Article pubs.acs.org/jced
Enthalpies of Dilution, Volumetric Properties, and Refractive Indices of N,N′‑Hexamethylenebisacetamide in Aqueous Xylitol or D‑Mannitol Solutions at T = 298.15 K Lina Dong, Min Liu,* Aiju Chen, and Dezhi Sun College of Chemistry and Chemical Engineering, Liao Cheng University, Liaocheng, Shandong, 252059, People’s Republic of China ABSTRACT: The enthalpies of dilution (ΔdilHm), apparent molar volumes (Vϕ), and refractive indices (nD) of N,N′-hexamethylenebisacetamide (HMBA) in aqueous solutions of xylitol and D-mannitol were respectively determined at 298.15 K with the methods of isothermal microcalorimetry, density, and refractive-index measurements. The enthalpic interaction coefficients (h2, h3, and h4), limiting partial molar volumes (V0ϕ), and transfer partial molar volumes (ΔtrsV0ϕ) from water to solutions and molar refractions at the sodium-D line (RD) were deduced from the experimental data in the polyols molality range (0 to 0.9) mol·kg−1. The important parameters were interpreted to understand the interactions among solvated solute molecules in HMBA−xylitol (or mannitol)−water ternary systems. The results indicated that the number of hydroxyls in the both polyols could evidently affect the parameters.
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INTRODUCTION Hybrid polar compounds could induce the tumor cell differentiation and inhibit their growth.1,2 Among this class of compounds, N, N′-hexamethylenebisacetamide (HMBA, its molecular structure is provided in Scheme 1) is a prototype
thermodynamic parameter which can clarify solvent-mediated solute−solute interactions. Volumetric properties, especially limiting partial molar volumes, can provide valuable information and lead to a deeper understanding of intermolecular interactions.14,15 Additionally, the refractive index is another thermodynamic parameter to illustrate the interactions occurring in aqueous system.16,17 In the present work, we report the enthalpies of dilution, volumetric properties, and refractive indices of HMBA in pure water and aqueous xylitol and D-mannitol solutions at T = 298.15 K. All of the involved parameters are discussed according to the interactions occurring in the (HMBA + xylitol or D-mannitol + water) systems.
Scheme 1. Molecular Structure of HMBA
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EXPERIMENTAL SECTION Materials. N, N′-Hexazmethylenebisacetamide (HMBA), xylitol, and D-mannitol purchased from Acros were dried for 72 h at ambient temperature in a vacuum dryer before use without further purification. The purities of the above three reagents are above 0.98, 0.98, and 0.99 mass fraction, respectively. Aqueous xylitol and D-mannitol solutions in the molality range from (0 to 0.9) mol·kg−1 were prepared with twice-distilled water and were used as solvents to prepare HMBA solutions. The above samples were degassed with ultrasonic waves and employed within 12 h after making to avoid bacterial contamination. The solutions mentioned above were prepared on a weight basis by using a Mettler Toledo AG 135 balance with high precision (± 1·10−8 kg). Calorimetric Measurements. A Thermometric 2277 thermal activity monitor (Thermometric, Sweden) was employed to measure the dilution enthalpies of HMBA in aqueous solutions of xylitol and D-mannitol at 298.15 K. The details of the thermodynamic procedures have been described elsewhere.18−20
compound, whose differentiation effect has been verified through an experiment on murine.3,4 Researchers focus much attention to HMBA and have done plenty of studies on it because of its revulsive function.5−7 The biological system is a very complex organism containing many organic substances such as polyhydroxy compounds. In various polyhydroxy compounds, xylitol, that is, 1,2,3,4,5-pentahydroxy pentane, is an important intermediate product in mammalian carbohydrate metabolism.8−10 It can be obtained from the reduction of xylose and has important applications on the treatment of diabetes and pulmonary infection. By contrast, D-mannitol, that is, (2R,3R,4R,5R)-hexane-1,2,3,4,5,6-hexol, is an important hexahydric alcohol. It plays an important role in the therapy of elevated intracranial pressure in brain trauma because of its function of decreasing brain water content as a hyperosmolar solution.11−13 The thermodynamic property study of HMBA in aqueous xylitol and D-mannitol solutions may aid in elucidating the nature and mechanisms of HMBA playing a curative effect in the biological systems. Among various thermodynamic parameters, the enthalpy of dilution (ΔdilHm) is a well-known © 2012 American Chemical Society
