Equilibrium Thermodynamic Properties of Aqueous Solutions of Ionic Liquid 1-Ethyl-3-Methylimidazolium Methanesulfonate [EMIM][MeSO3]

The ionic liquid 1-ethyl-3-methylimidazolium methanesulfonate ([EMIM][MeSO3]) has been considered as a promising alternative desiccant to triethylene glycol and lithium bromide commonly used in the industry. In this paper, the water activity coefficient of this binary system was measured from 303 K to 363 K with water concentration from 18% to 92%. The interaction energies between the ionic liquid molecules (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${g}_{22}$$\end{document}g22) and between the ionic liquid and water molecules (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${g}_{12}$$\end{document}g12) for the [EMIM][MeSO3]/water binary system were determined from the water activity coefficient data using the Non-Random Two-Liquid (NRTL) model. The magnitude of the interaction energy between the [EMIM][MeSO3] and water molecules (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${g}_{12}$$\end{document}g12) was found to be in the range of 45~49 kJ/mol, which was about 20% larger than that between the water molecules (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${g}_{11}$$\end{document}g11) in the [EMIM][MeSO3]/water system. The large (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${g}_{12}$$\end{document}g12) can explain many observed macroscopic thermodynamic properties such as strong hygroscopicity in the ionic liquid [EMIM][MeSO3]. These interaction energies were used to determine the heat of desorption of the [EMIM][MeSO3]/water system, and the obtained heat of desorption was in good agreement with that calculated from the conventional Clausius-Clapeyron Equation.

activity coefficients data. These interaction energies were used to determine the heat of desorption of the [EMIM] [MeSO 3 ]/water system, which was in good agreement with those calculated from the Clausius-Clapeyron Equation. A formula to predict heat of desorption from the interaction energies was also developed for the binary systems.

Theoretical Background
Water activity coefficient. The activity coefficient of water γ H o 2 is a fundamental thermodynamic parameter that accounts for deviations from ideal behavior in non-ideal solutions, such as the aqueous ionic liquid solutions, which is defined as 7,8 : 2 is often used for the comparison of the hygroscopicity or absorption strength of different desiccants 7 .
Non-random two-liquid (NRTL) model. The  where the subscripts 1 and 2 refer to component 1 and component 2 in the binary solution, respectively, ∆ − g 12 11 and ∆ − g 12 22 are the exchange in the interaction energy between molecules, α 12 is the non-randomness parameter, R is the molar gas constant, and T is the absolute temperature. In the case of infinite dilution, the NRTL equations reduce to 2, 12 22 12 11 12 12 11 The water activity coefficient at infinite dilution γ ∞ H O, 2 can be used to compare the hygroscopicity or absorption strength of different desiccants.
In the NRTL model, the exchange in the interaction energy ∆ = − − g g g 12 11 12 11 , which is the interaction energy change as a result of breaking a 1-1 interaction g 11 and forming a 1-2 interaction g 12 3 ]/water binary system. The interaction energy between the ionic liquid and water molecules g 12 can be determined using the formula: = ∆ + − g g g 12 12 11 11 if the interaction energy between water molecules g 11 is known. Similarly, the interaction energy between the ionic liquid molecules g 22 can be determined by = ∆ + − g g g 22 12 22 12 . These molecular interaction energy properties are related to many macroscopic thermodynamic properties such as heat of desorption, heat capacity, hygroscopicity, and water vapor pressure. One application of these molecular interaction energies is that they can be used to predict the heat of desorption of the aqueous ionic liquid solutions with water concentration from 0% to 100%. In comparison, the Clausius-Clapeyron Equation determines the heat of desorption at the water concentration where the vapor pressure and temperature are known.
(VLE) data (p and T) to the thermodynamic property, enthalpy of vaporization (∆H v ), which is given by 21 v where p is the vapor pressure at the temperature T, ∆H v is enthalpy of vaporization, R is the molar gas constant, and C is a constant. In Eq. (7), ∆H v is assumed to be independent of T.
where a is the temperature coefficient. So the modified Clausius-Clapeyron Equation for the ionic liquid solutions can be written as follows: Therefore ∆H v can be determined from Eqs. (8) and (9) when the VLE data are measured.
Uncertainty calculation. The experimental uncertainty in this experiment is estimated using the root-sum-square method suggested by Moffat 23 : In particular, whenever the equation describing the result is a pure "product form", as shown in Eq. (11): the relative uncertainty can be calculated by Eq. (12):  www.nature.com/scientificreports www.nature.com/scientificreports/ VLE measurement. The data logging and the conversion from RH and T to water vapor pressure were performed using the HW4-E software in a computer.

