Densities and Viscosities of Aqueous Amino Acid Ionic Liquids

May 9, 2017 - A semiempirical method to estimate the viscosity of aqueous [Cnmim][Ala] (n = 3, 4, 5) was put forward based on Eyring's theory, and the...
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Densities and Viscosities of Aqueous Amino Acid Ionic Liquids [Cnmim][Ala](n = 3, 4, 5) Jing Tong,*,† Xu Zheng,† Hui Li,† Jian Tong,† and Qingshan Liu‡ †

College of Chemistry, Liaoning University, Shenyang 110036, P. R. China College of Science, Shenyang Agricultural University, Shenyang, 110866, P. R. China

‡

S Supporting Information *

ABSTRACT: Amino acid ionic liquids [C nmim][Ala] (n = 3, 4, 5) (1-alkyl-3methylimidazolium alanine salt) were prepared by the neutralization method. The density and viscosity for aqueous solutions of the ionic liquids (ILs) with various molalities were measured at T = (288.15 to 328.15) K with an interval of 5 K. In terms of the Jones−Dole equation, the viscosity B-coefficients with large positive values and dB/dT < 0 were obtained, and these facts implied that the ionic liquids are water-structure-making. According to Feakins, the contribution of the solute per mole to the free energy of activation for viscous flow of the solution, Δμ2⧧0, or called as the standard molar activation free energy, was obtained at different temperatures. Under the constant molality of solution, ΔH2⧧0 (the activation enthalpy of the activation for viscous flow of aqueous [Cnmim][Ala] (n = 3, 4, 5)) is a temperature-independent constant. This implies that the activation process of the solute for viscous flow of aqueous [Cnmim][Ala] (n = 3, 4, 5) is an isoCoulombic reaction. A semiempirical method to estimate the viscosity of aqueous [Cnmim][Ala] (n = 3, 4, 5) was put forward based on Eyring’s theory, and the estimated viscosity values of the aqueous ILs are in good agreement with the corresponding experimental ones.

1. INTRODUCTION Much attention has been focused on the avoidance of environmentally unfriendly organic solvents.1 Therefore, the chemistry of ionic liquids (ILs) is nowadays a very important field of research. ILs are “adjustable”, because their properties can be tuned to a specific purpose.2 Natural amino acids are necessary for both humans and animals. These safe, biodegradable acids were utilized in functionalizing some of the ILs. This category of ILs is termed amino acid-based ionic liquids (AAILs).3 AAILs have several remarkable advantages over traditional ILs in that they are cheap, biodegradable, and noncorrosive and have particularly excellent solution properties.4AAILs could be used for various applications such as intermediates for peptide syntheses and chiral solvents.5 One of the barriers against replacing commonly used solvents with ionic liquids in various applications is the relatively high viscosity of ILs.6 High viscosity results in low diffusion coefficients and slow mass transfer;,6 the pumping and energy costs would become prohibitive.7 An effective method to overcome this disadvantage is to mix ILs with other solvents.8,9 However, it is necessary to study the fundamental physical properties of AAIL solutions for theoretical research and practical application.9−14 Therefore, as a continuation of our previous investigation,14−18 the apparent molar volume and viscosity of aqueous amino acid ionic liquids [Cnmim][Ala](n = 3, 4, 5) are investigated.

under reduced pressure. N-Methylimidazole (AR grade reagent) was vacuum distilled prior to use. 1-Bromopropane, 1-bromobutane, and 1-bromopentane (AR grade reagent) were distilled before use. Ethyl acetate and acetonitrile were distilled and then stored over molecular sieves in tightly sealed glass bottles, respectively. Anion-exchange resin (type 717) was purchased from Shanghai Chemical Reagent Co. Ltd. and activated by the regular method before use. The source and purity of the materials are listed in Table 1. 2.2. Preparation of the ILs [Cnmim][Ala] (n = 3, 4, 5). The AAILs [Cnmim][Ala](n = 3, 4, 5) were prepared by a neutralization method according to Fukumoto,12 and the detailed procedure has been described in previous articles.20 The structures of the resulting ILs were confirmed by NMR spectroscopy (Varian XL-300), and the 1H NMR spectra are shown in section A of the Supporting Information. Element analysis (Flash EA1112-type produced by THERMO) showed that the purities of the synthesized ionic liquids are more than 0.99 (mass fraction) (section B of the Supporting Information). The water content (w2) of the AAILs, determined by a Karl Fischer moisture titrator (ZSD-2 type), was (0.00360, 0.00300, 0.00330 ± 0.0001) (mass fraction). The synthetic products were tested by silver nitrate solution, and no halogen ions were found. 2.3. Measurement of the Density and Viscosity of the Aqueous [Cnmim][Ala]. (n = 3, 4, 5). In molarities of

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. 19 DL-Alanine was recrystallized twice from water and was dried

