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Study on the thermodynamic properties for ionic liquid [C6mim][OAc](1-hexyl-3-methylimidazolium acetate)
Fluid Phase Equilibria 371 (2014) 1–5
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Study on the thermodynamic properties for ionic liquid [C6 mim][OAc](1-hexyl-3-methylimidazolium acetate) Jie Wei, Qiu-Bo Zhang, Fang Tian, Ling Zheng, Wei Guan ∗ , Jia-Zhen Yang College of Chemistry, Liaoning University, Shenyang 110036, PR China
a r t i c l e
i n f o
Article history: Received 7 December 2013 Received in revised form 28 February 2014 Accepted 10 March 2014 Available online 19 March 2014 Keywords: Acetate ionic liquid Enthalpy of solution Molar heat capacity of solution Apparent molar heat capacity
a b s t r a c t Using the solution-reaction isoperibol calorimeter, molar enthalpies of solution in water, sol Hm , for ionic liquid [C6 mim][OAc] with different molalities were measured in the temperature range from (288.15 to 308.15 ± 0.01) K with an interval of 5 K. According to Archer’s method, the values of the standard molar enthalpies of solution, sol Hm , were obtained for [C6 mim][OAc], respectively. According to Glasser’s theory of lattice energy, the hydration enthalpy of cation and anion in infinite dilution aqueous [C6 mim][OAc] was calculated, (H+ + H− ) = −598 kJ mol−1 , at 298.15 K. The hydration enthalpy of the cation, H+ ([C6 mim]+ ) = −173 kJ mol−1 , was determined. In comparison with hydration enthalpy of [C2 mim]+ , the hydration enthalpy of [C6 mim]+ is a little bit weaker. A linear relationship was found by plotting the experimental values of sol Hm against (T—298.15) K. The standard molar heat capacity of solution, Cp,m = 313 J K−1 mol−1 , was obtained from the slope of the regression line, the specific heat capacity of solution, Cp = 1.38 J g−1 K−1 , and the apparent relative molar heat capacity, ˚ Cp , were also calculated for [C6 mim][OAc]. © 2014 Elsevier B.V. All rights reserved.
1. Introduction Due to minuscule vapor pressure, non-flammability and dual natural polarity, ionic liquids (ILs) have been applied in many physical–chemical fields [1]. As a new-generation “greener ionic liquid”, acetic acid ionic liquids (AcAILs) have attracted considerable attention from industry and the academic community because they have several unique properties including strong solubility and good catalytic properties, which are useful for an enzyme-‘friendly’ co-solvent for resolution of amino acids [2], ultrasonic irradiation towards synthesis of trisubstituted imidazoles [3], assisted transdermal delivery of sparingly soluble drugs [4], some catalytic reactions [5], and dissolve cellulose [6]. It is well known that enthalpy, molar heat capacity, specific heat capacity of solution, and the apparent relative molar heat capacity, C , for [C mim][OAc] are the basic thermodynamic data, and these p 6 basic data, as well as other thermodynamic properties, are of great importance to any industrial processes for application of AcAILs. The density, surface tension, and other physicochemical properties for the homologue of AcAILs were previously reported [7–9]. As a continuation of our previous investigation [7–13], this paper
∗ Corresponding author. Tel.: +86 24 62207797; fax: +86 24 62207797. E-mail addresses: [email protected], [email protected] (W. Guan). http://dx.doi.org/10.1016/j.fluid.2014.03.011 0378-3812/© 2014 Elsevier B.V. All rights reserved.
reports that (1) Using the water as solvent, the molar enthalpies of solution for IL [C6 mim][OAc] were measured in the temperature range of (288.15 to 308.15 ± 0.01) K with an interval of 5 K. (2) The values of the standard molar enthalpy of solution, , for [C mim][OAc] in the temperature range of (288.15 to sol Hm 6 308.15 ± 0.01) K were obtained according to of Archer’s method [14], and the hydration enthalpy of cation and anion in infinite dilution aqueous [C6 mim][OAc] was obtained at 298.15 K according to Glasser’s theory of lattice energy. The hydration enthalpy of the cation, H+ ([C6 mim]+ ), was obtained at 298.15 K. (3) The , for [C mim][OAc] standard molar heat capacity of solution, Cp,m 6
vs. was obtained from the slope of the straight line of sol Hm (T—298.15) K, the specific heat capacity of solution, Cp , and the
apparent relative molar heat capacity, ˚ Cp , were also calculated for [C6 mim][OAc].
2. Experimental 2.1. Chemicals KCl was placed into a vacuum oven and baked at 408.15 K for 6 h before use, as well as THAM (Tris-(hydroxymethyl) aminomethane) for 6 h. The ultrapure water was used. Pure IL [C6 mim][OAc] was purchased, the water content (w2 is the water mass fraction, w2 < 0.005) in the ILs was determined by use of a Karl Fischer
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J. Wei et al. / Fluid Phase Equilibria 371 (2014) 1–5
Table 1 The source and purity of the materials. Chemical name
Source
Purification method
Mass fraction purity (%)
KCl THAM (Tris-(hydroxymethyl) aminomethane) [C6 mim][OAc] Acetic acid Halogen
Shenyang Reagent Co. LTD Shenyang Reagent Co. LTD Lanzhou Institute of Chemical Physics
No further purification No further purification No further purification
>0.9999 >0.9997 ≥0.99 <0.002 <0.0012
H2 O
Ultrapure water
moisture titrator (ZSD-2 type). The source and purity of the materials and the mass fraction contribution of the impurities for [C6 mim][OAc] are listed in Table 1. 2.2. Determination of enthalpy of solution An on-line solution-reaction isoperibol calorimeter system was developed based on calorimetric apparatus previously reported in literature [15–17]. The calorimeter consists of a set of water thermostat, a 200 ml pyrex-glass plated silver Dewar, a 4 ml glass sample cell, a calibration heater, a glass-sheathed thermistor probe, an amplifier, a circuit used as an A/D converter and a personal computer for data acquisition and processing. The detailed experimental procedure has been described elsewhere [11]. The performance and accuracy of the calorimetric system were examined by measuring the molar enthalpy of solution of KCl in water and THAM [Tris-(hydroxymethyl) aminomethane] in 0.1 mol dm−3 HCl (aq) at (298.15 ± 0.01) K. The mean molar solution enthalpies are sol Hm =(17,542 ± 31) J mol−1 for KCl and (−29,794 ± 28) J mol−1 for THAM, which were in good agreement with the corresponding published data: (17,536 ± 9) J mol−1 for KCl [18,19] and (−29,739 ± 10) J mol−1 for THAM [19]. The accuracy of the temperature measurement device is ±0.0001. These results suggest that the calorimeter can be used for determining molar enthalpies of solution in the study. The molar enthalpies of solution in ultrapure water of [C6 mim][OAc] with different molalities, sol Hm , were measured at the temperature range of (288.15 to 308.15 ± 0.01) K with an interval of 5 K.