VLe measurements. Twelve [EMIM][MeSO 3 ]/water solutions with molar concentration of water from 18%
to 92% were prepared in the VLE measurements. For each solution, its RH was measured at temperatures 303 K, 323 K, 343 K, and 363 K. The sample solution with an approximate volume of 100 ml was placed in the reactant bottle. The oven temperature was set to the desired temperature, and the sample solution was heated and stirred vigorously with magnetic stirrers to get homogeneous mixing. At the same time, the data logging was started. After the system reached the equilibrium and the RH stayed unchanged for 30 minutes, the equilibrium temperature and RH were recorded. A series of equilibrium temperature and water vapor pressure (or RH) data were obtained for the [EMIM][MeSO 3 ]/water solutions.

Results and Discussion
Activity coefficient of water. The  were determined using the measured RH. The relative uncertainty of the measured mole fraction x(H 2 O) was found to be less than 5.02% using Eq. (12). The RH and T were measured simultaneously using the humidity sensor with an uncertainty of T = ±0.1 K and RH = ±0.8% of the RH reading. Figure 2 shows the measured water vapor pressure in [EMIM][MeSO 3 ]/water binary solutions versus the molar fraction of water in a temperature range of 303 K to 363 K.
The effect of the ionic liquid on the non-ideality of the aqueous solutions can be expressed by the activity coefficients of water γ H O 2 , which was calculated by Eq. (1). is in the range of 0.102 to 0.151 at temperatures from 303 K to 363 K, more than 4 times lower than that for triethylene glycol, which indicates that   Interaction energy between molecules and non-randomness parameters. The exchange in interaction energy ∆ − g 12 11 , and ∆ − g 12 22 (3-4)). These parameters are listed in Table 4. In Table 4, the subscript "1" represents water, while the "2" represents the ionic liquid [EMIM][MeSO 3 ]. ∆ − g 12 11 12 11 and ∆ − g 12 22 decreases with increasing temperature, which could be attributed to the increasing thermal motion of the molecules 18 .

is the interaction energy change as a result of breaking an H 2 O-H 2 O interaction and forming a [EMIM][MeSO 3 ]-H 2 O interaction. As shown in
For comparison, the exchange in interaction energy ∆ − g 12 11 and ∆ − g 12 22 in some other ionic liquids/water binary solutions were summarized in Table 5 19,20,24,25 . It should be noted that the ∆ − g 12 11 25 , which is another promising ionic liquid for moisture removal and shares similar chemical structure 26,27 . The difference in interaction energy may result from the shorter alkyl group in [EMIM][MeSO 3 ] anion, which is favorable for the bonding with water molecule 28,29 .