Special Issue: Memorial Issue in Honor of Ken Marsh

© 2017 American Chemical Society

Received: November 15, 2016 Accepted: April 28, 2017 Published: May 9, 2017 2501

DOI: 10.1021/acs.jced.6b00951 J. Chem. Eng. Data 2017, 62, 2501−2508

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Table 1. Source and Puritya of the Materials chemical name

source

anion-exchange resin (type 717) N-methylimidazole 1-bromopropane

Shanghai Reagent Co. Ltd. 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. Shanghai Reagent Co. Ltd. Shanghai Reagent Co. Ltd. synthesis synthesis synthesis

1-bromobutane 1-bromopentane DL-alanine

acetonitrile ethyl acetate sodium hydroxide methanol anhydrous ethanol [C3mim][Ala]b [C4mim][Ala]c [C5mim][Ala]d

purification method

where Mm is the average molar mass of solution, ρ is the density of aqueous [Cnmim][Ala] (n = 3, 4, 5)

final mole fraction purity

distillation distillation

granularity >0.950 >0.990 >0.980

distillation

>0.980

distillation

>0.980

recrystallization

>0.985

no further purification no further purification no further purification no further purification no further purification vacuum drying vacuum drying vacuum drying

>0.995

M m = xMsolute + (1 − x)Msolvent

(2)

where x (x = m/(m + 1/Msolvent)) is the molar fraction of solute, its value from quality molarity conversion.23 The values of Vm for aqueous [Cnmim][Ala] (n = 3, 4, 5) were calculated in accordance with eq 1, and the results are included in Table S1 of the Supporting Information. According to eq 3, the apparent molar volume, Vϕ B21 can be obtained from the density data: VϕB = [1000(ρ0 − ρ) + mMBρ0 ]/mρρ0

(3)

where ρ0 is the density of water, ρ and m are the density and molality of solution, respectively. MB is the molar mass of solute. Under the specified temperature, the relationship between Vϕ B and the molality of solution can be expressed as the following empirical equation:

>0.995 >0.960 >0.995

VϕB = a0 + a1m1/2

>0.997

(4)

where ai is the empirical constant. Plotting Vϕ B against m1/2, a series of good straight lines were obtained (see Figure S4). When the molality tends to zero, that is, m → 0, a0 = Vϕ B0; Vϕ B0 is the limiting apparent molar volume at infinite dilution and the values, the fitting correlation coefficient square r2 and the standard deviation s are listed in Table S2 of the Supporting Information. 3.2. The Values of Viscosity, η/Pa·s, and Viscosity B-Coefficients. The experimental values of viscosity of aqueous [Cnmim][Ala] (n = 3, 4, 5) with various molalities at different temperatures are listed in Table 3. Each value in the table is the average of triple measurements. The viscosity of the electrolyte aqueous solution can be described by Jones−Dole empirical equation:19−25

>0.990 >0.990 >0.990

a

The purity of the samples was given on the chemical bottles declared by suppliers. b[C3mim][Ala] = 1-propyl-3-methylimidazolium DL-alanine salt. c[C4mim][Ala] = 1-butyl-3-methylimidazolium DL-alanine salt. d [C5mim][Ala] = 1-pentyl-3-methylimidazolium DL-alanine salt.

0.01−1.1 mol·kg−1, a series of aqueous [Cnmim][Ala] (n = 3, 4, 5) samples were prepared with weight method. The water content in the ionic liquid was accounted for upon solution preparation. An Anton Paar DMA 4500 oscillating U-tube densitometer was used to measure the densities of the samples at T = (288.15 to 328.15) K. By using the calibrated densitometer, the density of water was measured in the above temperature range and the results were in good agreement with the literature,21 within an experimental error of ±0.00005 g·cm−3. The temperature in the cell was regulated to ±0.01 K with a solid state thermostat. The viscosities of aqueous [Cnmim][Ala] (n = 3, 4, 5) with various molalities were measured by means of an Ubbelohde viscometer at T = (288.15 to 328.15) K. The instrument coefficient k was determined by deionized water which was processed by the sub-boiling purification unit. The viscometer was kept in a water thermostat controlled to ±0.02 K.

η /η0 = 1 + Ac1/2 + Bc

(5)

where η and η0 are the viscosity of solution and solvent, respectively, c (c = m·1 kg/(m·1 kg·MB + 1000)/1000ρ) is the concentration of substance which can be converted by the measured solution density,23 and the results are listed in Table S3 of the Supporting Information. A is a parameter which reflects the effects of the ion−ion interactions, and the parameter B reflects the effects of ion−solvent interactions as the viscosity coefficient. By rearranging eq 5, a viscosity B-coefficients-working equation was obtained: η′ = (η /η0 − 1)/c1/2 = A + Bc1/2

