Article pubs.acs.org/jced
Thermodynamic Functions for Solubility of 1‑Hydroxybenzotriazole in Sixteen Solvents at Temperatures from (278.15 to 313.15) K and Mixing Property of Mixtures Jiao Chen, Gaoquan Chen, Chao Cheng, Yang Cong, Cunbin Du, and Hongkun Zhao* College of Chemistry & Chemical Engineering, YangZhou University, YangZhou, Jiangsu 225002, People’s Republic of China S Supporting Information *
ABSTRACT: Solubility of 1-hydroxybenzotriazole in 16 neat solvents including methanol, ethanol, n-propanol, isopropanol, acetone, butanone, isoamyl alcohol, nhexanol, n-heptanol, isooctyl alcohol, N,N-dimethylformamide (DMF), dimethyl sulfoxide (DMSO), ethyl acetate, acetonitrile, 1,4-dioxane, and toluene was measured using the method of isothermal saturation over a temperature range from (278.15 to 313.15) K under atmospheric pressure (101.1 kPa). The mole fraction solubility of 1hydroxybenzotriazole in the selected solvents increased with an increase of temperature. They followed the order from high to low in studied neat solvents: DMF > DMSO > ethanol > n-propanol > isopropanol > methanol > butanone > acetone >1,4-dioxane > n-heptanol > n-hexanol > isoamyl alcohol > isooctyl alcohol > ethyl acetate > acetonitrile > toluene. The obtained solubility data of 1hydroxybenzotriazole in the studied solvents were correlated with the λh equation, modified Apelblat equation, and NRTL and Wilson models. The largest value of root-mean-square deviation was 7.65 × 10−4, and relative average deviation, 4.21%. The values of root-mean-square deviation obtained with the modified Apelblat equation were smaller than those with the other equations for a given solvent. By and large, the four thermodynamic models all provided acceptable results for 1-hydroxybenzotriazole in the studied solvents. Moreover, the apparent dissolution enthalpy and the mixing enthalpy, mixing Gibbs energy, mixing entropy, reduced excess enthalpy, and activity coefficient at infinitesimal concentration were derived. The obtained solubility and thermodynamic studies could provide the fundamental data for optimizing the reaction and purification procedure of 1-hydroxybenzotriazole.
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INTRODUCTION 1-Hydroxybenzotriazole (CAS Reg. No. 2592-95-2, abbreviated as HOBT, structure shown in Figure S1) is used for reducing the racemization in peptide syntheses, in particular in syntheses of dicyclohexylcarbodiimide1,2 or active ester.3,4 In addition, it serves as particularly effective mediator substance in an enzymatic bleaching process by atmospheric oxidation in the paper and pulp industry.3−5 HOBT can also exhibit corrosion inhibitive properties toward Cu6,7 and Fe.8,9 Several methods have been proposed for synthesizing HOBT.10−14 The traditional preparation method of HOBT consumes a large amount of raw material and produces a large amount of wastewater.8−12 Recently, in order to overcome these disadvantages, an improved process for synthesis of HOBT was proposed in China, where organic solvent, such as alcohols with high boiling points,12 toluene,13 or dimethyl sulfoxide (DMSO) and N,N-dimethylformamide (DMF),14 is introduced into the reaction system. This is a very promising method for HOBT production. However, the solubility of HOBT in organic solvent affects greatly the reaction rate and the yield of product. In order to optimize the technical conditions and speed up the industrial process of this method, knowledge of solubility as well as solution thermodynamics for HOBT in different solvents is urgently needed. © XXXX American Chemical Society
Furthermore, as an important substance in peptide syntheses and enzymatic bleaching, pure 1-hydroxybenzotriazole must be needed, because impurities in the 1-hydroxybenzotriazole may influence the racemization and bleaching effect of synthesized material. Thus, it is a necessary step to purify the crude HOBT in industry. In recent years, Huang and co-workers put forward a purification method of crude HOBT via solvent crystallization in mixed solvents of dichloromethane and methanol.13 However, the boiling point of dichloromethane is very low. Considering the safety problem, it is not suitable for use in industry. So it is necessary to develop the crystallization process of HOBT in other solvent systems. It is well-known that crystallization in solvent is a common method in the purification process of solids. The solid solubility in solvent is of great significance and plays an essential role in understanding the phase equilibrium or solid−liquid equilibrium in the developing of a crystallization route. The solubility data are necessary in designing the crystallization process and conducting further thermodynamic research. Solvent crystallization is an effective method to purify HOBT. Although the solubility of HOBT is very important in the solvent selection Received: April 3, 2017 Accepted: June 9, 2017
A
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relationship between the solubility of solid in different solvents and temperature may be obtained and expressed as eq 4.20
and purification process, no solubility has been determined in open publications. On the basis of the considerations mentioned above, in this work, we determine the solubility of HOBT in some solvents and develop better models for describing these behaviors. From many species of organic solvents, we chose 16 commonly used organic solvents (methanol, ethanol, isopropanol, n-propanol, butanone, acetone, isoamyl alcohol, n-hexanol, n-heptanol, isooctyl alcohol, N,N-dimethylformamide (DMF), dimethyl sulfoxide (DMSO), acetonitrile, ethyl acetate, toluene, and 1,4dioxane) in the industrial purification process; and the purposes of the work are to (1) determine the solubility of HOBT in the 16 organic solvents at elevated temperatures; (2) correlate solubility by using different solubility models; and (3) compute the thermodynamic properties for the dissolution procedure of HOBT in different neat solvents.
