Article pubs.acs.org/IECR
Volumetric and Surface Properties of Aqueous 1‑Alkyl-3methylimidazolium Propionate {[Cnmim][Pro] (n = 4, 5, 6)} Ionic Liquids at 298.15 K Wei-Guo Xu, Chi Li, Ru-Jing Liu, Hong-Xu Yang, Jing Tong,* and Jia-Zhen Yang Key Laboratory of Green Synthesis and Preparative Chemistry of Advanced Materials, Liaoning University, Shenyang, 110036, People’s Republic of China S Supporting Information *
ABSTRACT: Three propionic acid ionic liquids (PrAILs), 1-alkyl-3-methylimidazolium propionate ([Cnmim][Pro] (n = 4, 5, 6)), were prepared by the neutralization method and characterized by 1H NMR spectroscopy. The values of the densities and surface tensions of aqueous [C4mim][Pro], [C5mim][Pro], and [C6mim][Pro] with various molalities were determined at 298 K, and the values of the parachor for these solutions were calculated. The values of the apparent molar volumes and partial molar volumes at infinite dilution for the ILs were estimated in terms of Pitzer’s theory. With the use of Li’s model of surface tension and the empirical equation of the parachor, the values of the surface tensions of these aqueous solutions for three PrAILs were estimated and the estimated values were in good agreement with experimental ones.
1. INTRODUCTION Ionic liquids (ILs), which consist solely of ions and are liquids at or near room temperature, are a new reaction medium with environmentally friendly properties and new soft functional materials developed in recent years.1 Since carboxylic acid ionic liquids (CAILs) can be synthesized through natural carboxylic acids, they have aroused great attention from industry and the academic community as a new-generation “greener ionic liquid”.2−7 Propionic acid has low toxicity, cheap price, good stability, and other advantages, especially as a widely used catalyst. Therefore, using propionic acid as the root of an ionic liquid anion, a new series of [Cnmim][Pro] (n = 4, 5, 6) alkaline ionic liquids were synthesized and have been expected to be applied in various fields, such as industrial chemistry and the pharmaceutical chemistry.6,7 Most of the research has focused on pure ionic liquids in past years, and few papers discuss the behavior of the IL solutions from a thermophysical point of view.8−11 However, the solutions of ILs increase enormously the above-cited tuning capability of ILs because there is an unlimited quantity of possible IL solutions. Potential uses and applications of an IL solution make it necessary to know its physical properties such as density, viscosity, surface tension, and conductivity which need to be measured experimentally. Therefore, in this paper we report the following: (1) Propionic acid ionic liquids (PrAILs) 1-alkyl-3-methylimidazolium propioniate ([Cnmim][Pro] (n = 4, 5, 6)) were prepared by the neutralization method and characterized by 1H NMR spectroscopy. (2) The values of densities and surface tensions for aqueous [Cnmim][Pro] (n = 4, 5, 6) with various molalities were measured at 298.15 K. (3) The values of apparent molar volumes and partial molar volumes at infinite dilution for the ILs were calculated in terms of Pitzer’s theory. (4) The dependence of the surface tension and the parachor on molality for aqueous [Cnmim][Pro] (n = 4, 5, 6) were discussed. (5) With the use of both Li’s model of © 2014 American Chemical Society
surface tension and the semiempirical methods of parachor, the surface tensions for the aqueous PrAILs were estimated.
2. EXPERIMENTAL SECTION 2.1. Chemicals. Deionized water was distilled in a quartz still, and its conductance was (0.8−1.2) × 10−4 S·m−1. NMethylimidazole AR grade reagent was obtained from ACROS and vacuum distilled prior to use. Propionic acid was distilled and dried under reduced pressure. N-Methylimidazole (ARgrade reagent) was vacuum distilled prior to use. 1Bromobutane, 1-bromopentane (AR-grade reagent), and 1bromohexane (AR-grade reagent) were distilled before use. Ethyl acetate and acetonitrile were distilled and then stored over molecular sieves in tightly sealed glass bottles. Anionexchange resin (type 717) was purchased from Shanghai Chemical Reagent Co. Ltd. and activated by the regular method before use. The sources and purities of the materials are listed in Table 1. 2.2. Preparation of PrAILs. The PrAILs [Cnmim][Pro] (n = 4, 5, 6) were prepared by a neutralization method.12−14 The structures of the resulting ionic liquids were confirmed by 1H NMR spectroscopy (see Figure A in the Supporting Information). The water content (w2 is the water mass fraction; w2 = (8.00 ± 0.01) × 10−3, (7.60 ± 0.01) × 10−3, and (7.80 ± 0.01) × 10−3 mass fraction for [C4mim][Pro], [C5mim][Pro], and [C6mim][Pro], respectively) in the ILs was determined by use of a Karl Fischer moisture titrator (ZSD-2 type). 2.3. Measurement of the Densities and Surface Tensions of the Aqueous Solutions of PrAILs. Each sample was used immediately after it was mixed well by Received: Revised: Accepted: Published: 9959
March 25, 2014 May 15, 2014 May 16, 2014 May 16, 2014 dx.doi.org/10.1021/ie501240t | Ind. Eng. Chem. Res. 2014, 53, 9959−9967
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error of ±0.1 mJ·m−2. Then the values of surface tensions of the samples were measured by the same method.
