Article pubs.acs.org/jced
Solubility Measurement and Correlation of (+)-Biotin Intermediate Lactone in Different Organic Solvents from 287.15 to 323.75 K Yun-Long Shi, Chao Qian, and Xin-Zhi Chen* Key Laboratory of Biomass Chemical Engineering of Ministry of Education, College of Chemical and Biological Engineering, Zhejiang University, Hangzhou, Zhejiang, 310027, P. R. China ABSTRACT: The solubilities of (+)-biotin intermediate lactone in methanol, toluene, tetrahydrofuran, dichloromethane, ethyl acetate, and N,N-dimethylformamide were determined at the investigated temperatures 287.15−323.75 K under pressure (p = 0.1 MPa) by a laser monitoring system. The solubilities of (+)-biotin intermediate lactone in pure solvents increase with increasing temperature and in the following order: methanol < toluene < ethyl acetate < tetrahydrofuran < dichloromethane < N,N-dimethylformamide. The solubilities were correlated by the equation for ideal solution model, modified Apelblat equation, λh equation, Wilson model, and NRTL equation. The calculated values are in good agreement with the measured experimental data. The modified Apelblat equation was found to provide further accurate representation of the experimental data in six organic solvents.
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INTRODUCTION (+)-Biotin intermediate lactone (CAS Registry No. 28092-62-8; (3aS,6aR)-tetrahydro-1,3-dibenzyl-hexahydro-1H-furo[3,4-d]imidazole-2,4-dione, shown in Figure 1) is currently of particular
proper solvents which use in reaction, separation and purification process. In this study, the solubilities of (+)-biotin intermediate lactone were investigated by the laser monitoring system. The six organic solvents including methanol, toluene, tetrahydrofuran (THF), dichloromethane (DCM), ethyl acetate, and N,N-dimethylformamide (DMF) were chosen in measuring the solubilities with the synthetic method at the temperature ranging from 287.15 to 323.75 K (p = 0.1 MPa). The equations for ideal solution model, modified Apelblat equation, λh equation, Wilson model, and NRTL equation were used to correlate the solubilities of (+)-biotin intermediate lactone in different solvents.
Figure 1. Chemical structure of (+)-biotin intermediate lactone.
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interest as a medium for (+)-biotin, derivative thereof and compounds related thereto. An approach of the synthesis of (+)-biotin, utilizing (+)-biotin intermediate lactone as the key intermediate,1−4 is presently the most competitive commercial route. The preparation of (+)-biotin intermediate lactone is an extremely vital step in the development of commercial asymmetric total synthesis of (+)-biotin. Many scientists devoted to the asymmetric synthesis of (+)-biotin intermediate lactone and amounts of studies have been reported in recent years.5,6 The solubilities of (+)-biotin intermediate lactone are bound up with purification and recrystallization process, and the solubility in different solvents is the basic property of (+)-biotin intermediate lactone, which provides essential information for its high quality production. Moreover, the purity of the lactone has a direct impact on the synthesis of (+)-biotin. However, there have been no report about the solubilities of (+)-biotin intermediate lactone so far. Hence, it is essential to measure its solubilities in different solvents. As the fundamental thermodynamic property for industrial process, the solubility data are indispensable for the choice of © XXXX American Chemical Society
EXPERIMENTAL SECTION
Materials. (+)-Biotin intermediate lactone was supplied by Xinchang Pharmaceutical Factory, Zhejiang Medicine Co., Ltd. and then was recrystallized two or more times from ethanol to yield a purified sample. The mass fraction purities of (+)-biotin intermediate lactone was higher than 0.992 (as determined by HPLC). In the present paper, all of the solvents were purchased from Sinopharm Chemical Reagent Co., Ltd. The solvents were analytical reagents and their purities were further identified by gas chromatograph (GC). The normal melting temperature of (+)-biotin intermediate lactone were determined using the differential scanning calorimetry (Mettler Toledo, DSC-1). The polymorphism behavior of (+)-biotin intermediate lactone was determined by X-ray diffractometer (PANalytical B.V., X’pert PRO).