⎤ ⎡ Λ12 Λ 21 ln γ1 = −ln(x1 + Λ12x 2) + x 2⎢ − ⎥ x 2 + Λ 21x1 ⎦ ⎣ x1 + Λ12x 2 (5)
⎤ ⎡ Λ 21 Λ12 ln γ2 = −ln(x 2 + Λ 21x1) + x1⎢ − ⎥ x1 + Λ12x 2 ⎦ ⎣ x 2 + Λ 21x1 (6)
SOLUBILITY MODELING So as to find an appropriate equation to express the solubility behavior of HOBT, four models are employed to correlate the determined solubility values, which are the modified Apelblat equation,15,16 λh equation,17 Wilson model,18 and NRTL model.19 Modified Apelblat Equation. The solubility in mole fraction dependence upon temperature T can be expressed with the modified Apelblat equation,15,16 which is described as B + C ln(T /K ) T /K
(1)
V2 ⎛ λ12 − λ 22 ⎞ V2 ⎛ Δλ12 ⎞ ⎟ = exp⎜ − ⎟ exp⎜ − V1 ⎝ RT ⎠ V1 ⎝ RT ⎠
(7)
Λ 21 =
⎛ Δλ ⎞ V1 ⎛ λ 21 − λ11 ⎞ V ⎟ = 1 exp⎜ − 21 ⎟ exp⎜ − V2 ⎝ RT ⎠ V2 ⎝ RT ⎠
(8)
N
ln γi =
∑ j = 1 τjiGjixj N
∑i = 1 Gijxi
N
+
∑ j=1
N ⎡ ∑ xτ G ⎤ ⎢τ − i = 1 i ij ij ⎥ ij N N ∑i = 1 Gijxi ⎢⎣ ∑i = 1 Gijxi ⎥⎦
xjGij
(9)
(2)
Gji = exp( −αjiτji)
(10)
αij = αji
(11)
τij =
where λ and h are adjustable equation parameters; Tm is the melting temperature of HOBT in kelvins. The λ and h are equation parameters. Wilson Model. Once a solid−liquid equilibrium is built at a fixed pressure and temperature, the solid solubility in neat solvents can be expressed in a universal form as eq 3,20 ln(x·γ ) =
Λ12 =
where Vi denotes the molar volume of component i. Δλij are the interaction parameters (J·mol−1) which are in relation to interaction energy between the components i and j. NRTL Model. Renon and Prausnitz19 put forward the NRTL equation based on the local composition model as eqs 9−12.