Table 1. Sources and Purities of Materials mass fraction purity
source
N-methylimidazole, ≥0.99 propionic acid, ≥0.99 1-bromobutane, >0.98 1-bromopentane, >0.98 1-bromohexane, >0.98 ethyl acetate, >0.99 acetonitrile, >0.99 anion-exchange resin (type 717, granularity >0.95) benzoic acid, >0.999
ACROS Shenyang Reagent Co. Ltd. Shenyang Reagent Co. Ltd. Shenyang Reagent Co. Ltd. Shenyang Reagent Co. Ltd. Shanghai Reagent Co. Ltd. Shanghai Reagent Co. Ltd. Shanghai Reagent Co. Ltd.
3. RESULTS AND DISCUSSION 3.1. Density and Surface Tension for Aqueous [Cnmim][Pro] (n = 4, 5, 6). The experimental values of densities and surface tensions for the samples of aqueous [C4mim][Pro], [C5mim][Pro], and [C6mim][Pro] with various molalities at 298.15 K are listed in Table 2. Each value in Table 2 is the average of triple measurements. Figures 1 and 2 are the plots of density and surface tension versus the molalities of aqueous [C4mim][Pro], [C5mim][Pro], and [C6mim][Pro] at 298.15 K. Rilo et al.8 studied the influence of density with alkyl chain length of four 1-alkyl-3-methylimidazolium tetrafluoroborates, [Cnmim][BF4], in aqueous solutions. They pointed out that the density of aqueous [Cnmim][BF4] decreases with the increase of the alkyl chain length of the cation and with decrease of the concentration. From Table 2 it can be seen that Rilo’s results are in good agreement with those in this work. 3.2. Apparent Molar Volume and Determination of the Partial Molar Volume at Infinite Dilution for Aqueous [Cnmim][Pro] (n = 4, 5, 6). The apparent molar volume is derived from the densities of solutions. The apparent molar volumes are given by16
NIMC
shaking. All solutions to be measured were prepared freshly and performed on an electronic balance (AL104) accurate to 0.1 mg with calibration of air buoyancy. The uncertainty of the molalities of all solutions is within ±1.0 × 10−4 mol·kg−1. With the use of an Anton Paar DMA 4500 oscillating U-tube densitometer, the density of each sample with molality ranging from 0.01 to 0.50 mol·kg−1 was measured at 298.15 K. The temperature in the cell was regulated to ±0.01 K with a solid state thermostat. The apparatus was calibrated once a day with dry air and double-distilled degassed fresh water. By use of the tensiometer of the forced bubble method (DPAW type produced by Sang Li Electronic Co.), the surface tension of water was measured at 298.15 ± 0.05 K and was in good agreement with the literature15 within the experimental
ϕ
V B = [1000(ρ0 − ρ) + mM 2ρ0 ]/mρρ0
(1)
Table 2. Experimental Values of Density and Surface Tension for Aqueous [Cnmim][Pro] (n = 4, 5, 6) with Various Molalities at 298.15 K m/mol·kg−1
ρ/g·cm−3
γ(Exp)/mJ·m−2
0.0111 0.0278 0.0556 0.1112 0.1670 0.2789 0.3351 0.3912 0.4470
0.997 19 0.997 39 0.997 74 0.998 47 0.999 21 1.000 73 1.001 48 1.002 23 1.002 95
71.7 71.4 70.7 69.9 68.7 66.3 65.0 63.6 62.4
0.0111 0.0278 0.0557 0.1112 0.1670 0.2774 0.3350 0.3913 0.4477
0.997 17 0.997 34 0.997 64 0.998 29 0.998 98 1.000 35 1.001 09 1.001 83 1.002 55
71.7 71.5 70.7 69.8 68.5 66.0 64.4 63.1 61.9
0.0115 0.0277 0.0547 0.1112 0.1673 0.2789 0.3350 0.3910 0.4475
0.997 16 0.997 30 0.997 56 0.998 13 0.998 75 1.000 06 1.000 71 1.001 39 1.002 10
