Densities and Viscosities of Sugar Alcohols in Vitamin B6 Aqueous

Article pubs.acs.org/jced

Densities and Viscosities of Sugar Alcohols in Vitamin B6 Aqueous Solutions at (293.15 to 323.15) K Xiaohui Xu,†,‡ Chunying Zhu,*,† and Youguang Ma*,† †

State Key Laboratory of Chemical Engineering, School of Chemical Engineering and Technology, Tianjin University, Tianjin 300072, P. R. China ‡ Tianjin Bohai Vocational Technical College, Tianjin, 300402, P. R. China S Supporting Information *

ABSTRACT: The densities and viscosities of ternary solutions (erythritol/xylitol/sorbitol/maltitol + vitamin B6 + water) were measured at 293.15 K, 303.15 K, 313.15 K, 323.15 K and atmospheric pressure. The experimental densities were correlated in terms of the Guimarães equation, and the apparent molar volumes (Vφ), the limiting partial molar volumes (Vφ0), and the limiting partial molar volumes of transfer (ΔtrVφ0) were calculated through the densities. The experimental viscosities were correlated according to the extended Jones−Dole equation to obtain the viscosity B coefficients, and the free energies of 0≠ activation per mole of solute (Δμ0≠ 2 ) and per mole of solvent (Δμ1 ) were calculated. These obtained thermodynamical properties and transport properties of multicomponents are useful to understand the structural change and strong solute−solvent interaction in the ternary solutions (sugar alcohols + vitamin B6 + water).

1. INTRODUCTION Densities and viscosities are two very important physicochemical properties of solution in chemical process design. Meanwhile, the derivative thermodynamical and transport properties of solution from its densities and viscosities are usually used for describing the intermolecular interactions to understand their real behavior. Recently, much attention of researchers has been attracted to the sugar alcohol ternary solution. Banipal et al.1 presented the densities and viscosities of mannitol and sorbitol in water and in mixed aqueous solutions in the range of (288.15 to 318.15) K. Hu, Y. F. et al.2 reported the viscosity and density of the nonelectrolyte system (mannitol + sorbitol + sucrose + H2O) and its binary and ternary subsystems at 298.15 K. Shekaari, H. et al.3 measured the densities and viscosities of D-xylose + ionic liquid (1-alkyl-3methylimidazolium bromide) + water solutions at 298.15 K. Jiang et al.4,5 investigated the densities and viscosities of ternary solutions (sugar alcohols + L-ascorbic acid + water) in the range of (293.15 to 323.15) K. Sugar alcohols, as a kind of carbohydrate, have been widely applied as artificial nutritive sweeteners in food and beverages (including diet drinks), and vitamin B6 is an important vitamin © XXXX American Chemical Society

for the production of red blood cells and cells of the immune system, and for maintaining healthy nerve and muscle cells.6 Sugar alcohols and vitamin B6 often appear simultaneously in food. However, less information about the densities and viscosities of sugar alcohol in vitamin B6 aqueous solutions could be found systematically in the literature. As a continuation of our previous studies on thermodynamical properties of sugar alcohols,4,5,7 in this work, the volumetric and viscometric properties for sugar alcohol−vitamin B6−water system were studied. The densities and viscosities of the ternary systems (erythritol/xylitol/sorbitol/maltitol + vitamin B6 + water) were measured at temperature from 293.15 to 323.15 K and atmospheric pressure. Some volumetric and viscometric properties were respectively obtained from experimental data. These quantities were then used to interpret the solute−solvent interactions of the ternary mixtures of erythritol/xylitol/ sorbitol/maltitol+ vitamin B6 + water. Received: August 8, 2014 Accepted: April 17, 2015

A

DOI: 10.1021/acs.jced.5b00114 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

Journal of Chemical & Engineering Data

Article

2. EXPERIMENTAL SECTION 2.1. Materials. Vitamin B6 (2-methyl-3-hydroxy-4,5-bis(hydroxymethyl) pyridine hydrochloride), is a biochemistry reagent. (2R,3S)-Butane-1,2,3,4-tetrol (erythritol), (2R,3R,4S)pentane-1,2,3,4,5-pentol (xylitol), (2R,3S,4S,5S)-hexane1,2,3,4,5,6-hexol (sorbitol), and 4-O-α-D-glucopyranosyl-Dglucitol (maltitol) were of analytical grade. The specifications of vitamin B6 and the four sugar alcohols are given in Table 1,

than its length (120 mm), thus the kinetic energy and the end corrections could be ignored. The viscosity η of the solutions was calculated by the following equation:9 η ρt = ηw ρw tw (1) where η, ρ, t and ηw, ρw, tw are viscosities, densities, and flow times of the experimental solutions and pure water, respectively. The viscosity of pure water was obtained from the available literature.10 The uncertainty of the experimental viscosity is 1 %.

Table 1. Specification of Studied Chemicals molar mass chemical name

CAS No.

g·mol−1

source

vitamin B6

58-56-0

205.64

erythritol

149-32-6

122.12

xylitol

87-99-0

152.15

sorbitol

50-70-4

182.17

maltitol

585-88-6

344.31

Sinopharm Chemical Reagent Co., Ltd. (China) O’Laughlin (Tianjin) Biotechnology Company Zhengzhou Jianda Chemicals, Inc. Zhengzhou Jianda Chemicals Inc.Co., Ltd. Zhengzhou Jianda Chemicals, Inc.