Received: April 9, 2012 Accepted: August 21, 2012 Published: August 27, 2012 2456
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Table 1. Values of the Molar Enthalpies of Dilution (ΔdilHm) of HMBA in Aqueous Xylitol and D-Mannitol Solutions at T = 298.15 Ka mi
mf
ΔdilHm
δ
mi
mf
ΔdilHm
δ
mol·kg−1
mol·kg−1
J·mol−1
J·mol−1
mol·kg−1
mol·kg−1
J·mol−1
J·mol−1
0.0500 0.0800 0.1000 0.1200 0.1500 0.1800
0.0263 0.0422 0.0525 0.0631 0.0784 0.0941
−41.53 −75.35 −98.41 −120.58 −155.15 −188.42
−0.03 0.00 0.01 0.07 0.02 −0.10
0.2000 0.2200 0.2500 0.2800 0.3000 0.3200
0.1048 0.1148 0.1300 0.1454 0.1554 0.1650
−210.16 −233.25 −267.71 −301.61 −324.94 −349.38
−0.06 0.06 −0.04 0.11 0.00 −0.05
0.0500 0.0800 0.1000 0.1200 0.1500 0.1800
0.0259 0.0411 0.0515 0.0617 0.0768 0.0927
−45.86 −77.67 −98.44 −119.62 −151.92 −182.70
mxylitol = 0.1000 mol·kg−1 −0.03 0.2000 0.07 0.2200 0.00 0.2500 −0.05 0.2800 0.06 0.3000 −0.06 0.3200
0.1023 0.1120 0.1273 0.1421 0.1518 0.1617
−205.38 −227.87 −259.75 −292.91 −315.38 −337.29
0.01 −0.07 0.03 0.06 0.00 −0.01
−44.61 −76.16 −96.30 −116.45 −146.57 −178.94
mxylitol = 0.2000 mol·kg−1 −0.02 0.2000 0.14 0.2200 −0.14 0.2500 −0.05 0.2800 0.01 0.3000 0.02 0.3200
0.0999 0.1095 0.1239 0.1390 0.1493 0.1582
−199.77 −221.17 −253.29 −283.78 −303.46 −325.64
0.03 0.04 0.03 −0.11 −0.02 0.05
−38.24 −66.13 −85.90 −106.21 −137.43 −168.92
mxylitol = 0.3000 mol·kg−1 0.04 0.2000 0.11 0.2200 0.12 0.2500 −0.05 0.2800 0.01 0.3000 0.11 0.3200
0.1009 0.1107 0.1254 0.1402 0.1498 0.1590
−189.62 −211.31 −243.60 −275.28 −296.55 −318.49
0.12 −0.09 0.09 −0.13 0.10 −0.07
0.1014 0.1112 0.1279 0.1412 0.1503 0.1601
−173.05 −194.01 −221.65 −256.64 −279.37 −300.59
−0.14 −0.09 0.04 0.14 −0.06 −0.01
Water
0.0500 0.0800 0.1000 0.1200 0.1500 0.1800 0.0500 0.0800 0.1000 0.1200 0.1500 0.1800
0.0254 0.0398 0.0500 0.0602 0.0756 0.0899 0.0252 0.0407 0.0507 0.0608 0.0757 0.0907
0.0500 0.0800 0.1000 0.1200 0.1500 0.1800
0.0256 0.0409 0.0511 0.0613 0.0763 0.0916
−31.57 −57.34 −75.02 −93.52 −122.81 −152.14
mxylitol = 0.5000 mol·kg−1 0.03 0.2000 −0.14 0.2200 0.09 0.2500 0.05 0.2800 −0.01 0.3000 0.11 0.3200
0.0500 0.0800 0.1000 0.1200 0.1500 0.1800
0.0249 0.0401 0.0502 0.0602 0.0741 0.0891
−29.72 −52.31 −68.62 −86.16 −115.31 −144.25
mxylitol = 0.7000 mol·kg−1 −0.06 0.2000 0.04 0.2200 0.08 0.2500 0.02 0.2800 −0.07 0.3000 −0.14 0.3200
0.1005 0.1102 0.1255 0.1387 0.1489 0.1584
−161.71 −182.41 −212.63 −247.09 −267.79 −289.25
0.06 0.05 0.09 −0.03 −0.09 0.05
0.0500 0.0800 0.1000 0.1200 0.1500 0.1800
0.0254 0.0416 0.0524 0.0618 0.0772 0.0925
−22.89 −41.21 −54.62 −71.03 −95.73 −122.61
mxylitol = 0.9000 mol·kg−1 −0.02 0.2000 −0.03 0.2200 0.08 0.2500 0.00 0.2800 0.07 0.3000 −0.06 0.3200
0.1024 0.1125 0.1277 0.1424 0.1524 0.1626
−141.61 −160.94 −190.23 −221.42 −241.69 −262.10
−0.07 −0.08 0.13 −0.04 0.10 −0.07
−44.85 −75.12 −96.30 −117.77 −150.84 −183.37
mD‑mannitol = 0.1000 mol·kg−1 −0.02 0.2000 −0.03 0.2200 0.06 0.2500 0.08 0.2800 −0.01 0.3000 −0.13 0.3200
0.1017 0.1115 0.1270 0.1413 0.1509 0.1622
−204.99 −227.41 −259.00 −292.91 −315.10 −333.22
−0.04 0.01 0.11 0.04 −0.06 0.00
0.0500 0.0800 0.1000 0.1200 0.1500 0.1800
0.0257 0.0413 0.0513 0.0614 0.0763 0.0916
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Table 1. continued mi mol·kg
ΔdilHm
mf −1
mol·kg
−1
J·mol
−1
0.0500 0.0800 0.1000 0.1200 0.1500 0.1800
0.0258 0.0412 0.0515 0.0616 0.0769 0.0921
−45.71 −73.59 −92.91 −113.06 −144.20 −176.15
0.0500 0.0800 0.1000 0.1200 0.1500 0.1800
0.0262 0.0417 0.0521 0.0623 0.0779 0.0929
−40.75 −67.20 −85.80 −105.69 −135.76 −167.95
0.0500 0.0800 0.1000 0.1200 0.1500 0.1800
0.0262 0.0418 0.0522 0.0626 0.0781 0.0934
−33.83 −57.52 −74.93 −93.01 −121.94 −152.68
0.0500 0.0800 0.1000 0.1200 0.1500 0.1800
0.0260 0.0417 0.0519 0.0624 0.0777 0.0928
−27.45 −47.22 −62.57 −78.72 −105.42 −134.19
0.0500 0.0800 0.1000 0.1200 0.1500 0.1800
0.0262 0.0420 0.0524 0.0626 0.0781 0.0935
−18.91 −35.85 −48.84 −63.49 −87.07 −112.76
δ
mi −1
J·mol
mD‑mannitol −0.04 0.02 0.09 0.04 −0.08 −0.14 mD‑mannitol −0.03 0.03 0.06 −0.07 0.00 −0.04 mD‑mannitol −0.03 0.05 −0.04 0.10 −0.07 −0.10 mD‑mannitol −0.05 0.06 0.07 −0.05 −0.10 0.04 mD‑mannitol −0.02 0.02 0.05 −0.01 −0.09 0.05