(6)

where η′ is an extrapolation function which can be calculated from experimental data and the calculated values are listed in Table S4 of the Supporting Information. Plotting η′ vs c1/2, a set of good straight lines was obtained; the slopes of straight lines are viscosity B-coefficients. Figure 1 is the plotting of η′ vs c1/2 for [C3mim][Ala] ([C4mim][Ala] and [C5mim][Ala] are similar to [C3mim][Ala], see Figure S5). According to eq 6, the B-coefficients, parameter A, the correlation coefficient square r2, and the standard deviation s can be obtained and are listed in Table 4. From Table 4, it can be seen that the parameter A in eq 6 increases with the increase of temperature, and the parameter B in eq 6 decreases with the increase of temperature. These values can be expressed by the following equations:

3. RESULTS AND DISCUSSION 3.1. The Average Molar Volume, Vm, and Apparent Molar Volume, Vϕ B (R3−5). The experimental values of density for the samples of aqueous [Cnmim][Ala] (n = 3, 4, 5) with various molalities at T = (288.15 to 328.15) K are listed in Table 2. Each value in the table is the average of triple measurements. A comparison of the experimental values of density for [C4mim][Ala] with the reference data,22 in the temperature range from 293.15 K to 313.15 K shows that the experimental data are in good agreement with the reference data; the maximum deviation is 0.05%. By using the experimental data of density, the average molar volume, Vm, can be calculated by the following equation: Vm = M m /ρ (1)

A = q0 + q1T 2502

(7) DOI: 10.1021/acs.jced.6b00951 J. Chem. Eng. Data 2017, 62, 2501−2508

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Table 2. Values of Density, ρ/g·cm−3, for Aqueous [Cnmim][Ala] (n = 3, 4, 5) with Various Molalities in the Temperature Range from 288.15 to 328.15 Ka m/mol·kg−1

x

288.15 K

293.15 K

298.15 K

303.15 K

308.15 K

313.15 K

318.15 K

323.15 K

328.15 K

0b

0

0.99910

0.99820

0.99704

0.99564

0.99222

0.99021

0.98804

0.98569

0.0167 0.0222 0.0275 0.0558 0.1672 0.2788 0.3914 0.5039 0.6170 0.7316 0.8451 1.0167

0.0003 0.0004 0.0005 0.0010 0.0030 0.0050 0.0070 0.0090 0.0110 0.0130 0.0150 0.0180

0.99955 0.99970 0.99984 1.00058 1.00357 1.00664 1.00971 1.01281 1.01585 1.01890 1.02188 1.02620

0.99863 0.99877 0.99890 0.99962 1.00250 1.00546 1.00844 1.01135 1.01431 1.01727 1.02015 1.02442

0.99745 0.99758 0.99771 0.99839 1.00114 1.00397 1.00680 1.00969 1.01249 1.01538 1.01818 1.02214

0.99604 0.99617 0.99629 0.99695 0.99961 1.00236 1.00512 1.00793 1.01064 1.01334 1.01606 1.02001

0.99260 0.99272 0.99284 0.99348 0.99607 0.99874 1.00138 1.00411 1.00675 1.00947 1.01210 1.01593

0.99060 0.99072 0.99084 0.99147 0.99404 0.99666 0.99933 1.00198 1.00463 1.00731 1.00990 1.01368

0.98842 0.98854 0.98866 0.98928 0.99181 0.99442 0.99706 0.99969 1.00225 1.00488 1.00746 1.01129

0.98608 0.98620 0.98632 0.98693 0.98945 0.99202 0.99466 0.99723 0.99986 1.00245 1.00504 1.00881

0.0163 0.0218 0.0277 0.0543 0.1629 0.2778 0.3939 0.5049 0.6189 0.7406 0.8516 1.0065

0.0003 0.0004 0.0005 0.0010 0.0029 0.0050 0.0070 0.0090 0.0110 0.0132 0.0151 0.0178

0.99954 0.99968 0.99983 1.00053 1.00342 1.00651 1.00963 1.01254 1.01557 1.01873 1.02159 1.02545

0.99862 0.99876 0.99890 0.99956 1.00231 1.00528 1.00823 1.01107 1.01402 1.01707 1.01981 1.02353

0.99744 0.99757 0.99771 0.99833 1.00095 1.00377 1.00658 1.00933 1.01205 1.01502 1.01768 1.02127

0.99603 0.99616 0.99629 0.99690 0.99944 1.00221 1.00499 1.00760 1.01030 1.01314 1.01560 1.01919

0.99258 0.99270 0.99283 0.99341 0.99585 0.99847 1.00116 1.00370 1.00631 1.00899 1.01144 1.01501

0.99058 0.99070 0.99083 0.99140 0.99381 0.99641 0.99906 1.00158 1.00412 1.00683 1.00934 1.01274

0.98840 0.98852 0.98864 0.98921 0.99160 0.99423 0.99686 0.99937 1.00191 1.00458 1.00700 1.01045

0.98606 0.98618 0.98630 0.98687 0.98926 0.99183 0.99444 0.99695 0.99946 1.00221 1.00464 1.00808