Received: October 9, 2015 Accepted: March 16, 2016
A
DOI: 10.1021/acs.jced.5b00857 J. Chem. Eng. Data XXXX, XXX, XXX−XXX
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Table 1. Specific Information of the Chemicals in Our Experiments
a
chemical name
CAS Registry No.
actual mass fraction
purification method
analysis method
source
(+)-biotin intermediate lactone methanol toluene ethyl acetate tetrahydrofuran dichloromethane N,N-dimethylformamide
28092-62-8 67-56-1 108-88-3 141-78-6 109-99-9 75-09-2 68-12-2
≥0.992 ≥0.997 ≥0.997 ≥0.996 ≥0.997 ≥0.995 ≥0.997
none distillation distillation distillation distillation distillation distillation
HPLCa GCb GC GC GC GC GC
Xinchang Pharmaceutical Factory Sinopharm Chemical Reagent Co., Ltd. Sinopharm Chemical Reagent Co., Ltd. Sinopharm Chemical Reagent Co., Ltd. Sinopharm Chemical Reagent Co., Ltd. Sinopharm Chemical Reagent Co., Ltd. Sinopharm Chemical Reagent Co., Ltd.
HPLC: high-performance liquid chromatography. bGC: gas chromatography.
Table 2. Experimental and Calculated Solubilities of (+)-Biotin Intermediate Lactone in Selected Solvents with the Temperature T = 287.15−323.75 K and Pressure p = 0.1 MPaa and Their Relative Deviations εb the equation for ideal solution model
modified Apelblat equation
T/K
xi
xical
ε/%
xical
287.15 293.15 298.15 303.25 308.05 313.45 318.15
0.0034 0.0049 0.0067 0.0088 0.0119 0.0160 0.0211
0.0033 0.0048 0.0066 0.0090 0.0119 0.0162 0.0210
3.3341 1.7867 1.8923 2.0963 0.0591 1.3926 0.8012
0.0034 0.0049 0.0066 0.0089 0.0118 0.0161 0.0210
291.15 298.15 303.05 308.65 313.25 317.95 323.75
0.0073 0.0101 0.0125 0.0157 0.0197 0.0242 0.0316
0.0069 0.0098 0.0124 0.0162 0.0199 0.0244 0.0312
5.6796 2.4716 0.2694 2.6275 0.9466 1.0418 1.1144
0.0072 0.0099 0.0124 0.0160 0.0197 0.0243 0.0314
293.65 298.35 304.15 308.25 314.15 318.15 323.75
0.0221 0.0271 0.0332 0.0391 0.0487 0.0576 0.0716
0.0215 0.0263 0.0335 0.0395 0.0497 0.0578 0.0709
2.7787 2.8046 0.8810 1.0900 1.9360 0.2652 0.9677
0.0220 0.0266 0.0335 0.0393 0.0494 0.0576 0.0711
293.35 298.15 303.15 308.15 313.05 318.15 323.25
0.0740 0.0845 0.0971 0.1106 0.1258 0.1425 0.1649
0.0732 0.0842 0.0969 0.1111 0.1264 0.1440 0.1634
1.0309 0.3516 0.1365 0.4186 0.5117 1.0647 0.9548
0.0744 0.0845 0.0966 0.1103 0.1256 0.1437 0.1643
293.25 296.45 299.35 302.25 305.45 308.15 311.35
0.1213 0.1271 0.1322 0.1375 0.1438 0.1490 0.1555
0.1212 0.1270 0.1323 0.1377 0.1438 0.1491 0.1554
0.0433 0.0896 0.0511 0.1318 0.0154 0.0233 0.0650
0.1213 0.1270 0.1322 0.1376 0.1437 0.1491 0.1555
293.15 298.15 303.15 308.15 312.65
0.1503 0.1632 0.1795 0.1957 0.2112
0.1490 0.1638 0.1795 0.1962 0.2119
0.8183 0.4042 0.0411 0.2413 0.3315
0.1500 0.1639 0.1790 0.1954 0.2114
λh equation
ε/%
xical
