Imidazolium-based ionic liquids containing FAP anion: Thermodynamic study

Imidazolium-based ionic liquids containing FAP anion: Thermodynamic study

Journal of Molecular Liquids 287 (2019) 110959 Contents lists available at ScienceDirect Journal of Molecular Liquids journal homepage: www.elsevier...

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Journal of Molecular Liquids 287 (2019) 110959

Contents lists available at ScienceDirect

Journal of Molecular Liquids journal homepage: www.elsevier.com/locate/molliq

Imidazolium-based ionic liquids containing FAP anion: Thermodynamic study Dzmitry H. Zaitsau a,⁎⁎, Sergey P. Verevkin a,b,⁎ a b

Department of Physical Chemistry and Department of “Science and Technology of Life, Light and Matter”, University of Rostock, 18059, Dr-Lorenz-Weg 2, Rostock, Germany Department of Physical Chemistry, Kazan Federal University, Kremlevskaya str. 18, 420008 Kazan, Russia

a r t i c l e

i n f o

Article history: Received 23 March 2019 Received in revised form 9 May 2019 Accepted 10 May 2019 Available online 16 May 2019 Keywords: Ionic liquid Enthalpy of vaporization Enthalpy of solution Vapor pressure Enthalpy of formation

a b s t r a c t New experimental vapor pressures and vaporization enthalpies of the ionic liquids (ILs) [C2mim][FAP], [C4mim] [FAP] , and [C6mim][FAP] with [FAP] = tris(pentafluoroethyl)trifluorophosphate have been measured by the Langmuir method combined with the Quartz Crystal Microbalance. Linear dependence of vaporization enthalpies on alkyl chain length was observed. Gas-phase enthalpies of formation of ILs were calculated by quantum chemistry. Solution enthalpies of ILs available from the literature were used for calculation the aqueous enthalpy of formation of the ΔfHom(FAP− aq) anion in combination with quantum-chemical results. These results will facilitate chemical engineering calculations of processes involving ILs. © 2019 Elsevier B.V. All rights reserved.

1. Introduction Last decades ionic liquids (ILs) have been in focus of scientific and practical endeavours. Due to their unusual physicochemical properties ILs are offering prospects for unusual technological innovations. Variation on structures of the cation and anion constituting an IL is countless. Thus, physicochemical properties of ILs could be tailored to any specific application. In this context, an accurate knowledge of the structure-property relations in ILs families is important to reduce the synthetic efforts and obtain materials with desired properties. ILs with fluorinated anions are commonly used for different practical applications. Admittedly, the most broadly used anions are bis(trifluoromethylsulfonyl)imide [N (CF2SO3)2] and hexafluorophosphate, [PF6]. However, the ILs with hydrophobic [PF6]-anion are hydrolytically unstable, especially at elevated temperature [1]. The HF elimination and reaction with water exclude the [PF6]-containing ILs from practical applications. To address this disadvantage of the hexafluorophosphate anion, the replacement of some fluorine atoms by hydrophobic perfluoroalkyl-groups looks promising as a way to increase the hydrolytic stability of fluorophosphates [2]. Based on this idea Merck made commercially available a group of ILs based on tris (pentafluoroethyl)trifluorophosphate ([FAP]) anion [2,3]. These new ILs

⁎ Correspondence to: S.P. Verevkin, Department of Physical Chemistry and Department of “Science and Technology of Life, Light and Matter”, University of Rostock, 18059, DrLorenz-Weg 2, Rostock, Germany. ⁎⁎ Corresponding author. E-mail addresses: [email protected] (D.H. Zaitsau), [email protected] (S.P. Verevkin).

https://doi.org/10.1016/j.molliq.2019.110959 0167-7322/© 2019 Elsevier B.V. All rights reserved.

exhibit excellent thermal and electrochemical stability [2], they are also very hydrophobic, but miscible with polar organic solvents [4]. These remarkable properties can be useful for development of new technologies in electrochemistry [5] and gas absorption [6,7]. This paper extends our previous studies on the ILs containing fluorinated anions [8–10] and deals with vapor pressure measurements on imidazolium based ILs with the [FAP] anion (see Fig. 1). 2. Experimental section 2.1. Materials The sample of 1-ethyl-3-methylimidazolium tris(pentafluoroethyl) trifluorophosphate [C2mim][FAP] (CAS # 377739–43-0, C12H11F18N2P, molecular weight 556.17 g·mol−1) 1-butyl-3-methylimidazolium tris (pentafluoroethyl)trifluorophosphate [C4mim][FAP] (CAS # 917762–915, C14H15F18N2P, molecular weight 584.23 g·mol−1) and 1-hexyl-3methylimidazolium tris(pentafluoroethyl)trifluorophosphate [C6mim] [FAP] (CAS # 713512–19-7, C16H19F18N2P, molecular weight 612.28 g·mol−1) used in this work were purchased from Sigma-Aldrich (see Table 1) with the purity assay of N99% mass determined by the HPLC method with the halide content ≤100 ppm, and water amount ≤ 100 ppm according to the analysis certificate. Prior to the experiments, samples were subjected to vacuum evaporation at 413 K and 10−5 Pa for N24 h to reduce possible traces of solvents and moisture. Samples used in vaporization studies were additionally conditioned inside of the vacuum chamber at the highest temperature of experiment within 12 h. This additional purification allowed for removing of residual traces of water