electrical resistivity, (M cm)
18.2
Table 3 Values of molar solution enthalpy for ionic liquid [C6 mim][OAc], sol Hm (kJ mol−1 ), and extrapolation function, Y (kJ mol−1 ), at 293.15 K, pressure p = 0.1 MPa. Wa (g)
m (mol kg−1 )
−Hm (kJ mol−1 )
Tb (K)
−Y (kJ mol−1 )
0.3809 0.4638 0.5021 0.5497 0.6079 0.6597 0.7139 0.7734 0.8317 0.8971 0.9354 0.9787
0.01685 0.02050 0.02221 0.02430 0.02690 0.02919 0.03159 0.03421 0.03680 0.03970 0.04139 0.04330
52.11 ± 0.023 51.98 ± 0.027 51.85 ± 0.027 51.69 ± 0.030 51.54 ± 0.034 51.40 ± 0.038 51.22 ± 0.040 51.08 ± 0.043 50.93 ± 0.046 50.80 ± 0.051 50.64 ± 0.051 50.49 ± 0.053
0.1824 ± 0.0001 0.2144 ± 0.0001 0.2176 ± 0.0001 0.2368 ± 0.0001 0.2696 ± 0.0001 0.3000 ± 0.0001 0.3208 ± 0.0001 0.3456 ± 0.0001 0.3704 ± 0.0001 0.4064 ± 0.0001 0.4096 ± 0.0001 0.4248 ± 0.0001
52.33 ± 0.023 52.22 ± 0.027 52.10 ± 0.027 51.95 ± 0.030 51.81 ± 0.034 51.68 ± 0.038 51.51 ± 0.040 51.39 ± 0.043 51.25 ± 0.046 51.12 ± 0.051 50.98 ± 0.051 50.83 ± 0.053
a b
Sample mass, W = ±0.0001, m = ±5.04 × 10−6 . Experimental temperature difference, T = ±0.0001.
K are listed in Tables 2–6 suggesting that the dissolution process of the AcAIL is a typical exothermal. According to Archer’s method [14], in terms of a Debye–Hückel limiting term, the values of the standard molar enthalpy of solu , can be obtained using the following tion for [C6 mim][OAc], sol Hm equation at the given temperature: Y = sol Hm −
A H
b
ln 1 + bI 1/2 = sol Hm + ˇm
(1)
The measured values of molar solution enthalpy, sol Hm , of [C6 mim][OAc] and various molarities at (288.15 to 308.15 ± 0.01)
where m is molality, I is ionic strength (I = m for the 1:1 electrolyte [C6 mim][OAc]), b is a constant to be 1.2 [20], AH is the Debye–Hückel parameter for enthalpy and its value at different temperatures was taken from the literature [20], ˇ is empirical constant, Y is extrapolation function calculated from experimental data and are listed in Tables 2–6. According to Eq. (1), plotting the values of Y against various molarities, the good straight lines were and ˇ were obtained obtained (see Fig. 1). The values of sol Hm from the intercepts and the slopes of linear regressions, respectively, and the values of the correlation coefficients, r, and the
Table 2 Values of molar solution enthalpy for ionic liquid [C6 mim][OAc], sol Hm (kJ mol−1 ), and extrapolation function, Y (kJ mol−1 ), at 288.15 K, pressure p = 0.1 MPa.
Table 4 Values of molar solution enthalpy for ionic liquid [C6 mim][OAc], sol Hm (kJ mol−1 ), and extrapolation function, Y (kJ mol−1 ), at 298.15 K, pressure p = 0.1 MPa.
3. Results and discussion , for AcAIL 3.1. The standard molar enthalpy of solution, sol Hm [C6 mim][OAc]
Wa (g)
m (mol kg−1 )
−s Hm (kJ mol−1 )
Tb (K)
−Y (kJ mol−1 )
Wa (g)
m (mol kg−1 )
−s Hm (kJ mol−1 )
Tb (K)
−Y (kJ mol−1 )
0.3843 0.4452 0.4839 0.5529 0.5945 0.6539 0.6872 0.7453 0.7898 0.8548 0.9054 0.9818
0.01700 0.01970 0.02141 0.02446 0.02630 0.02890 0.03040 0.03297 0.03494 0.03782 0.04006 0.04344
53.46 ± 0.025 53.31 ± 0.026 53.20 ± 0.029 53.07 ± 0.032 52.91 ± 0.034 52.79 ± 0.039 52.64 ± 0.040 52.50 ± 0.044 52.36 ± 0.047 52.18 ± 0.048 52.04 ± 0.051 51.90 ± 0.054
0.1960 ± 0.0001 0.2112 ± 0.0001 0.2312 ± 0.0001 0.2536 ± 0.0001 0.2704 ± 0.0001 0.3128 ± 0.0001 0.3216 ± 0.0001 0.3480 ± 0.0001 0.3744 ± 0.0001 0.3848 ± 0.0001 0.4064 ± 0.0001 0.4344 ± 0.0001
53.66 ± 0.025 53.53 ± 0.026 53.42 ± 0.029 53.31 ± 0.032 53.15 ± 0.034 53.05 ± 0.039 52.90 ± 0.040 52.78 ± 0.044 52.64 ± 0.047 52.47 ± 0.048 52.34 ± 0.051 52.21 ± 0.054
0.4094 0.4501 0.5026 0.5604 0.6008 0.6557 0.7003 0.7525 0.8078 0.9012 1.0157 1.1374
0.01811 0.01991 0.02224 0.02480 0.02658 0.02901 0.03098 0.03329 0.03574 0.03987 0.04494 0.05032
50.58 ± 0.022 50.46 ± 0.024 50.34 ± 0.027 50.17 ± 0.029 50.02 ± 0.031 49.89 ± 0.033 49.79 ± 0.036 49.67 ± 0.039 49.55 ± 0.041 49.32 ± 0.045 49.15 ± 0.051 48.91 ± 0.056
0.1776 ± 0.0001 0.1928 ± 0.0001 0.2144 ± 0.0001 0.2344 ± 0.0001 0.2472 ± 0.0001 0.2600 ± 0.0001 0.2840 ± 0.0001 0.3088 ± 0.0001 0.3246 ± 0.0001 0.3624 ± 0.0001 0.4072 ± 0.0001 0.4488 ± 0.0001
50.89 ± 0.022 50.73 ± 0.024 50.63 ± 0.027 50.46 ± 0.029 50.32 ± 0.031 50.20 ± 0.033 50.05 ± 0.036 49.94 ± 0.039 49.82 ± 0.041 49.67 ± 0.045 49.53 ± 0.045 49.38 ± 0.056
a b
Sample mass, W = ± 0.0001, m = ±5.04 × 10−6 . Experimental temperature difference, T = ±0.0001.
a b
Sample mass, W = ±0.0001, m = ±5.04 × 10−6 . Experimental temperature difference, T = ±0.0001.