where x is the solubility of HOBT in mole fraction in ten organic solvents; A, B, and C are the adjustable parameters in this equation. λh Equation. The λh equation is described as eq 2.17 The equation has an excellent effect for describing the solubility behavior of HOBT in neat solvent: ⎛ 1 ⎡ λ(1 − x) ⎤ 1 ⎞ ln⎢1 + − ⎟ ⎥ = λh⎜ ⎦ ⎣ x Tm/K ⎠ ⎝ T /K
(4)
In a binary liquid−solid system, the activity coefficient can be described by the Wilson equation as18
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ln x = A +
ΔfusH ⎛ 1 1 ⎞ − ⎜ ⎟ R ⎝ Tm/K T /K ⎠
ln(x i·γi) =
gij − gjj RT
=
Δgij RT
(12)
Δgij are model parameters relevant to the energy of interaction between molecular pairs. The value of nonrandom parameter α usually varies from 0.20 to 0.47. Assuming that the temperature dependence of the parameters of interaction in the NRTL model and Wilson model is linear,22 τij in the NRTL model and Λij in the Wilson model may be described as eqs 13 and 14,
⎞ ΔV Ttp ΔHtp ⎛ 1 1 ⎞ ΔCp ⎛ Ttp ⎜ − ⎟⎟ − − + 1⎟ − (p − ptp ) ⎜ln R ⎜⎝ Ttp T⎠ R ⎝ T T RT ⎠
(3)
τij = aij +
where ΔCp and ΔV refer respectively to the difference of volume and heat capacity between in liquid state and in solid state at fusion temperature; also x is the mole fraction solubility of HOBT; γ represents the activity coefficient of solute; ΔHtp denotes melting enthalpy at triple point temperature Ttp. Under a given pressure, the terms comprising ΔCp in eq 3 may be neglected.21 In addition, for liquid−solid equilibrium, slight variation of pressure does not affect significantly on equilibrium.21 It is not easy to obtain the triple point temperature Ttp and enthalpy ΔHtp for many substances. On the other hand, the fusion temperature Tm is very close to the triple point temperature Ttp. So, substituting Ttp and ΔHtp with Tm and ΔfusH, respectively, a simple equation describing the
Λij =
bij T/K
⎡ ⎛ bij ⎞⎤ exp⎢ −⎜aij + ⎟⎥ ⎢⎣ ⎝ T /K ⎠⎥⎦ Vi
(13)
Vj
(14)
where aij and bij designate the parameters that are independent of composition and temperature.
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EXPERIMENTAL SECTION Materials and Apparatus. HOBT having a purity of 0.980 in mass fraction was bought from Beijing HWRK Chemical Co., Ltd. The crude HOBT was crystallized in methanol three times. The purified material had a mass fraction of 0.992, which B
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was withdrawn with the 3 mL syringe connected with a 0.2 μm pore filter precooled or preheated in the thermostatic bath. The extracted liquid was transferred immediately to a 25 mL preweighed volumetric flask. Then it was diluted to 25 mL with the same solvent, and 1 μL of the liquid was removed to analyze by HPLC. When the solubility determined was made at one temperature, the residue was heated to another one, and the measurement process was carried out repeatedly. During the experimental process, the local atmospheric pressure was about 101.1 kPa. The mole fraction solubility (xe) of HOBT in neat solvent was evaluated using eq 15,
was confirmed using an Agilent-1260 high-performance liquid phase chromatograph (HPLC). The solvents of ethanol, methanol, isopropanol, n-propanol, acetone, butanone, toluene, acetonitrile, 1,4-dioxane, and ethyl acetate were purchased from Sinopharm Chemical Reagent Co., Ltd., China. The purities of the solvents were no less than 0.993 in mass fraction, which were confirmed by gas chromatography (Agilent 7890). The details of HOBT and the solvents were collected and are tabulated in Table S1. The mass of the solvent, solute, and saturated solution was analyzed by using an analytical balance (model CPA225D) purchased from Sartorius Scientific Instrument (Beijing), of which the standard uncertainty was 0.0001 g. The experimental apparatus is given in Figure S2. It comprised a 100 mL jacketed glass vessel, a magnetic stirrer system, and