2

D.H. Zaitsau, S.P. Verevkin / Journal of Molecular Liquids 287 (2019) 110959

where the K´ = (9.5 ± 1.1) × 10−6 Pa·s·kg1/2·Hz−1·K−1/2·mol−1/2 is the empirical constant containing all parameters of the Sauerbrey equation as well as the parameters specific for the geometry of the experimental setup [10]; T is the temperature in K; M is the molar mass of the studied compound in the gas phase in kg·mol−1. The K´-value for our apparatus was evaluated with the help of reliable vapor pressure data available for imidazolium and pyridinium based ILs [10]. Using the experimental vapor pressures psat measured with the QCM technique the molar enthalpy of vaporization, Δgl Hom(T) at experimental temperatures is obtained according to the Clarke-Glew equation [13]: Δgl Gm° ðT av Þ þ Δgl H m° ðT av Þ T av      1 1 T av T ° ; −1 þ ln − þ Δgl C p;m T T av T T av

R ln ðpsat =po Þ ¼ −

ð3Þ

where Tav is the average temperature for the interval of the study, R = 8.3144598 J·K−1·mol−1 is the ideal gas constant and Δgl G°m(Tav) is the change in standard Gibb's energy during vaporization . The value Δgl Cp, o o o m = Cp, m(g) – Cp, m(liq) is the difference between the molar heat capacities of the gaseous, Cop, m(g), and the liquid phase, Cop, m(liq), respectively. The vaporization enthalpy Δgl Hom(298.15 K) at the reference temperature is calculated according to the Kirchhoff's equation: Fig. 1. ILs under study in this work: 1-ethyl-3-methylimidazolium tris(pentafluoroethyl)trifluorophosphate [C2mim][FAP]; 1-butyl-3-methylimidazolium tris(pentafluoroethyl)and 1-hexyl-3-methylimidazolium tris trifluorophosphate [C4mim][FAP], (pentafluoroethyl)-trifluorophosphate [C6mim][FAP].

and volatile impurities as well as for collecting the amount of the vaporized IL required for the FTIR analysis. 2.2. Determination of the molar vaporization enthalpy and absolute vapor pressures with Quartz-Crystal Microbalance (QCM) Vapor pressures and standard molar enthalpies of vaporization of [Cnmim][FAP] series were determined by using the QCM method [11]. Vaporization enthalpies were derived from the temperature dependencies of the experimentally measured change in the vibrational frequency of the quartz crystal. In our method a sample of an IL is placed in an open cavity (Langmuir evaporation) inside of the thermostat block and it is exposed to vacuum (10−5 Pa) with the whole open surface of the loaded compound. The QCM is placed directly above the measuring cavity containing the sample. During the vaporization into a vacuum, a certain amount of sample is deposited on the quartz crystal. The change of the vibrational frequency Δf was directly related to the mass deposition Δm on the crystal according to the Sauerbrey equation [12]:

Δgl H om ð298:15 KÞ ¼ Δgl Hom ðT av Þ þ Δgl C op;m ð298:15−T av Þ

ð4Þ

To detect and avoid any possible effect of impurities on the measured frequency loss rate (df·dt−1), a typical experiment was performed in a few consequent series with increasing and decreasing temperature steps. Every series consisted of 7 to 11 temperature points of mass loss rate determination. Several runs have been performed to test the reproducibility of the results. The study was finished when the enthalpy of vaporization, Δgl Hom(Tav), obtained in the sequential runs by adjusting Eq. (3) to the temperature dependent rates (df·dt−1) agreed within the assessed experimental uncertainty of about ±1 kJ·mol−1. In order to confirm the absence of decomposition of IL under the experimental conditions, the residual IL in the crucible and the IL-deposit on QCM were analyzed by ATR-FTIR spectroscopy. As can be seen in Figs. S1 – S3 of the Supporting Information no changes in the spectra have been detected. Primary experimental results of the QCM studies are given in Table S1 in the Supporting Information. The final uncertainty of the absolute vapor pressure determination is estimated to be 50% and mostly determined by the uncertainty of K′ coefficient. 2.3. Quantum-chemical calculation

Δf ¼ −C  f  Δm  SC −1 2

ð1Þ

where f is the fundamental frequency of the crystal (6 MHz in this case) with Δf b b f, SC is the surface of the crystal, and C is a constant [10]. The measured frequency change rates (df·dt−1) can be used for calculation of absolute vapor pressures psat according to the equation: df psat ¼ K0 dt

rffiffiffiffiffiffi T : M

ð2Þ

Table 1 Provenance and purity of [Cnmim][FAP] ILs used in this work. ILa

CAS

Source

Purity

Analysis method

[C2mim][FAP] [C4mim][FAP] [C6mim][FAP]

377739-43-0 917762-91-5 713512-19-7

Sigma-Aldrich Sigma-Aldrich Sigma-Aldrich

≥0.99 ≥0.99 ≥0.99

HPLC HPLC HPLC

a

The abbreviation [FAP] = tris(pentafluoroethyl)trifluorophosphate.