in the [EMIM][MeSO 3 ]/ water binary solution was found to be larger than that in 1-ethyl-3-methylimidazolium ethylsulfate ([EMIM] [EtSO 4 ])/water solution
The interaction energy between water molecules g 11 is the molar vaporization energy of water (i.e., cohesive energy) but has a negative sign on it 30 , which is available in liteature 31 . The interaction energy between the ionic liquid and water molecules g 12 can be calculated using the formula: = ∆ + − g g g 12 12 11 11 . Similarly, the interaction energy between the ionic liquid molecules g 22 can be determined by = ∆ + − g g g 22 12 22 12 . The obtained interaction energies g g , 11 12 and g 22 are summarized in Table 4. These molecular interaction energies have negative signs due to the intermolecular attractive forces. It is found in Table 4 that the molecular interaction energies become less negative when the temperature increases. The magnitude of the interaction energy between the [EMIM] [MeSO 3 ] and water molecules was found to be in the range of 45~49 kJ/mol, which was 20% larger than that     3 ] and water molecules can explain many reported macroscopic thermodynamic properties, such as small water activity coefficient and strong hygroscopicity.
The parameters α 12 is related to the non-randomness in the liquid mixture; when α 12 is zero, the local distribution around the center molecule is completely random. The non-randomness parameters α 12 in the [EMIM] [MeSO 3 ]/water binary solutions were found to be around 0.5, as shown in Table 4. The values of α 12 are generally consistent with those reported for other water/hygroscopic ionic liquid binary solutions 17,20,24  The extent of the correlation between the experimental data and the NRTL model was evaluated by calculating the absolute relative deviation (ARD) 24 : where n is the number of data points, γ exp is the γ value calculated from experimental data, and γ NRTL is the γ value calculated from the NRTL model. The values of ARD are also listed in Table 4, which implies a satisfactory correlation in the test temperature range.
Heat of desorption. One application of these molecular interaction energies is that they can be used to determine the heat of desorption of the aqueous ionic liquid solutions. The internal energy in the aqueous ionic liquid solution U l is the sum of the excess internal energy of the solution U E and the molar internal energy of the pure component U i : where n 1 and n 2 are the mole number of component 1 (i.e., water) and component 2 (i.e., ionic liquid), respectively. In the evaporation process, the intermolecular interaction energy is dominant, and therefore the intramolecular interaction energy can be neglected in the internal energy. The excess internal energy of the aqueous ionic liquid solution U E can be evaluated as 18,32 : where g 11 and g 22 are the molar interaction energy between water molecules and between the ionic liquid and water molecules, respectively, and g (1) and g (2) represent the molar residual Gibbs energy for molecule cells having component 1 and component 2 at the center respectively 33 . g (1) and g (2) can be calculated as: www.nature.com/scientificreports www.nature.com/scientificreports/ The formula can be used to predict the heat of desorption in the aqueous binary solutions when the interaction energies are given. Figure 4 shows the heat of desorption calculated from the interaction energies in the [EMIM][MeSO 3 ]/water binary solutions with water fraction from 0% to 100% at temperatures 303 K, 323 K, 343 K, and 363 K. The desorption heat calculated by the Clausius-Clapeyron Equation is also shown for comparison. As shown in Fig. 4, they are in good agreement. The desorption heat ∆H v decreases with increasing temperature for a given water concentration. This trend is consistent with the temperature dependence of the interaction energy parameters ∆ − g 12 11 and ∆ − g 12 22 listed in Table 4, which could be attributed to the increasing thermal motion of the molecules at elevated temperatures. Due to the strong bonding forces between water and [EMIM][MeSO 3 ], the desorption heat or enthalpy of vaporization of water in the [EMIM][MeSO 3 ]/water solutions is always higher than the enthalpy of vaporization of pure water at the same temperature, but the difference becomes smaller when the water concentration approaches 100%.

conclusion
In this work, molecular thermodynamic properties such as interaction energies and non-randomness parameter of the [EMIM][MeSO 3 ]/water binary system were determined from the water activity coefficient data using the Non-Random Two-Liquid (NRTL) model. The water activity coefficient of this binary system was measured with molar concentrations of water from 18% to 92% at temperatures 303 K, 323 K, 343 K, and 363 K. The interaction energy between the ionic liquid [EMIM][MeSO 3 ] and water molecules (g 12 ) was found to be ~20% larger than that between the water molecules (g 11 ). The exchange in interaction energy ∆g followed the order [

Data availability
All data generated or analyzed during this study are included in this published article.