71.6 71.2 70.3 69.3 68.0 65.5 64.2 62.6 61.0
ϕ
V/cm3·mol−1
Pm(Calc)
Pm
Aqueous Solution of [C4mim][Pro] 216.09 52.68 52.72 215.32 52.79 52.85 214.71 52.92 53.08 214.03 53.30 53.53 213.64 53.59 53.98 213.00 54.14 54.88 212.80 54.38 55.33 212.62 54.59 55.78 212.50 54.83 56.22 Aqueous Solution of [C5mim][Pro] 217.90 52.69 52.72 217.15 52.83 52.87 216.56 52.97 53.11 215.68 53.37 53.60 215.07 53.68 54.09 214.39 54.28 55.05 214.05 54.51 55.55 213.73 54.78 56.03 213.50 55.07 56.52 Aqueous Solution of [C6mim][Pro] 219.10 52.69 52.73 218.58 52.80 52.89 217.87 52.93 53.14 217.17 53.36 53.67 216.52 53.72 54.20 215.55 54.41 55.24 215.27 54.73 55.76 214.94 54.97 56.28 214.60 55.20 56.81 9960
Pm(Est)
ΔP = Pm(Calc) − Pm
γ(Est)/mJ·m−2
52.68 52.77 52.91 53.20 53.49 54.07 54.35 54.64 54.92
−0.03 −0.06 −0.15 −0.23 −0.39 −0.74 −0.94 −1.18 −1.39
71.7 71.3 70.7 69.4 68.2 65.9 64.9 63.8 62.8
52.72 52.78 52.94 53.26 53.57 54.19 54.52 54.83 55.14
−0.03 −0.04 −0.14 −0.23 −0.41 −0.77 −1.03 −1.25 −1.46
71.9 71.3 70.6 69.2 68.0 65.6 64.4 63.3 62.3
52.70 52.80 52.96 53.31 53.65 54.32 54.66 54.99 55.33
−0.05 −0.09 −0.21 −0.31 −0.48 −0.83 −1.03 −1.31 −1.61
71.6 71.2 70.5 69.0 67.6 65.1 63.9 62.7 61.6
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Figure 3. Plot of apparent molar volume versus molality m. ■, [C4mim][Pro]; ●, [C5mim][Pro]; ▲, [C6mim][Pro].
Figure 1. Plot of density versus molality of aqueous solution at 298.15 K. ■, [C4mim][Pro]; ●, [C5mim][Pro]; ▲, [C6mim][Pro].
ln γ± = −|z Mz X|Aϕ[I1/2/(1 + bI1/2) + (2/b) ln(1 + bI1/2)] + 2(2νXνMm /ν) {β (0)MX + (β (1)MX /α 2I ) [1 − (1 + αI1/2 − α 2I /2)] exp(−αI1/2)} + (3/2)[(νXνM)3/2 /ν]m2C ϕ MX
(4)
(1/2)∑mizi2,
where I is the ionic strength, I = and zM and zX are ionic charges for the cation and anion in electronic units, respectively. Likewise, νM and νX are the numbers of cations and anions in the formula of the ionic liquid, respectively, where ν = νM+ νX; Aϕ is the Debye−Hückel parameter for the osmotic coefficient given as Aϕ = (1/3)(2πN0ρW /1000)1/2 (e 2 /DkBT )3/2
where N0 is Avogadro’s number, ρW is the density of the solvent, D is the static dielectric constant of pure water, kB is the Boltzmann constant, and e the absolute electronic charge. Since the values of νM, νX, and ν for electrolyte of 1−1 type, [Cnmim][Pro] (n = 4, 5, 6), are 1, 1, and 2, respectively, the factors (2νXνM)/ν and 2[(νXνM)3/2 /ν] equal 1. The leading term in eqs 3 and 4 arises from the long-range electrostatic interactions; the parameters β(0)MX, and β(1)MX account for various types of short-range interactions between M and X, and for indirect forces arising from the solvent; the third coefficient CϕMX is for triple ion interactions and is important only at high concentrations. The parameter b is given the value 1.2 for all electrolytes and α is 2.0 for all electrolytes of 1−1 type in eqs 3 and 4; b and α are taken as temperature independent. The quantities β(0)MX, β(1)MX, and CϕMX are adjusted for a given salt at fixed temperature by a least-squares fit of osmotic or activity coefficient data. The total volume, V, of the solution is given by
Figure 2. Plot of surface tension versus molality of aqueous solution at 298.15 K. ■, [C4mim][Pro]; ●, [C5mim][Pro]; ▲, [C6mim][Pro].