0.0167 0.0222 0.0279 0.0562 0.1681 0.2834 0.3868 0.5075 0.6214 0.7266 0.8339 1.0157

0.0003 0.0004 0.0005 0.0010 0.0030 0.0051 0.0069 0.0091 0.0111 0.0129 0.0148 0.0180

0.99953 0.99966 0.99980 1.00050 1.00331 1.00624 1.00889 1.01197 1.01479 1.01746 1.02012 1.0157

0.99860 0.99873 0.99886 0.99952 1.00222 1.00501 1.00753 1.01047 1.01321 1.01577 1.01833 0.0180

0.99742 0.99754 0.99767 0.99829 1.00085 1.00351 1.00596 1.00867 1.01131 1.01374 1.01618 1.02449

0.99601 0.99612 0.99624 0.99683 0.99930 1.00194 1.00428 1.00702 1.00953 1.01194 1.01430 1.02254

0.99403 [C3mim][Ala] 0.99442 0.99455 0.99467 0.99531 0.99794 1.00063 1.00335 1.00610 1.00880 1.01149 1.01412 1.01804 [C4mim][Ala] 0.99441 0.99453 0.99466 0.99525 0.99773 1.00041 1.00311 1.00572 1.00837 1.01104 1.01363 1.01714 [C5mim][Ala] 0.99439 0.99450 0.99462 0.99520 0.99761 1.00017 1.00249 1.00516 1.00774 1.01001 1.01239 1.02028

0.99256 0.99267 0.99278 0.99335 0.99570 0.99819 1.00052 1.00309 1.00567 1.00803 1.01030 1.01824

0.99056 0.99067 0.99078 0.99135 0.99368 0.99617 0.99849 1.00107 1.00359 1.00596 1.00828 1.01634

0.98838 0.98849 0.98860 0.98916 0.99150 0.99394 0.99626 0.99885 1.00142 1.00368 1.00614 1.01421

0.98604 0.98615 0.98626 0.98682 0.98915 0.99162 0.99395 0.99657 0.99906 1.00138 1.00374 1.01205

a Pressure p = 100.3 kPa. Standard uncertainties u are u(T) = 0.02 K, u(p) = 1.0 kPa, u(x) = 0.001, u(m) = 0.005 mol·kg−1 and the combined expanded uncertainty U(ρ) = 0.0021 g·cm−3 with 0.95 level of confidence (k ≈ 2). bThe density of pure water.

B = q2 + q3T

corresponding experimental values ηexp, produces a good straight line (see Figure 2). 3.3. Thermodynamic Parameters of the Activation for Viscous Flow. On the basis of Eyring transition state theory,26 Feakins19,25 and co-workers derived the relationship between the viscosity B-coefficient and the activation free energy for viscous flow of the solution:

(8)

By fitting A and B vs T, respectively, the parameters q0, q1, q2, q3 with the correlation coefficient square r2 and the standard deviation s can be determined and are listed in Table 5. Combining eqs 7 and 8 with eq 6 gives eq 9: η η0

−1

c1/2

= q0 + q1T + q2c1/2 + q3Tc1/2

(9)

B = (V1 − V2)/1000 + V1(Δμ2 ⧧ 0 − Δμ1⧧ 0 )/1000RT

In the temperature range of T = (288.15 to 328.15) K, when the molality is less than 1 mol·kg−1, the viscosity of the aqueous [Cnmim][Ala] (n = 3, 4, 5) can be predicted by using eq 9, and the predicted values, ηpre, are listed in Table S5 of the Supporting Information. The maximum percentage deviation from experimental values is 0.020866. Plotting the predicted values, ηpre for aqueous [Cnmim][Ala] (n = 3, 4, 5) against the

(10)

where V1 and V2 are the molar volume of solvent and solute, respectively. Δμ1⧧0 is the molar free energy of activation for viscous flow of solvent, Δμ2⧧0 is the standard molar free energy of activation of solute for viscous flow of the solution. Jianji Wang and his co-workers27,28 pointed that the value of Δμ1⧧0 2503

DOI: 10.1021/acs.jced.6b00951 J. Chem. Eng. Data 2017, 62, 2501−2508

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Table 3. Viscosity of Aqueous [Cnmim][Ala] (n = 3, 4, 5) at Different Temperatures and Compositions 106η/Pa·s in the Temperature Range from 288.15 to 328.15 K, p = 100.3 kPaa 106η/Pa·s −1

m/mol·kg

x

288.15 K

293.15 K

298.15 K

303.15 K

308.15 K

313.15 K

318.15 K

323.15 K

328.15 K

0b

0

1138.9

1002.2

889.7

798.8

652.5

596.0

547.0

504.3

0.0167 0.0222 0.0275 0.0558 0.1672 0.2788 0.3914 0.5039 0.6170 0.7316 0.8451 1.0167