3. RESULTS AND DISCUSSION 3.1. The Density of Ternary Solutions. The experimental densities and viscosities of ternary solutions (erythritol/xylitol/ sorbitol/maltitol + vitamin B6 + water) at 293.15 K, 303.15 K, 313.15 K, 323.15 K and atmospheric pressure are listed in Table 2. The figures for the experimental densities and viscosities for vitamin B6 + water solutions in comparison with the literature values11,12 are shown in the Supporting Information (Figure S1 and Figure S2). Figures S1 and S2 show that variation tendencies of experimental densities and viscosities are in agreement with the literature. From Table 2, it could be found that the densities increase monotonously with the increasing molalities of erythritol, xylitol, sorbitol, maltitol in vitamin B6 aqueous solution, and vitamin B6 in water, but the densities decrease monotonously with increasing temperature. Because the solution is heated, the thermal energy of molecules increases and accordingly the intermolecular distance increases, which leads to the decrease of the density. The densities of the four sugar alcohols solutions decrease in the order maltitol > sorbitol > xylitol > erythritol for the same molality of sugar alcohols and vitamin B6 at the same temperature, which proves that the density is higher for the larger molar weight. The relationships of the densities of the erythritol, xylitol, sorbitol, maltitol in vitamin B6 aqueous solution, versus temperature T and the solute molality m were presented vividly in Figure 1. From Figure1, it could be easily found that the density shows a very good linear relationship with the temperature and solute molality m. Thus, the Guimarães equation was applied to correlate the experimental density.13 ρ = A1 + A 2 T + A3m (2)

mass fraction purity ≥ 0.990 ≥ 0.995 ≥ 0.990 ≥ 0.990 ≥ 0.990

and these chemicals were used without further purification. The deionized water was distilled in the experiment for the preparation of the aqueous solutions. All solutions were prepared at 293.15 K by mass using an analytical balance (FA2204B, Shanghai Jingke, China) with an uncertainty of 0.0001 g, and the uncertainty of molality was 0.0001 mol·kg−1. The molality of vitamin B6 in water was from 0.1 to 0.4 mol· kg−1 with an interval of 0.1 mol·kg−1. 2.2. Density Measurement. The density of all ternary solutions and the pure water were measured at atmospheric pressure and at T = (293.15, 303.15, 313.15, and 323.15) K using a vibrating tube density meter DMA 4500 (Anton Paar, Austria) with an uncertainty of 5.0 × 10−5 g·cm−3. The doubly distilled water and the dry air were used to calibrate the density meter before the experimental solutions were measured. At 293.15 K and 101.325 kPa, the standard density of water and dry air are 0.998203 g·cm−3 and 0.001199 g·cm−3 for calibration.8 The temperature of the density measuring cell was automatically controlled within ± 0.03 K. Every measurement was repeated for three times. The experimental densities of pure water are (0.99821, 0.99568, 0.99222, and 0.98801) g· cm−3 at (293.15, 303.15, 313.15, and 323.15) K, respectively, and the corresponding values in the literature8 are (0.998203, 0.995645, 0.992212, and 0.988030) g·cm−3, which validates the experimental accuracy. 2.3. Viscosity Measurement. An iVisc capillary viscometer (LAUDA, Germany) was used to measure the viscosities of erythritol/xylitol/sorbitol/maltitol in vitamin B6 aqueous solutions. An Ubbelohde viscometer filled with experimental solutions was immersed in a glass-sided water thermostat (ET 15S, LAUDA, Germany) with an uncertainty of 0.05 K. The efflux time of liquids was measured by an infrared detection system and recorded automatically by computer software. The uncertainty of the time measurement is 0.01 s. Every experiment was repeated for three times and the deviation was less than 0.2 s. The flow time was larger than 100 s in the experiment and the capillary diameter (0.5 mm) was far less

where A1, A2, and A3 are the empirical constants, T is the temperature, and m is the molality of solute in the ternary solutions (erythritol/xylitol/sorbitol/maltitol + vitamin B6 + water). The fitting parameters A1, A2, and A3, the standard deviation (SD), and the average deviation (AD) are shown in Table 3. The standard deviation (SD) and the average deviation (AD) are calculated as follows: n

SD = [∑ (yexp, i − ycal, i )2 /(n − k − 1)]1/2 i=1

AD =

1 n

n

∑ i=1

(3)

yexp, i − ycal, i yexp, i

(4)

where yexp,i and ycal,i are the experimental values and the calculated values, respectively. n is the total number of experimental data points, and k is the number of fitted B



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Table 2. Densities, ρ, Viscosities, η, and Apparent Molar Volumes, Vφ, of Erythritol/Xylitol/Sorbitol/Maltitol + Vitamin B6 + Water at Temperature 293.15 K, 303.15 K, 313.15 K, and 323.15 K and Atmospheric Pressure T/K = 293.15 ma mol·kg