a circulating water bath employed for keeping the solution temperature. The system temperature was regulated by using a thermostatic water bath with a model of DZKW-4 and having standard uncertainty of 0.02 K, which was provided by Ningbo Scientz Biotechnology Co., Ltd. In order to avoid escaping of the solvent, a condenser was employed and attached to the jacketed glass vessel. Before experiment, the reliability of experimental apparatus was verified by measuring the benzoic acid solubility in toluene.22,23 Melting Properties Determination. The fusion temperature Tm of HOBT was reported in the previous publications,10,24−26 but the fusion enthalpy (ΔfusH) of HOBT has not been reported so far. Besides, there is a large difference among the determined values of melting temperature. In order to describe the solubility behavior with thermodynamic models, the fusion temperature and melting enthalpy of HOBT were determined by a Simultaneous Thermal Analyzer (STA 409PC Luxx, NETZSCH) under a nitrogen gas. With indium as the reference material, the instrument was precalibrated in advance. Around 3 mg of HOBT was introduced to a pan and heated with 2 K·min−1 at temperatures ranging from (300 to 433) K. The standard uncertainties of the experiments were evaluated to be 0.5 K for temperature, and 0.4 kJ·mol−1 for the melting enthalpy. Solubility Determination. In the present work, the liquid−solid equilibria for the HOBT + solvent mixtures were constructed by using the isothermal dissolution method27−30 from (278.15 to 313.15) K under atmospheric pressure, and the HPLC was employed to determine the HOBT solubility in the selected solvents. Around 60 mL of solvent and some excessive amount of HOBT were introduced into the 100 mL jacketed glass vessel. The temperature of the system was kept at a desired value by circulating water through the outer jacket. A mercury glass microthermometer having a standard uncertainty of 0.02 K showed the true temperature of the solution. A magnetic stirrer was employed to make the solution mixed sufficiently. So as to get the equilibration time, the liquor was withdrawn at intervals of 2 h with a 3 mL syringe attached with a 0.2 μm pore syringe filter, and then tested by the high-performance liquid phase chromatograph (HPLC, Agilent-1260). Once the composition of liquor did not vary, the solution was assumed to have reached equilibrium. In order to make sure that sampling was carried out at equilibration conditions, a primary experiment was made where the liquid composition was determined as a function of time. The results illustrated that 13 h was sufficient to make the solution equilibrium. The magnetic stirrer was stopped. 30 min later, about 3 mL of equilibrium liquid phase
xe =
m1/M1 m1/M1 + m2 /M 2
(15)
where m1 and m2 are the mass of HOBT and corresponding solvent, respectively, and M1 and M2 are the molar mass of HOBT and the solvent. Analysis Method. The content of HOBT in equilibrium liquor was analyzed using the Agilent-1260 high-performance liquid-phase chromatograph (HPLC). The chromatographic column was a reverse phase column with a model of LP-C18 (250 mm × 4.6 mm), the temperature of which was set to 303.15 K during the analysis. The wavelength of the UV detector was 244 nm, which was determined by continuous UV scanning. Pure methanol was used as the mobile phase, the flow rate of which was 1.2 mL·min−1. Each measurement was made three times, and three samples were withdrawn for certain solution at a fixed temperature. The relative standard uncertainty of solubility in mole fraction was estimated to be 2.7%.
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RESULTS AND DISCUSSION Melting Properties of HOBT. The DSC curve of HOBT is shown in Figure 1. From the results of DSC analysis, the fusion
Figure 1. DSC scan of HOBT.