Methanol 0.2184 0.0033 0.4703 0.0048 1.7999 0.0066 1.4941 0.0090 0.7949 0.0119 1.0234 0.0162 0.4062 0.0210 Toluene 2.3452 0.0070 1.5320 0.0099 0.4011 0.0124 1.8576 0.0161 0.1469 0.0198 0.6086 0.0244 0.5634 0.0313 Ethyl Acetate 0.6085 0.0217 1.9088 0.0264 0.7600 0.0335 0.5795 0.0394 1.3352 0.0495 0.0861 0.0576 0.6066 0.0710 Tetrahydrofuran 0.4694 0.0738 0.0180 0.0844 0.5097 0.0968 0.2829 0.1107 0.1302 0.1260 0.8594 0.1438 0.3662 0.1638 Dichloromethane 0.0418 0.1217 0.0848 0.1270 0.0130 0.1320 0.0781 0.1373 0.0557 0.1435 0.0183 0.1490 0.0012 0.1559 N,N-Dimethylformamide 0.1839 0.1500 0.4426 0.1639 0.2535 0.1790 0.1374 0.1954 0.0774 0.2113 B
Wilson model
NRTL equation
ε/%
xical
ε/%
xical
ε/%
2.7789 1.5223 1.8209 2.0325 0.1766 1.3133 0.7396
0.0031 0.0051 0.0070 0.0090 0.0120 0.0159 0.0208
7.5090 3.2780 4.2624 2.2723 0.8885 0.7190 1.5602
0.0033 0.0051 0.0064 0.0092 0.0118 0.0156 0.0213
2.4681 3.4973 4.8779 4.2735 1.1310 2.3744 0.9680
4.2003 1.9201 0.2096 2.3268 0.5621 0.7834 0.8719
0.0072 0.0102 0.0126 0.0158 0.0198 0.0241 0.0314
2.2891 0.8147 1.0856 0.6141 0.4313 0.0879 0.5850
0.0075 0.0099 0.0125 0.0157 0.0195 0.0249 0.0312
2.2892 1.7919 0.5100 0.5626 1.0715 2.8878 1.0741
1.8546 2.3963 0.8328 0.8439 1.6216 0.0725 0.7545
0.0220 0.0272 0.0333 0.0392 0.0488 0.0576 0.0714
0.6606 0.2635 0.2424 0.2686 0.0928 0.0009 0.1956
0.0220 0.0269 0.0332 0.0394 0.0479 0.0584 0.0714
0.5504 0.6749 0.0732 0.7746 1.7989 1.3696 0.2863
0.2662 0.1170 0.2826 0.0764 0.1678 0.9287 0.6579
0.0739 0.0845 0.0972 0.1107 0.1258 0.1425 0.1649
0.1205 0.0096 0.0754 0.0668 0.0385 0.0197 0.0474
0.0739 0.0845 0.0972 0.1107 0.1258 0.1425 0.1649
0.1205 0.0096 0.0754 0.0668 0.0385 0.0197 0.0474
0.3393 0.0721 0.1336 0.1322 0.2221 0.0158 0.2395
0.1214 0.1271 0.1322 0.1375 0.1438 0.1490 0.1554
0.0727 0.0475 0.0172 0.0083 0.0245 0.0440 0.0607
0.1213 0.1271 0.1322 0.1375 0.1438 0.1490 0.1555
0.0071 0.0217 0.0046 0.0181 0.0069 0.0030 0.0042
0.1710 0.4640 0.2484 0.1535 0.0543
0.1503 0.1631 0.1795 0.1957 0.2112
0.0053 0.0153 0.0156 0.0128 0.0044
0.1503 0.1632 0.1795 0.1957 0.2112
0.0025 0.0090 0.0267 0.0005 0.0149
DOI: 10.1021/acs.jced.5b00857 J. Chem. Eng. Data XXXX, XXX, XXX−XXX
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Table 2. continued the equation for ideal solution model T/K 316.05 320.35
xical
xi 0.2235 0.2417
0.2243 0.2407
ε/% 0.3535 0.4202
modified Apelblat equation xical 0.2242 0.2415
λh equation
ε/%
xical
N,N-Dimethylformamide 0.3132 0.2242 0.0522 0.2416
Wilson model
NRTL equation
ε/%
xical
ε/%
xical
ε/%
0.3016 0.0176
0.2235 0.2417
0.0050 0.0071
0.2235 0.2417
0.0137 0.014
Standard uncertainties u are u(T) = ±0.01 K, ur(p) = 0.05, and ur(x) = 0.01. The solubility (xical) calculated from corresponding equations (eqs 3, 4, 5, and 7). bRelative deviations calculated using eq 2. a
where m1 and m2 represent the quantity of the solute and solvent, respectively. The molecular weights were expressed severally as M1 and M2. All of the experimental quantities of the solute and solvents were obtained by three times.