ρ

C −1

mol·dm

−3

g·cm

−3

T/K = 303.15 η

mPa·s

ρ

Vφ −1

cm ·mol 3

−3

g·cm

T/K = 313.15 η

mPa·s

ρ

Vφ −1

cm ·mol 3

−3

g·cm

T/K = 323.15 η

ρ

Vφ −1

−3

η

Vφ

mPa·s

cm ·mol−1

mPa·s

cm ·mol

0.679 0.716 0.756 0.796 0.839 0.884

87.85 87.93 87.99 88.02 88.09

0.99381 1.00048 1.00692 1.01299 1.01906 1.02479

0.568 0.597 0.627 0.658 0.692 0.726

88.49 88.54 88.62 88.69 88.73

0.703 0.743 0.785 0.828 0.871 0.918

87.91 87.99 88.08 88.13 88.16

0.99927 1.00592 1.01233 1.01835 1.02420 1.02998

0.587 0.618 0.650 0.683 0.717 0.753

88.45 88.53 88.58 88.64 88.66

0.729 0.770 0.813 0.859 0.905 0.955

87.97 88.02 88.05 88.13 88.18

1.00474 1.01129 1.01761 1.02366 1.02952 1.03516

0.608 0.641 0.674 0.708 0.744 0.782

88.51 88.54 88.64 88.67 88.73

0.755 0.798 0.843 0.891 0.940 0.991

88.09 88.13 88.16 88.19 88.26

1.01001 1.01650 1.02275 1.02875 1.03454 1.04004

0.629 0.663 0.697 0.734 0.772 0.810

88.53 88.58 88.65 88.70 88.77

0.678 0.725 0.774 0.827 0.883 0.944

103.59 103.76 103.86 103.94 104.06

0.99380 1.00323 1.01200 1.02073 1.02905 1.03709

0.568 0.604 0.641 0.683 0.726 0.773

104.53 104.62 104.68 104.71 104.82

0.704 0.754 0.804 0.861 0.919 0.983

103.88 103.94 103.99 104.09 104.17

0.99949 1.00879 1.01751 1.02623 1.03430 1.04237

0.589 0.626 0.665 0.710 0.754 0.802

104.68 104.71 104.79 104.83 104.89

0.729 0.780 0.835 0.891 0.955 1.018

103.87 103.96 104.07 104.12 104.20

1.00483 1.01407 1.02292 1.03104 1.03930 1.04719

0.609 0.649 0.691 0.735 0.783 0.831

104.72 104.74 104.83 104.87 104.92

0.755 0.808 0.866 0.926 0.992 1.059

103.93 104.07 104.15 104.24 104.28

1.01002 1.01916 1.02800 1.03616 1.04437 1.05175

0.629 0.669 0.717 0.761 0.813 0.864

104.78 104.83 104.87 104.94 105.00

3

g·cm

3

−1

0 0.1998 0.4002 0.5966 0.8004 0.9996

0.0000 0.1972 0.3884 0.5695 0.7514 0.9234

1.00423 1.01116 1.01785 1.02419 1.03051 1.03651

1.044 1.111 1.182 1.255 1.335 1.418

86.61 86.68 86.71 86.78 86.79

0 0.2008 0.4022 0.5983 0.7961 0.9978

0.0000 0.1993 0.3924 0.5742 0.7516 0.9266

1.01000 1.01688 1.02353 1.02978 1.03586 1.04185

1.084 1.155 1.230 1.307 1.389 1.477

86.73 86.77 86.80 86.84 86.88

0 0.1999 0.4000 0.6000 0.8000 1.0001

0.0000 0.1995 0.3924 0.5788 0.7589 0.9334

1.01567 1.02246 1.02900 1.03530 1.04137 1.04724

1.127 1.201 1.279 1.362 1.449 1.540

86.73 86.79 86.84 86.90 86.93

0 0.2000 0.4001 0.6000 0.8000 0.9980

0.0000 0.2007 0.3945 0.5817 0.7627 0.9361

1.02112 1.02782 1.03428 1.04052 1.04652 1.05227

1.169 1.247 1.329 1.416 1.508 1.603

86.90 86.93 86.93 86.98 87.01

0 0.2007 0.3958 0.5982 0.7989 1.0028

0.0000 0.1975 0.3820 0.5660 0.7415 0.9130

1.00423 1.01407 1.02325 1.03235 1.04102 1.04941

1.044 1.126 1.213 1.308 1.411 1.523

101.89 101.93 102.04 102.10 102.23

0 0.1999 0.3953 0.5997 0.7965 1.0020

0.0000 0.1979 0.3837 0.5705 0.7434 0.9172

1.01019 1.01991 1.02901 1.03812 1.04651 1.05494

1.085 1.172 1.263 1.366 1.473 1.592

101.99 102.06 102.15 102.25 102.32

0 0.2001 0.4000 0.5919 0.7948 0.9972

0.0000 0.1991 0.3901 0.5664 0.7457 0.9177

1.01574 1.02540 1.03464 1.04311 1.05168 1.05987

1.127 1.218 1.317 1.418 1.532 1.657

102.03 102.10 102.22 102.34 102.45

0 0.1995 0.4011 0.5951 0.7992 0.9904

0.0000 0.1996 0.3931 0.5721 0.7531 0.9163

1.02116 1.03071 1.03992 1.04841 1.05693 1.06462

1.172 1.266 1.370 1.478 1.601 1.723

102.14 102.27 102.35 102.49 102.55

Erythritol + 0.1000 mol·kg Vitamin B6 1.00157 0.830 0.99804 1.00842 0.879 87.16 1.00479 1.01502 0.931 87.25 1.01130 1.02126 0.984 87.31 1.01745 1.02747 1.045 87.41 1.02362 1.03332 1.102 87.49 1.02941 Erythritol + 0.1992 mol·kg−1 Vitamin B6 1.00723 0.861 1.00365 1.01404 0.913 87.22 1.01036 1.02059 0.968 87.34 1.01683 1.02675 1.024 87.39 1.02288 1.03271 1.083 87.48 1.02878 1.03857 1.147 87.56 1.03460 Erythritol + 0.3000 mol·kg−1 Vitamin B6 1.01281 0.893 1.00915 1.01951 0.948 87.32 1.01576 1.02596 1.005 87.39 1.02213 1.03216 1.065 87.47 1.02827 1.03812 1.128 87.55 1.03416 1.04388 1.193 87.60 1.03986 Erythritol + 0.3999 mol·kg−1 Vitamin B6 1.01815 0.926 1.01445 1.02479 0.983 87.35 1.02098 1.03117 1.043 87.43 1.02727 1.03731 1.106 87.49 1.03333 1.04322 1.172 87.56 1.03918 1.04886 1.241 87.62 1.04473 Xylitol + 0.0999 mol·kg−1 Vitamin B6 1.00156 0.829 0.99803 1.01124 0.890 102.84 1.00760 1.02025 0.954 102.92 1.01647 1.02920 1.024 103.01 1.02529 1.03774 1.099 103.04 1.03368 1.04597 1.180 103.19 1.04181 Xylitol + 0.2025 mol·kg−1 Vitamin B6 1.00742 0.862 1.00385 1.01698 0.925 102.93 1.01326 1.02592 0.992 103.02 1.02207 1.03489 1.067 103.08 1.03091 1.04313 1.145 103.20 1.03903 1.05138 1.231 103.29 1.04717 Xylitol + 0.3014 mol·kg−1 Vitamin B6 1.01288 0.894 1.00921 1.02238 0.961 102.97 1.01857 1.03146 1.034 103.05 1.02751 1.03978 1.107 103.18 1.03571 1.04822 1.189 103.27 1.04406 1.05627 1.278 103.37 1.05201 Xylitol + 0.4001 mol·kg−1 Vitamin B6 1.01819 0.926 1.01446 1.02758 0.996 103.08 1.02372 1.03664 1.073 103.19 1.03264 1.04498 1.152 103.29 1.04087 1.05341 1.241 103.35 1.04915 1.06093 1.328 103.46 1.05662