temperature (Tm) and melting enthalpy ΔfusH of HOBT are 424.26 K and 20.05 kJ·mol−1, respectively. The fusion temperature Tm obtained in this work is smaller than the values reported by Ikawa,25 and greater than that reported by Hammud24 and Borsche,26 but is very close to that reported by Huang.10 The case may be due to difference in samples, equipment, and/or determination conditions. Based on the fusion enthalpy ΔfusH of HOBT, the value of fusion entropy ΔfusS for HOBT is computed to be 47.26 J·(K· mol)−1 with the classical thermodynamics property: C
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Table 1. Experimental Mole Fraction Solubility (x) of HOBT in Different Solvents at the Temperature Range from T = (278.15 to 313.15) K under 101.1 kPaa 100x T/K
methanol
ethanol
n-propanol
isopropanol
2-butanone
acetone
278.15 280.65 283.15 285.65 288.15 290.65 293.15 295.65 298.15 300.65 303.15 305.65 308.15 310.65 313.15
2.232 2.388 2.542 2.739 2.935 3.138 3.363 3.581 3.861 4.152 4.445 4.799 5.218 5.622 6.093
3.181 3.311 3.553 3.771 4.057 4.327 4.621 4.928 5.281 5.655 6.050 6.508 6.967 7.457 8.017
2.972 3.185 3.397 3.622 3.871 4.124 4.402 4.721 5.018 5.352 5.731 6.119 6.553 6.976 7.490
2.476 2.613 2.813 3.006 3.199 3.415 3.672 3.920 4.208 4.508 4.806 5.147 5.530 5.919 6.370
1.574 1.694 1.814 1.954 2.105 2.245 2.408 2.590 2.785 2.988 3.225 3.467 3.720 4.018 4.327
1.389 1.486 1.596 1.712 1.842 1.983 2.138 2.294 2.464 2.659 2.855 3.060 3.302 3.549 3.833
100x T/K
ethyl acetate
acetonitrile
toluene
278.15 280.65 283.15 285.65 288.15 290.65 293.15 295.65 298.15 300.65 303.15 305.65 308.15 310.65 313.15
0.5050 0.5548 0.6062 0.6763 0.7449 0.8206 0.9077 1.009 1.152 1.298 1.487 1.686 1.928 2.194 2.474
0.2291 0.2488 0.2707 0.2952 0.3221 0.3476 0.3805 0.4143 0.4491 0.4882 0.5309 0.5802 0.6311 0.6854 0.7493
0.001105 0.001203 0.001496 0.001605 0.001985 0.002167 0.002487 0.002849 0.003256 0.003615 0.004282 0.004871 0.005561 0.006199 0.006923
1,4-dioxane
isoamyl alcohol
n-hexanol
1.452 1.582 1.713 1.869 2.024 2.245 2.466 2.721 2.976 3.309 3.642
1.092 1.135 1.182 1.228 1.275 1.321 1.370 1.426 1.483 1.549 1.609 1.673 1.743 1.810 1.882
1.139 1.182 1.234 1.289 1.340 1.394 1.452 1.519 1.589 1.660 1.738 1.818 1.898 1.976 2.058
100x T/K
n-heptanol
isooctyl alcohol
DMF
DMSO
278.15 280.65 283.15 285.65 288.15 290.65 293.15 295.65 298.15 300.65 303.15 305.65 308.15 310.65 313.15
1.188 1.235 1.290 1.342 1.396 1.457 1.519 1.584 1.653 1.731 1.818 1.901 2.005 2.098 2.203
1.080 1.115 1.153 1.193 1.232 1.275 1.319 1.372 1.428 1.485 1.543 1.610 1.677 1.748 1.819
4.124 4.644 5.220 5.865 6.456 7.199 7.942 8.843 9.800 10.90 12.13 13.43 14.85 16.37 17.98
3.369 3.770 4.213 4.746 5.287 5.918 6.639 7.377 8.205 9.205 10.26 11.43 12.75 14.16 15.71
a
x denotes the experimental mole fraction solubility of HOBT at the studied temperature T; RD and RAD denote the relative deviation and the average absolute deviation, respectively. Standard uncertainties u are u(T) = 0.02 K, u(p) = 0.45 kPa; relative standard uncertainty ur is ur(x) = 0.027.
ΔfusS =
ΔfusH Tm
butanone, isoamyl alcohol, n-hexanol, n-heptanol, isooctyl alcohol, DMSO, DMF, acetonitrile, ethyl acetate, toluene, and 1,4-dioxane within the temperature range from (278.15 to 313.15) K is presented in Table 1 and graphically shown in Figure 2. Figure S3 is the van’t Hoff plots of ln(x) versus 1/T in
(16)
Solubility Data. The measured solubility of HOBT in mole fraction in ethanol, methanol, n-propanol, isopropanol, acetone, D
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Figure 2. Mole fraction solubility (x) of HOBT in selected solvents at different temperatures: ●, ethanol; ▲, n-propanol; ★, isopropanol; ■, methanol; ◇, n-heptanol; ○, n-hexanol; □, isoamyl alcohol; ☆, isooctyl alcohol; ▼, acetone; ◀, 1-butanone; ▶, DMF; ◆, DMSO; Δ; acetonitrile; ▽, ethyl acetate; ◁, toluene; ▷, dioxane. , calculated values via modified Apelblat equation.