The bulky [FAP] anion have a flexible structure and comprehensive search of the conformers of the ion pair for [C2mim][FAP] is a challenging task [14]. It is well established, that the dispersion forces contribute N10% of the total intermolecular interactions in ILs, what can totally change the calculated distribution of the conformers for bulky molecules [15,16]. Therefore, we have carried out a careful search for stable conformers by using the “shaking” and “annealing” MD procedure implemented in the GFn-xtb semi-empirical method by Grimme et al. [17]. At a first step, two most stable anion conformers of the anion found with at B3LYP/6-31+G(2d,2p) [14] were combined with rotational conformers of [C2mim] cation forming the set of “in-plane” (front and rear) and “on-top” conformers of the ionic pairs. The set of conformers constructed in this way was optimized by the GFn-xtb procedure [17] and 30 stable conformers were obtained. These conformers were further optimized at BP86/def2-SVP-D3(BJ) level of theory. Admittedly, conformers with the energy difference ≥ 10 kJ·mol−1 are practically not populated in the gas phase. Thus, from this set we selected nine conformers with the lowest energies (energy difference lower

D.H. Zaitsau, S.P. Verevkin / Journal of Molecular Liquids 287 (2019) 110959

than 10 kJ·mol−1 from the most stable) and they were additionally optimized at the B3LYP/def2-TZVPP level of the theory [18,19] with the D3 dispersion correction [20] and Becky-Jonson damping [21]. Due to this optimization step the number of the distinguishable conformers was reduced to five. For these five conformers the total energies E were calculated at the RI-MP2-JK/def2-TZVPP level of theory. The total enthalpy of the equilibrium mixture of conformers was calculated as the H298–value of the most stable conformer plus a correction 〈ΔH〉 for the presence of the mixture of low-energetic conformers, calculated by the statistical thermodynamics, assuming that all conformers have the same entropy value (ΔS = 0 J·K−1·mol−1 and ΔG = ΔH):    ΔH i exp −ΔHi RT −ΔH   ; P i exp RT

P hΔH i ¼

ð5Þ

where ΔHi is the energy (enthalpy) of ith conformer in comparison to the most stable conformer, 〈ΔH〉 is the correction to the final value of H298. Total energies H298 of [Cnmim][FAP] conformers were calculated with DLPNO-CCSD(T) method [22]. Due to the large amount of computational work only two single point calculations with DLPNO-CCSD(T)method were performed by using the def2-TZVPP basis set [19]. A thermal correction was calculated at rigid rotator, harmonic oscillator approximation. All computations were carried out by using ORCA 3.0.3 package [23]. The conformational correction was calculated to be 〈ΔH〉 =1.45 kJ·mol−1 for [C2mim][FAP]. 3. Results and discussion 3.1. Absolute vapor pressures of [Cnmim][FAP] Modern catalytic processes like Solid Catalyst with Ionic Liquid Layer (SCILL) [13] or Supported Ionic Liquid Phase (SILP) [24] require the knowledge of vapor pressure of an IL at any temperature in order to assess a possible long-term uptake of the IL. The frequency changes rates (df·dτ−1) measured by the QCM were used for calculation of the absolute vapor pressures psat of [Cnmim][FAP] according to Eq. (2) (see Table 2) with help of the empirical constant K´ evaluated for our experimental setup recently [10]. It is well-established [25], that the fitting of the experimental vapor pressures by using the Clarke and Glew equation [13] is able to provide reliable interpolation and extrapolations of vapor pressures. The Clarke and Glew equation referenced to T = 298.15 K is given as follows:

3

phases, J·K−1·mol−1; T is the temperature of the vapor pressure experiment, K. Temperatures 373 K and 473 K seem to be of reasonable choice for many practical applications and extremely low values of vapor pressures of the [FAP] based ILs at these temperatures (see Table 2) indicate that the negligible mass uptake of the IL in different catalytic or separation applications can be expected even at elevated temperatures. The absolute vapor pressure data on ILs are still seldom available in the literature and it is interesting to compare the general vapor pressure levels within the families of imidazolium-based ILs with fluorinated anions [N(CF2SO3)2]−, [PF6]−, [BF4]−, and [FAP]− (see Fig. 2). It is apparent from Fig. 2 that the vapor pressures of ILs with the [FAP] and [N(CF2SO3)2] ions are of 200 to 300 times higher than those for the [BF4] and the [PF6] ILs. Values of absolute vapor pressures of the [FAP] and [N(CF2SO3)2] series are not significantly different. The values of absolute vapor pressures of the [PF6] and the [BF4] series are also rather close. It makes oneself conspicuous, that the vapor pressure chain-length dependence for all imidazolium-based ILs demonstrates very similar behavior. The obvious decrease of the vapor pressure for ILs with the [C2mim] ion in comparison to those with the [C4mim] ion seems to be common for these series of ILs, but we are still reticent with explanation of this artefact. 3.2. Standard molar vaporization enthalpies from vapor pressure measurements 3.2.1. Adjustment of vaporization enthalpies to the reference temperature 298.15 K Standard molar enthalpies of vaporization of [C2mim][FAP], [C4mim] [FAP], and [C6mim][FAP] were derived from the temperature dependence of the vapor pressures measured by the QCM (see Table 3, column 4) are referenced to the average temperature Tav (see Table 3, column 3), which is the middle of the temperature range under study. Admittedly, for the adjustment of vaporization enthalpies to any desired temperature, the Kirchhoff's equation can be used (see Eq. (4)). Isobaric heat capacity differences Δgl Cop, m which are required for temperature adjustment according to Eq. (4) are usually derived with help of at least four well-established methods: from experimental vapor pressures,