C



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Table 2. continued T/K = 293.15 a

m

C

mol·kg−1

mol·dm−3

ρ g·cm−3

T/K = 303.15 η

Vφ

mPa·s

cm3·mol−1

0 0.1999 0.3946 0.5929 0.7959 0.9992

0.0000 0.1961 0.3785 0.5560 0.7298 0.8961

1.00423 1.01661 1.02804 1.03913 1.04989 1.06009

1.044 1.148 1.259 1.383 1.524 1.672

118.53 118.75 118.90 119.10 119.33

0 0.2000 0.3993 0.5984 0.8018 0.9986

0.0000 0.1973 0.3849 0.5639 0.7386 0.9004

1.01010 1.02237 1.03400 1.04506 1.05579 1.06565

1.085 1.194 1.315 1.448 1.596 1.754

118.78 118.87 118.97 119.11 119.27

0 0.2000 0.4000 0.5937 0.7895 0.9902

0.0000 0.1983 0.3875 0.5626 0.7319 0.8979

1.01567 1.02784 1.03942 1.05011 1.06037 1.07041

1.127 1.243 1.370 1.507 1.658 1.827

118.95 119.02 119.09 119.23 119.34

0 0.1999 0.4001 0.5973 0.8001 0.9927

0.0000 0.1993 0.3896 0.5685 0.7443 0.9040

1.02111 1.03317 1.04465 1.05540 1.06589 1.07538

1.169 1.291 1.426 1.573 1.735 1.911

119.14 119.23 119.34 119.49 119.61

0 0.2002 0.4000 0.5998 0.7999 1.0000

0.0000 0.1927 0.3696 0.5329 0.6842 0.8245

1.00428 1.02886 1.05134 1.07199 1.09089 1.10843

1.044 1.260 1.532 1.898 2.255 2.760

215.83 216.07 216.33 216.79 217.07

0 0.1999 0.4000 0.5943 0.8009 0.9994

0.0000 0.1935 0.3715 0.5312 0.6881 0.8278

1.01009 1.03452 1.05677 1.07676 1.09611 1.11326

1.085 1.314 1.595 1.936 2.379 2.898

215.87 216.49 216.62 217.11 217.48

0 0.2000 0.3997 0.6006 0.8000 0.9947

0.0000 0.1946 0.3731 0.5386 0.6905 0.8281

1.01566 1.03987 1.06201 1.08227 1.10093 1.11768

1.127 1.368 1.668 2.041 2.488 3.041

216.49 216.70 217.24 217.42 217.71

0 0.1999 0.4000 0.5970 0.7954 1.0003

0.0000 0.1955 0.3752 0.5383 0.6902 0.8355

1.02112 1.04516 1.06718 1.08698 1.10539 1.12291

1.169 1.424 1.741 2.124 2.611 3.216

216.75 216.97 217.37 217.62 217.88

ρ g·cm−3 Sorbitol 1.00157 1.01377 1.02505 1.03595 1.04651 1.05653 Sorbitol 1.00734 1.01945 1.03090 1.04177 1.05233 1.06204 Sorbitol 1.01281 1.02482 1.03624 1.04675 1.05684 1.06674 Sorbitol 1.01815 1.03008 1.04141 1.05203 1.06238 1.07172 Maltitol 1.00161 1.02590 1.04815 1.06853 1.08725 1.10460 Maltitol 1.00734 1.03147 1.05355 1.07326 1.09239 1.10949 Maltitol 1.01281 1.03673 1.05863 1.07877 1.09717 1.11370 Maltitol 1.01815 1.04195 1.06372 1.08337 1.10157 1.11878

T/K = 313.15 η

Vφ

mPa·s

cm3·mol−1

+ 0.1000 0.830 0.907 0.988 1.080 1.180 1.288 + 0.2016 0.861 0.942 1.031 1.127 1.234 1.349 + 0.3000 0.894 0.980 1.073 1.172 1.281 1.401 + 0.3999 0.926 1.017 1.115 1.222 1.337 1.464 + 0.1008 0.830 0.989 1.184 1.422 1.705 2.060 + 0.2016 0.861 1.035 1.235 1.477 1.792 2.158 + 0.3000 0.893 1.070 1.290 1.554 1.873 2.255 + 0.3999 0.926 1.114 1.344 1.620 1.959 2.382

ρ g·cm−3

mol·kg−1 Vitamin B6 0.99804 119.59 1.01007 119.76 1.02121 119.96 1.03199 120.20 1.04245 120.44 1.05243 mol·kg−1 Vitamin B6 1.00375 119.73 1.01571 119.89 1.02700 120.04 1.03774 120.18 1.04820 120.33 1.05776 mol·kg−1 Vitamin B6 1.00915 119.90 1.02102 119.99 1.03229 120.11 1.04270 120.27 1.05266 120.36 1.06248 mol·kg−1 Vitamin B6 1.01445 119.95 1.02620 120.10 1.03738 120.20 1.04785 120.37 1.05812 120.52 1.06736 mol·kg−1 Vitamin B6 0.99810 217.54 1.02214 217.67 1.04415 217.98 1.06440 218.37 1.08298 218.62 1.10026 mol·kg−1 Vitamin B6 1.00374 217.63 1.02763 217.96 1.04946 218.21 1.06903 218.69 1.08804 218.88 1.10492 mol·kg−1 Vitamin B6 1.00915 218.21 1.03287 218.32 1.05460 218.65 1.07456 218.92 1.09275 219.24 1.10918 mol·kg−1 Vitamin B6 1.01445 218.22 1.03802 218.49 1.05955 218.77 1.07901 219.05 1.09711 219.44 1.11419