ΔdilHm
mf
mol·kg
−1
−1
δ
J·mol
J·mol−1
0.1020 0.1120 0.1269 0.1419 0.1518 0.1617
−197.94 −220.03 −253.27 −286.25 −308.58 −330.12
0.10 −0.05 0.08 0.09 −0.14 0.04
0.1029 0.1131 0.1292 0.1430 0.1531 0.1630
−189.87 −211.55 −242.69 −278.31 −299.91 −321.71
0.00 0.07 −0.03 −0.02 0.04 −0.02
0.1038 0.1136 0.1284 0.1437 0.1542 0.1629
−173.51 −194.81 −229.01 −261.02 −281.88 −305.70
0.01 0.10 0.02 −0.10 0.09 −0.03
0.1030 0.1131 0.1283 0.1433 0.1531 0.1632
−154.16 −174.72 −205.82 −237.60 −259.31 −280.15
0.09 −0.12 0.01 0.13 −0.11 0.02
0.1038 0.1135 0.1291 0.1441 0.1540 0.1637
−131.00 −150.69 −179.43 −210.34 −231.21 −252.57
0.06 −0.08 0.02 0.01 −0.02 0.00
mol·kg
−1
−1
= 0.2000 mol·kg 0.2000 0.2200 0.2500 0.2800 0.3000 0.3200 = 0.3000 mol·kg−1 0.2000 0.2200 0.2500 0.2800 0.3000 0.3200 = 0.5000 mol·kg−1 0.2000 0.2200 0.2500 0.2800 0.3000 0.3200 = 0.7000 mol·kg−1 0.2000 0.2200 0.2500 0.2800 0.3000 0.3200 = 0.9000 mol·kg−1 0.2000 0.2200 0.2500 0.2800 0.3000 0.3200
The symbols mi and mf represent the initial and final molality of HMBA, respectively. The symbols δ = ΔdilHm − ΔdilHm(calcd), where ΔdilHm(calcd) was calculated using eq 4 with coefficients obtained by fitting the data at the corresponding msolvent. mxylitol is the molality of xylitol, while mD‑mannitol is the molality of D-mannitol in the aqueous solutions. Standard uncertainties u are u(T) = 0.01 K, u(mi) = u(mf) = u(mxylitol) = u(mD‑mannitol) = 0.0001 mol·kg−1, and the combined expand uncertainties uc are uc(ΔdilHm) ≤ 0.04 J·mol−1 (level of confidence = 0.95). a
Shanghai, China) after calibration with twice-distilled water at 293.15 K (1.3325). 23 Distilled water was circulated into the apparatus through a thermostatically controlled bath maintained constant to ± 0.02 K. The experiments were repeated three times, and the results were presented as mean ± SD (standard deviation). The uncertainties of measured refractive indices were found to be within 0.0003.
The mixing-flow system is consist of a mixing cell, a reference cell, and a VS2-10R MIDI dual-channel pump. The pump was used to deliver the aqueous HMBA solutions and the polyol solvents through the mixing cell and the reference cell in succession. The determination of the flow rates was based on the weight of liquids through the pump during six minutes. The change of the flow rates before and after the experiment was no more than 0.1 %. Density Measurements. Densities of the solutions were determined with a quartz vibrating-tube densimeter (Anton Paar DMA 5000) controlled within ± 0.001 K with the precision of ± 2·10−3 kg·m−3. The densimeter was calibrated at 293.15 K with twice-distilled, freshly degassed water (9.98203·102 kg·m−3)21 and dry air (1.205 kg·m−3).22 Measurements were carried out in triplicate. The uncertainties of measured densities were found to be within 0.5 kg·m−3. Refractive Index Measurements. Refractive indices were determined with a model-2W refractometer (made in
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RESULTS AND DISCUSSION Enthalpy of Dilution. The enthalpies of dilution (ΔdilHm) of the solutions are calculated by the dilution thermal power (P) and the flow rate ( f 2):24 Δdil Hm − P(1 + m i M )/m i f2
(1)
in which mi is the initial molality before dilution of HMBA in pure water and aqueous xylitol or D-mannitol solutions and M is the molar mass of HMBA. The uncertainties of f 2, P, and mi 2458
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are ± 2·10−9 kg·s−1, ± 2·10−7 W, and ± 0.0001 mol·kg−1, respectively. The calculation equation of the final molality after dilution (mf) is as follows: mf = m i f2 /[f1 (1 + m i M ) + f2 ]
As for relative partial molar enthalpy (L2), it can be calculated from relative apparent molar enthalpy (L2ϕ) based on the following expression: ⎛ ∂L 2ϕ ⎞ L 2 = L 2ϕ + m ⎜ ⎟ ⎝ ∂m ⎠T , P , n
(2)
where f1 is the flow rate of water or mixed solvent. The determined results of ΔdilHm along with the uncertainties, the values of δ (defined in footnote of Table 1), mi and mf are listed in Table 1. The uncertainty of ΔdilHm was estimated to be within ± 0.04 J·mol−1. Excess enthalpy is a basic thermodynamic parameter when a solution with molality m is diluted. The relation between molar excess enthalpy (HmE) and molality m based on the assumption that aqueous xylitol or D-mannitol solution could be regarded as solvent can be expressed as: HmE = L 2ϕ = h2m + h3m2 + h4m3 + ...