where ρ0 and ρ are the densities of pure water and IL aqueous solutions, respectively, m is molality, and M2 is the molar mass of the IL. The values of apparent molar volume calculated with eq 1 are listed in Table 2. Figure 3 is the plot of the apparent molar volume versus the molality m for aqueous [Cnmim][Pro] (n = 4, 5, 6). According to Pitzer’s theory,17 the total excess Gibbs energy is GEX = νnW mRT(1 − ϕ + ln γ±)
(2)
where nW is the number of kilograms of solvent (neutral molecules), m is the molality of an ionic liquid, R is the gas constant, and ν is the number of ions in the formula of the ionic liquid. T is the thermodynamic temperature, ϕ is the osmotic coefficient, and γ± is the activity coefficient. According to Pitzer’s theory, ϕ and ln γ± can be calculated by the following equations:
V = n0V0 0 + nBVB̅ 0 + (∂GEX /∂P)T , m
[β (0)MX + β (1)MX exp( −αI1/2)] + 2[(νXνM)
2
/ν]m C
ϕ MX
(6)
where V00 is the molar volume of the solvent, and V̅ 0B is the partial molar volume of the salt at infinite dilution. The apparent molar volume, ϕVB, of the solute is given by
ϕ − 1 = −|z Mz X|Aϕ[I1/2/(1 + bI1/2)] + (2νXνMm /ν) 3/2
(5)
ϕ
(3)
V B = (V − n0V0 0)/nB
(7)
so that 9961
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V B = V̅B0(1/nB)(∂GEX /∂P)T , m
methylene, but the values of the Pitzer parameter β(1)VMX are almost constant. 3.3. Dependence of Surface Tension on Molarity of the Aqueous PrAILs. In a large concentration range, the following empirical equation18 was applied to the relationship between the surface tension and the molarity:
(8)
Substitution of Pitzer’s equations into eq 8 yields ϕ
V B = VB̅ 0 + ν|z Mz X|(AV /2b) ln(1 + bI1/2)] + (2νXνM RT )[mB′MX + (z MνM)m2C′MX
(9)
γ = γ0 − kc
where
where k = −(∂γ/∂c)T is an empirical constant, γ0 is the surface tension of water, and c is molarity. The conversion relationship between molality and molarity is c = mρ/(1 + 0.001mM2), where ρ is the density of the aqueous PrAILs and M2 is the mass of the solute. The calculated values of the molarity of [Cnmim][Pro] (n = 4, 5, 6) according to the molality at 298.15 K are listed in Table S1 of the Supporting Information. The definition of the surface pressure, π, is
B′MX = (∂B EX /∂P)T , I = β (0)V MX + (β (1)V MX /α 2I )[1 − (1 + αI1/2) exp(−αI1/2)]
(18)
(10)
β (0)V MX = (∂β (0)MX /∂P))T , I
(11)
β (1)V MX = (∂β (1)MX /∂P)T , I
(12)
π = γ0 − γ = k′c
(19)
C′MX = (z Mz X)−1/2 C ϕV MX /2
(13)
k′ = (∂π /∂c)T
(20)
C ϕV MX = (∂C ϕ MX /∂P)T , I
(14)
AV = 2AϕRT[3(∂ ln D/∂P)T + (∂ ln V0 0/∂P)T ]
(15)
When k′ > 0, there is positive adsorption on the surface of solution; when k′ < 0, there is negative adsorption. Figure 4 is a
The apparent molar volumes of aqueous [Cnmim][Pro] (n = 4, 5, 6) can be expressed by Pitzer’s equation (9). The third coefficient C′MX in eq 9 is for triple ion interactions and is important only at high concentrations (m > 2.0 mol·kg−1). Because the molality of aqueous [C4mim][Pro], [C5mim][Pro] and [C6mim][Pro] is less than 0.50 mol·kg−1, the term of C′MX can be neglected. Therefore, rearranging eq 9, the working equation for aqueous [Cnmim][Pro] (n = 4, 5, 6) yields Y = ϕV B − (AV /1.2) ln(1 + 1.2I1/2) = V̅B0 + 2RTmβ (0)V MX + 2RTmy′β (1)V MX
(16)
where Y is the extrapolation function which may be calculated from experimental data and y′ is defined by the following equation: y′ = [1 − (1 + 2I
1/2
) exp( −2I
1/2
)]/2I
Figure 4. Plot of surface pressure versus molarity for aqueous [Cnmim][Pro] (n = 4, 5, 6) at 298.15 K. ■, [C4mim][Pro]; ●, [C5mim][Pro]; ▲, [C6mim][Pro].