T/K = 323.15 η

Vφ

mPa·s

cm3·mol−1

0.679 0.738 0.800 0.869 0.944 1.024

120.66 120.78 120.93 121.12 121.27

0.704 0.765 0.833 0.906 0.986 1.069

ρ

η

Vφ

mPa·s

cm3·mol−1

0.99381 1.00569 1.01668 1.02735 1.03771 1.04752

0.568 0.614 0.663 0.715 0.775 0.835

121.68 121.82 121.91 122.07 122.27

120.70 120.90 121.01 121.10 121.28

0.99943 1.01126 1.02245 1.03309 1.04340 1.05290

0.587 0.636 0.688 0.744 0.806 0.870

121.62 121.75 121.86 122.00 122.13

0.729 0.795 0.866 0.939 1.022 1.112

120.82 120.94 121.01 121.18 121.23

1.00474 1.01650 1.02767 1.03795 1.04789 1.05758

0.608 0.660 0.714 0.770 0.835 0.903

121.64 121.75 121.87 121.93 122.03

0.755 0.824 0.898 0.978 1.064 1.157

121.06 121.15 121.25 121.32 121.46

1.01001 1.02167 1.03277 1.04313 1.05327 1.06246

0.629 0.683 0.740 0.803 0.868 0.941

121.78 121.85 122.01 122.13 122.22

0.679 0.801 0.946 1.124 1.333 1.594

219.15 219.28 219.43 219.76 219.91

0.99386 1.01767 1.03949 1.05952 1.07800 1.09499

0.568 0.663 0.778 0.912 1.069 1.267

220.74 220.81 221.01 221.22 221.51

0.703 0.832 0.986 1.165 1.396 1.665

219.19 219.58 219.69 220.07 220.33

0.99943 1.02311 1.04480 1.06415 1.08316 1.09991

0.587 0.689 0.809 0.942 1.117 1.317

220.68 220.92 221.16 221.30 221.57

0.729 0.863 1.029 1.222 1.461 1.735

219.57 219.64 219.99 220.32 220.58

1.00474 1.02830 1.04987 1.06965 1.08784 1.10412

0.608 0.712 0.840 0.988 1.168 1.373

220.82 220.92 221.33 221.47 221.78

0.755 0.898 1.069 1.277 1.521 1.829

219.73 220.06 220.30 220.46 220.81

1.01001 1.03343 1.05485 1.07417 1.09214 1.10916

0.629 0.740 0.873 1.032 1.214 1.448

220.93 221.19 221.48 221.65 221.94

g·cm−3

a The symbol m stands for the molality of erythritol/xylitol/sorbitol/maltitol in vitamin B6 aqueous solution. Standard uncertainty: in molality u(m) = 1·10−4 mol·kg−1; in density u(ρ) = 5·10−4 g·cm−3, u(T) = 0.03 K; in viscosities u(η) = 1 %, u(T) = 0.05 K.

D



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where M is the molar weight of the solute, m is the molality of erythritol/xylitol/sorbitol/maltitol in the mixture solvent (vitamin B6 + water), ρ and ρ0 are the density of the solution and the mixture solvent, respectively. The calculated apparent molar volumes are also presented in Table 2. Vφ is found to have a good linear relationship with m at different temperatures; thus, the limiting partial molar volumes Vφ0 at infinite dilution were obtained by a regression analysis based on leastsquares method through the following equation. Vφ = V φ0 + Svm

In eq 6, Sv is the slope of the straight line, which indicates the strength of solute−solute interactions, and is influenced by a number of effects.16 The calculated values V0φ at different temperatures and their errors are given in Table 4. The limiting partial molar volume (V0φ) is a vital parameter to describe the solute−solvent interactions. A perusal of Table 4 reveals that the values V0φ are positive for all ternary solutions at the studied scale of molality and at different temperatures, and the values V0φ increase with either the elevating temperature or the increasing molality of vitamin B6. It is clear from the V0φ of four sugar alcohols, the variation tendency of the solute− solvent interactions of the sugar alcohols is in the order: erythritol < xylitol < sorbitol < maltitol. And the increase of V0φ with elevating temperature may be due to the release of some solvent molecules from the loose solvation layers of the solutes in solution.17 For a ternary system, the limiting partial molar volume of transfer, ΔtrV0φ, is a very important parameter for describing transfer property. The limiting partial molar volumes of erythritol/xylitol/sorbitol/maltitol in pure water could be obtained from the literature.4,5 The limiting partial molar volumes of transfer for erythritol/xylitol/sorbitol/maltitol from pure water to vitamin B6 aqueous solutions were calculated according to the following equation:

Figure 1. Density (ρ) of sugar alcohols in 0.1 mol·kg−1 vitamin B6 aqueous solution: red ■, maltitol; blue ▲, sorbitol; green ★, xylitol; black ●, erythritol.

Table 3. Fitting Coefficients A1, A2, and A3 of eq 2 for Erythritol/Xylitol/Sorbitol/Maltitol + Vitamin B6 + Water Ternary Solutions mVB6a mol·kg

a

−1

g·cm

10−3A3

104A2

A1 −3

0.1000 0.1992 0.3000 0.3999

1.1137 1.1217 1.1293 1.1362

0.0999 0.2025 0.3014 0.4001

1.1174 1.1257 1.1331 1.1405

0.1000 0.2016 0.3000 0.3999

1.1189 1.1268 1.1339 1.1408

0.1008 0.2016 0.3000 0.3999

1.1261 1.1332 1.1401 1.1474

−3

−1

g·cm ·K

−3

Erythritol −3.6942 −3.7724 −3.8383 −3.8895 Xylitol −3.8068 −3.8894 −3.9528 −4.0197 Sorbitol −3.8473 −3.9161 −3.9726 −4.0214 Maltitol −4.0130 −4.0588 −4.1067 −4.1689

SD·103 100AD

g·cm−3

0.0316 0.0313 0.0309 0.0306

0.04 0.04 0.04 0.04

0.6 0.5 0.5 0.5

0.0440 0.0436 0.0433 0.0429

0.05 0.05 0.05 0.05

0.7 0.7 0.7 0.7

0.0547 0.0545 0.0542 0.0537

0.07 0.07 0.07 0.06

0.9 0.9 0.9 0.9

0.1024 0.1016 0.1009 0.1001

0.2 0.2 0.2 0.2

2 2 2 2

g ·cm ·mol 2

−1

Δtr V φ0 = V φ0[vitamin B6 + water] − V φ0[water]

parameters. The maximum values of AD and SD are only 0.2 % and 0.002 g·cm−3, respectively. 3.2. Volumetric Properties. The apparent molar volume is very important to describe the solvation behavior of molecules in aqueous solutions since it contains much information about the immersed solute structure and the specific solute−solvent interactions.14 The apparent molar volume (Vφ) was calculated through the experimental density values using the following equation:15 1000(ρ − ρ0 ) M − ρ mρρ0

(7)