J. Wei et al. / Fluid Phase Equilibria 371 (2014) 1–5 Table 5 Values of molar solution enthalpy for ionic liquid [C6 mim][OAc], sol Hm (kJ·mol−1 ), and extrapolation function, Y (kJ mol−1 ), at 303.15 K, pressure p = 0.1 MPa. Wa (g)
m (mol kg−1 )
−s Hm (kJ mol−1 )
Tb (K)
−Y (kJ mol−1 )
0.4216 0.4897 0.5268 0.5529 0.6424 0.7596 0.8493 0.9272 0.9811 1.0054 1.1351 1.2147
0.01865 0.02167 0.02331 0.02446 0.02842 0.03361 0.03758 0.04102 0.04341 0.04448 0.05022 0.05374
49.05 ± 0.015 48.92 ± 0.020 48.80 ± 0.022 48.70 ± 0.024 48.55 ± 0.028 48.40 ± 0.033 48.22 ± 0.037 48.09 ± 0.039 47.95 ± 0.042 47.85 ± 0.044 47.72 ± 0.048 47.60 ± 0.053
0.1175 ± 0.0001 0.1600 ± 0.0001 0.1734 ± 0.0001 0.1946 ± 0.0001 0.2250 ± 0.0001 0.2638 ± 0.0001 0.2960 ± 0.0001 0.3103 ± 0.0001 0.3397 ± 0.0001 0.3498 ± 0.0001 0.3851 ± 0.0001 0.4223 ± 0.0001
49.32 ± 0.015 49.21 ± 0.020 49.11 ± 0.022 49.00 ± 0.024 48.88 ± 0.028 48.75 ± 0.033 48.60 ± 0.037 48.48 ± 0.039 48.35 ± 0.042 48.26 ± 0.044 48.15 ± 0.048 48.04 ± 0.053
a b
Sample mass, W = ±0.0001, m = ±5.04 × 10−6 . Experimental temperature difference, T = ±0.0001.
Wa (g)
m (mol kg−1 )
−s Hm (kJ mol−1 )
Tb (K)
−Y (kJ mol−1 )
0.5026 0.5976 0.6405 0.6720 0.7390 0.8314 0.8733 0.9675 1.0638 1.1342 1.2410 1.3059
0.02224 0.02644 0.02834 0.02973 0.03270 0.03678 0.03864 0.04281 0.04707 0.05018 0.05491 0.05778
47.23 ± 0.019 47.05 ± 0.022 46.95 ± 0.024 46.83 ± 0.025 46.68 ± 0.028 46.50 ± 0.031 46.38 ± 0.033 46.21 ± 0.036 45.98 ± 0.041 45.84 ± 0.044 45.66 ± 0.047 45.53 ± 0.051
0.1491 ± 0.0001 0.1748 ± 0.0001 0.1914 ± 0.0001 0.1974 ± 0.0001 0.2270 ± 0.0001 0.2510 ± 0.0001 0.2637 ± 0.0001 0.2918 ± 0.0001 0.3258 ± 0.0001 0.3486 ± 0.0001 0.3784 ± 0.0001 0.4064 ± 0.0001
47.55 ± 0.019 47.44 ± 0.022 47.34 ± 0.024 47.20 ± 0.025 47.04 ± 0.028 46.90 ± 0.028 46.68 ± 0.033 46.54 ± 0.036 46.44 ± 0.041 46.30 ± 0.044 46.19 ± 0.047 46.05 ± 0.051
a
[C6mim][OAc] (l)
ΔsolHmθ H 2O
[C6mim]+ (aq) + [OAc]- (aq)
UPOT
ΔH+ + ΔH[C6mim]+ (g) + [OAc]- (g)
Fig. 2. The thermodynamic cycle for estimation the values of the hydration enthalpy of [C6 mim][OAc].
standard deviations, s, were also from the linear regressions. All above the parameters are listed in Table 7. 3.2. The estimation of hydration enthalpy of [C6 mim][OAc]
Table 6 Values of molar solution enthalpy for ionic liquid [C6 mim][OAc], sol Hm (kJ mol−1 ), and extrapolation function, Y (kJ mol−1 ), at 308.15 K, pressure p = 0.1 MPa.
b
3
Sample mass, W = ±0.0001, m = ±5.04 × 10−6 . Experimental temperature difference, T = ±0.0001.
The hydration enthalpy of the ionic liquid [C6 mim][OAc] was of the pure ionic liquid in terms estimated using the value of sol Hm of the following thermodynamic cycle (see Fig. 2): (H+ + H− ) = sol Hm − UPOT
(2)
where UPOT is crystal lattice energy which can be estimated by Glasser’s [21,22] theory of lattice energy:
−1/3
UPOT = 2 ˛Vm
+ˇ
(3)
where ˛ and ˇ are fitting coefficients, ionic strength I = 1, and the molecular volume was presented in nm3 . According to the suggestion from Gutowski et al. [23], the values of ˛ and ˇ are, respectively, 83.3 nm kJ mol−1 and 157.3 kJ mol−1 for the ILs which are 1:1 salts but contain organic cations. These ˛ and ˇ values have been recently used to calculate thermodynamic properties of some ILs [24,25]. The crystal energies for the ILs investigated in the present work were calculated from, the values of UPOT for [C6 mim][OAc] is 546.77 kJ mol−1 , so that the hydration enthalpy of cation and anion in infinite dilution aqueous [C6 mim][OAc], (H+ + H− ) = −598 kJ mol−1 , at 298.15 K. It is believed that there are only ion–water interactions, no ion–ion interactions in infinite dilution, hence the contributions of the cation and the anion to molar hydration enthalpy of the [C6 mim][OAc] have additivity. Consequently, according to hydration enthalpy of acetic acid anion, H− ([CH3 COO]− ) = −425 kJ mol−1 , obtained by Marcus [26], the hydration enthalpy of the cation, H+ ([C6 mim]+ ) = −173 kJ mol−1 , was determined. In comparison with hydration enthalpy of [C2 mim]+ , H+ ([C2 mim]+ ) = −233 kJ mol−1 [27], the hydration enthalpy of [C6 mim]+ is a little bit weaker. 3.3. The standard molar heat capacity of solution, Cp,m
Fig. 1. The plot of Y (extrapolation function calculated from Eq. (1) against m for [C6 mim][OAc] in temperature range of 288.15–308.15 K.