(17)
With the use of the experimental data of the apparent molar volume to fit eq 16, the values of β(0)VMX, β(1)VMX, the partial molar volume of the salt at infinite dilution V̅ 0B, and the correlation coefficient, r, were obtained and are listed in Table 3. The very small standard deviation for the fitting to eq 16 implies that Pitzer’s equation is also appropriate for aqueous [C4mim][Pro], [C5mim][Pro], and [C6mim][Pro]. From Table 3 it can be seen that the values of the partial molar volumes of these ILs at infinite dilution, V̅ 0B, increase and the values of Pitzer parameter β(0)VMX decrease with the increase of
plot of surface pressure versus molarity for aqueous [C4mim][Pro], [C5mim][Pro], and [C6mim][Pro] at 298.15 K. From Figure 4 it can be seen that k′ > 0; this means that the PrAILs have a certain surface activity and the surface activity increases with the increase of the methylene number for ILs. This result is in good agreement with that obtained by Rilo et al.,8 who measured surface tensions of four ILs [Cnmim][BF4] in aqueous solutions. Rilo et al. observed that the surface tension decreases with the increase of the alkyl chain length of the cation. 3.4. Estimating Surface Tension of Aqueous PrAILs Using the Parachor. The parachor, P, is a relatively old concept and is available as a link between the structure, density, and surface tension of a liquid and was defined using the following equation:19,20
Table 3. Values of the Partial Molar Volume of the IL at Infinite Dilution V̅ 0B (cm3·mol−1), Pitzer’s Parameters, and Related Coefficients r of Aqueous [Cnmim][Pro] (n = 4, 5, 6) for the Fitting to eq 16 at 298.15 K V̅ 0B/cm3·mol−1 105β(0)VMX 103β(1)VMX r
[C4mim][Pro]
[C5mim][Pro]
[C6mim][Pro]
206.1 31.2 2.26 0.999
207.9 −7.30 2.26 0.999
210.6 −49.1 1.93 0.999
P = (Mγ 1/4)/ρ
(21)
where γ is the surface tension, M is the molar mass, and ρ is the density of a substance. 9962
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In 2008, Balasubrahmanyam21 pointed out that the following equation was used to estimate the parachor of a solution: Pm = xP2 + (1 − x)P1
(22)
Pm is the parachor of the solution, P2 and P1 are the parachors of the solute and solvent, and x is the mole fraction of the solute and can be calculated with x = mM1/(1000 + mM1), where M1 is the molar mass of the solvent in grams. When calculating the experimental values of the parachor for the aqueous PrAILs with eq 21, M should be replaced with the average molar mass: M = xM 2 + (1 − x)M1
(23)
where M2 and M1 are the molar mass of the solute and the solvent, respectively. The values of Pm calculated by eq 22 are also listed in Table 2. From Table 2, it can be seen that the difference, ΔP = Pm(Calc) − Pm, between Pm(Calc) and Pm means the measurement of the solute−solvent interaction and can be expressed in the following empirical equation: ΔP = Pm(Calc) − Pm = A pm
Figure 6. Plot of estimated values of surface tension, γ(Est), versus experimental values, γ(Exp), at 298.15 K. ■, [C4mim][Pro]; ●, [C5mim][Pro]; ▲, [C6mim][Pro]. y = 2.30 + 0.965x; r = 0.996; s = 0.296.
(24)
where Ap is an empirical parameter and m is the molality. The following values of Ap were obtained: Ap = −2.90 for aqueous [C4mim][Pro], Ap = −3.07 for aqueous [C5mim][Pro], and Ap = −3.30 for aqueous [C6mim][Pro]. Equation 25, an empirical equation, may be used to estimate the values of the parachor, Pm(Est), for the PrAILs; the estimated values are also listed in Table 2. Pm(Est) = xPsolute + (1 − x)Psolvent + A pm
versus γ(Exp), for aqueous [C4mim][Pro], [C5mim][Pro], and [C6mim][Pro] at 298.15 K. From Figure 6, it can be seen that the estimated surface tension and the experimental values are highly correlated (correlation coefficient, r = 0.996; standard deviation, s = 0.306) and extremely similar (gradient = 0.995; intercept = 0.0910). 3.5. Li’s Model of Surface Tension for Electrolyte Aqueous Solutions. Li et al. proposed the surface tension model of electrolyte solution which was built on the basis of the following assumptions:22−25 (1) There exists a surface phase located between the bulk liquid and vapor phases, assuming that the surface phase is electrically neutral with a uniform concentration of ionic liquid phase that is different from the
(25)
Figure 5 is a comparative plot of calculated parachor values, Pm(Est), as a function of corresponding experimental values,
Figure 7. Scheme of the surface phase in an electrolyte solution. V, bulk vapor phase; S, surface phase; L, bulk liquid phase.
body phase (Figure 7). (2) For [Cnmim][Pro] (n = 4, 5, 6), an electrolyte of 1−1 valence type
Figure 5. Plot of calculated parachor values, Pm(Est), versus experimental values, Pm(Calc), at 298.15 K. ■, [C4mim][Pro]; ●, [C5mim][Pro]; ▲, [C6mim][Pro]. y = −1.29 + 1.02x; r = 0.997; s = 0.0630.