0.0003 0.0004 0.0005 0.0010 0.0030 0.0050 0.0070 0.0090 0.0110 0.0130 0.0150 0.0180

1155.7 1162.1 1167.5 1203.4 1361.5 1512.9 1658.1 1821.6 1957.7 2101.2 2246.7 2460.3

1016.9 1022.2 1026.5 1057.0 1197.5 1325.9 1446.7 1575.5 1697.8 1819.4 1941.4 2109.1

900.3 907.1 911.2 937.6 1057.1 1163.2 1273.4 1368.5 1478.1 1580.6 1677.6 1826.5

810.1 813.2 816.7 838.1 939.1 1027.8 1119.1 1209.5 1301.6 1380.3 1469.2 1599.2

661.4 663.9 666.4 684.6 759.0 827.5 894.2 958.9 1027.0 1089.0 1157.3 1254.2

604.2 606.0 608.4 625.8 688.3 749.4 805.8 867.6 929.1 985.9 1037.1 1115.5

554.0 556.5 558.7 573.0 629.4 684.9 736.1 781.3 831.9 887.7 932.2 1000.3

510.8 513.4 515.5 529.1 580.2 625.1 672.6 716.8 764.1 807.4 850.8 912.1

0.0163 0.0218 0.0277 0.0543 0.1629 0.2778 0.3939 0.5049 0.6189 0.7406 0.8516 1.0065

0.0003 0.0004 0.0005 0.0010 0.0029 0.0050 0.0070 0.0090 0.0110 0.0132 0.0151 0.0178

1155.6 1162.1 1167.5 1203.4 1361.3 1512.7 1658.0 1821.1 1957.2 2100.8 2246.1 2458.5

1016.5 1022.2 1026.5 1056.9 1197.3 1325.7 1446.4 1575.1 1697.4 1819.0 1940.7 2107.3

900.3 907.1 911.2 937.5 1056.9 1163.0 1273.2 1368.1 1477.4 1580.0 1676.8 1825.0

810.4 813.0 816.7 838.1 939.0 1027.6 1119.0 1209.1 1301.2 1380.0 1468.6 1597.9

661.1 663.9 666.4 684.6 758.9 827.3 894.0 958.5 1026.6 1088.5 1156.5 1253.1

604.0 606.0 608.4 625.8 688.2 749.2 805.6 867.2 928.6 985.5 1036.5 1114.5

554.0 556.5 558.7 572.9 629.2 684.8 736.0 781.1 831.7 887.5 931.8 999.5

510.8 513.4 515.4 529.1 580.1 625.0 672.4 716.6 763.8 807.2 850.5 911.5

0.0167 0.0222 0.0279 0.0562 0.1681 0.2834 0.3868 0.5075 0.6214 0.7266 0.8339 1.0157

0.0003 0.0004 0.0005 0.0010 0.0030 0.0051 0.0069 0.0091 0.0111 0.0129 0.0148 0.0180

1155.6 1162.1 1167.4 1203.3 1361.2 1512.3 1656.7 1820.1 1955.7 2098.2 2242.8 2456.2

1015.4 1022.1 1026.5 1056.8 1197.2 1325.3 1445.4 1574.1 1696.0 1816.7 1937.9 2105.2

900.3 907.1 911.2 937.5 1056.8 1162.7 1272.4 1367.2 1476.3 1578.0 1674.3 1823.2

809.8 813.0 816.6 838.0 938.8 1027.3 1118.2 1208.4 1300.2 1378.3 1466.7 1596.4

718.4 [C3mim][Ala] 726.9 731.7 734.8 755.2 841.7 916.9 997.7 1070.6 1147.1 1225.2 1292.9 1394.4 [C4mim][Ala] 726.2 731.7 734.8 755.2 841.5 916.7 997.5 1070.2 1146.6 1224.7 1292.3 1393.2 [C5mim][Ala] 725.2 731.6 734.8 755.2 841.4 916.5 996.8 1069.6 1145.9 1223.4 1290.7 1392.1

661.0 663.9 666.4 684.5 758.7 827.1 893.4 957.9 1025.9 1087.5 1155.2 1252.1

604.3 606.0 608.4 625.7 688.1 749.0 805.2 866.8 928.1 984.6 1035.4 1113.8

554.0 556.4 558.7 572.9 629.2 684.6 735.5 780.7 831.2 886.7 931.0 998.8

510.8 513.4 515.4 529.1 580.1 624.9 672.1 716.3 763.4 806.5 849.7 910.9

Standard uncertainties u are u(x) = 0.001,u(m) = 0.005 mol·kg−1, u(T) = 0.02 K, u(p) = 1.0 kPa, and the expand uncertainty U is U(η) = 7.2 × 10−5 Pa·s. bThe dynamic viscosity of pure water. a

a1= −1.027, −1.024, and −1.043 kJ·mol−1·K−1 for [Cnmim][Ala] (n = 3, 4, 5), respectively. The fitting correlation coefficient square is more than 0.99. According to the thermodynamic relationship, the other activation functions for viscous flow of the solution: activation entropy, ΔS2⧧0, activation enthalpy, ΔH2⧧0, can be calculated by the following empirical equation:

in eq 10 can be calculated by Eyring equation: η1 = (ℏNA /V1) exp(Δμ1⧧ 0 /RT )