are As shown in Fig. 3, the experimental values of sol Hm linearly associated with (T—298.15) K for AcAIL. The [C6 mim][OAc] regression equation is sol Hm /kJ mol−1 = −51.63 + 0.313 (T—298.15) K with a correlation coefficient, r = 0.999, and standard deviation, s = 0.12. The standard molar heat capacity of solution,
Table 7 (kJ mol−1 ) in temperature range of 288.15–308.15 K. Values of standard molar solution enthalpy for ionic liquid [C6 mim][OAc], sol Hm T (K) −sol Hm a
(kJ mol ˇ (kJ kg mol−2 ) b s (kJ mol−1 ) rc a b c
−1
)
Empirical constant. Standard deviation. Correlation coefficient.
288.15
293.15
298.15
303.15
308.15
54.66 ± 0.03 57.24 0.03 0.998
53.35 ± 0.04 57.36 0.03 0.998
51.64 ± 0.05 47.82 0.05 0.995
49.96 ± 0.04 36.56 0.04 0.996
48.52 ± 0.03 43.69 0.03 0.999
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J. Wei et al. / Fluid Phase Equilibria 371 (2014) 1–5
Table 8 Values of the apparent relative molar heat capacity of [C6 mim][OAc], Cp (J K−1 mol−1 ) at 298.15 K. −sol Hm (kJ mol−1 )
m (mol kg−1 )
0.01500 0.02100 0.02300 0.02600 0.02800 0.03100 0.03400 0.03500 0.03700 0.04000 0.04400 0.04600 a
288.15 (K)
293.15 (K)
298.15 (K)
303.15 (K)
308.15 (K)
53.48 53.09 52.96 52.76 52.64 52.45 52.26 52.19 52.07 51.88 51.63 51.51
52.17 51.77 51.64 51.45 51.32 51.13 50.94 50.88 50.75 50.56 50.32 50.19
50.60 50.26 50.15 49.99 49.88 49.72 49.56 49.50 49.40 49.24 49.02 48.92
49.09 48.82 48.73 48.60 48.51 48.39 48.26 48.22 48.13 48.01 47.84 47.76
47.54 47.23 47.13 46.98 46.87 46.73 46.58 46.53 46.43 46.28 46.09 45.99
(∂sol Hm /∂T)p,m
ra
299.03 293.28 291.37 288.49 286.58 283.70 280.83 279.87 277.96 275.08 271.25 269.33
0.9996 0.9996 0.9995 0.9994 0.9993 0.9991 0.9989 0.9988 0.9986 0.9982 0.9977 0.9974
746 740 738 735 734 731 728 727 725 722 718 716
Cp (J K−1 mol−1 )
Correlation coefficient.
Cp,m = 313 J K−1 mol−1 , was obtained from the slope, and the spe-
cific heat capacity of solution, accordingly.
Cp
= 1.38 J g−1
K−1 ,
was calculated
3.4. The apparent relative molar heat capacity, ˚ Cp for [C6 mim][OAc] The apparent relative molar heat capacity for [C6 mim][OAc], may be expressed as:
C , p
Cp =
∂sol Hm ∂T
4. Conclusions
+ Cp (ILs)
(4)
p,m
The molar heat capacity of [C4 mim][OAc], Cp (ILs) is 383.2 J K−1 mol−1 , per molar methylene’s contribution to the heat capacity is about 32 J K−1 mol−1 [28], and so the molar heat capacity of [C6 mim][OAc], Cp (ILs), is about 447 J K−1 mol−1 . According to Archer’s method [14], the values of molar solution enthalpy, sol Hm , of [C6 mim][OAc] with various molalities at (288.15 to 308.15 ± 0.01) K were calculated. Plotting the values of sol Hm against T, the values of (∂sol Hm /∂T)p,m were obtained from the slopes of linear regressions. According to Eq. (4), the values of Cp were calculated. All above the parameters are listed in Table 8.
According to the experiment values of the molar enthalpies of solution, sol Hm , for ionic liquid [C6 mim][OAc], the val for ues of the standard molar enthalpies of solution sol Hm [C6 mim][OAc] were obtained in the temperature range of (288.15 to 308.15 ± 0.01) K, respectively. According to Glasser’s theory of lattice energy, the hydration enthalpy of cation, (H+ + H− ) = −598 kJ mol−1 at 298.15 K was obtained. The hydration enthalpy of the cation, H+ ([C6 mim]+ ) = −173 kJ mol−1 , was determined. In comparison with hydration enthalpy of [C2 mim]+ , the hydration enthalpy of [C6 mim]+ is a little bit weaker. A linear relationship was found by plotting the experimental values of against (T—298.15) K, The standard molar heat capacity sol Hm of solution, Cp,m = 313 J K−1 mol−1 , was obtained from the slope of the regression line, the specific heat capacity of solution, Cp
= 1.38 J g−1 K−1 , and the apparent relative molar heat capacity, ˚ Cp , were also calculated for [C6 mim][OAc]. Acknowledgment This project was supported by NSFC (21173107), Peoples Republic of China. References
-48 -49
θ -1 ΔsolHm /kJ·mol
-50 -51 -52 -53 -54 -55 -10
-5
0
5
10
( T-298.15) /K Fig. 3. The plot of the standard molar enthalpy of solution, sol Hm (kJ mol−1 ), against (T—298.15) K for [C6 mim][OAc].
