function of pressure

Fig 5-22 Solubility of CO2 in [C2CNCnim]DOSS ILs as a function of pressure

Fig 5-23 Solubility of CO₂ in dual functionalized-based ILs as a function of pressure

0.0 0.1 0.2 0.3 0.4 0.5 0.6

0 5 10 15 20

P/(bar)

_CO

2

[C₂CNHim]DDS [C₂CNHim]TFMS [C₂CNHim]SBA [C₂CNHim]BS

0.0 0.2 0.4 0.6 0.8

0 5 10 15 20

P/(bar)

CO₂

[C₂CNDim]DOSS [C₂CNOim]DOSS [C₂CNHim]DOSS [C2CNBim]DOSS

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7

0 5 10 15 20

P/(bar)

_CO

2

[C₂CNHeim]DOSS [C₂CNBzim]DOSS [C₂CNAyim]DOSS

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Fig 5-24 Solubility of CO2 in phosphonium-based ILs as a function of pressure These solubility behaviors are more clearly understood in terms of the thermodynamic excess functions (excess Gibbs, excess enthalpy, and excess entropy TSE energies); sufficiently negative values in excess Gibbs usually indicate some chemical complex formations; the heat of mixing (or excess enthalpy) is more negative than TSE. A minimum in excess Gibbs occurs around 50 mol % of the CO2 + IL system, suggesting the 1:1 complex formation, whereas excess Gibbs minimum around 33 mol % of CO2 in indicates the 1:2 (CO2: IL) complex formation [122].

As shown in Table 5-5, the DOSS-based IL shows the lower value compared to the other anions. The [C2CDim]DOSS, [C2C Heim]DOSS and [P8,8,8,14]DOSS show the lower values among the three categories. Moreover, [C2CDim]DOSS shows the lower value among all the studied ILs. The effect of temperature in the solubility of CO2 in the [C2CNDim]DOSS, [C2CNHeim]DOSS and [P8,8,8,14]DOSS ILs was studied and the results are shown in Fig 5-25 and reported in Table 5-6 and Table 5-7.

Henry‘s law constants for these ILs are estimated using equation 5-3 and the results are presented in Table 5-5.

The CO₂ solubility decreases with the increasing temperature, which is in accordance with the results found in most cases of gas dissolution into liquid [181].

Increased temperature causes an increase in kinetic energy. The higher kinetic energy causes more motion in molecules which break intermolecular bonds and escape from solution. In addition, this may be due to the decrease in the inter-ion space as the ions

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7

0 5 10 15 20

P/(bar)

_CO

2

[P_8,8,8,14]DOSS [P_6,6,6,14]DOSS [P_8,8,8C₆P_8,8,8]DOSS₂ [P_8,8,8C₁₀P_8,8,8]DOSS₂

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become active with the increased kinetic energy and are more irregularly distributed.

The effect of temperature is important for the study of the thermodynamic properties.

Table 5-5 Henry‘s law constant and correlation coefficients for the studied ILs Property [C2CNHim]

DDS

[C2CNHim]

SBA

[C2CNHim]

BS

[C2CHim]

TFMS

kH (298 K) 20.07 18.93 22.09 17.02

R² 0.998 0.999 0.997 0.999

[C2CNBim]

DOSS

[C2CNHim]

DOSS

[C2CNOim]

DOSS

[P6,6,6,14] DOSS

kH(298 K) 19.21 15.79 10.16 13.33

R² 0.999 0.999 0.998 0.999

[C2CNBzim]

DOSS

[C2CNAyim]

DOSS

[P8,8,8 C6

P_8,8,8]DOSS₂

[P8,8,8 C10

P_8,8,8] DOSS₂

k_H(298 K) 14.64 19.13 17.47 19.17

R² 0.997 0.998 0.999 0.999

[C₂C Dim]

DOSS

[C₂CNHeim]

DOSS

[P_8,8,8,14] DOSS

k_H (298 K) 7.45 11.40 11.62

R² 0.998 0.999 0.999

k_H (313 K) 10.56 30.01 31.88

R² 0.998 0.999 0.999

k_H (343 K) 19.11 43.09 48.02

R² 0.998 0.999 0.999

Moreover, Henry‘s law constant as an indication of the gas solubility in the solvent was applied to study the effect of temperature on the CO₂ solubility capacity of these ILs. The experimental solubility data for [C₂CN Dim]DOSS, [C₂CN Heim]DOSS and [P8,8,8,14]DOSS at 313 and 343 K are reported in Table 5-6 and Table 5-7 and also plotted in Fig 5-25. Henry‘s law constants for these ILs are estimated using equation 5-3 and the results are presented in Table 5-5.

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Table 5-6 Experimental solubility data for CO₂ in [C₂CN Dim]DOSS, [C₂CN Heim]DOSS and [P8,8,8,14]DOSS at 313 K

Pressure (bar)

CO2 (mol fraction)

[C₂CN Dim]DOSS [C₂CN Heim]DOSS [P_8,8,8,14]DOSS

1±0.01 0.066739 0.025730 0.024222

5±0.01 0.222589 0.104131 0.098029

10±0.03 0.386501 0.174275 0.164063

15±0.04 0.495395 0.225430 0.212220

20±0.05 0.573745 0.271642 0.255724

gCO2/g IL

1±0.01 0.00459 0.00170 0.00159

5±0.01 0.01839 0.00747 0.00698

10±0.03 0.04047 0.01356 0.01261

15±0.04 0.06306 0.01869 0.01730

20±0.05 0.08646 0.02396 0.02207

Table 5-7 Experimental solubility data for CO2 in [C2CN Dim]DOSS, [C2CN Heim]DOSS and [P_8,8,8,14]DOSS at 343 K

Pressure (bar)

CO2 (mol fraction)

[C2CN Dim]DOSS [C2CN Heim]DOSS [P8,8,8,14]DOSS

1±0.01 0.036888 0.017921 0.016081

5±0.01 0.123028 0.072527 0.065078

10±0.03 0.213624 0.121383 0.108917

15±0.04 0.273811 0.157012 0.140887

20±0.05 0.317116 0.189199 0.169768

gCO2/g IL

1±0.01 0.00246 0.00117 0.00105

5±0.01 0.00901 0.00502 0.00447

10±0.03 0.01745 0.00887 0.00785

15±0.04 0.02422 0.01196 0.01053

20±0.05 0.02983 0.01499 0.01313

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Fig 5-25 Solubility of CO₂ in [C₂CNDim]DOSS, [C₂CNHeim]DOSS and [P8,8,8,14]DOSS ILs at different temperatures