Δg G ° ð298:15 KÞ þ Δgl Hm° ð298:15 KÞ R ln ðpsat =po Þ ¼ − l m 298:15      1 1 298:15 T ° ð298:15 KÞ − þ Δgl C p;m −1 þ ln 298:15 T T 298:15 ð6Þ where psat is the saturated vapor pressure of the sample, Pa; po = 105 Pa is the standard pressure; Δgl Gom(298.15 K) is the change of the standard Gibbs energy during vaporization of the sample at the reference temperature, J·mol−1; Δgl Hom(298.15 K) is the enthalpy change during vaporization of the sample at Τ = 298.15 K, J·mol−1; Δgl Cop, m(298.15 K) is the isobaric heat capacity difference between gaseous and condensed Table 2 Absolute vapor pressures of ILs [Cnmim][FAP] with n = 2, 4 and 6 at 373 K and at 473 K. Cation

[C2mim] [C4mim] [C6mim]

psat × 10-6 [Pa]

psat × 10-6 [Pa]

373 K

473 K 13 15 8.2

1032 1652 1037

Fig. 2. Chain-length dependence of absolute vapor pressures scaled with k at T = 423.15 K for homologous series [Cnmim][N(CF2SO3)2] (○) from [8,10] (k = 1/3), [Cnmim][PF6] (◊) from [10] (k = 3), [Cnmim][BF4] (Δ) from [9] (k = 3), and [Cnmim][FAP] (☆) this work (k = 1/3). For illustrative reason the absolute vapor pressures of ILs were scaled with the coefficients k given in parenthesis.

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D.H. Zaitsau, S.P. Verevkin / Journal of Molecular Liquids 287 (2019) 110959

Table 3 Compilation of data on molar heat capacities Cop, m and heat capacity differences (in J.K−1.mol−1) at 298.15 K. Cop, m(liq)a

Cop, m(liq)b

Cop, m(liq)c

Δgl C op;m d

Δgl C op;m e

Δgl C op;m f

1

2

3

4

[C2mim][FAP] [C4mim][FAP]

– 769 [27] (697) [28] (730) [4] 1441 [29]

[C6mim][FAP] [P6,6,6,14][FAP] a b c d e f

5

6

7

740 806

703

−114 ± 20 −131 ± 20

−105 ± 15 −105 ± 15

−108 ± 12 −114 ± 12

871 1595

827

−146 ± 20

−112 ± 15

−124 ± 12

Experimental results. Calculated according to the group-additivity procedure suggested by Ahamadi et al. [30]. Calculated by scaling Copm(liq) from column 3 with factor 0.95. Values given in bold have been used for calculations of Δgl C op;m in column 5. o Calculated according to Eq. (9) with the Cpm (liq)-values given in bold in this table. Calculated according by using volumetric properties according to Eqs. 7 and 8. Weighted average value calculated taking individual uncertainties as the weighting factor.

from empirical and theoretical heat capacities Cop, m(liq) and Cop, m(g), from the Cop, m(liq)-based empirical correlations, and from volumetric properties. Details on these methods could be found elsewhere [8,25,26]. In general, all four methods should be applied and Δgl Cop, mresults compared, provided that sufficient amount of the input data are available. In the frame of this work we used the volumetric properties based method to assess the Δgl Cop, m-values. In series of our recent works [8,25], we demonstrated that a general thermodynamic equation:  Δgl C op;m ¼ −2R– C opm −C ovm

−1

liq

R ¼ 8:3144598 JK −1 mol

:

ð7Þ

can be successfully used for reliable assessment of the Δgl Cop, m-values ILs. The crucial advantage of Eq. (7) is that the contribution (Copm −

for Covm)liq is derived from the experimental volumetric properties with help of equation [8]:  C opm −C ovm

liq

¼

α 2p V m T; κT

ð8Þ

where αp, is the thermal expansion coefficient, K−1; κT, is the isothermal compressibility, Pa−1; Vm, is the molar volume, m3·mol−1, and T, is the temperature, K. Data on volumetric properties for the [Cnmim][FAP] family available in the literature were collected and evaluated in Table S2. Values of Δgl Cop, m calculated according to Eqs. 7 and 8 are given in Table 3, column 6. In order to get more confidence in the Δgl Cop, m-values estimated from the volumetric properties, the empirical method based on the liquid phase molar heat capacities Cop, m(liq) was additionally applied in this work. From our experiences this method is very practical because Cop, m(liq)-values can be easily measured by using differential scanning calorimetry or even reliably calculated by numerous group-additivity procedures [8,30]. The idea of this method is that the Δgl Cop, m –values, if correlated with the experimental Cop, m(liq, 298.15 K) show a simple

Table 4 Calculations of the heat capacity differences for imidazolium based ILs and molecular compounds using equation: Δgl Cop, m/J·K−1·mol−1 = k×Cop, m(liq) + m. Compoundsa

k

m

R2

Reference

[Cnmim][N(CF2SO3)2] [Cnmim][PF6] Molecular compounds

−0.26 ± 0.05 −0.40 ± 0.07 −0.26 ± 0.05

69 ± 37 91 ± 29 10.6 ± 15

0.950 0.986 0.97

[8] [10] [31]

a Values of Δgl Cop, m and Cop, m(liq) used for correlation were taken from our previous studies. Uncertainties are presented as the extended uncertainties corresponding to the 0.95 confidence level and k = 2.