(11)

where ℏ is Planck constant, NA is Avogadro constant, V1 is the molar volume of solvent (water). The values of Δμ1⧧0 calculated by eq 11, and Δμ2⧧0 calculated by eq 10 are listed in Table 6. From Table 6, the relationship between Δμ2⧧0 and T can use the following empirical equation: Δμ2 ⧧ 0 = a0 + a1T

(12)

ΔS2 ⧧ 0 = −a1

(13)

ΔH2 ⧧ 0 = Δμ2 ⧧ 0 + T ΔS2 ⧧ 0

(14)

According to eqs 13 and 14, the calculated results are listed in Table 6. From Table 6, the activation enthalpy, ΔH2⧧0, of the activation for viscous flow of aqueous [Cnmim][Ala] (n = 3, 4, 5) almost is a temperature-independent constant so that the molar

where ai (i = 0, 1) is the empirical parameter. According to eq 12, fitting Δμ2⧧0 vs T, the values of ai (i = 0, 1) were obtained: a0 = 516.26, 518.35, and 530.17 kJ·mol−1 ; 2504

DOI: 10.1021/acs.jced.6b00951 J. Chem. Eng. Data 2017, 62, 2501−2508

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equation is used for binary solution, V in eq 15 should be replaced by Vm, which means the average molar volume of the solution, ΔG⧧, is the average Gibbs free energy of activation for viscous flow of the solution. ΔG⧧ is defined by the equation: ΔG⧧ = x1Δμ1⧧ + x 2Δμ2 ⧧

(16)

where Δμ1⧧ and Δμ2⧧ are the contribution of solvent and solute to ΔG⧧. By using Δμ1⧧0 and Δμ2⧧0 instead of Δμ1⧧ and Δμ2⧧ which are independent of molality, the eq 16 changes to ΔG⧧ = x1Δμ1⧧ 0 + x 2Δμ2 ⧧ 0 + Δμ E ⧧

(17)

where Δμ is the excess activation Gibbs free energy, which has similar meaning to the system excess Gibbs energy GE.30 Therefore, eq 15 changes to E⧧

η = (ℏN /V ) exp[(x1Δμ1⧧ 0 + x 2Δμ2 ⧧ 0 + Δμ E ⧧ )/RT ]

Figure 1. Plotting of the extrapolation function η′ vs c1/2 for [C3mim][Ala]: black ■, 288.15 K; red ●, 293.15 K; green ▲, 298.15 K; blue ▼, 303.15 K; aqua ◆, 308.15 K; pink ◀, 313.15 K; yellow ▶, 318.15 K; brown ⬢, 323.15 K; black ★, 328.15 K.

Taking the logarithm so that the following equation was obtained: ln η = ln(ℏN /V ) + (x1Δμ1⧧ 0 + x 2Δμ2 ⧧ 0 )

activation heat capacity Δcp2⧧0 ≈ 0 which implies that the process of the activation process for viscous flow of aqueous [Cnmim][Ala] (n = 3, 4, 5) is an isoCoulombic reaction.29

/RT + Δμ E ⧧ /RT

The relationship between ΔμE≠/RT and the molality of solution, m, can be expressed in the following empirical equation:

4. THE PREDICTION OF THE VISCOSITY BY USING SEMIEMPIRICAL METHOD Eyring applied the transition state theory of reaction rate to the transportation, and a simple viscosity equation was obtained: ⧧

η = (ℏN /V ) exp(ΔG /RT )

(18)

Δμ E ⧧ /RT = β0 + β1m + β2m2

(19)

where βi is the empirical constant. If ΔμE≠/RT vs m is fitted according to eq 19, the correlation coefficient square r2 is larger than 0.99, implying that eq 19 can describe the relationship between ΔμE≠/RT and m the molality of the solution accurately. The values of βi, the correlation coefficient square r2, and the standard deviation s, were obtained and are listed at the bottom of Table S6. A new Eyring semiempirical equation

(15) ⧧

where η means the viscosity, ΔG is Gibbs free energy of activation for viscous flow of the ionic liquid and V is the molar volume. This equation explains the change of η vs T, and it can also be used to calculate viscosity of solution. When the

Table 4. Values of Parameter A and Viscosity B-coefficient of Aqueous [Cnmim][Ala] (n = 3, 4, 5) with the Correlation Coefficient Square r2 and the Standard Deviation s at (288.15 to 328.15) K 288.15 K