Table 1 presents the specific information on the chemicals employed in our experiments. Apparatus and Procedure. The solubilities of (+)-biotin intermediate lactone were determined by the synthetic method.7 The experimental apparatus is similar to the facility in the literature.8,9 The existing apparatus mainly includes the weighing device, temperature control system, dissolving system, and detecting system. The laser monitoring system was used as the primary detecting system and was applied to the dissolving procedures of different solutes. For existing apparatus, there are two main methods for measurement of the solubility. One is that solute is added to a certain quantity of solvent until the dissolution capacity is exceeded. The other is that solvent is added to a known quantity of solute until the solute is dissolved. In contrast of the two methods’ results, the differences are often minor and also negligible. In this paper, the former method was adopted. In order to obtain accurate results of the experiment, we used a 200 mL jacked vessel as the container to dissolve the solutes and an electromagnetic agitator to stir the solute which could dissolve in the solvents increasingly. A microthermometer was used to determine the mixture’s temperature in the container. To keep constant temperature of the solution, the thermostatic bath (type CH1015, Selon, Shanghai, China, u = 0.03 K) was applied to provide the circulating water in the set temperature. An electronic analytical balance (type BS210S, Napco, Guangdong, China, u = 0.1 mg) could measure the changed mass of the solutes accurately. A condenser pipe was added to the jacked vessel for preventing the evaporation of the solvent. The laser monitoring system (type F-GX1000, Force, Beijing, China, u = 0.1 μW), which included a laser generator, a laser receiver, and a light signal display, was used to determine the dissolution’s equilibrium point in terms of varying laser signal. In the early stages of the experiments, predetermined amounts of solute and solvent were taken by the electronic analytical balance and then were put in the jacked vessel which was in the condition of water bath heating at a stable temperature as well as magnetic stirring, and an unsaturated solution was obtained. The intensity of the laser penetrated through the solution was regarded as the maximum. Then an additional solute of known mass was introduced into the vessel. When the supersaturated solution was obtained, the intensity would decrease. In the following process, a known quantity of solute was added until the intensity was below the maximum. Finally, the total amount of the solute added was used to compute the solubility at the current temperature. After removing the solvent by reduced pressure distillation, the solute was obtained and put on the board smoothly. Then the samples were determined by XRD. The solubility (mole fraction) x of (+)-biotin intermediate lactone was calculated as follows: x=
m1/M1 m1/M1 + m2 /M 2
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RESULTS AND DISCUSSION Solubility Data of (+)-Biotin Intermediate Lactone. Table 2 lists the experimental solubilities (xi) of (+)-biotin intermediate lactone in methanol, toluene, ethyl acetate, tetrahydrofuran, dichloromethane, and N,N-dimethylformamide ranging from 287.15 to 323.75 K (p = 0.1 MPa). From Table 2, the data indicate that the rise of temperature result in higher dissolving capacity. As seen in Figure 2, the solubility of
Figure 2. Mole fraction solubility of (+)-biotin intermediate lactone (x) in six organic solvents from 287.15 to 323.75 K: ▽, methanol; ▲, toluene; ◇, ethyl acetate; ⧫, tetrahydrofuran; ☆, dichloromethane; ★, N,N-dimethylformamide. Solid red curves are fits to eq 4.