linear equation. For example, in our previous study of the [Cnmim][N (CF2SO3)2]-family we obtained the following linear equation (see Table 4): Δgl C op;m ¼ C op;m ðliq; 298:15 KÞ  ð−0:26  0:05Þ þ ð69  37Þ

ð9Þ

For generalization, we have additionally analyzed relationships between Δgl Cop, m and Copm(liq, 298.15 K) for imidazolium ([Cnmim] [Anion]) based ILs with the [N(CF2SO3)2]− and [PF6]− anions (see Table 4). Coefficients of a general empirical equation: Δgl C op;m =J  K−1  mol

−1

¼ k  C op;m ðliqÞ þ m

ð10Þ

for these ILs with the fluorinated anion are compiled in Table 4. It has turned out that the nature of the anion hardly affects the Δgl Cop, m –values (at least within the significant uncertainties of the empirical coefficients k and m). Surprisingly, the coefficients k and m even for the molecular compounds (derived from analysis of data for 135 compounds cross over organic chemistry [31]) are very close to those of the fluorinated ILs [Cnmim][N(CF2SO3)2] and [Cnmim][PF6]. These observations have justified the assessment of the Δgl Cop, m– values for imidazolium based ILs with tris(pentafluoroethyl) trifluorophosphate anion [FAP] with help of Eq. (9), which in our opinion is the best statistically established empirical correlations of this type. It has turned out that the heat capacities Cop, m(liq) required for calculations according to Eq. (9), have been found (see Table 3) only for [C4mim][FAP] and [C6mim][FAP]. Unfortunately, these values seem to be highly inconsistent, because the available heat capacity of the [C6mim][FAP] is expected to be higher than those of the [C4mim][FAP], but such expectation is not supported having the scattered experimental Cop, m(liq)-values for the latter IL (see Table 3). A simple way to establish consistency of the available Cop, m(liq)-values is to use any group-additivity (GA) method. There is not a fault of differently shaped GA methods for estimation of isobaric heat capacities [8,30,32]. Taking into account that evaluation and testing of GA methods for [FAP] containing ILs was not in focus of the current study, we arbitrary selected the most simple and straightforward additive approach for assessment of Cop, m(liq, 298.15 K) developed by Ahamadi et al. [30]. The empirical formula and contributions for constituent elements are collected in Table S3. The Cop, m(liq)-estimates for [C2mim][FAP], [C4mim][FAP], and [C6mim][FAP] are collected in Table 3, column 3. As it can be seen from this table, the additive method provides systematically higher values in comparison to the available experiment. For validation of the GA method for the [FAP] containing ILs we additionally used the experimental value Cop, m(liq) = 1441 J·K−1·mol−1 for [P666,14][FAP] reported by Ferreira et al. [29]. The estimate Cop, m(liq) = 1595 J·K−1·mol−1 according to Ahamadi et al. [30]. was also about 10% higher in comparison to the experiment. Nevertheless, the GA estimates have been helpful at least to

D.H. Zaitsau, S.P. Verevkin / Journal of Molecular Liquids 287 (2019) 110959

set preferences and to select the experimental result Cop, m(liq) = 769 J·K−1·mol−1 for [C4mim][FAP], reported by Ge et al. [27] as the reliable value. The latter result was used to obtain the scaling factor 0.95 and assess the Cop, m(liq)-values for [C2mim][FAP] and [C6mim][FAP] by scaling the GA estimates (see Table 3, column 4). Values of Δgl Cop, m calculated according to Eq. (8) by using the Cop, m(liq)-values (Table 3, column 4) are given in Table 3, column 5. Now we have assessed the Δgl Cop, m-values (Table 3, columns 3 and 4) with help of two independent procedures. These values are in agreement within their uncertainties and it is reasonable to derive the average weighted value (Table 3, column 6), taking individual uncertainties as the weighting factor. The latter evaluated Δgl Cop, m-values have been applied in Eq. (4) for the temperature adjustment of experimental vaporization enthalpies, given in Table 5, column 7.

3.2.2. Comparison of vaporization enthalpies of Δgl Hom(298.15 K) with available data A careful search in the literature has revealed that experimental studies of vaporization enthalpy for FAP based ILs are practically absent in the literature. The only available for comparison experimental enthalpy of vaporization of [C6mim][FAP] 131.0 ± 2.0 kJ·mol−1 at 430 K was measured by using the TPD-LOSMS method [33]. We adjusted this result to the reference temperature in the same way as own vaporization enthalpies and the value Δgl Hom (298.15 K) = 147.3 ± 3.8 kJ·mol−1 is in poor but still acceptable agreement (within the combined uncertainties) with our result. In the virtual absence of experimental data, it is of importance to test the performance of few theoretical and half-empirical methods available in the literature. For example, the quantum-chemistry based COSMO-RS method [34], which nowadays is very popular in chemical engineering, can be validated with experimental vaporization enthalpies evaluated in Table 5. It is apparent from Table 6, that enthalpies of vaporization Δgl Hom (298.15 K) of [C2mim][FAP] and [C4mim][FAP] calculated by COSMORS were in acceptable agreement with experimental values (see Table 6, column 2 and 3). Also the empirical predictive model developed by Licence and Jones [33,35] (in which Δgl Hom(298 K) is decomposed into a Coulombic component and a van der Waals components from the anion and cation) provide reliable vaporization enthalpies (see Table 6, columns 4 and 5) vaporization enthalpies for all representatives of the [Cnmim][FAP] family.