1
(5)
The combination of eqs 4 and 5 results in the following equation: L 2 = 2h2m + 3h3m2 + 4h4m3 + ...
(6)
Figures 1 and 2 show the nearly linear relationship between L2 obtained from eq 6 and the molality m of aqueous xylitol and
(3)
in which L2ϕ represents the relative apparent molar enthalpy, h2, h3, and h4 are the enthalpic pairwise, triplet, and quartet interaction coefficients which reflect the interaction among two, three, or four solvated solute molecules, respectively. Therefore, when the HMBA solution is diluted from mi to mf, ΔdilHm can be obtained from the following equation: Δdil Hm = Hm E(mf ) − Hm E(m i ) = h2(mf − m i ) + h3(mf 2 − m i 2) + h4(mf 3 − m i 3) + ...
(4)
where HmE (mi) is the molar excess enthalpy of HMBA before dilution and HmE (mf) is that after dilution. The values of h2, h3, and h4 together with the standard derivations obtained from multiple regression analysis of experimental results are provided in Table 2.
Figure 1. Relative partial molar enthalpy L2 of HMBA versus the molality m of xylitol in aqueous solutions at 298.15 K. ▲, pure water; ▽, mxylitol = 0.1000 mol·kg−1; △, mxylitol = 0.2000 mol·kg−1; ▼, mxylitol = 0.3000 mol·kg−1; □, mxylitol = 0.5000 mol·kg−1; ●, mxylitol = 0.7000 mol·kg−1; ■, mxylitol = 0.9000 mol·kg−1.
Table 2. Enthalpic Interaction Coefficients (h2, h3, and h4) of HMBA in Aqueous Xylitol and D-Mannitol Solutions at T = 298.15 Ka msolvent
h2
h3
h4
SD
mol·kg−1
J·kg·mol−2
J·kg2·mol−3
J·kg3·mol−4
J·mol−1
0.0000
2489 ± 9
0.1000 0.2000 0.3000 0.5000 0.7000 0.9000
2113 ± 7 1959 ± 10 1711 ± 13 1489 ± 14 1158 ± 11 821 ± 11
0.1000 0.2000 0.3000 0.5000 0.7000 0.9000
1943 ± 10 1640 ± 13 1460 ± 6 1189 ± 11 829 ± 12 644 ± 7
Water −506 ± 34 Xylitol 209 ± 27 426 ± 42 1324 ± 50 1493 ± 54 2171 ± 42 2786 ± 44 D-Mannitol 950 ± 38 1590 ± 51 2183 ± 24 2725 ± 42 3260 ± 49 2988 ± 28
651 ± 51
0.07
−271 ± 41 −692 ± 37 −1832 ± 77 −1560 ± 82 −2166 ± 64 −2696 ± 67
0.06 0.09 0.10 0.11 0.09 0.09
−1471 −1895 −2653 −3112 −3484 −2648
0.08 0.10 0.05 0.08 0.10 0.06
± ± ± ± ± ±
58 78 37 64 74 42
Figure 2. Relative partial molar enthalpy L2 of HMBA versus the molality m of D-mannitol in aqueous solutions at 298.15 K. ▲, pure water; ▽, mD‑mannitol = 0.1000 mol·kg−1; △, mD‑mannitol = 0.2000 mol·kg−1; ▼, mD‑mannitol = 0.3000 mol·kg−1; □, mD‑mannitol = 0.5000 mol·kg−1; ●, mD‑mannitol = 0.7000 mol·kg−1; ■, mD‑mannitol = 0.9000 mol·kg−1. D-mannitol solutions, respectively. The phenomenon is a strong evidence that the interactions among three or more HMBA molecules could be neglected in the studied systems. So only h2
a
msolvent is the molality of solvent (xylitol or D-mannitol) in aqueous solutions, and SD is standard deviation. Standard uncertainties u are u(T) = 0.01 K, u(msolvent) = 0.0001 mol·kg−1. 2459
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are emphatically discussed here. The change tendencies of h2 with the increasing of molalities of solvent are demonstrated in Figure 3. Additionally, it is worth mentioning that polyols and saccharides are both polyhydroxy compounds. So it is necessary and meaningful to compare the influence of polyols and saccharides on the h2 of HMBA. The h2 values of HMBA in aqueous glucose solutions at 298.15 K7 are also included in Figure 3 to be compared with that in aqueous xylitol and D-mannitol solutions. Moreover, considering the thermodynamic meanings and revealed approximate regularity of h3 and h4, we also briefly discuss the interactions among three or four solvent mediated solute molecules. The values of the enthalpic interaction coefficients are decided by several weak interactions occurring among solute and solute as well as among solute and solvent. The interaction types in the HMBA−xylitol or mannitol−water system include: (i) hydrophobic−hydrophobic interaction among the apolar groups (hexamethylenes) of HMBA molecules (endothermic process leading to positive h2); (ii) hydrogen bond interactions (exothermic process), which include the carbonyl−amino group interaction and the carbonyl−hydroxyl interaction; (iii)
Figure 3. Enthalpic pairwise interaction coefficients (h2) of HMBA versus the molality of solvent in aqueous solutions at 298.15 K. △, glucose; ■, xylitol; ▲, D-mannitol. Enthalpic pairwise interaction coefficients of HMBA in aqueous glucose solutions can be obtained from ref 7.