(+)-biotin intermediate lactone is associated with the temperature, and the increases in temperature correspond to increases in solubility obviously. Besides, Figure 2 illustrates that the solubility of lactone in selected solvents was ranked from small to large order: methanol < toluene < ethyl acetate < THF < DCM < DMF. At a certain temperature, the solubility of lactone in DMF is superior to other selected solvents. In contrast, methanol is the lowest one in six organic solvents. The solubilities in methanol is far below the level of other solvents, while it is pretty suitable for the recrystallization of lactone. Ethyl acetate has the similar ester group with (+)-biotin intermediate lactone so that it is used as extractant generally. Considering the high solubilities of lactone in dichloromethane and the lower boiling point of dichloromethane, DCM is applied to liquid−liquid extraction process. Tetrahydrofuran and N,N-dimethylformamide are relatively applicable solvents for chemical synthesis procedure.
(1) C
DOI: 10.1021/acs.jced.5b00857 J. Chem. Eng. Data XXXX, XXX, XXX−XXX
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Figure 3. X-ray powder diffraction pattern of (+)-biotin intermediate lactone crystals obtained from different solvents: (A) methanol; (B) toluene.
In addition, the crystals of (+)-biotin intermediate lactone obtained from these solvents by the distillation. To confirm no polymorphism behavior of (+)-biotin intermediate lactone, XRD powder analysis is given, and the results are shown in Figure 3, which identify that they are the same material. Solubility Data Correlation. In our study, the temperature dependence of the solubilities of (+)-biotin intermediate
lactone in six organic solvents was correlated by the equation for ideal solution model, modified Apelblat equation, λh equation, Wilson model, and NRTL equation. These equations, with mathematical expressions, have been constantly employed in solubility data correlation of other compounds.10,11 The calculated solubilities (xical) are obtained from above equations and corresponding relative deviations D
DOI: 10.1021/acs.jced.5b00857 J. Chem. Eng. Data XXXX, XXX, XXX−XXX
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λh Equation. The λh equation was initially put forward by Buchowski et al.15 to describe the relationship of solubility data and temperature, whose formula is given as follows:
(ε) are also collected in Table 2. The relative deviations (ε) is defined as ε=
|xical − xi| × 100% xi
⎛ ⎛1 1 − xi ⎞ 1 ⎞ ln⎜1 + λ ⎟ = λh⎜ − ⎟ xi ⎠ Tm ⎠ ⎝T ⎝
(2)
where xical is the solubility data calculated by the correlated equation and xi is the experimental value. The Equation of Ideal Solution Model. Referring to an ideal solution, the equation for ideal solution model was used to predict the relation of ln xi and reciprocal absolute temperature. The formula is given as follows: ln xi = a +
b T
where λ and h are model parameters and Tm is the normal melting temperature of (+)-biotin intermediate lactone (Tm = 391.85 K, standard uncertainties u are u(T) = ± 0.01 K). The λh equation is a semiempirical equation and two parameter (λ and h) in this equation can greatly correlate the experimental solubility data. The value of λ stands for the approximate mean association number of solute molecules, which reveals the nonideality of the solution system, while that of h denotes the enthalpy of solution.16 Activity Coefficient Models. There is a commonly used solubility model according to solid−liquid equilibrium criteria, which can be expressed below:17
(3)
where xi is the mole fraction solubility of (+)-biotin intermediate lactone in different solvents, T is the absolute temperature in Kelvin, and a and b are model parameters (shown in Table 3), Table 3. Parameters of the Equation for Ideal Solution Model (eq 3), Fitting Degree (R2), Average Relative Deviations (RAD), and Deviations (RMSD) for (+)-Biotin Intermediate Lactone in Different Organic Solventsa
a
solvent
a
B
R2
102 RAD
104 RMSD
methanol toluene ethyl acetate THF DCM DMF
13.3266 10.0016 8.9800 6.0577 2.1624 3.7403
−5469.6184 −4360.3710 −3764.2219 −2543.8055 −1252.8646 −1654.5077
0.9993 0.9983 0.9983 0.9988 0.9999 0.9993
1.6231 2.0215 1.5319 0.6384 0.0599 0.3729
0.4269 1.5726 2.3249 2.8839 0.1983 4.6476
ln x1γ1 =
⎞ ΔfusHtp ⎛ 1 Ttp 1 ⎞ ΔCp ⎛ Ttp ⎜⎜ − ⎟⎟ − − + 1⎟ ⎜ln R ⎝ Ttp T⎠ R ⎝ T T ⎠ ΔV − (P − Ptp) (6) RT
Generally, the negligible difference between triple point (Ttp) and normal melting point (Tm) makes it suitable to replace ΔfusHtp and Ttp by the enthalpy of melting (ΔfusHm) and Tm.18 Additionally, ΔCp and ΔV represent the correction of heat capacity and pressure difference, and the last two terms have mutual compensation functions. Therefore, these terms are general negligible; then the equation can be simplified as19
Relative uncertainty is ur(α) = 2%, ur(b) = 2%.