different solvents. Figure 2 shows that the solubilities of HOBT in different solvents increase with increasing temperature. At a given temperature, the mole fraction solubility of HOBT is largest in DMF, and lowest in toluene. Figure 2 further reveals that the mole fraction solubility decreases according to the following order in different solvents: DMF > DMSO > ethanol > n-propanol > isopropanol > methanol > butanone > acetone >1,4-dioxane > n-heptanol > n-hexanol > isoamyl alcohol > isooctyl alcohol > ethyl acetate > acetonitrile > toluene. For the solvent of DMSO, the solubilities of HOBT have strong dependence on temperature. So this solvent is a suitable solvent to purify the crude HOBT. For the systems of HOBT + alcohol, the mole fraction solubility of HOBT decreases approximately with the decrease in solubility parameter of the selected alcohols except for methanol and isoamyl alcohol.31 The solubility parameter of toluene is lowest, so the HOBT solubility in toluene is lowest among the studied solvents. Besides, the solubility parameter of acetone molecule is larger than that of 2-butanone molecule, however the solubility of HOBT is smaller in acetone than in 2butanone. The trend in solubility for the acetone/2-butanone pair is the opposite of that for the similar structural change in the series acetone/2-butanone. It is noted that the solubility parameter of methanol molecule is larger than those of the other alcohols, however the solubility of HOBT is smaller in methanol than in ethanol, n-propanol, and isopropanol at a certain temperature. In addition, the HOBT molecule has a five-membered unsaturated ring structure composed of three nitrogen atoms, so it has large dipole moments and hence shows strong interactions of nonspecific dipole−dipole with the neat solvent molecules. It can form H-bonds with DMSO and DMF molecules with electron donor sites, which has a direct impact on the solubility. As a result, the solubility of HOBT in DMSO and DMF is relatively high. Generally, it is too complicated to elucidate the solubility behavior presented in Table 1 based on a single reason. This behavior may be due to many factors, e.g., solvent−solvent interactions, solute−solvent interactions, molecular shapes and sizes, and so on. Correlation and Calculation of Solubility. The solubilities of HOBT in the studied solvents are correlated by using eqs 1−12 via the nonlinear regression method. For the NRTL and Wilson model models, the objective function is expressed as eq 17.
F=
∑ (ln γie − ln γic)2
(17)
i=1
And for the λh equation and the modified Apelblat equation, the objective function is given as F=
∑ (xie − xic)2
(18)
i=1
Moreover, in order to evaluate the studied solubility models, the relative average deviation (RAD), relative deviation (RD), and root-mean-square deviation (RMSD) are used, which are defined as eqs 19, 20, and 21, respectively, RAD =
1 N e
RD =
N
∑ i=1
x −x xe
xie − xic xie
(19)
c
(20)
⎡ ∑N (x c − x e)2 ⎤1/2 i i ⎥ RMSD = ⎢ i = 1 ⎢⎣ ⎥⎦ N
(21)
γei
where ln denotes the logarithm of activity coefficient which is computed from eq 4; and ln γci is the logarithm of activity coefficient computed using solubility models. N denotes the number of experimental data points; xci is the evaluated solubility values of HOBT; and xei , the experimental ones. During the regression procedure, the densities of the selected solvents tabulated in Table S1 are taken from ref 32. The density of HOBT is computed with the Advanced Chemistry Development (ACD/Laboratories) Software V11.02 (© 1994− 2016 ACD/Laboratories); and the fusion temperature (Tm) and fusion enthalpy (ΔfusH) of HOBT are taken from this work. The regressed values of parameters A, B, and C in the modified Apelblat equation, λ and h in the λh equation, Δλij in the Wilson model, and Δgij in the NRTL model, together with the RMSD values, are listed in Tables S3 and S4. On the basis of the obtained parameters’ values, the solubilities of HOBT in the studied solvents at different temperature are computed. The obtained values of RD and RAD are tabulated in Table S5. In order to show the difference between the experimental and the calculated solubility, the evaluated solubilities using the modified Apelblat equation are shown graphically in Figure 2. Tables S3−S5 illustrate that the calculated solubility of HOBT in 16 solvents agrees well with the experimental ones. E
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The maximum value of RMSD is 15.84 × 10−4 attained using the Wilson equation for DMSO; and the maximum value of RAD is 4.21%. The RAD values acquired with the modified Apelblat equation are no more than 1.91%. On the whole, for a given solvent, the modified Apelblat equation provides lower RAD and RMSD values than the other two models, indicating that the modified Apelblat equation gives the best correlation results for the solubility of HOBT in the studied solvents. In general, the four equations may all be suitable for correlating the HOBT solubility in the studied solvents. Mixing Properties of Solution. On the basis of the Lewis−Randall rule, the actual states of the pure components are the standard states. So the mixing property of mixture may be obtained. For an ideal mixture, the mixing properties including mixing Gibbs energy, mixing enthalpy, and mixing entropy in neat solvent are described as28,33 Δmix Gid = RT (x1 ln x1 + x 2 ln x 2)
(22)
Δmix S id = −R(x1 ln x1 + x 2 ln x 2)
(23)
Δmix H id = 0
(24)
Figure S4 and Table S6 show that the ΔmixG values are all negative and increase with the decrease in temperature, therefore, the dissolution process of HOBT is spontaneous and favorable in the selected solvents.