293.15 K

298.15 K

303.15 K

102A/m3/2·mol−1/2 102s/m3/2·mol−1/2 B/m3·mol−1 102s/ m3·mol−1 r2 2 3/2 10 s/m ·mol−1/2

−0.264 0.023 0.00142 0.00122 0.9992 0.038

−0.231 0.018 0.00136 0.00094 0.9996 0.029

−0.215 0.524 0.00130 0.00089 0.9996 0.027

−0.201 0.017 0.00123 0.00109 0.9992 0.034

102A/m3/2·mol−1/2 102s/m3/2·mol−1/2 B/m3·mol−1 102s/ m3·mol−1 r2 2 3/2 10 s/m ·mol−1/2

−0.257 0.033 0.00143 0.00176 0.9984 0.054

−0.227 0.026 0.00137 0.00142 0.9990 0.044

−0.208 0.206 0.00130 0.00140 0.9988 0.043

−0.194 0.030 0.00123 0.00164 0.9982 0.050

102A/m3/2·mol−1/2 102s/m3/2·mol−1/2 B/m3·mol−1 102s/ m3·mol−1 r2 2 3/2 10 s/m ·mol−1/2

−0.298 0.033 0.00146 0.00181 0.9984 0.055

−0.275 0.024 0.00140 0.00133 0.9992 0.040

−0.246 0.025 0.00133 0.00135 0.9990 0.041

−0.234 0.027 0.00126 0.00149 0.9986 0.045 2505

308.15 K [C3mim][Ala] −0.164 0.012 0.00116 0.00063 0.9998 0.019 [C4mim][Ala] −0.165 0.020 0.00117 0.00110 0.9992 0.034 [C5mim][Ala] −0.210 0.023 0.00120 0.00127 0.9988 0.038

313.15 K

318.15 K

323.15 K

328.15 K

−0.155 0.019 0.00112 0.00100 0.9992 0.031

−0.133 0.015 0.00107 0.00082 0.9994 0.025

−0.100 0.014 0.00101 0.00073 0.9994 0.022

−0.075 0.012 0.00098 0.00064 0.9996 0.020

−0.153 0.028 0.00113 0.00151 0.9982 0.046

−0.130 0.020 0.00107 0.00110 0.9990 0.034

−0.095 0.018 0.00102 0.00099 0.9990 0.030

−0.069 0.019 0.00098 0.00108 0.9988 0.033

−0.187 0.026 0.00115 0.00140 0.9986 0.042

−0.158 0.022 0.00110 0.00120 0.9988 0.036

−0.126 0.021 0.00104 0.00115 0.9988 0.035

−0.100 0.020 0.00100 0.00108 0.9988 0.032

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Table 5. Parameters q0, q1, q2, and q3a with the Correlation Coefficient Square r2 and the Standard Deviation s

a

parameter

[C3mim][Ala]

[C4mim][Ala]

[C5mim][Ala]

parameter

[C3mim][Ala]

[C4mim][Ala]

[C5mim][Ala]

q0 dm3/2·mol−1/2 q1 dm3/2·mol−1/2·K−1 r2 S dm3/2·mol−1/2

−0.4954 0.00143 0.99 0.00212

−0.4900 0.00142 0.991 0.00202

−0.5404 0.00154 0.992 0.00198

q2 L1/2·mol−1/2 q3 L1/2·mol−1/2·K−1 r2 S L1/2·mol−1/2

4.648 −0.0112 0.993 0.0131

4.673 −0.0113 0.993 0.0136

4.784 −0.0116 0.994 0.0131

Coefficient q0, q1, q2, and q3 were obtained from eqs 7 and 8

was obtained by combining eq 18 and eq 19: ln η = ln(ℏN /V ) + (x1Δμ1⧧ 0 + x 2Δμ2 ⧧ 0 ) /RT + β0 + β1m + β2m2

(20)

The predicted values of viscosity of solution, ηpre′/μPa·s, were obtained and are listed in Table S7. The maximum percentage deviation from experimental values is 0.014192. Plotting the predicted values, ηpre′/μPa·s, for the aqueous [Cnmim][Ala] (n = 3, 4, 5) against the corresponding experimental values produces a good straight line (see Figure 3), for which slopes are close to 1 and r2 values are more than 0.999. The results show that the predicted values, ηpre′/μPa·s, and the corresponding experimental ones are highly correlated and extremely similar, implying that the Eyring semiempirical equation is a useful tool for predicting the viscosity of aqueous [Cnmim][Ala] (n = 3, 4, 5). To the best of our knowledge, it is still a difficult problem to predict the viscosity of mixed electrolyte solution.31,32

Figure 2. Plotting the predicted values, ηpre/μPa·s for the aqueous [Cnmim][Ala] (n = 3, 4, 5) by eq 9 vs the corresponding experimental values, ηexp/μPa·s: black ■, [C3mim][Ala]; red ●, [C4mim][Ala]; green ▲, [C5mim][Ala].