3.2.3. Structure-property correlations of vaporization enthalpies: chainlength dependence The enthalpy of vaporization usually correlates linearly with the chain length within the homologues series of molecular and ionic compounds [8–10]. For the series [Cnmim][FAP] studied in this work, the dependence of vaporization enthalpy on the number of C-atoms, (NC), in

5

Table 6 Comparison of experimental and theoretical vaporization enthalpies Δgl Hom(298.15 K) of [Cnmim][FAP] family (in kJ·mol−1). Δgl Hom(298.15 K)

Cation Exp.a

COSMOb

Empiricc

Empiricd

MD

1

2

3

4

5

6

[C2mim] [C4mim] [C6mim] [C8mim]

126.4 ± 1.9 134.2 ± 1.9 141.5 ± 1.9 149.1 ± 2.0g

125.6 ± 3.0 129.5 ± 3.0 139 150

133 133 139 149

166e 212f

a

Experimental data on Δgl Hom(298.15 K, [Cnmim][FAP]) from Table 5. Estimated with COSMO-RS by Schroeder et al. [34] with expected uncertainty of ±3.0 kJ·mol−1. c Estimated with empirical procedure developed by Licence and Jones [35]. d Estimated with refined empirical procedure developed by Licence and Jones [33]. e Obtained from molecular dynamic simulations [36]. f Obtained from molecular dynamic simulations [37]. g Calculated from the experimental data on Δgl Hom(298.15 K, [C6mim][FAP] by addition of two contributions for [CH2] = (3.8 ± 0.5) kJ·mol−1 according to Eq. (11). b

the alkyl chains of the imidazolium cation follows the linear equation: −1

Δgl H om ð298:15KÞ=kJ  mol

¼ 3:8  ðNCÞ

þ 115:0 with R2 ¼ 0:999



ð11Þ

The linear trends have been also observed (see Table 7) for the imidazolium-based ILs with the fluorinated cations [NTf2]−, [PF6]−, [BF4]−. It is apparent from Table 7, that slopes of all considered linear dependencies are very close and they are generally representing the very similar “additive” contribution of the CH2-group to the vaporization enthalpy Δgl Hom(298.15 K) independent on the structure of the cation and anion. Consequently, the coefficients of linear equations Δgl Hom(298.15 K)/ kJ·mol−1 = Q×(NC) + Y can be safely used for reasonable extrapolation in order to assess vaporization enthalpies of the unknown but similarly structured ILs. For example, the value Δgl Hom(298.15 K, [C8mim][FAP]) = 149.2 kJ·mol−1 was estimated according to Eq. (11). The latter value is in excellent agreement with the estimates collected in Table 6. Such a good agreement could be considered as the mutual validation of both empirical and theoretical methods. 3.3. Gas- and liquid-phase enthalpies of formation for [FAP] containing ILs Standard molar enthalpies of formation, ΔfHom, in the liquid or gaseous phase are broadly used in chemical engineering for optimization of the technological processes and temperature management in chemical reactors. Enthalpies of formation are connected over the vaporization enthalpy according to the general thermodynamic equation: Δ f H om ðg; 298:15KÞ ¼ Δ f Hom ðliq; 298:15 KÞ þ Δgl H om ð298:15 KÞ

ð12Þ

Table 5 Thermodynamics of vaporization of [Cnmim][FAP family derived from experimental results. Cation

T-range

Tav

[K]

Δgl Hom(Tav) [kJ·mol

−1

Δgl Gom(Tav)a

]

Δgl Hom(298.15 K)c

Δgl Cob p, m [J·K

−1

·mol

−1

]

[kJ·mol−1]

1

2

3

4

5

6

7

[C2mim] [C4mim] [C6mim]

350–398 346–393 353–398 –

373.4 368.4 375.0 430.0

118.3 ± 1.0 126.1 ± 1.0 130.0 ± 1.0 131.0 ± 2.0 [33]

70.70 ± 1.3 70.81 ± 1.3 71.79 ± 1.3 –

−114 −131 −146 −146

126.4 ± 1.9 134.2 ± 1.9 139.5 ± 2.2 147.3 ± 3.8 141.5 ± 1.9d

a The standard Gibbs energies of vaporization was calculated according to Eq. (6) with help of calibration coefficient developed in our recent work [10]. b Calculated from the evaluated Δgl Cop, m–data (see Table 3, column 6). c Adjusted to 298.15 K using Eq. (4) by using the Δgl Cop, m–values from column 6. The experimental QCM uncertainties were extended with uncertainty of the heat capacity difference assessed to be of 20 J·K−1·mol−1. d Weighted average value from the QCM (this work) and TPD (temperature programmed desorption [33]) methods. Uncertainties of vaporization enthalpies were used as the weighting factor. Values in bold were recommended for thermochemical calculations.

6

D.H. Zaitsau, S.P. Verevkin / Journal of Molecular Liquids 287 (2019) 110959

Table 7 Alkyl chain length (NC)a dependence of Δgl Hom(298.15 K) for ILs under study according to general equations: Δgl Hom(298.15 K)/kJ·mol−1 = Q×(NC) + Y. IL

NC-rangea

Q

Y

R2

Reference

[Cnmim][NTf2] [Cnmim][PF6] [Cnmim][BF4] [Cnmim][FAP]

2–18 8–10 2–10 2–6

3.9 3.3 3.5 3.8

115.7 128.9 124.3 115.0

0.995 0.999 0.992 0.999

[8] [10] [9] this work

a

Number of C-atoms in all alkyl chains attached to 1-N-atom.