which are obtained from regression of the experimental data. Here, for a real solution, it is rational to utilize this equation in consideration of the nonideality caused by the solvent effect.12 Modified Apelblat Equation. The relationship of temperature and solubility was described by the modified Apelblat equation,13,14 which is frequently used in correlation of solid− liquid equilibrium. For the majority of solution systems, this equation provides the preferable fitting results. The form of modified Apelblat equation is ln xi = A + B /(T /K) + C ln(T /K)
(5)
ln x1γ1 =
ΔfusHm ⎛ 1 1⎞ − ⎟ ⎜ R ⎝ Tm T⎠
(7)
where x1 is the mole fraction of the solute, γ1 is the liquid-phase activity coefficient of solute, ΔfusHm is the enthalpy of fusion of solute at the melting point, and Tm is the melting temperature of (+)-biotin intermediate lactone. The values of ΔfusHm and Tm can be measured with the differential scanning calorimetry (DSC). A small amount of (+)-biotin intermediate lactone was put in tablet machine and analyzed with the differential scanning calorimetry. Figure 4 shows the heating DSC curves of (+)-biotin intermediate lactone at the heating rate of 10 K/min from 303.15 to 433.15 K and the values of melting temperature and enthalpy of fusion. The values of enthalpy of fusion and the melting temperature are determined to be 30.29 KJ·mol−1 (ur(ΔfusHm) = 0.03) and 391.85 K (u(Tfus) = 0.5 K) for (+)-biotin intermediate lactone.
(4)
where A, B, and C represent dimensionless parameters, which are listed in Table 4. The values of A, B, and C signify the change in the solution activity, the influence of solution nonidealities on dissolution process, and the relationship of temperature and enthalpy of fusion, respectively.
Table 4. Parameters of the Modified Apelblat Equation (eq 4), Fitting Degree (R2), Average Relative Deviations (RAD), and Deviations (RMSD) for (+)-Biotin Intermediate Lactone in Different Organic Solventsa
a
solvent
A
B
C
R2
102 RAD
104 RMSD
methanol toluene ethyl acetate THF DCM DMF
−112.8637 −115.2115 −91.5837 −93.0843 −16.9788 −56.2564
291.7832 1423.6602 890.0604 2015.3892 −390.2480 1086.3990
18.7565 18.5733 14.9120 14.7174 2.8517 8.9168
0.9995 0.9993 0.9998 0.9994 0.9999 0.9997
0.8867 1.0650 0.8407 0.3765 0.0418 0.2086
0.0280 0.6494 0.5091 1.3131 0.1917 1.0443
Relative uncertainty is ur(A, B, C) = 2%. E
DOI: 10.1021/acs.jced.5b00857 J. Chem. Eng. Data XXXX, XXX, XXX−XXX
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Figure 4. Heating differential scanning calorimetry (DSC) curves of (+)-biotin intermediate lactone.