Table 3. Values of Densities (ρ) and Apparent Molar Volumes (Vϕ) of HMBA in Aqueous Xylitol and D-Mannitol Solutions at T = 298.15 Ka mHMBA
10−3 ρ
106 Vϕ
mHMBA
10−3 ρ
106 Vϕ
mHMBA
10−3 ρ
106 Vϕ
mHMBA
mol·kg−1
kg·m−3
m3·mol−1
mol·kg−1
kg·m−3
m3·mol−1
mol·kg−1
kg·m−3
m3·mol−1
mol·kg−1
a
0.0000 0.1000 0.1500 0.2000
0.997047 0.997981 0.998443 0.998931
0.0000 0.1000 0.1500 0.2000
1.002002 1.002837 1.003263 1.003699
0.0000 0.1000 0.1500 0.2000
1.006925 1.007655 1.008036 1.008423
0.0000 0.1000 0.1500 0.2000
1.011756 1.012392 1.012725 1.013077
0.0000 0.1000 0.1500 0.2000
1.020961 1.021401 1.021651 1.021914
0.0000 0.1000 0.1500 0.2000
1.029873 1.030129 1.030296 1.030481
0.0000 0.1000
1.038327 1.038407
Water 0.2500 191.30 0.3000 191.24 0.3500 191.04 0.4000 mxylitol = 0.1000 mol·kg−1 0.2500 191.40 0.3000 191.27 0.3500 191.11 0.4000 mxylitol = 0.2000 mol·kg−1 0.2500 191.56 0.3000 191.39 0.3500 191.23 0.4000 mxylitol = 0.3000 mol·kg−1 0.2500 191.62 0.3000 191.46 0.3500 191.25 0.4000 mxylitol = 0.5000 mol·kg−1 0.2500 191.86 0.3000 191.63 0.3500 191.42 0.4000 mxylitol = 0.7000 mol·kg−1 0.2500 192.01 0.3000 191.73 0.3500 191.49 0.4000 mxylitol = 0.9000 mol·kg−1 0.2500 192.13 0.3000
10−3 ρ
106 Vϕ
kg·m−3
m3·mol−1
1.039103 1.039299
190.69 190.46
1.005355 1.005798 1.006244 1.006692
190.95 190.78 190.63 190.48
1.010997 1.011385 1.011779 1.012186
191.06 190.89 190.73 190.56
1.016819 1.017163 1.017523 1.017887
191.04 190.85 190.65 190.47
1.027483 1.027732 1.027988 1.028279
191.23 191.01 190.82 190.58
1.037876 1.038039 1.038212 1.038419
191.31 191.05 190.83 190.57
1.047688 1.047767 1.047861 1.047991
191.58 191.26 190.98 190.68
−1
0.999413 0.999901 1.000372 1.000882
190.90 190.76 190.68 190.50
1.004145 1.004594 1.005043 1.005502
190.93 190.78 190.65 190.50
1.008825 1.009231 1.009643 1.010059
191.05 190.88 190.73 190.58
1.013437 1.013805 1.014179 1.014572
191.07 190.89 190.73 190.55
1.022191 1.022488 1.022786 1.023104
191.22 191.00 190.82 190.63
1.030693 1.030922 1.031159 1.031412
191.23 190.98 190.77 190.56
1.038751 1.038914
191.24 190.96
0.1500 0.2000
1.038494 1.038611
0.0000 0.1000 0.1500 0.2000
1.003272 1.004081 1.004498 1.004927
0.0000 0.1000 0.1500 0.2000
1.009201 1.009885 1.010247 1.010614
0.0000 0.1000 0.1500 0.2000
1.015288 1.015852 1.016158 1.016484
0.0000 0.1000 0.1500 0.2000
1.026508 1.026835 1.027034 1.027251
0.0000 0.1000 0.1500 0.2000
1.037429 1.037522 1.037613 1.037731
0.0000 0.1000 0.1500 0.2000
1.047802 1.047644 1.047630 1.047644
mxylitol = 0.9000 mol·kg 191.82 0.3500 191.52 0.4000 mD‑mannitol = 0.1000 mol·kg−1 0.2500 191.44 0.3000 191.27 0.3500 191.09 0.4000 mD‑mannitol = 0.2000 mol·kg−1 0.2500 191.61 0.3000 191.41 0.3500 191.25 0.4000 mD‑mannitol = 0.3000 mol·kg−1 0.2500 191.69 0.3000 191.47 0.3500 191.24 0.4000 mD‑mannitol = 0.5000 mol·kg−1 0.2500 191.94 0.3000 191.68 0.3500 191.44 0.4000 mD‑mannitol = 0.7000 mol·kg−1 0.2500 192.17 0.3000 191.88 0.3500 191.60 0.4000 mD‑mannitol = 0.9000 mol·kg−1 0.2500 192.61 0.3000 192.22 0.3500 191.89 0.4000
mHMBA is the molality of HMBA in aqueous xylitol or D-mannitol solutions. Standard uncertainties u are u(T) = 0.01 K, u(mHMBA) = u(mxylitol) = u(mD‑mannitol) = 0.0001 mol·kg−1, and the combined expand uncertainties uc are u(ρ) ≤ 0.5 kg·m−3, u(Vϕ) ≤ 4·10−8 m3·mol−1. 2460
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Table 4. Limiting Partial Molar Volumes (Vϕ0), Transfer Partial Molar Volumes (ΔtrsVϕ0), and Experimental Slopes (SV) of HMBA in Aqueous Xylitol and D-Mannitol Solutions at T = 298.15 K msolvent mol·kg
−1
106 Vϕ0 m ·mol 3
−1
106 ΔtrsVϕ0 m ·mol 3
−1
106 SV m ·kg·mol 3
106 Vϕ0 −2
−1