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: the standard molar heat capacity of solution Cp,m
Cp : the specific heat capacity of solution Cp (ILs): molar heat capacity Cp : the apparent relative molar heat capacity : the standard molar enthalpies of solution sol Hm I: ionic strength m: molality M: molar mass r: correlation coefficient s: standard deviation T: is the adiabatic temperature change of the solution process W: sample mass Y: extrapolation function Greek Letters
Glossary ˇ: empirical constant AH : the Debye–Hückel parameter b: constant
5
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Fluid Phase Equilibria journal homepage: www.elsevier.com/locate/fluid
Study on the thermodynamic properties for ionic liquid [C6 mim][OAc](1-hexyl-3-methylimidazolium acetate) Jie Wei, Qiu-Bo Zhang, Fang Tian, Ling Zheng, Wei Guan ∗ , Jia-Zhen Yang College of Chemistry, Liaoning University, Shenyang 110036, PR China
a r t i c l e
i n f o
Article history: Received 7 December 2013 Received in revised form 28 February 2014 Accepted 10 March 2014 Available online 19 March 2014 Keywords: Acetate ionic liquid Enthalpy of solution Molar heat capacity of solution Apparent molar heat capacity
a b s t r a c t Using the solution-reaction isoperibol calorimeter, molar enthalpies of solution in water, sol Hm , for ionic liquid [C6 mim][OAc] with different molalities were measured in the temperature range from (288.15 to 308.15 ± 0.01) K with an interval of 5 K. According to Archer’s method, the values of the standard molar enthalpies of solution, sol Hm , were obtained for [C6 mim][OAc], respectively. According to Glasser’s theory of lattice energy, the hydration enthalpy of cation and anion in infinite dilution aqueous [C6 mim][OAc] was calculated, (H+ + H− ) = −598 kJ mol−1 , at 298.15 K. The hydration enthalpy of the cation, H+ ([C6 mim]+ ) = −173 kJ mol−1 , was determined. In comparison with hydration enthalpy of [C2 mim]+ , the hydration enthalpy of [C6 mim]+ is a little bit weaker. A linear relationship was found by plotting the experimental values of sol Hm against (T—298.15) K. The standard molar heat capacity of solution, Cp,m = 313 J K−1 mol−1 , was obtained from the slope of the regression line, the specific heat capacity of solution, Cp = 1.38 J g−1 K−1 , and the apparent relative molar heat capacity, ˚ Cp , were also calculated for [C6 mim][OAc]. © 2014 Elsevier B.V. All rights reserved.
1. Introduction Due to minuscule vapor pressure, non-flammability and dual natural polarity, ionic liquids (ILs) have been applied in many physical–chemical fields [1]. As a new-generation “greener ionic liquid”, acetic acid ionic liquids (AcAILs) have attracted considerable attention from industry and the academic community because they have several unique properties including strong solubility and good catalytic properties, which are useful for an enzyme-‘friendly’ co-solvent for resolution of amino acids [2], ultrasonic irradiation towards synthesis of trisubstituted imidazoles [3], assisted transdermal delivery of sparingly soluble drugs [4], some catalytic reactions [5], and dissolve cellulose [6]. It is well known that enthalpy, molar heat capacity, specific heat capacity of solution, and the apparent relative molar heat capacity, C , for [C mim][OAc] are the basic thermodynamic data, and these p 6 basic data, as well as other thermodynamic properties, are of great importance to any industrial processes for application of AcAILs. The density, surface tension, and other physicochemical properties for the homologue of AcAILs were previously reported [7–9]. As a continuation of our previous investigation [7–13], this paper
∗ Corresponding author. Tel.: +86 24 62207797; fax: +86 24 62207797. E-mail addresses: [email protected], [email protected] (W. Guan). http://dx.doi.org/10.1016/j.fluid.2014.03.011 0378-3812/© 2014 Elsevier B.V. All rights reserved.
reports that (1) Using the water as solvent, the molar enthalpies of solution for IL [C6 mim][OAc] were measured in the temperature range of (288.15 to 308.15 ± 0.01) K with an interval of 5 K. (2) The values of the standard molar enthalpy of solution, , for [C mim][OAc] in the temperature range of (288.15 to sol Hm 6 308.15 ± 0.01) K were obtained according to of Archer’s method [14], and the hydration enthalpy of cation and anion in infinite dilution aqueous [C6 mim][OAc] was obtained at 298.15 K according to Glasser’s theory of lattice energy. The hydration enthalpy of the cation, H+ ([C6 mim]+ ), was obtained at 298.15 K. (3) The , for [C mim][OAc] standard molar heat capacity of solution, Cp,m 6
vs. was obtained from the slope of the straight line of sol Hm (T—298.15) K, the specific heat capacity of solution, Cp , and the
apparent relative molar heat capacity, ˚ Cp , were also calculated for [C6 mim][OAc].
2. Experimental 2.1. Chemicals KCl was placed into a vacuum oven and baked at 408.15 K for 6 h before use, as well as THAM (Tris-(hydroxymethyl) aminomethane) for 6 h. The ultrapure water was used. Pure IL [C6 mim][OAc] was purchased, the water content (w2 is the water mass fraction, w2 < 0.005) in the ILs was determined by use of a Karl Fischer
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J. Wei et al. / Fluid Phase Equilibria 371 (2014) 1–5
Table 1 The source and purity of the materials. Chemical name
Source
Purification method
Mass fraction purity (%)
KCl THAM (Tris-(hydroxymethyl) aminomethane) [C6 mim][OAc] Acetic acid Halogen
Shenyang Reagent Co. LTD Shenyang Reagent Co. LTD Lanzhou Institute of Chemical Physics
No further purification No further purification No further purification
>0.9999 >0.9997 ≥0.99 <0.002 <0.0012
H2 O
Ultrapure water
moisture titrator (ZSD-2 type). The source and purity of the materials and the mass fraction contribution of the impurities for [C6 mim][OAc] are listed in Table 1. 2.2. Determination of enthalpy of solution An on-line solution-reaction isoperibol calorimeter system was developed based on calorimetric apparatus previously reported in literature [15–17]. The calorimeter consists of a set of water thermostat, a 200 ml pyrex-glass plated silver Dewar, a 4 ml glass sample cell, a calibration heater, a glass-sheathed thermistor probe, an amplifier, a circuit used as an A/D converter and a personal computer for data acquisition and processing. The detailed experimental procedure has been described elsewhere [11]. The performance and accuracy of the calorimetric system were examined by measuring the molar enthalpy of solution of KCl in water and THAM [Tris-(hydroxymethyl) aminomethane] in 0.1 mol dm−3 HCl (aq) at (298.15 ± 0.01) K. The mean molar solution enthalpies are sol Hm =(17,542 ± 31) J mol−1 for KCl and (−29,794 ± 28) J mol−1 for THAM, which were in good agreement with the corresponding published data: (17,536 ± 9) J mol−1 for KCl [18,19] and (−29,739 ± 10) J mol−1 for THAM [19]. The accuracy of the temperature measurement device is ±0.0001. These results suggest that the calorimeter can be used for determining molar enthalpies of solution in the study. The molar enthalpies of solution in ultrapure water of [C6 mim][OAc] with different molalities, sol Hm , were measured at the temperature range of (288.15 to 308.15 ± 0.01) K with an interval of 5 K.