m±S = km± L m±L
(26)
m±S
where and are mean ionic molalities of aqueous ILs in the bulk liquid and surface phases, k is a proportional constant, and superscript “L” and “S” mean bulk liquid and surface phases. (3) Assuming the partial molar surface area of water, SW ̅ , in aqueous [Cnmim][Pro] (n = 4, 5, 6) to be equal to the molar area of pure water, SW, eq 27 was obtained:
Pm(Calc), for aqueous ILs. From Figure 5, it can be seen that Pm(Est) and Pm(Calc) are highly correlated (correlation coefficient, r = 0.997; standard deviation, s = 0.0637) and extremely similar (gradient = 0.998; intercept = 0.0613). According to eq 21, the surface tension of the aqueous PrAILs can be estimated by the values of Pm(Est). Figure 6 is a comparative plot of estimated values of the surface tension, γ(Est), as a function of corresponding experimental values,
2/3 1/3 SW = SW ̅ = (VW ) (NA )
(27)
where VW is molar volume of water, NA is Avogadro’s constant, and subscript “W” means water. (4) The osmotic coefficients of 9963
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Table 4. Values of Surface Tensions and Activity Coefficients of Bulk Liquid and Surface Phases for [Cnmim][Pro] (n = 4, 5, 6)a
a
m/mol·kg−1
γ(Exp)/mJ·m−2
f±B
0.0111 0.0278 0.0556 0.1112 0.1670 0.2789 0.3351 0.3912 0.4470
71.7 71.4 70.7 69.9 68.7 66.3 65.0 63.6 62.4
0.8798 0.8151 0.7481 0.6648 0.6096 0.5360 0.5094 0.4872 0.4682
0.0111 0.0278 0.0557 0.1112 0.1670 0.2774 0.3350 0.3913 0.4477
71.7 71.5 70.7 69.8 68.5 66.0 64.7 63.0 62.0
0.8733 0.8016 0.7259 0.6318 0.5696 0.4888 0.4591 0.4350 0.4146
0.0115 0.0277 0.0547 0.1112 0.1673 0.2789 0.3350 0.3910 0.4475
71.6 71.2 70.3 69.3 68.0 65.5 64.2 62.6 61.0
0.8950 0.8509 0.8087 0.7579 0.7258 0.6829 0.6667 0.6528 0.6404
γ(Calc)/mJ·m−2
f±B(D)
In Aqueous [C4mim][Pro] 71.7 0.8995 71.3 0.8565 70.7 0.8184 69.4 0.7792 68.2 0.7586 65.9 0.7397 64.7 0.7361 63.5 0.7350 62.4 0.7357 In Aqueous [C5mim][Pro] 71.7 0.8995 71.3 0.8565 70.6 0.8183 69.4 0.7792 68.1 0.7586 65.7 0.7398 64.4 0.7361 63.2 0.7350 61.9 0.7357 In Aqueous [C6mim][Pro] 71.6 0.8980 71.2 0.8567 70.5 0.8193 69.1 0.7792 67.7 0.7585 65.1 0.7397 63.7 0.7361 62.4 0.7350 61.1 0.7357
f±F
m±F/mol·kg−1
a±F
0.6591 0.5587 0.4816 0.4082 0.3682 0.3212 0.3055 0.2926 0.2819
0.2204 0.5512 1.1028 2.2080 3.3150 5.5364 6.6506 7.7651 8.8733
0.1453 0.3079 0.5312 0.9014 1.2204 1.7785 2.0317 2.2724 2.5012
0.6530 0.5514 0.4739 0.4013 0.3618 0.3163 0.3005 0.2879 0.2773
0.2281 0.5705 1.1439 2.2843 3.4305 5.6998 6.8817 8.0395 9.1972
0.1490 0.3146 0.5421 0.9168 1.2413 1.8028 2.0679 2.3146 2.5507
0.6487 0.5542 0.4798 0.4051 0.3646 0.3174 0.3015 0.2885 0.2775
0.2603 0.6261 1.2365 2.5137 3.7817 6.3023 7.5716 8.8360 10.1128
0.1688 0.3470 0.5933 1.0183 1.3789 2.0005 2.2829 2.5495 2.8066
γ(Exp) and γ(Calc) are the experimental value and calculated value.