m ·mol 3
Xylitol 0.0000 0.1000 0.2000 0.3000 0.5000 0.7000 0.9000
191.60 191.71 191.88 191.98 192.25 192.46 192.66
± ± ± ± ± ± ±
0.04 0.02 0.01 0.01 0.02 0.03 0.03
0.11 0.28 0.38 0.65 0.86 1.06
± ± ± ± ± ±
0.06 0.05 0.05 0.06 0.07 0.07
106 ΔtrsVϕ0 −1
m ·mol 3
106 SV m ·kg·mol−2 3
D-Mannitol
−2.74 −3.05 −3.29 −3.59 −4.09 −4.84 −5.59
± ± ± ± ± ± ±
0.15 0.06 0.04 0.05 0.06 0.10 0.10
hydrophilic−hydrophobic interaction of hydroxyl with hexamethylene (endothermic process); (iv) partial desolvation effects (endothermic process). The competitive balance of the above interactions leads to the difference of enthalpic interaction coefficients. First, Table 2 shows that the values of h2 are all positive which suggest that the interactions i, iii, and iv are predominant over interaction ii. Second, the h2 values monotonically decrease with the increasing molality of the solvent. It can be interpreted from the fact that the higher molality of polyols results in the stronger solute−solvent hydrogen bond interaction, which leads to the more negative contribution to h2. Third, the h2 values for the same molality of glucose, xylitol, and D-mannitol are in the order of h2 (HMBA in glucose solutions) > h2 (HMBA in xylitol solutions) > h2 (HMBA in D-mannitol solutions). The change tendency of h2 in aqueous D-mannitol and xylitol solutions may be due to the stronger hydrogen bond interactions (negative contribution to h2) in D-mannitol solutions caused by the more hydroxyl number of D-mannitol molecules. Additionally, glucose exists in aqueous solution mainly in the form of hexatomic ring called pyranose. The inductive effect of the hemiacetal oxygen makes the intramolecular interactions be strengthened. So the intermolecular hydrogen bond interactions between solute and solvent molecules are weakened, which lead to the increasing of h2 values. Finally, the values of h3 and h4 are positive and negative, respectively, over the whole polyol molality range except for in pure water. On one hand, when more than two molecules containing alkyl groups interact in aqueous solutions, two molecules will have more chance to associate side-by-side.25 If another or more molecules then participate in the triplet or quartet interaction in a way similar to the two cosphere molecules, the change tendency of h3 and h4 would be similar to that of h2. For example, the values of h3 and h4 would be positive in our investigated system. On the other hand, solventseparated association could take place under the participation of polyol molecules.26 The solvent separated association will increase the hydrophobic hydration shell of the alkyl groups by means of mutual shielding effects. This will increase the difficulty of hydrophobic−hydrophobic interaction, accompanied by the reduction of the positive contribution to hn. That is, the solvent-separated association will cause a negative contribution to enthalpic interaction coefficients.27 It is the competition of the above contrary interaction that leads to the positive h3 and negative h4.
191.60 191.75 191.94 192.07 192.36 192.67 193.19
± ± ± ± ± ± ±
0.04 0.01 0.01 0.02 0.02 0.03 0.04
0.15 0.34 0.47 0.76 1.07 1.59
± ± ± ± ± ±
0.05 0.05 0.06 0.06 0.07 0.08
−2.74 −3.19 −3.48 −4.06 −4.45 −5.32 −6.35
± ± ± ± ± ± ±
0.15 0.04 0.04 0.07 0.08 0.10 0.14
Figure 4. Variation of limiting partial molar volume of HMBA (Vϕ0) versus the molality of solvent in aqueous solution at 298.15 K. ■, xylitol; ▲, D-mannitol.
Figure 5. Variation of experimental slope (SV) versus the molality of solvent in aqueous solution at 298.15 K. ■, xylitol; ▲, D-mannitol.