electrical resistivity, (M cm)
18.2
Table 3 Values of molar solution enthalpy for ionic liquid [C6 mim][OAc], sol Hm (kJ mol−1 ), and extrapolation function, Y (kJ mol−1 ), at 293.15 K, pressure p = 0.1 MPa. Wa (g)
m (mol kg−1 )
−Hm (kJ mol−1 )
Tb (K)
−Y (kJ mol−1 )
0.3809 0.4638 0.5021 0.5497 0.6079 0.6597 0.7139 0.7734 0.8317 0.8971 0.9354 0.9787
0.01685 0.02050 0.02221 0.02430 0.02690 0.02919 0.03159 0.03421 0.03680 0.03970 0.04139 0.04330
52.11 ± 0.023 51.98 ± 0.027 51.85 ± 0.027 51.69 ± 0.030 51.54 ± 0.034 51.40 ± 0.038 51.22 ± 0.040 51.08 ± 0.043 50.93 ± 0.046 50.80 ± 0.051 50.64 ± 0.051 50.49 ± 0.053
0.1824 ± 0.0001 0.2144 ± 0.0001 0.2176 ± 0.0001 0.2368 ± 0.0001 0.2696 ± 0.0001 0.3000 ± 0.0001 0.3208 ± 0.0001 0.3456 ± 0.0001 0.3704 ± 0.0001 0.4064 ± 0.0001 0.4096 ± 0.0001 0.4248 ± 0.0001
52.33 ± 0.023 52.22 ± 0.027 52.10 ± 0.027 51.95 ± 0.030 51.81 ± 0.034 51.68 ± 0.038 51.51 ± 0.040 51.39 ± 0.043 51.25 ± 0.046 51.12 ± 0.051 50.98 ± 0.051 50.83 ± 0.053
a b
Sample mass, W = ±0.0001, m = ±5.04 × 10−6 . Experimental temperature difference, T = ±0.0001.
K are listed in Tables 2–6 suggesting that the dissolution process of the AcAIL is a typical exothermal. According to Archer’s method [14], in terms of a Debye–Hückel limiting term, the values of the standard molar enthalpy of solu , can be obtained using the following tion for [C6 mim][OAc], sol Hm equation at the given temperature: Y = sol Hm −
A H
b
ln 1 + bI 1/2 = sol Hm + ˇm
(1)
The measured values of molar solution enthalpy, sol Hm , of [C6 mim][OAc] and various molarities at (288.15 to 308.15 ± 0.01)
where m is molality, I is ionic strength (I = m for the 1:1 electrolyte [C6 mim][OAc]), b is a constant to be 1.2 [20], AH is the Debye–Hückel parameter for enthalpy and its value at different temperatures was taken from the literature [20], ˇ is empirical constant, Y is extrapolation function calculated from experimental data and are listed in Tables 2–6. According to Eq. (1), plotting the values of Y against various molarities, the good straight lines were and ˇ were obtained obtained (see Fig. 1). The values of sol Hm from the intercepts and the slopes of linear regressions, respectively, and the values of the correlation coefficients, r, and the
Table 2 Values of molar solution enthalpy for ionic liquid [C6 mim][OAc], sol Hm (kJ mol−1 ), and extrapolation function, Y (kJ mol−1 ), at 288.15 K, pressure p = 0.1 MPa.
Table 4 Values of molar solution enthalpy for ionic liquid [C6 mim][OAc], sol Hm (kJ mol−1 ), and extrapolation function, Y (kJ mol−1 ), at 298.15 K, pressure p = 0.1 MPa.
3. Results and discussion , for AcAIL 3.1. The standard molar enthalpy of solution, sol Hm [C6 mim][OAc]
Wa (g)
m (mol kg−1 )
−s Hm (kJ mol−1 )
Tb (K)
−Y (kJ mol−1 )
Wa (g)
m (mol kg−1 )
−s Hm (kJ mol−1 )
Tb (K)
−Y (kJ mol−1 )
0.3843 0.4452 0.4839 0.5529 0.5945 0.6539 0.6872 0.7453 0.7898 0.8548 0.9054 0.9818
0.01700 0.01970 0.02141 0.02446 0.02630 0.02890 0.03040 0.03297 0.03494 0.03782 0.04006 0.04344
53.46 ± 0.025 53.31 ± 0.026 53.20 ± 0.029 53.07 ± 0.032 52.91 ± 0.034 52.79 ± 0.039 52.64 ± 0.040 52.50 ± 0.044 52.36 ± 0.047 52.18 ± 0.048 52.04 ± 0.051 51.90 ± 0.054
0.1960 ± 0.0001 0.2112 ± 0.0001 0.2312 ± 0.0001 0.2536 ± 0.0001 0.2704 ± 0.0001 0.3128 ± 0.0001 0.3216 ± 0.0001 0.3480 ± 0.0001 0.3744 ± 0.0001 0.3848 ± 0.0001 0.4064 ± 0.0001 0.4344 ± 0.0001
53.66 ± 0.025 53.53 ± 0.026 53.42 ± 0.029 53.31 ± 0.032 53.15 ± 0.034 53.05 ± 0.039 52.90 ± 0.040 52.78 ± 0.044 52.64 ± 0.047 52.47 ± 0.048 52.34 ± 0.051 52.21 ± 0.054
0.4094 0.4501 0.5026 0.5604 0.6008 0.6557 0.7003 0.7525 0.8078 0.9012 1.0157 1.1374
0.01811 0.01991 0.02224 0.02480 0.02658 0.02901 0.03098 0.03329 0.03574 0.03987 0.04494 0.05032
50.58 ± 0.022 50.46 ± 0.024 50.34 ± 0.027 50.17 ± 0.029 50.02 ± 0.031 49.89 ± 0.033 49.79 ± 0.036 49.67 ± 0.039 49.55 ± 0.041 49.32 ± 0.045 49.15 ± 0.051 48.91 ± 0.056
0.1776 ± 0.0001 0.1928 ± 0.0001 0.2144 ± 0.0001 0.2344 ± 0.0001 0.2472 ± 0.0001 0.2600 ± 0.0001 0.2840 ± 0.0001 0.3088 ± 0.0001 0.3246 ± 0.0001 0.3624 ± 0.0001 0.4072 ± 0.0001 0.4488 ± 0.0001
50.89 ± 0.022 50.73 ± 0.024 50.63 ± 0.027 50.46 ± 0.029 50.32 ± 0.031 50.20 ± 0.033 50.05 ± 0.036 49.94 ± 0.039 49.82 ± 0.041 49.67 ± 0.045 49.53 ± 0.045 49.38 ± 0.056
a b
Sample mass, W = ± 0.0001, m = ±5.04 × 10−6 . Experimental temperature difference, T = ±0.0001.
a b
Sample mass, W = ±0.0001, m = ±5.04 × 10−6 . Experimental temperature difference, T = ±0.0001.