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CONCLUSION The equilibrium solubilities were obtained for HOBT in 16 neat solvents at the temperatures from (278.15 to 313.15) K under atmospheric pressure of 101.1 kPa. The mole fraction solubility of HOBT in these neat solvents increased with increasing temperature. At a given temperature, the mole fraction solubility ranked as DMF > DMSO > ethanol > npropanol > isopropanol > methanol > butanone > acetone >1,4-dioxane > n-heptanol > n-hexanol > isoamyl alcohol > isooctyl alcohol > ethyl acetate > acetonitrile > toluene. The determined solubilities were correlated with the λh equation, modified Apelblat equation, and NRTL and Wilson models. The maximum values of RMSD and RAD were 15.84 × 10−4 and 4.21%, respectively. On the whole, the four solubility models were all satisfactory for expressing the solubility behavior of HOBT in the studied solvents. According to the Wilson model, the mixing properties such as mixing enthalpy, Gibbs energy, mixing entropy, infinite dilution activity coefficient, and reduced excess enthalpy were calculated according to the solubility data of HOBT in neat solvent. The ΔmixG values were all negative, therefore the solution process of HOBT is favorable and spontaneous in the studied solvents.
where x1 is the solubility of solute in mole fraction; and x2, the solvent. For a real solution, the mixing properties may be described with eq 25. Δmix M = ME + Δmix M id
(25)
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E
for M = G, H, and S, where M stands for the excess property in real solutions. ΔmixG, ΔmixH, and ΔmixS are the mixing Gibbs energy, mixing enthalpy, and mixing entropy, respectively. The superscript id refers to ideal state. Based on the Wilson equation, these mixing properties are expressed as eqs 26−28.34
S Supporting Information *
The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jced.7b00316. Chemical structure of HOBT, experimental apparatus, van’t Hoff plots, mixing Gibbs energy, information on materials, solubility parameters, parameters of the equations, RD and RAD values, and mixing properties (PDF)
GE = RT (x1 ln γ1 + x 2 ln γ2) = −RT[x1 ln(x1 + x 2 Λ12) + x 2 ln(x 2 + x1Λ 21)]
(26)
⎡ ∂(GE /T ) ⎤ H E = − T 2⎢ ⎥ ⎣ ∂T ⎦ ⎛ b Λ b21Λ 21 ⎞ = Rx1x 2⎜ 12 12 + ⎟ x 2 + Λ 21x1 ⎠ ⎝ x1 + Λ12x 2
SE =
HE − GE T
■
*Tel: + 86 514 87975568. Fax: + 86 514 87975244. E-mail:
[email protected].
(27)
ORCID
Hongkun Zhao: 0000-0001-5972-8352
(28)
ln γ1∞ = −ln Λ12 + 1 − Λ 21
Funding
This work was supported by the Priority Academic Program Development of Jiangsu Higher Education Institutions. The authors would like to express their gratitude for the Innovation Project of Jiangsu Province for Post Graduate Students (Project No.: KYLX16_1396).
(29)
The thermodynamic relationship between excess enthalpy at infinite dilution and temperature is described as36,37 = P ,x
AUTHOR INFORMATION
Corresponding Author
The activity coefficient (γ∞ 1 ) at infinitesimal concentration can be calculated on the basis of the Wilson model35 by
⎡ ∂ ln γ ∞ ⎤ 1 ⎢ ⎥ ⎣ ∂(1/T ) ⎦
ASSOCIATED CONTENT
Notes
The authors declare no competing financial interest.
H1E, ∞ R
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REFERENCES
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The value of HE,∞ may be achieved from the slope of a ln γ∞ 1 1 vs l/T curve. On the basis of the obtained parameters in the Wilson model and the determined solubility data, the ΔmixG, E,∞ ΔmixH, ΔmixS, ln γ∞ are computed and tabulated in 1 , and H1 Table S6. The mixing Gibbs energy (ΔmixG) for a solution may be employed to illustrate the dissolving capacity of a solid. F
DOI: 10.1021/acs.jced.7b00316 J. Chem. Eng. Data XXXX, XXX, XXX−XXX
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DOI: 10.1021/acs.jced.7b00316 J. Chem. Eng. Data XXXX, XXX, XXX−XXX