The ΔtrV0φ values are given in Table 4. The ΔtrV0φ values for the four sugar alcohols are all positive and increase monotonically with the molality of vitamin B6 in mixed solvents. The cosphere overlap model18,19 could be used to explain the ΔtrVφ0 . In principle, there exist hydrophilic−hydrophilic, hydrophilic−hydrophobic, and hydrophobic−hydrophobic interactions between sugar alcohols and vitamin B6 molecules. In three structure interactions, The hydrophilic−hydrophilic interactions between −OH groups of vitamin B6 molecules and −OH groups of sugar alcohol molecules weaken the breaking effect of vitamin B6 on the water structure, and more water molecules are released from the hydration shells into bulk water, which contributes positively to the ΔtrV0φ, while the hydrophilic−hydrophobic interactions between the −OH group and the alkyl chain and the hydrophobic−hydrophobic interactions between the alkyl chains lead to a negative contribution to the ΔtrV0φ.4,19 The positive ΔtrV0φ values indicate that the hydrophilic−hydrophilic interaction is predominant. In addition, the ΔtrV0φ values increase monotonically with the molality of vitamin B6 in mixed solvents, which implies that the predominant effect of the hydrophilic−hydrophilic interactions become more distinct with the increasing molality of vitamin B6, and the presence of vitamin B6 molecules facilitates the solute−solvent interaction.

mVB6 is the molality of vitamin B6 aqueous solution.

Vϕ =

(6)

(5) E



Article

Table 4. Limiting Apparent Molar Volumes (V0φ) and Limiting Apparent Molar Volumes of Transfer (ΔtrV0φ) of Erythritol/ Xylitol/Sorbitol/Maltitol + Vitamin B6 + Water Solutions at T = (293.15 to 323.15) K T/K = 293.15

T/K = 303.15

T/K = 313.15

T/K = 323.15

mVB6a

Vφ0

ΔtrVφ0

Vφ0

ΔtrVφ0

Vφ0

ΔtrVφ0

Vφ0

ΔtrVφ0

mol·kg−1

cm3·mol−1

cm3·mol−1

cm3·mol−1

cm3·mol−1

cm3·mol−1

cm3·mol−1

cm3·mol−1

cm3·mol−1

0.0000 0.1000 0.1992 0.3000 0.3999

86.24b 86.59(±0.02) 86.69(±0.00) 86.69(±0.01) 86.87(±0.01)

0.35 0.45 0.45 0.63

86.96b 87.09(±0.01) 87.15(±0.02) 87.25(±0.01) 87.29(±0.01)

87.71b 87.83(±0.02) 87.86(±0.02) 87.91(±0.01) 88.05(±0.01)

0.12 0.15 0.20 0.34

88.39b 88.43(±0.01) 88.41(±0.02) 88.45(±0.02) 88.47(±0.01)

0.04 0.02 0.06 0.08

0.0000 0.0999 0.2025 0.3014 0.4001

101.50b 101.78(±0.03) 101.90(±0.01) 101.90(±0.02) 102.05(±0.02)

0.28 0.40 0.40 0.55

102.48b 102.76(±0.03) 102.84(±0.02) 102.86(±0.01) 103.00(±0.02)

0.03 0.32 0.32 0.39

104.46b 104.47(±0.02) 104.62(±0.01) 104.66(±0.02) 104.72(±0.01)

0.01 0.16 0.20 0.26

0.0000 0.1000 0.2016 0.3000 0.3999

118.34c 118.34(±0.02) 118.63(±0.03) 118.83(±0.03) 119.00(±0.02)

0.00 0.29 0.49 0.64

119.326c 119.35(±0.03) 119.59(±0.01) 119.76(±0.02) 119.80(±0.02)

120.473c 120.49(±0.02) 120.59(±0.04) 120.72(±0.03) 120.96(±0.02)

0.02 0.12 0.22 0.49

121.470c 121.52(±0.03) 121.49(±0.01) 121.55(±0.02) 121.65(±0.02)

0.05 0.02 0.08 0.18

0.0000 0.1008 0.2016 0.3000 0.3999

214.81c 215.46(±0.07) 215.56(±0.12) 216.16(±0.10) 216.45(±0.05)

0.65 0.75 1.35 1.64

216.86c 217.18(±0.08) 217.31(±0.07) 217.87(±0.07) 217.89(±0.04)

218.80c 218.91(±0.06) 218.94(±0.07) 219.21(±0.09) 219.50(±0.06)

0.11 0.14 0.41 0.70

220.35c 220.47(±0.07) 220.48(±0.04) 220.52(±0.08) 220.69(±0.03)

0.12 0.13 0.17 0.34

Erythritol

a

0.13 0.19 0.29 0.33 Xylitol 0.28 0.36 0.38 0.52 Sorbitol 0.02 0.26 0.43 0.47 Maltitol 0.32 0.45 1.01 1.03

103.48b 103.51(±0.03) 103.80(±0.02) 103.80(±0.02) 103.87(±0.03)

mVB6 is the molality of vitamin B6 aqueous solution. bReference 4. cReference 5.

From Table 4, it could also be seen that most ΔtrV0φ values of maltitol show maximal in the four sugar alcohols due to the most −OH groups and the largest molar weight. The ΔtrV0φ values decrease with the increase of temperature for four sugar alcohols. Although the limiting partial molar volume increases with rising temperature for four sugar alcohols in both pure water and vitamin B6 aqueous solutions, comparatively, the increase of the limiting partial molar volume in vitamin B6 aqueous solution is less than that in pure water. As a result, the transfer limiting partial molar volume decreases with the increase of temperature. 3.3. Viscometric Properties. The experimental viscosities η of erythritol/xylitol/sorbitol/maltitol in vitamin B6 aqueous solutions at temperatures from 293.15 to 323.15 K are listed in Table 2. Figure 2 shows the viscosities of erythritol/xylitol/ sorbitol/maltitol in 0.1 mol·kg−1 vitamin B6 aqueous solutions at T = 293.15 K. From Figure 2, it could be seen that the viscosities increase nonlinearly with the increase of the molarity of erythritol/xylitol/sorbitol/maltitol at constant temperature. For a given molarity of vitamin B6 and a constant temperature, the viscosities of the four sugar alcohols increase in the order erythritol < xylitol < sorbitol < maltitol. From Table 2, it is worth noting that the viscosities decrease with elevating temperature due to the rapid molecular motion. The relative viscosities of erythritol/xylitol/sorbitol/maltitol in vitamin B6 aqueous solutions could be analyzed using the extended Jones−Dole equation.20 ηr =

η = 1 + BC + DC 2 η0

Figure 2. Viscosities of sugar alcohols in 0.1 mol·kg−1 vitamin B6 aqueous solutions at T = 293.15 K: red ■, maltitol; blue ▲, sorbitol; green ★, xylitol; black ●, erythritol.