Table 6. Thermodynamic Parameters of the Activation for Viscous Flow of Aqueous [Cnmim][Ala] (n = 3, 4, 5) T/K

Δμ1⧧0/kJ·mol−1

Δμ2⧧0 /kJ·mol−1

288.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15 328.15

9.4 9.3 9.2 9.0 8.9 8.8 8.7 8.6 8.6

220.8 216.2 210.7 204.1 197.7 194.5 190.1 183.6 181.0

288.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15 328.15

9.4 9.3 9.2 9.0 8.9 8.8 8.7 8.6 8.6

223.6 219.1 213.4 206.7 200.9 197.5 193.0 186.4 183.8

288.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15 328.15

9.4 9.3 9.2 9.0 8.9 8.8 8.7 8.6 8.6

229.8 225.8 219.5 213.1 207.5 203.5 198.6 192.2 189.6

ΔS2⧧0/J·mol−1 [C3mim][Ala] 1027 1027 1027 1027 1027 1027 1027 1027 1027 [C4mim][Ala] 1024 1024 1024 1024 1024 1024 1024 1024 1024 [C5mim][Ala] 1043 1043 1043 1043 1043 1043 1043 1043 1043 2506

ΔH2⧧0/kJ·mol−1

V1/cm3·mol−1

V2/cm3·mol−1

516.7 517.2 516.8 515.4 514.1 516.0 516.7 515.4 517.9

18.03 18.05 18.07 18.09 18.12 18.16 18.19 18.23 18.28

188.81 190.24 191.70 192.52 193.29 193.85 194.66 195.06 195.52

518.8 519.4 518.8 517.2 516.5 518.2 518.9 517.5 519.9

18.03 18.05 18.07 18.09 18.12 18.16 18.19 18.23 18.28

203.10 204.43 205.89 206.69 207.79 208.60 209.46 210.01 210.47

530.3 531.5 530.4 529.2 528.8 530.0 530.4 529.2 531.8

18.03 18.05 18.07 18.09 18.12 18.16 18.19 18.23 18.28

218.56 220.27 221.70 222.95 223.77 224.80 225.65 226.17 226.65

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AUTHOR INFORMATION

Corresponding Author

*Tel.: +86 24 62207801. E-mail: [email protected]. ORCID

Jing Tong: 0000-0002-0607-0179 Funding

This project was supported by NSFC−China (21273003 and 21673107), program for Liaoning Excellent Talents in University (LJQ2015099). Notes

The authors declare no competing financial interest.

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Figure 3. Plotting the viscosity values, ηpre′/μPa·s, of aqueous [Cnmim][Ala] (n = 3, 4, 5) estimated by eq 20 vs the corresponding experimental ones, ηexp/μPa·s: black ■, [C3mim][Ala]; red ●, [C4mim][Ala]; green ▲, [C5mim][Ala].

However, the new method in our work is easily used for mixed electrolyte solutions. The working equation is n

ln η = ln(ℏN /V ) + ( ∑ x iΔμi ⧧ 0 )/RT + i=1

m

∑

βjm j

j=0

(21)

where subscript i means species, i = 1 is solvent, others are solute, n is the number of species in the aqueous ionic liquids, and j is the number of terms in the polynomial.

5. CONCLUSIONS According to the values of the density of the aqueous [Cnmim][Ala] (n = 3, 4, 5), the average molar volume Vm and apparent molar volume Vϕ B can be calculated. On the basis of the Jones−Dole empirical equation, by using the values of the viscosity of the aqueous [Cnmim][Ala] (n = 3, 4, 5), the viscosity B-coefficients were obtained. According to Feakins’ theory, the values of the Gibbs free energy of activation of the solute for viscous flow, Δμ2⧧0, were obtained, and the relationship between Δμ2⧧0 and temperature is linear so that the standard molar activation entropy ΔS2⧧0 and enthalpy, ΔH2⧧0, were obtained. On the basis of Eyring’s theory, a semiempirical method to predict the viscosity of aqueous [Cnmim][Ala] (n = 3, 4, 5) was put forward and the predicted viscosity values with the corresponding experimental ones are highly correlated and extremely similar. Compare Figure 2 with Figure 1; the semiempirical method is a better way to predict viscosity of aqueous [Cnmim][Ala] (n = 3, 4, 5).

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REFERENCES

ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jced.6b00951. 1 H NMR of [Cnmim][Ala] (n = 3, 4, 5); the values of molar volume Vm and the apparent molar volume Vϕ B for aqueous [Cnmim][Ala] (n = 3, 4, 5) with various molalities at 288.15−328.15 K; the values of concentration of substance c, the extrapolation function η′, the values of ΔμE≠/RT, the predicted values ηpre and ηpre′ for aqueous [Cnmim][Ala] (n = 3, 4, 5); plot of η′ vs c1/2 for [C4mim][Ala] and [C5mim][Ala] (PDF) 2507

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