the bulk liquid and surface phases are all calculated by Pitzer equations.17 According to thermodynamics, in aqueous [Cnmim][Pro] (n = 4, 5, 6) the chemical potential of water for bulk liquid and surface phases, μWL and μWS, can be expressed by μ W L = μ° W L + RT ln(a L W )
(28)
μ W S = μ° W S + RT ln(aS W ) − γS W ̅
(29)
μ°WL
φ = 1 − AφI1/2/(1 + 1.2I1/2) + mβ (0) + mβ (1) exp( − 2I1/2) + m2C ϕ
C is for triple ion interactions and is important only at high concentrations, so it was neglected in this work. I is ionic strength. Substituting eq 33 into eq 32 and rearranging, the working equation yields Y = 55.51(γ − γW )S W /(2mRT ) + Aφ[I L1/2/(1 + I L1/2) − kI S1/2/(1 + I S1/2)]
μ°WS
where and are standard chemical potentials for bulk liquid and surface phases; a and γ are the activity and surface tension, respectively. In the equilibrium state, μWL = μWS. Equation 29 minus eq 28 can be obtained as eq 30:
= (1 − k) + (1 − k 2)mβ (0) + m[exp(− 2I L1/2) − k 2 exp( − 2I S1/2)]β (1)
S L γ = (μ° W S − μ° W L )/S W ̅ + (RT /S W ̅ ) ln(a W /a W )
(34) S
For pure water = a W = 1 and S̅W = SW. With eq 30, the surface tension of pure water was given: L
γW = (μ° W S − μ° W L )/S W
Y = A 0 + X1β (0) + X 2β (1)
(31)
(35)
where A0 = (1 − k); variables X1 = (1 − k )m and X2 = m[exp(−2IL1/2) − k2 exp(−2IS1/2)]. In Y, X1, and X2, k is an undetermined value so that it is necessary that an initial value be assigned to k(0). According to eq 35, the regression of extrapolation function Y against X1 and X2 was made using the least-squares program so that the values of A0, β(0), and X2β(1) were obtained. Using the value of A0, the new value of k(1) was 2
Substituting eq 31 and the relation between the activity of water and the osmotic coefficient, φ, of an electrolyte solution into eq 30, 16 the following equation was obtained: γ = γW + (2mRT /55.51S W )(φL − kφS)
L
where I = kI = km; Y is the extrapolation function which may be calculated from experimental data. Equation 34 is equivalent to the multivariate linear equation (35):
(30)
aSW
(33)
ϕ
(32)
For aqueous [Cnmim][Pro] (n = 4, 5, 6), Pitzer’s equation17 is 9964
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calculated so that new values of Y, X1, and X2 were obtained and a new regression was made until |k(n) − k(n − 1)| < 0.01, where n is iterative times. According to the working equation, the multiple linear regression has good convergence. The values of k, β(0), and β(1) were obtained: k = 19.85, β(0) = −1.043 × 10−4, and β(1) = −0.7378 for [C4mim][Pro]; k = 20.78, β(0) = 3.299 × 10−3, and β(1) = −1.205 for [C5mim][Pro]; k = 22.60, β(0) = −4.496 × 10−3, and β(1) = 0.2837 for [C6mim][Pro]. For [Cnmim][Pro] (n = 4, 5, 6), the values of k are greater than 1. The results indicate that the surface concentration of the ionic liquid is greater than that in the bulk solution and the ionic liquids have some surface activity. The value of k increases with increase of methylene, which means that methylene increases the surface activity of the ILs. Using the values of β(0) and β(1), and Pitzer’s equations
surface tension according to eq 32, and the predicted values of γ(Calc)/mJ·m−2 for the ILs are listed in Table 4. Figure 9 is a
f± = exp{−Aφ[I1/2/(1 + 1.2I1/2) + (2/1.2) ln(1 + 1.2I1/2)] + 2mβ (0) + (mβ (1)/2I ) [1 − (1 + 2I1/2 − I ) exp( −I1/2)]}
Figure 9. Plot of γ(Calc) predicted by Li’s model versus experimental values, γ(Exp). ■, [C4mim][Pro]; ●, [C5mim][Pro]; ▲, [C6mim][Pro]. y = −0.289 + 1.002x; r = 0.998; s = 0.214.
(36)
The ionic mean activity coefficients, f±, of the bulk liquid and surface phases for the ILs can be calculated, and the results are listed in Table 4. In order to evaluate the values of activity coefficients calculated by Pitzer’s equation, Davies’ equation
comparative plot of predicted values, γ(Calc)/mJ·m−2, as a function of corresponding experimental values, γ(Exp)/mJ·m−2, for aqueous ILs. From Figure 9, it can be seen that γ(Calc) and γ(Exp) are highly correlated (correlation coefficient, r = 0.998; standard deviation, s = 0.214 mJ m−2 which is very close to experimental error) and extremely similar (gradient = 1.002; intercept = −0.2886). The results show that Li’s model is more reliable than the parachor semiempirical method in the prediction of the surface tension of aqueous ILs.