where Δg12 and Δg21 are two parameters which stand for the cross interaction energy (J·mol−1) and α12 is considered as a third adjustable parameter. Tables 3−7 summarize the values of parameters for diverse equations (a, b, A, B, C, λ, h, Δλ12, Δλ21, Δg12, Δg21, and α12),
1. Wilson Model. Wilson proposed a local composition model because he recognized that the distribution of molecules is not purely random in a mixture with specific interactions. The activity coefficient of this model can be easily obtained as20 ⎞ ⎛ Λ12 Λ 21 ln γ1 = −ln(x1 + Λ12x 2) + x 2⎜ − ⎟ x 2 + Λ 21x1 ⎠ ⎝ x1 + Λ12x 2
Table 5. Parameters of λh Equation (eq 5), Fitting Degree (R2), Average Relative Deviations (RAD), and Deviations (RMSD) for (+)-Biotin Intermediate Lactone in Different Organic Solventsa
(8)
Λ12 =
Λ 21 =
⎛ Δλ ⎞ ν2 ⎛ λ12 − λ11 ⎞ ν ⎟ = 2 exp⎜ − 12 ⎟ exp⎜ − RT ⎠ ν1 ⎝ ν1 ⎝ RT ⎠ ⎛ Δλ ⎞ ν1 ⎛ λ 21 − λ 22 ⎞ ν ⎟ = 1 exp⎜ − 21 ⎟ exp⎜ − ⎝ ⎠ RT ν2 ν2 ⎝ RT ⎠
(9)
(10)
where x1 and x2 represent the mole fraction of the solute and the selected solvent, respectively. Δλ12 and Δλ21 are two adjustable parameters per binary. ν1 and ν2 are the molar volumes of solute and selected solvent. The values of ν2 are obtained from the literature,21 and that of (+)-biotin intermediate lactone is calculated from its density (ρ = 1.312 g·cm−3). The density of (+)-biotin intermediate lactone is measured with the densitometer (type DMAM, Anton Paar GmbH, Austria, ±0.001 g·cm−3). 2. NRTL Equation. The NRTL model proposed by Renon and Prausnitz22 has been applicable to a large variety of systems. The equation contains three parameters per binary and gives a better representation by proper selection of Δg12, Δg21, and α12. The equation can be written:
a
τ12 = τ21 =
⎞ ⎟ [x 2 + x1 exp( −α12τ12)] ⎠
(g12 − g22) RT (g21 − g11) RT
exp(−α12τ12)
2
=
Δg12
=
Δg21
RT
RT
λ
h
R2
102 RAD
104 RMSD
methanol toluene ethyl acetate THF DCM DMF
0.5189 0.2741 0.4519 0.4758 0.0349 0.2871
10418.97 15126.07 7882.94 4729.86 7449.96 3888.52
0.9994 0.9989 0.9989 0.9994 0.9994 0.9998
1.4834 1.5535 1.1966 0.3566 0.1649 0.2015
0.3559 1.1630 1.5517 0.7447 1.5557 0.9710
Relative uncertainty is ur(λ) = 3% and ur(h) = 3%.
Table 6. Parameters of Wilson Equation (eq 8), Fitting Degree (R2), Average Relative Deviations (RAD), and Deviations (RMSD) for (+)-Biotin Intermediate Lactone in Different Organic Solventsa
⎛ exp(− 2α12τ21) ln γ1 = x 22⎜τ21 2 ⎝ [x1 + x 2 exp( −α12τ21)] + τ12
solvent
solvent
Δλ12
Δλ21
R2
102 RAD
104 RMSD
methanol toluene ethyl acetate THF DCM DMF
15738.75 16129.62 13399.28 9723.809 7781.21 7746.441
11460.56 15023.82 15046.27 15198.63 124487 17059.99
0.9986 0.9999 0.9999 0.9999 0.9999 0.9999
2.9271 0.8440 0.2463 0.0540 0.0393 0.0093
0.9617 0.6338 0.5527 0.3372 0.3332 0.0298
a
Relative uncertainty is ur(Δλ12) = 3% and ur(Δλ21) = 3%.