In the equation, ηr is the relative viscosity, η and η0 are respectively the viscosities of ternary solutions and the mixed solvents (vitamin B6 + water), and C is the concentration of the solute in vitamin B6 aqueous solutions at 293.15 K; it could be computed from the molality (m) through density values. B and D are the coefficients estimated by the least-squares regression method. These coefficients B and D for each of the ternary systems average deviation (AD) and the standard deviation (SD) are shown in Table 5. And the maximum values of AD

(8) F



Article

0≠ Table 5. Viscosity B and D Coefficients Δμ0≠ 1 , Δμ2 , of Erythritol/Xylitol/Sorbitol/Maltitol + Vitamin B6 + Water Ternary Solutions at T = (293.15 to 323.15) K

mVB6a mol·kg

−1

0.1000

0.1992

0.3000

0.3999

0.0999

0.2025

0.3014

0.4001

0.1000

0.2016

0.3000

0.3999

0.1008

0.2016

T K

B

SD·102

D −1

dm ·mol 3

293.15 303.15 313.15 323.15 293.15 303.15 313.15 323.15 293.15 303.15 313.15 323.15 293.15 303.15 313.15 323.15

0.3050 0.2853 0.2651 0.2466 0.3074 0.2863 0.2691 0.2540 0.3089 0.2889 0.2692 0.2513 0.3090 0.2880 0.2683 0.2505

293.15 303.15 313.15 323.15 293.15 303.15 313.15 323.15 293.15 303.15 313.15 323.15 293.15 303.15 313.15 323.15

0.3639 0.3417 0.3223 0.2977 0.3662 0.3415 0.3239 0.3003 0.3708 0.3504 0.3294 0.3073 0.3669 0.3491 0.3230 0.3086

293.15 303.15 313.15 323.15 293.15 303.15 313.15 323.15 293.15 303.15 313.15 323.15 293.15 303.15 313.15 323.15

0.4490 0.4239 0.4014 0.3788 0.4468 0.4205 0.3998 0.3784 0.4530 0.4282 0.4002 0.3782 0.4555 0.4314 0.4060 0.3812

293.15 303.15 313.15 323.15 293.15 303.15

0.6895 0.6079 0.5869 0.5718 0.6320 0.6273

−2

dm ·mol 6

Erythritol 0.0894 0.0768 0.0664 0.0594 0.0896 0.0778 0.0649 0.0551 0.0900 0.0764 0.0666 0.0577 0.0930 0.0799 0.0698 0.0613 Xylitol 0.1510 0.1331 0.1156 0.1064 0.1544 0.1361 0.1165 0.1047 0.1525 0.1277 0.1125 0.0986 0.1598 0.1357 0.1274 0.1082 Sorbitol 0.248 0.2142 0.1846 0.1636 0.2614 0.2292 0.1960 0.1727 0.2641 0.2258 0.2027 0.1779 0.2687 0.2287 0.1992 0.1801 Maltitol 1.5510 1.4169 1.2473 1.0944 1.6474 1.4160

G

Δμ0≠ 1 −1

kJ·mol

Δμ0≠ 2 kJ·mol−1

100AD

mPa·s

0.03 0.05 0.03 0.03 0.03 0.04 0.04 0.02 0.03 0.02 0.03 0.05 0.03 0.03 0.02 0.02

0.06 0.1 0.06 0.06 0.06 0.07 0.09 0.05 0.05 0.05 0.07 0.1 0.06 0.07 0.04 0.03

9.42 9.17 8.96 8.78 9.55 9.30 9.09 8.90 9.67 9.42 9.21 9.03 9.79 9.54 9.34 9.15

59.25 57.92 56.37 54.88 59.07 57.55 56.44 55.45 58.75 57.42 55.97 54.59 58.29 56.81 55.39 54.02

0.06 0.05 0.02 0.01 0.05 0.03 0.05 0.02 0.07 0.04 0.03 0.04 0.04 0.03 0.04 0.08

0.1 0.1 0.05 0.03 0.1 0.06 0.1 0.05 0.2 0.09 0.09 0.09 0.07 0.06 0.1 0.2

9.42 9.17 8.96 8.78 9.55 9.30 9.09 8.91 9.67 9.42 9.21 9.04 9.79 9.54 9.34 9.15

69.14 67.84 66.69 64.65 68.80 67.17 66.32 64.43 68.78 67.76 66.48 64.84 67.70 67.01 65.02 64.46

0.05 0.05 0.03 0.04 0.09 0.1 0.04 0.08 0.1 0.09 0.1 0.09 0.1 0.1 0.1 0.1

0.1 0.1 0.07 0.1 0.2 0.2 0.07 0.2 0.2 0.2 0.2 0.2 0.4 0.4 0.3 0.4

9.42 9.17 8.96 8.78 9.55 9.30 9.09 8.90 9.67 9.42 9.21 9.03 9.79 9.54 9.34 9.15

82.71 81.44 80.31 78.94 81.64 80.21 79.31 78.10 81.70 80.49 78.61 77.32 81.27 80.15 78.69 77.02

0.8 0.9 0.8 0.8 0.9 0.9

3 2 2 2 3 2

9.42 9.17 8.96 8.78 9.55 9.30

127.76 120.24 120.55 121.46 118.82 121.61



Article

Table 5. continued mVB6a

T

B

D

mol·kg−1

K

dm3·mol−1

dm6·mol−2

313.15 323.15 293.15 303.15 313.15 323.15 293.15 303.15 313.15 323.15

0.5946 0.5921 0.6297 0.6259 0.6084 0.5887 0.6241 0.6230 0.6125 0.5928

1.2547 1.0786 1.6828 1.442 1.2581 1.1053 1.7309 1.4826 1.2838 1.1348

100AD

SD·102

Δμ0≠ 1

Δμ0≠ 2

mPa·s

kJ·mol−1

kJ·mol−1

9.09 8.90 9.67 9.42 9.21 9.03 9.79 9.54 9.34 9.15

120.34 123.06 117.39 120.22 121.01 121.27 115.51 118.59 120.35 120.60

Maltitol

0.3000

0.3999

a

0.8 0.8 1 0.9 0.8 0.6 1 0.9 0.7 0.7

2 2 3 2 2 2 3 2 2 2

mVB6 is the molality of vitamin B6 aqueous solution.