The liquid phase enthalpies of formation of ILs can be measured by the combustion calorimetry [38,39] or reaction calorimetry [40,41]. Unfortunately, both these methods are hardly applicable in the case of [Cnmim][FAP]. However, Eq. (12) can be used in order to derive the ΔfHom(liq, 298.15 K)-values with help of vaporization enthalpies of [Cnmim][FAP], measured in this work (see Table 5, column 7) and the enthalpy of formation ΔfHom(g, 298.15 K) of [C2mim][FAP] computed at DLPNO-CCSD(T)/def2-TZVP//B3LYP/def2-TZVP-D3(BJ) level of theory by using a set of isodesmic reactions (see Table 8). The primary data on H298 and the enthalpies of formation for the reactants are given in Table S4. Thus, the combination of the ΔfHom(g, 298.15 K, [C2mim][FAP]) = −4057.0 ± 4.2 kJ·mol−1 (see Table 8) with the experimental vaporization enthalpy of [C2mim][FAP] (see Table 5, column 7 and Table 9, column 4) provided the liquid phase enthalpy of formation ΔfHom(g, 298.15 K) = −3931 ± 5.3 kJ·mol−1 (see Table 9, column 5) which have been used in this work to obtain the standard molar enthalpy of formation of the aqueous tris (pentafluoroethyl)trifluorophosphate anion. 3.4. Aqueous-phase enthalpy of formation for the [FAP] anion The aqueous standard molar enthalpy of formation, ΔfHom(FAP− aq) of the tris(pentafluoroethyl)trifluorophosphate anion is an important brick stone for prediction of thermodynamic properties of ILs. This value can be used for quick appraisal of the liquid phase standard enthalpies of formation ΔfHom(liq) of ILs. The idea of such thermodynamic procedure is that energetics of the dissolution of an IL in water can be used to derive energetics of aqueous cation and anion. The standard enthalpy of formation of an ion in the aqueous solution, ΔfHom(ionaq), is referenced to the formation of the hydrated ion. They are obtained by arbitrarily assigning a value of zero to H+ ion; that is, ΔfHom(ionaq) = 0. Then the enthalpies of formation of all other aqueous ions can be determined relative to the heat of formation of the H+ aq ion by using the experimentally measured enthalpy of solution ΔsolH∞ m(salt or IL) at infinite dilution. The enthalpy of formation of a salt or an IL in aqueous solution,

ΔfHom(ILaq), can be considered as a sum of appropriate contributions from the aqueous cation and the anion constituting the IL:     − o Δ f H om ILaq ¼ Δ f Hom cationþ aq þ Δ f H m anionaq

ð13Þ

The enthalpy of reaction 13 is defined as the standard molar enthalpy of solution of an IL at infinite dilution ΔsolH∞ m(IL), under assumption of full dissociation of IL in water (at conditions of the infinite dilution). ΔsolH∞ m(IL)-values are precisely measured with help of the solution calorimetry. Standard molar enthalpies of formation of aqueous cations and anions specific for typical salts are well known from the literature [43]. Experimental enthalpies of formation of aqueous cations and anions specific for the ILs are in progress now [10,44–46]. Thus, for many ILs the ΔfHom(ILaq)-value can be principally obtained from sumo − mation of ΔfHom(cation+ aq) and ΔfHm(anionaq) contributions according to Eq. (13). Combining the aqueous enthalpy of formation of an IL with the calorimetrically measured enthalpy of solution of IL in water, the liquid phase enthalpy of formation of an IL can be derived:     Δ f H om ILliq ¼ Δ f H om ILaq −Δsol H ∞m ðILÞ

ð14Þ

The liquid-phase enthalpies of formation ΔfHom(liq) have been evaluated in Table 8, column 5. Standard molar enthalpies of solution at infinite dilution, ΔsolH∞ m(IL), of [C2mim][FAP] and [C4mim][FAP] were measured by solution calorimetry (see Table 9, column 2). We used these results to calculate for the first time the enthalpy of formation of the aqueous anion ΔfHom(FAP− aq) anion according to Eqs. 13 and 14 as follows, e.g. for imidazolium based ILs:   þ o o Δ f H om FAP− aq ¼ Δ f H m ð½Cnmim½FAP; liqÞ−Δ f H m Cnmimaq þ Δsol H ∞m ðILÞ

ð15Þ

−1 Taking into account values ΔfHom(C2mim+ aq) = −13.1 ± 3.1 kJ·mol −1 and ΔfHom(C4mim+ ) = −52.5 ± 2.5 kJ·mol available from in the litaq erature [10], the aqueous enthalpy of formation of ΔfHom(FAP− aq) = −3891 ± 6.0 kJ·mol−1 was calculated (see Table 9, column 6). This contribution is helpful for a quick appraisal of aqueous energetics of not only imidazolium-based ILs with e.g. longer chain length, but also for pyridinium, pyrrolidinium, and ammonium based ILs with the [FAP] anion (provided that the ΔsolH∞ m(IL)-values are available or assessed for these ILs.