(11)
corresponding fitting degree (R2), average relative deviations (RAD), and root-mean-square deviations (RMSD) in selected solvents. The average relative deviations and root-mean-square deviations are crucial indexes to be used to evaluate the model for the solubility of (+)-biotin intermediate lactone. The RAD and RMSD are defined with eqs 14 and 15, respectively.
(12)
(13) F
DOI: 10.1021/acs.jced.5b00857 J. Chem. Eng. Data XXXX, XXX, XXX−XXX
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Table 7. Parameters of NRTL Equation (eq 11), Fitting Degree (R2), Average Relative Deviations (RAD), and Deviations (RMSD) for (+)-Biotin Intermediate Lactone in Different Organic Solventsa
a
solvent
Δg12
Δg21
α
R2
102 RAD
104 RMSD
methanol toluene ethyl acetate THF DCM DMF
671.768 355.066 239.989 244.091 1055.769 1000.306
−732.933 175.807 358.742 357.304 800.328 764.454
−0.5448 −1.0806 −1.6111 −1.0851 0.4132 0.4139
0.9992 0.9991 0.9994 0.9992 0.9999 0.9999
2.7986 1.4553 0.7897 0.0540 0.0094 0.0116
0.3161 0.6339 0.4605 0.3372 0.0327 0.0143
Relative uncertainty is ur(Δg12, Δg21, α) = 4%.
RAD =
1 N
N
xical − xi × 100% xi
∑ i=1
⎡1 RMSD = ⎢ ⎢⎣ N
N
∑
(xical
Funding
The authors are grateful for the financial support from the Natural Science Foundation of China (21376213, 21476194), the Research Fund for the Doctoral Program of Higher Education of China (20120101110062), and the Zhejiang Provincial Public Technology Research of China (2014C31123).
(14)
⎤1/2
2⎥
− xi)
i=1
⎥⎦
(15)
Notes
The authors declare no competing financial interest.
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xical
where and xi are the calculated and experimental mole fraction solubilities of the solute in the solution and N signifies the number of experimental points. The experimental points and fitted curves were presented in Figure 2, and the calculated data with different equations were all consistent with the data of experiments. As shown in Table 2, all of the relative deviations (ε) calculated by the equation of ideal solution model, modified Apelblat equation, λh equation, Wilson model, and NRTL equation in selected solvents are respectively no more than 5.6796%, 2.3452%, 4.2003%, 7.5090%, and 4.8779%. For comparison, the maximum 102 RAD and 104 RMSD values in modified Apelblat equation are 1.0650 and 1.3131, less than that in other four equations. In addition, all of the R2 values in each solvents vary within the range between 0.9983 and 0.9999. The fitting degree of the modified Apelblat equation for different systems is highest and indicates the excellent accuracy of this equation. Therefore, the modified Apelblat equation are more suitable than the equation of ideal solution model, λh equation, Wilson model, and NRTL equation for our investigated systems.
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CONCLUSIONS The solubility of (+)-biotin intermediate lactone in methanol, toluene, ethyl acetate, tetrahydrofuran, dichloromethane, and N,N-dimethylformamide were measured by the laser monitoring technique. In the investigated temperature range of 287.15− 323.75 K, N,N-dimethylformamide showed the best solubility of the six organic solvents and the solubility in methanol is minimum. The solubility in each solvent was increasing following the increasing tendency of the temperature. The equation for ideal solution model, modified Apelblat equation, λh equation, Wilson model, and NRTL equation were applied to correlate the solubility of (+)-biotin intermediate lactone in different solvents, and satisfactory correlative results were obtained. In contrast to other equations, the modified Apelblat equation gave the more fitting results in experimental range. The overall values of the ε, RAD, and 104 RMSD in the modified Apelblat equation are less than 2.3452%, 1.0650%, and 1.3131, respectively.
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REFERENCES
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DOI: 10.1021/acs.jced.5b00857 J. Chem. Eng. Data XXXX, XXX, XXX−XXX
Journal of Chemical & Engineering Data
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DOI: 10.1021/acs.jced.5b00857 J. Chem. Eng. Data XXXX, XXX, XXX−XXX