Volumetric Properties. The calculations of the apparent molar volumes (Vϕ) of HMBA were based on the following equation:28 Vϕ = M /ρ − 1000(ρ − ρ0 )/(mρρ0 )
(7)
where ρ, ρ0, M, and m are the density of solution and solvent and molar mass and molality of the solute (HMBA), respectively. The uncertainty of m was ± 0.0001 mol·kg−1. 2461
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Table 5. Refractive Indices (nD) and Molar Refraction at the Sodium-D line (RD) of HMBA in Aqueous Xylitol and D-Mannitol Solutions at T = 298.15 Ka 106 RD
mHMBA mol·kg
a
−1
nD
0.0000 0.1000 0.1500 0.2000
1.3320 1.3348 1.3363 1.3382
0.0000 0.1000 0.1500 0.2000
1.3341 1.3371 1.3386 1.3400
0.0000 0.1000 0.1500 0.2000
1.3361 1.3389 1.3404 1.3420
0.0000 0.1000 0.1500 0.2000
1.3382 1.3411 1.3427 1.3441
0.0000 0.1000 0.1500 0.2000
1.3423 1.3448 1.3467 1.3480
0.0000 0.1000 0.1500 0.2000
1.3460 1.3489 1.3503 1.3517
0.0000 0.1000
1.3494 1.3524
−1
m ·mol 3
106 RD
mHMBA mol·kg
−1
Water 3.7054 0.2500 3.7981 0.3000 3.8458 0.3500 3.8976 0.4000 mxylitol = 0.1000 mol·kg−1 3.7579 0.2500 3.8541 0.3000 3.9024 0.3500 3.9498 0.4000 mxylitol = 0.2000 mol·kg−1 3.8093 0.2500 3.9049 0.3000 3.9539 0.3500 4.0041 0.4000 mxylitol = 0.3000 mol·kg−1 3.8620 0.2500 3.9600 0.3000 4.0107 0.3500 4.0595 0.4000 mxylitol = 0.5000 mol·kg−1 3.9675 0.2500 4.0641 0.3000 4.1195 0.3500 4.1685 0.4000 mxylitol = 0.7000 mol·kg−1 4.0694 0.2500 4.1730 0.3000 4.2244 0.3500 4.2758 0.4000 mxylitol = 0.9000 mol·kg−1 4.1692 0.2500 4.2766 0.3000
nD
106 RD
mHMBA
−1
m ·mol 3
mol·kg
−1
nD
−1
m ·mol 3
106 RD
mHMBA mol·kg
−1
nD
m3·mol−1
1.3592 1.3602
4.5385 4.5869
1.3420 1.3434 1.3448 1.3461
4.0106 4.0583 4.1062 4.1531
1.3440 1.3453 1.3467 1.3480
4.0734 4.1209 4.1696 4.2172
1.3467 1.3481 1.3493 1.3510
4.1427 4.1921 4.2394 4.2923
1.3512 1.3526 1.3538 1.3551
4.2751 4.3261 4.3750 4.4250
1.3560 1.3574 1.3588 1.3600
4.4110 4.4636 4.5164 4.5669
1.3597 1.3612 1.3625 1.3640
4.5362 4.5915 4.6447 4.7002
−1
1.3393 1.3409 1.3419 1.3431
3.9413 3.9903 4.0332 4.0781
1.3416 1.3429 1.3442 1.3456
3.9994 4.0459 4.0926 4.1404
1.3434 1.3449 1.3462 1.3475
4.0522 4.1016 4.1489 4.1964
1.3457 1.3470 1.3483 1.3498
4.1105 4.1584 4.2064 4.2566
1.3492 1.3505 1.3521 1.3533
4.2166 4.2658 4.3184 4.3667
1.3530 1.3542 1.3556 1.3569
4.3263 4.3756 4.4273 4.4780
1.3565 1.3578
4.4338 4.4856
0.1500 0.2000
1.3538 1.3551
0.0000 0.1000 0.1500 0.2000
1.3349 1.3379 1.3391 1.3408
0.0000 0.1000 0.1500 0.2000
1.3367 1.3398 1.3412 1.3425
0.0000 0.1000 0.1500 0.2000
1.3398 1.3423 1.3440 1.3451
0.0000 0.1000 0.1500 0.2000
1.3440 1.3470 1.3485 1.3499
0.0000 0.1000 0.1500 0.2000
1.3490 1.3516 1.3530 1.3545
0.0000 0.1000 0.1500 0.2000
1.3532 1.3561 1.3573 1.3585
mxylitol = 0.9000 mol·kg 4.3293 0.3500 4.3810 0.4000 mD‑mannitol = 0.1000 mol·kg−1 3.7724 0.2500 3.8690 0.3000 3.9144 0.3500 3.9650 0.4000 mD‑mannitol = 0.2000 mol·kg−1 3.8291 0.2500 3.9283 0.3000 3.9766 0.3500 4.0239 0.4000 mD‑mannitol = 0.3000 mol·kg−1 3.8983 0.2500 3.9931 0.3000 4.0453 0.3500 4.0913 0.4000 mD‑mannitol = 0.5000 mol·kg−1 4.0191 0.2500 4.1225 0.3000 4.1743 0.3500 4.2252 0.4000 mD‑mannitol = 0.7000 mol·kg−1 4.1486 0.2500 4.2512 0.3000 4.3037 0.3500 4.3573 0.4000 mD‑mannitol = 0.9000 mol·kg−1 4.2711 0.2500 4.3804 0.3000 4.4323 0.3500 4.4843 0.4000
Standard uncertainties u are u(T) = 0.01 K, u(mHMBA) = 0.0001 mol·kg−1, and the combined expand uncertainties uc are u(nD) ≤ 0.0003, u(RD) ≤ 6.4·10−9 m3·mol−1.