formation of a transition state in the presence of vitamin B6.24 For a given temperature and molality of vitamin B6, the Δμ0≠ 2 values decrease in the order maltitol >sorbitol > xylitol > erythritol. Among the four sugar alcohols, the Δμ0≠ 2 value of erythritol is the smallest, which revealed that erythritol is the most favorable to the formation of a transition state. In addition, the Δμ0≠ values decrease with the increase of 2 temperature for erythritol/xylitol/sorbitol in a mixture solvent (vitamin B6 + water), which implies that high temperature favors the formation of the transition state. However, the variation Δμ0≠ 2 value of maltitol with temperature is complex, the influencing mechanism of the temperature on the transition state of maltitol in vitamin B6 aqueous solution remains still unclear and needs further study.

and SD are 1 % and 0.03 mPa·s, respectively. The viscosity B coefficient reflects the effect of solute−solvent interactions, and the D coefficient accounts for solute−solute interactions.20,21 Table 5 shows that the positive B coefficient values remain in an increasing trend with increasing molality of vitamin B6, but decrease with rising temperature. Usually, the dB/dT is a better criterion for determining the structure-making/breaking nature of any solute. The negative dB/dT values in the studied systems are indicative of their structure-making propensity.22 The viscosity of erythritol/xylitol/sorbitol/maltitol in vitamin B6 aqueous solutions could be used to analyze the free energy of activation per mole of solvent (Δμ0≠ 1 ) and the free energy of activation per mole of solute (Δμ0≠ 2 ). On the basis of the Feakin’s transition state theory,23 the B coefficient could be expressed as B=

(V1̅ 0

−

V2̅ 0)

+

⎛ Δμ 0 ≠ V1̅ 0⎜⎜ 2 ⎝

− Δμ10 ≠ ⎞ ⎟⎟ RT ⎠

4. CONCLUSIONS The densities and viscosities of erythritol, xylitol, sorbitol, and maltitol in vitamin B6 aqueous solutions were measured, and the apparent molar volumes (Vφ), the limiting partial molar volumes (Vφ0), the limiting partial molar volumes of transfer (ΔtrV0φ), and the viscosity B coefficients were obtained through the experimental densities and viscosities of the ternary solution. In summary, the V0φ values increase with rising temperature as well as the molality of vitamin B6 in the solvent mixture. V0φ of four sugar alcohols increase in the order erythritol < xylitol < sorbitol < maltitol. The ΔtrV0φ becomes larger with the increase of the molality of vitamin B6, while it decreases with the increase of temperature. In addition, the viscosity B coefficients and the free energy of activation per mole of solvent (Δμ0≠ 1 ) were applied to analyze the free energy of activation per mole of solute (Δμ20≠). For a given temperature and a given molality of vitamin B6, the (Δμ0≠ 2 ) decreases in the order maltitol >sorbitol > xylitol > erythritol.

(9)

Therefore the free energy of activation per mole of solute, Δμ0≠ 2 , could be calculated using the viscosity B coefficient by the following relation: Δμ20 ≠ = Δμ10 ≠ +

RT [B − (V1̅ 0 − V2̅ 0)] V1̅ 0

(10)

where V1̅ 0(=∑xiMi/ρ0) is the mean molar volume of the solvent, in which the terms xi and Mi specify respectively the mole fraction and molar weight of water and vitamin B6 in mixtures solvent, ρ0 is the density of mixtures solvent (vitamin B6 + water), V2̅ 0 (= V0φ) is the standard partial molar volume of the solute at infinite dilution, and R is the gas constant. The free energy of activation per mole of solvent (Δμ0≠ 1 ) could be calculated through following equation:3 Δμ10 ≠ = RT ln

■

η0V1̅ 0 hNA

ASSOCIATED CONTENT

S Supporting Information *

(11)

Comparison of experimental densities and viscosities for vitamin B6 + water solutions with the literature values. This material is available free of charge via the Internet at http:// pubs.acs.org.

where NA is Avogadro’s number, h is Planck’s constant, and η0 is the viscosity of the solvent. Δμ0≠ 1 is almost invariant for the same solvent composition and temperature. The calculated 0≠ values of Δμ0≠ 1 and Δμ2 at different temperatures are also shown in Table 5. From Table 5, it could be seen that the values of both Δμ0≠ 2 0≠ 0≠ and Δμ0≠ 1 are positive, and Δμ2 is higher than Δμ1 at various temperatures, which indicates the existence of the stronger solute−solvent interaction. The interaction militates against the

■

AUTHOR INFORMATION

Corresponding Authors

*E-mail: [email protected]. *E-mail: [email protected]. H



Article

Notes

(20) Jones, G.; Dole, D. The viscosity of aqueous solutions of strong electrolytes with special reference to barium chloride. J. Am. Chem. Soc. 1929, 51, 2950−2964. (21) Seuvre, A. M.; Mathlouthi, M. Solutions properties and solute− solvent interactions in ternary sugar−salt−water solutions. Food Chem. 2010, 122, 455−461. (22) Li, Y.; Li, Y.; Wang, F.; Ren, B. Volumetric and viscometric studies of cefepime hydrochloride in water and normal saline from (278.15 to 313.15) K. J. Chem. Thermodyn. 2013, 66, 14−21. (23) Feakins, D.; Freemantle, D.; Lawrence, K. G. Transition state treatment of the relative viscosity of electrolytic solutions, applications to aqueous, non-aqueous and methanol + water systems. J. Chem. Soc., Faraday Trans. 1974, 70, 795−806. (24) Kumar, H.; Kaur, K. Viscosities of glycine and L-alanine in (0.2, 0.4, 0.6, and 0.8) mol·kg−1 aqueous dipotassium hydrogen phosphate solutions at different temperatures. J. Chem. Eng. Data 2012, 57, 3416−3421.

The authors declare no competing financial interest.

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REFERENCES

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Densities and Viscosities of Sugar Alcohols in Vitamin B6 Aqueous

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