Table 8 Isodesmic reactions applied for computation of the ΔfHom(g, 298.15 K) for [C2mim][FAP]. Reactiona

ΔrHom kJ·mol

1 2 3 4 5 6 7 8 9 10 11 12 13 14 a b

Me-Im + PF5 + 2C2F6 + 2C2H6 + F2 = [C2mim][FAP] + 3H2 + HF Me-Im + 3C2F6 + PH3 + C2H6 = [C2mim][FAP] + 2H2 P(CH3)3 + N2H4 + 3C2F6 + 2C2H2 = [C2mim][FAP] + H2 CH4 OP(CH3)3 + N2H4 + 3C2F6 + 2C2H2 = [C2mim][FAP] + H2O CH4 P(OCH3)3 + 2NH3 + 3C2F6 + 2C2H4 = [C2mim][FAP] + CH4 + H2O + H2 Me-Im + PF5 + 2C6H5-CF3 + HF + H2 + C2F6 = [C2mim][FAP] + 4/3C6H6 Me-Im + P(C2H5)3 + 3C2F6 + H2 = [C2mim][FAP] + 2C2H6 Me-Im + HP(C2H5)2 + 3C2F6 = [C2mim][FAP] + C2H6 Me-Im + H2P-C2H5 + 3C2F6 + H2 = [C2mim][FAP] Me-Im + HP(CH3)2+ 3C2F6 + H2 = [C2mim][FAP] H2P-C2H5 + N2H4 + 3C2F6 + C6H6 = [C2mim][FAP] + C2H6 P(C2H5)3 + 2NH3 + 3C2F6 = [C2mim][FAP] + 5H2 HP(C2H5)2 + N2H4 + 3C2F6 + C6H6 + H2 = [C2mim][FAP] + 2C2H6 HP(CH3)2 + 2NH3 + 3C2F6 + C6H6 = [C2mim][FAP] + 2C2H6 + H2 Average

Abbreviation Me-Im = 1-methyl imidazole. Uncertainty is twice standard deviation of the mean corresponding to the expanded uncertainty (0.95 confidence level, k = 2).

ΔfHom −1

−18.5 −61.2 −539.9 −478.6 −144.7 322.5 −176.6 −145.2 −107.5 −89.5 −251.7 221.2 −289.4 −45.3

−4070.9 −4046.8 −4049.4 −4063.3 −4068.0 −4047.5 −4066.2 −4056.3 −4050.3 −4050.8 −4057.3 −4055.9 −4063.3 −4057.1 −4057.0 ± 4.2b

D.H. Zaitsau, S.P. Verevkin / Journal of Molecular Liquids 287 (2019) 110959

7

Table 9 −1 ). Thermochemical properties of imidazolium-based ILs with the [FAP− aq] anion at 298.15 K (in kJ·mol IL

a ΔsolH∞ m

1

2

3

4

5

6

[C2mim][FAP] [C4mim][FAP]

23.2 ± 0.4 [34] 25.7 ± 0.7 [35]

−4057 ± 5.0b −4099.0 ± 5.0f

126.4 ± 1.9 134.2 ± 1.9

−3931 ± 5.3 −3965 ± 5.4

−3894 ± 6.2 −3887 ± 6.0 −3891 ± 6.0g

ΔfHom(g)

Δgl Homc

ΔfHom(liq)d

e ΔfHom(FAP− aq)

a

Measured by the solution calorimetry. Calculated using DLPNO/def2-TZVPP level of theory (see text). c From Table 5. d Calculated as the difference ΔfHom(l, 298.15 K) = ΔfHom(g, 298.15 K) - Δgl Hom (298.15 K). e Calculated using Eq. (15). f Calculated by addition of two contributions for [CH2] = (−20.75 ± 0.50) kJ·mol−1 adopted for ILs in our previous study [42] to the ΔfHom(g, 298.15 K, [C2mim][FAP]) = −4057.0 ± 5.0 kJ·mol−1. g Weighted average value calculated using the uncertainty as the weighing factor. b

4. Conclusions The experimental thermodynamic study of the [Cnmim][FAP] series of ILs has been performed. New experimental vapor pressures and vaporization enthalpies were measured by the QCM method. These results were adjusted to the reference temperature 298.15 K and tested for consistency. Absolute vapor pressures of ILs [Cnmim][FAP] with n = 2,4 and 6 at 373 K and at 473 K were calculated in order to asses the level for practical applications. Experimental enthalpies of vaporization Δgl Hom (298.15 K) have been used for calculation the aqueous enthalpy of formation of the ΔfHom(FAP− aq) anion. These results will facilitate chemical engineering calculations of processes involving ILs. Acknowledgments This work has been supported by the German Science Foundation (DFG) in the frame of the priority program SPP 1807 “Control of London Dispersion Interactions in Molecular Chemistry”, as well as of the priority program SPP 1708 “Material Synthesis Near Room Temperature”. DHZ acknowledges the financial support from DFG, grant ZA 872/3-1, 407078203. This work has been also partly supported by the Russian Government Program of Competitive Growth of Kazan Federal University and Russian Foundation for Basic Research No. 15-03-07475.

[9]

[10]

[11]

[12]

[13]

[14]

[15]

[16]

[17]

Appendix A. Supplementary data Supplementary data to this article can be found online at https://doi. org/10.1016/j.molliq.2019.110959.

[18] [19]

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