f± (D) = exp{−0.50 ln 10)[I L1/2/(1 + I L1/2) − 0.30I L]} (37)
was used to calculate the activity coefficients of aqueous [Cnmim][Pro] (n = 4, 5, 6) and the results, f±(D), are listed in Table 4. Figure 8 is a plot of f± and f±(D) versus the molality of
4. CONCLUSIONS Three propionic acid ionic liquids (PrAILs) [Cnmim][Pro] (n = 4, 5, 6) were prepared by the neutralization method. The values of density and surface tension of aqueous [Cnmim][Pro] (n = 4, 5, 6) with various molalities were determined at 298 K, and the experimental values of the parachor for these solutions were calculated. The values of apparent molar volumes and partial molar volumes at infinite dilution for the ILs were calculated in terms of Pitzer’s theory. With the use of Li’s model of surface tension and the empirical equation of the parachor, the values of the surface tensions of these aqueous solutions for three PrAILs were estimated. The results show that Li’s model is more reliable than the parachor semiempirical method in the prediction of the surface tensions of the aqueous ILs.
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Figure 8. Plot of f±L calculated by both Pitzer’s equation and Davies’ equation versus molality for [C4mim][Pro]. ■, with Pitzer’s equation; ●, with Davies’ equation.
ASSOCIATED CONTENT
S Supporting Information *
1
H NMR spectrum of the PrAILs [Cnmim][Pro] (n = 4, 5, 6). Plot of the ionic mean activity coefficients, f±L, of bulk liquid calculated by both Pitzer’s equation and Davies’ equation versus molality for [C5mim][Pro] and [C6mim][Pro]. Calculated values of molarity of [Cnmim][Pro] (n = 4, 5, 6) according to molality at 298.15 K. This material is available free of charge via the Internet at http://pubs.acs.org.
aqueous [C4mim][Pro]. The plots of aqueous [C5mim][Pro] and [C6mim][Pro] are in the Supporting Information (Figures S1 and S2). However, from Table 4 and Figure 8 it can be seen that the activity coefficients calculated by both the Pitzer equation and the Davies equation not only have very different values, but also changes with the concentration are not the same. Therefore, whether the values of β(0) and β(1) can be recommended to calculate activity coefficients and osmotic coefficients of the ILs also needs to be further validated. However, the values of β(0) and β(1) can be used to predict
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AUTHOR INFORMATION
Corresponding Author
*Tel.: +86 02462207801. Fax: +86 02462202380. E-mail:
[email protected]. 9965
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Notes
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The authors declare no competing financial interest.
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ACKNOWLEDGMENTS
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GLOSSARY
This project was supported by NSFC (21273003 and 21173107), the Education Bureau of Liaoning Province (LJQ2013001), Liaoning BaiQianWan Talents Program (2013921029), and the Foundation of 211 Project for Innovative Talents Training, Liaoning University.
Aϕ = Debye−Hückel parameter Ap = empirical parameter c = molarity D = static dielectric constant of pure water DSC = differential scanning calorimetry e = absolute electronic charge GEX = total excess Gibbs energy 1 H NMR = proton nuclear magnetic resonance I = ionic strength, I = (1/2)∑mi zi2 kB = Boltzmann constant k = empirical constant M = molar mass m = molality M2 = molar mass of the solute M1 = molar mass of solvent in grams NA = Avogadro’s constant nW = number of kilograms of solvent (neutral molecules) N0 = Avogadro’s number Pm = parachor of solution P2 = parachors of solute P1 = parachors of solvent R = gas constant T = thermodynamic temperature ϕ VB = apparent molar volumes ν = number of ions in the formula of the ionic liquid νM = numbers of cation in the formula of the ionic liquid νX = numbers of anion in the formula of the ionic liquid V00 = molar volume of the solvent V̅ 0B = partial molar volume of the salt at infinite dilution VW = molar volume of water x = mole fraction of solute Y = extrapolation function zM = ionic charges for the cation in electronic units zX = ionic charges for the anion in electronic units
Greek Symbols
γ = surface tension ρW = density of the solvent ρ = density ϕ = osmotic coefficient γ± = activity coefficient γ0 = surface tension of water ρ0 = density of pure water ϕ = osmotic coefficient a = activity μ°WB = standard chemical potential for bulk liquid μ°WF = standard chemical potential for surface phases
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REFERENCES
(1) Zhang, S. J.; Wang, J. J.; Lu, X. M.; Zhou, Q. Structures and Interactions of Ionic Liquids; Springer: Heidelberg, 2013. 9966
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(24) Tong, J.; Kong, Y. X.; Wang, P. P.; Dai, L. L.; Yang, J. Z. The surface tension of aqueous glycine ionic liquid: C3mim][Gly] and [C4mim][Gly]. Sci. China Chem. 2012, 42 (6), 776−783. (25) Huang, Z. Q. The Introduction of Electrolyte Solution Theory, 2nd ed.; Science Press: Beijing, 1983.
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