J. Wei et al. / Fluid Phase Equilibria 371 (2014) 1–5 Table 5 Values of molar solution enthalpy for ionic liquid [C6 mim][OAc], sol Hm (kJ·mol−1 ), and extrapolation function, Y (kJ mol−1 ), at 303.15 K, pressure p = 0.1 MPa. Wa (g)
m (mol kg−1 )
−s Hm (kJ mol−1 )
Tb (K)
−Y (kJ mol−1 )
0.4216 0.4897 0.5268 0.5529 0.6424 0.7596 0.8493 0.9272 0.9811 1.0054 1.1351 1.2147
0.01865 0.02167 0.02331 0.02446 0.02842 0.03361 0.03758 0.04102 0.04341 0.04448 0.05022 0.05374
49.05 ± 0.015 48.92 ± 0.020 48.80 ± 0.022 48.70 ± 0.024 48.55 ± 0.028 48.40 ± 0.033 48.22 ± 0.037 48.09 ± 0.039 47.95 ± 0.042 47.85 ± 0.044 47.72 ± 0.048 47.60 ± 0.053
0.1175 ± 0.0001 0.1600 ± 0.0001 0.1734 ± 0.0001 0.1946 ± 0.0001 0.2250 ± 0.0001 0.2638 ± 0.0001 0.2960 ± 0.0001 0.3103 ± 0.0001 0.3397 ± 0.0001 0.3498 ± 0.0001 0.3851 ± 0.0001 0.4223 ± 0.0001
49.32 ± 0.015 49.21 ± 0.020 49.11 ± 0.022 49.00 ± 0.024 48.88 ± 0.028 48.75 ± 0.033 48.60 ± 0.037 48.48 ± 0.039 48.35 ± 0.042 48.26 ± 0.044 48.15 ± 0.048 48.04 ± 0.053
a b
Sample mass, W = ±0.0001, m = ±5.04 × 10−6 . Experimental temperature difference, T = ±0.0001.
Wa (g)
m (mol kg−1 )
−s Hm (kJ mol−1 )
Tb (K)
−Y (kJ mol−1 )
0.5026 0.5976 0.6405 0.6720 0.7390 0.8314 0.8733 0.9675 1.0638 1.1342 1.2410 1.3059
0.02224 0.02644 0.02834 0.02973 0.03270 0.03678 0.03864 0.04281 0.04707 0.05018 0.05491 0.05778
47.23 ± 0.019 47.05 ± 0.022 46.95 ± 0.024 46.83 ± 0.025 46.68 ± 0.028 46.50 ± 0.031 46.38 ± 0.033 46.21 ± 0.036 45.98 ± 0.041 45.84 ± 0.044 45.66 ± 0.047 45.53 ± 0.051
0.1491 ± 0.0001 0.1748 ± 0.0001 0.1914 ± 0.0001 0.1974 ± 0.0001 0.2270 ± 0.0001 0.2510 ± 0.0001 0.2637 ± 0.0001 0.2918 ± 0.0001 0.3258 ± 0.0001 0.3486 ± 0.0001 0.3784 ± 0.0001 0.4064 ± 0.0001
47.55 ± 0.019 47.44 ± 0.022 47.34 ± 0.024 47.20 ± 0.025 47.04 ± 0.028 46.90 ± 0.028 46.68 ± 0.033 46.54 ± 0.036 46.44 ± 0.041 46.30 ± 0.044 46.19 ± 0.047 46.05 ± 0.051
a
[C6mim][OAc] (l)
ΔsolHmθ H 2O
[C6mim]+ (aq) + [OAc]- (aq)
UPOT
ΔH+ + ΔH[C6mim]+ (g) + [OAc]- (g)
Fig. 2. The thermodynamic cycle for estimation the values of the hydration enthalpy of [C6 mim][OAc].
standard deviations, s, were also from the linear regressions. All above the parameters are listed in Table 7. 3.2. The estimation of hydration enthalpy of [C6 mim][OAc]
Table 6 Values of molar solution enthalpy for ionic liquid [C6 mim][OAc], sol Hm (kJ mol−1 ), and extrapolation function, Y (kJ mol−1 ), at 308.15 K, pressure p = 0.1 MPa.
b
3
Sample mass, W = ±0.0001, m = ±5.04 × 10−6 . Experimental temperature difference, T = ±0.0001.
The hydration enthalpy of the ionic liquid [C6 mim][OAc] was of the pure ionic liquid in terms estimated using the value of sol Hm of the following thermodynamic cycle (see Fig. 2): (H+ + H− ) = sol Hm − UPOT
(2)
where UPOT is crystal lattice energy which can be estimated by Glasser’s [21,22] theory of lattice energy:
−1/3
UPOT = 2 ˛Vm
+ˇ
(3)
where ˛ and ˇ are fitting coefficients, ionic strength I = 1, and the molecular volume was presented in nm3 . According to the suggestion from Gutowski et al. [23], the values of ˛ and ˇ are, respectively, 83.3 nm kJ mol−1 and 157.3 kJ mol−1 for the ILs which are 1:1 salts but contain organic cations. These ˛ and ˇ values have been recently used to calculate thermodynamic properties of some ILs [24,25]. The crystal energies for the ILs investigated in the present work were calculated from, the values of UPOT for [C6 mim][OAc] is 546.77 kJ mol−1 , so that the hydration enthalpy of cation and anion in infinite dilution aqueous [C6 mim][OAc], (H+ + H− ) = −598 kJ mol−1 , at 298.15 K. It is believed that there are only ion–water interactions, no ion–ion interactions in infinite dilution, hence the contributions of the cation and the anion to molar hydration enthalpy of the [C6 mim][OAc] have additivity. Consequently, according to hydration enthalpy of acetic acid anion, H− ([CH3 COO]− ) = −425 kJ mol−1 , obtained by Marcus [26], the hydration enthalpy of the cation, H+ ([C6 mim]+ ) = −173 kJ mol−1 , was determined. In comparison with hydration enthalpy of [C2 mim]+ , H+ ([C2 mim]+ ) = −233 kJ mol−1 [27], the hydration enthalpy of [C6 mim]+ is a little bit weaker. 3.3. The standard molar heat capacity of solution, Cp,m
Fig. 1. The plot of Y (extrapolation function calculated from Eq. (1) against m for [C6 mim][OAc] in temperature range of 288.15–308.15 K.