plotted in Figures 4 and 5. From the data in the tables, we can conclude: (a) The values of V0ϕ and ΔtrsV0ϕ are all positive in our experimental conditions, which are contrary to the negative values of SV. This discrepancy may be interpreted from the different solute−solute interactions (embodied in the value of SV) and solute−solvent interactions (reflected by the value V0ϕ and ΔtrsV0ϕ). The negative values of SV suggest that the hydrophobic− hydrophobic interactions (negative contribution to SV) are predominant over the hydrogen bond interactions (positive contribution to SV) between two HMBA molecules. The conclusion coincides with the above discussion on enthalpic interaction coefficient h2. At the same time, the positive values of V0ϕ and ΔtrsV0ϕ may be interpreted from the fact that the carbonyl− hydroxyl hydrogen bond interactions (positive contribution to V0ϕ and ΔtrsV0ϕ) surpass the hydrophilic− hydrophobic interaction of hydroxyl with hexamethylene (negative contribution to V0ϕ and ΔtrsV0ϕ) in the studied ternary systems. Combined with the discussion of enthalpic interaction coefficients, it can be drawn that
Densities (ρ) of HMBA in pure water, aqueous xylitol, and D-mannitol solutions at 298.15 K and the calculated values of Vϕ along with the uncertainties of ρ and ρ0 are listed in Table 3. The uncertainty of Vϕ calculated using the law of propagation of uncertainty was found to be within ± 4·10−8 m3·mol−1. The limiting partial molar volume of HMBA (V0ϕ) was obtained by least-squares fitting to the following equation Vϕ = V ϕ0 + SV m
(8)
where SV is the fitted slope. Partial molar volume of transfer at infinite dilution (ΔtrsV0ϕ) of HMBA from pure water to the aqueous xylitol or D-mannitol solutions was calculated from the equation: ΔtrsV ϕ0 = V ϕ0(in aqueous xylitol or D‐mannitol solutions) − V ϕ0(in pure water)
(9)
The calculated values of V0ϕ, SV, and ΔtrsV0ϕ along with their standard deviations are summarized in Table 4. The variations of V0ϕ and SV versus the molalities of xylitol and D-mannitol are 2462
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hydrophobic−hydrophobic interactions of the apolar group of solute molecules (HMBA) may be the most dominant force. (b) Both V0ϕ and ΔtrsV0ϕ values of D-mannitol are larger than that of xylitol of the same molality, while the SV value for D-mannitol system is more negative than that for the xylitol system. The more positive values of V0ϕ and ΔtrsV0ϕ of D-mannitol may be due to the more number of OH groups in D-mannitol which results in stronger hydrogen bond interactions. The higher negative value of SV for D-mannitol may be derived from the supposition that the enhancement of solute−solvent interactions caused by the number of OH groups weakens the hydrogen bond interactions between two HMBA molecules. (c) The values of SV decrease with the increasing molalities of D-mannitol or xylitol solutions, while the change trend for the values of V0ϕ is contrary. The interpretation for this phenomenon is similar to the discussion of the hydroxyl group effect on V0ϕ and SV of D-mannitol and xylitol of the same molality. Refractive Index. Molar refraction at the sodium-D line (RD) were computed with the Lorentz−Lorenz equation29 RD = [(nD2 − 1)/(nD2 + 2)]( ∑ xiMi /ρ)
determined with isothermal microcalorimetry at T = 298.15 K. The enthalpic interaction coefficients (h2, h3, and h4) have been obtained according to the excess enthalpy theory, and their variation trends have been interpreted on the basis of various weak intermolecular interactions that take place in the investigated ternary systems. The results show that the number of hydroxyl in polyols has an important effect on the interaction of HMBA molecules. (2) Apparent molar volumes (Vϕ), limiting partial molar volumes (Vϕ0 ), and transfer partial molar volumes (ΔtrsV0ϕ) of HMBA from water to aqueous xylitol or D-mannitol solutions have been acquired from the values of densities (ρ). The values of V0ϕ and ΔtrsV0ϕ are all positive in our experimental conditions. Both V0ϕ and ΔtrsV0ϕ values of D-mannitol are larger than that of xylitol of the same molality. (3) Molar refractions at the sodium-D line have been calculated from refractive indices (nD). The calculated values of RD are all positive and increase with the molalities of solvent.
■
(10)
where nD, Mi, and xi are the refractive indices, molecular weight, and mole fraction of the i-th component of the mixture, respectively. The calculated values of RD and the measured values of nD along with the uncertainties of RD and nD are given in Table 5. The uncertainty of RD was calculated to be within ± 6.4·10−9 m3·mol−1. Owing to the more stronger solute−solvent interactions, an obvious increasing trend of RD with the increase of molality of solvent is shown in Figure 6.
*E-mail:
[email protected]. Funding
This work was financially supported by the National Science Foundation of China (No. 21103079) and Innovation Program for Graduate Education of Shandong Province (SDYC 10044/ LCUYZ 10008). Notes
The authors declare no competing financial interest.
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REFERENCES
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Figure 6. Variation of molar refraction at the sodium-D line (RD) versus the molality of HMBA in pure water and aqueous xylitol solutions at 298.15 K. ■, pure water; ●, mxylitol = 0.1000 mol·kg−1; ▲, mxylitol = 0.2000 mol·kg−1; ▼, mxylitol = 0.3000 mol·kg−1; △, mxylitol = 0.5000 mol·kg−1; ▽, mxylitol = 0.7000 mol·kg−1; □, mxylitol = 0.9000 mol·kg−1. (Since the tendency of RD versus mHMBA in aqueous D-mannitol solutions is very close to xylitol, RD versus mHMBA in aqueous D-mannitol solutions can be omitted.)
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AUTHOR INFORMATION
Corresponding Author
CONCLUSIONS
(1) The dilution enthalpies of HMBA in aqueous solutions of xylitol and D-mannitol of different molalities have been 2463
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