are As shown in Fig. 3, the experimental values of sol Hm linearly associated with (T—298.15) K for AcAIL. The [C6 mim][OAc] regression equation is sol Hm /kJ mol−1 = −51.63 + 0.313 (T—298.15) K with a correlation coefficient, r = 0.999, and standard deviation, s = 0.12. The standard molar heat capacity of solution,
Table 7 (kJ mol−1 ) in temperature range of 288.15–308.15 K. Values of standard molar solution enthalpy for ionic liquid [C6 mim][OAc], sol Hm T (K) −sol Hm a
(kJ mol ˇ (kJ kg mol−2 ) b s (kJ mol−1 ) rc a b c
−1
)
Empirical constant. Standard deviation. Correlation coefficient.
288.15
293.15
298.15
303.15
308.15
54.66 ± 0.03 57.24 0.03 0.998
53.35 ± 0.04 57.36 0.03 0.998
51.64 ± 0.05 47.82 0.05 0.995
49.96 ± 0.04 36.56 0.04 0.996
48.52 ± 0.03 43.69 0.03 0.999
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J. Wei et al. / Fluid Phase Equilibria 371 (2014) 1–5
Table 8 Values of the apparent relative molar heat capacity of [C6 mim][OAc], Cp (J K−1 mol−1 ) at 298.15 K. −sol Hm (kJ mol−1 )
m (mol kg−1 )
0.01500 0.02100 0.02300 0.02600 0.02800 0.03100 0.03400 0.03500 0.03700 0.04000 0.04400 0.04600 a
288.15 (K)
293.15 (K)
298.15 (K)
303.15 (K)
308.15 (K)
53.48 53.09 52.96 52.76 52.64 52.45 52.26 52.19 52.07 51.88 51.63 51.51
52.17 51.77 51.64 51.45 51.32 51.13 50.94 50.88 50.75 50.56 50.32 50.19
50.60 50.26 50.15 49.99 49.88 49.72 49.56 49.50 49.40 49.24 49.02 48.92
49.09 48.82 48.73 48.60 48.51 48.39 48.26 48.22 48.13 48.01 47.84 47.76
47.54 47.23 47.13 46.98 46.87 46.73 46.58 46.53 46.43 46.28 46.09 45.99
(∂sol Hm /∂T)p,m
ra
299.03 293.28 291.37 288.49 286.58 283.70 280.83 279.87 277.96 275.08 271.25 269.33
0.9996 0.9996 0.9995 0.9994 0.9993 0.9991 0.9989 0.9988 0.9986 0.9982 0.9977 0.9974
746 740 738 735 734 731 728 727 725 722 718 716
Cp (J K−1 mol−1 )
Correlation coefficient.
Cp,m = 313 J K−1 mol−1 , was obtained from the slope, and the spe-
cific heat capacity of solution, accordingly.
Cp
= 1.38 J g−1
K−1 ,
was calculated
3.4. The apparent relative molar heat capacity, ˚ Cp for [C6 mim][OAc] The apparent relative molar heat capacity for [C6 mim][OAc], may be expressed as:
C , p
Cp =
∂sol Hm ∂T
4. Conclusions
+ Cp (ILs)
(4)
p,m
The molar heat capacity of [C4 mim][OAc], Cp (ILs) is 383.2 J K−1 mol−1 , per molar methylene’s contribution to the heat capacity is about 32 J K−1 mol−1 [28], and so the molar heat capacity of [C6 mim][OAc], Cp (ILs), is about 447 J K−1 mol−1 . According to Archer’s method [14], the values of molar solution enthalpy, sol Hm , of [C6 mim][OAc] with various molalities at (288.15 to 308.15 ± 0.01) K were calculated. Plotting the values of sol Hm against T, the values of (∂sol Hm /∂T)p,m were obtained from the slopes of linear regressions. According to Eq. (4), the values of Cp were calculated. All above the parameters are listed in Table 8.
According to the experiment values of the molar enthalpies of solution, sol Hm , for ionic liquid [C6 mim][OAc], the val for ues of the standard molar enthalpies of solution sol Hm [C6 mim][OAc] were obtained in the temperature range of (288.15 to 308.15 ± 0.01) K, respectively. According to Glasser’s theory of lattice energy, the hydration enthalpy of cation, (H+ + H− ) = −598 kJ mol−1 at 298.15 K was obtained. The hydration enthalpy of the cation, H+ ([C6 mim]+ ) = −173 kJ mol−1 , was determined. In comparison with hydration enthalpy of [C2 mim]+ , the hydration enthalpy of [C6 mim]+ is a little bit weaker. A linear relationship was found by plotting the experimental values of against (T—298.15) K, The standard molar heat capacity sol Hm of solution, Cp,m = 313 J K−1 mol−1 , was obtained from the slope of the regression line, the specific heat capacity of solution, Cp
= 1.38 J g−1 K−1 , and the apparent relative molar heat capacity, ˚ Cp , were also calculated for [C6 mim][OAc]. Acknowledgment This project was supported by NSFC (21173107), Peoples Republic of China. References
-48 -49
θ -1 ΔsolHm /kJ·mol
-50 -51 -52 -53 -54 -55 -10
-5
0
5
10
( T-298.15) /K Fig. 3. The plot of the standard molar enthalpy of solution, sol Hm (kJ mol−1 ), against (T—298.15) K for [C6 mim][OAc].
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: the standard molar heat capacity of solution Cp,m
Cp : the specific heat capacity of solution Cp (ILs): molar heat capacity Cp : the apparent relative molar heat capacity : the standard molar enthalpies of solution sol Hm I: ionic strength m: molality M: molar mass r: correlation coefficient s: standard deviation T: is the adiabatic temperature change of the solution process W: sample mass Y: extrapolation function Greek Letters
Glossary ˇ: empirical constant AH : the Debye–Hückel parameter b: constant
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