Determination and Thermodynamic Analysis of the Solubility of

Article pubs.acs.org/jced

Cite This: J. Chem. Eng. Data XXXX, XXX, XXX−XXX

Determination and Thermodynamic Analysis of the Solubility of Limonin in Eight Organic Solvents and Ethyl Acetate + 2‑Propanol Binary Solvents from 283.2 to 323.2 K Jie-Ping Fan,*,†,‡ Tian-Tao Yuan,† Jia-Xin Yu,† Xue-Hong Zhang,§ and Ya-Hui Cao† †

School of Resource, Environmental and Chemical Engineering, ‡Key Laboratory of Poyang Lake Ecology and Bio-Resource Utilization of Ministry of Education, and §School of Foreign Language, Nanchang University, Nanchang 330031, China S Supporting Information *

ABSTRACT: In the present study, the solubility of limonin in eight organic solvents and a binary solvent system (ethyl acetate + 2-propanol) was determined by the high-performance liquid chromatography analysis method within the temperature range from 283.2 to 323.2 K. The results showed that the solubility of limonin increased with temperature in the eight pure solvents and the binary solvent mixtures. In the binary solvent system ethyl acetate + 2-propanol, the solubility decreased with the initial mole fraction of ethyl acetate. The experimental solubility of limonin was well correlated with temperature by the simplified thermodynamic equation, modified Apelblat equation, λh equation, and NRTL equation. Furthermore, the solubility of limonin in the binary solvent mixtures was correlated with both temperature and initial solvent composition of the binary solvent mixtures by the Jouyban−Acree model, van’t Hoff−Jouyban−Acree model, modified Apelblat−Jouyban−Acree model, Ma model, Sun model, and NRTL model. Finally, the thermodynamic properties of the mixing process, including mixing Gibbs energy, mixing enthalpy, and mixing entropy, were also calculated.

1. INTRODUCTION Limonoids, unique substances with highly oxygenated triterpenoid backbones, are only found in the families of Rutaceae and Meliaceae.1 Limonin (C26H30O8, molar mass 470.51 g mol−1, CAS Registry No. 1180-71-8, Figure 1) is one

property of enhancing osteoblasto genesis and cytotoxic activity.8,9 Limonin often coexists with other components in the citrus fruits.10 Therefore, to separate and purify limonin, it is very important to know the solubility of limonin in different solvents and at various temperatures. The solubility of limonin was reported only in some aqueous media11 and several organic solvents and buffer solutions at 310.15 K.12 In our previous work we also have reported the solubility of limonin in acetone + water mixtures at various temperatures.13 However, the solubility of limonin at various temperatures in the eight organic solvents (listed in Table 1) and ethyl acetate + 2propanol mixtures has not been systematically studied. These solvents are common and widely used to dissolve and separate chemicals in pharmaceutical and chemical industry. Therefore, in our present work the solubility of limonin in the eight organic solvents and a binary solvent system (ethyl acetate + 2propanol) with various initial mole fractions was measured by high-performance liquid chromatography (HPLC) analysis method at different temperatures ranging from 283.2 to 323.2 K, and the thermodynamic properties of the mixing process, including mixing Gibbs energy, mixing enthalpy, and mixing entropy, were also calculated.

Figure 1. Chemical structure of limonin.

of the most prevalent limonoids and often found in citrus fruits.2,3 Limonin demonstrates a diversity of important bioactivities, such as antiviral, antimicrobial, anti-HIV, anticancer and antioxidant activities.4−7 Furthermore, ongoing studies have already revealed that limonin has the potential © XXXX American Chemical Society

Received: September 25, 2017 Accepted: February 22, 2018

A

DOI: 10.1021/acs.jced.7b00851 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

Journal of Chemical & Engineering Data

Article

Table 1. Provenance and Mass Fraction Purity of Chemicals

a

chemicals

mass fraction purity

limonin acetonitrile ethyl acetate butyl acetate chloroform tetrahydrofuran ethanol 2-propanol 1-butanol

≥0.980 ≥0.997 ≥0.995 ≥0.995 ≥0.995 ≥0.995 ≥0.995 ≥0.995 ≥0.995

analysis method HPLC GCc GC GC GC GC GC GC GC

CAS Registry No.a

provenance

1180-71-8 75-05-8 141-78-6 123-86-4 67-66-3 109-99-9 64-17-5 67-63-0 71-36-3

Nanjing Zelan Biotechnology Co. Ltd. Guangdong Xilong Chemical Co., Ltd. Tianjin Hengxin Chemical Preparation Co., Ltd. Shanghai Sinopharm Chemical Reagent Co., Ltd. Shanghai Rich Joint Chemical ReagentsCo., Ltd. Tianjin Hengxin Chemical Preparation Co. Ltd. Tianjin Hengxin ChemicalPreparation Co. Ltd. Guangdong Xilong Chemical Co., Ltd. Shanghai Rich Joint Chemical Reagents Co., Ltd.

b

CAS Registry Numbers are provided by the author. bHigh performance liquid chromatography. cGas chromatography.

2. EXPERIMENTAL SECTION 2.1. Materials. The materials used in this work were listed in Table 1 and were used in the experiment without any further purification. 2.2. Solubility Measurement. According to our previous work, the solubility of limonin was measured by the HPLC analytic method and the experiment in full detail can be found in refs 13−16. The verification for reliability of of our experimental technique can be found in our previous work;13,17,18 the experimental solubility data agreed well with those in the literature. So the experimental method used is reasonable and reliable. The amount of limonin in the samples was also determined by an Agilent 1100 HPLC system according to our previous work.13 In this study, the combined standard uncertainty was used to calculate the relative uncertainty of the experimental solubility data, and all of the relative uncertainties were within the range 2.0−5.0%. The mole fraction solubility of limonin in pure and binary solvents was calculated on the basis of eqs 1 and 2, respectively. Pure solvents: x1 =

m1/M1 m1/M1 + m2 /M 2

3. THERMODYNAMIC AND CORRELATING MODELS 3.1. Correlation of Solubility with Temperature. In this work, the van’t Hoff model (eq 3),19,20 the modified Apelblat model (eq 4),21,22 and the λh model (eq 5)23,24 were used to correlate the solubility with temperature. a ln x1 = +b (3) T /K ln x1 = A +

m1/M1 m1/M1 + m2 /M 2 + m3 /M3

(4)

⎡ ⎛ 1 λ(1 − x1) ⎤ 1 ⎞ ln⎢1 + − ⎥ = λh⎜ ⎟ x1 Tm/K ⎠ ⎦ ⎣ ⎝ T /K

(5)

where x1 is the mole fraction solubility of limonin at temperature T (K), Tm is the melting temperature of limonin, and a, b, A, B, C, λ, and h are parameters of the models. 3.2. Correlation of Solubility with Both Temperature and Initial Solvent Composition of the Binary Solvents. To describe the effect of both solvent composition and temperature on the solubility of limonin, the Jouyban−Acree model (eq 6),25,26 the van’t Hoff−Jouyban−Acree model (eq 7),27,28 and the modified Apelblat−Jouyban−Acree model (eq 8)29,30 were used to correlate the solubility data.

(1)

where x1 is the mole fraction solubility of limonin, m1 and M1 are the mass and molecular mass of limonin, respectively, and m2 and M2 refer to the mass and molecular mass of the solvents, respectively. Binary solvents: x1 =

B + C ln(T /K ) T /K

ln x1 = m2 ln x 2 + m3 ln x3 +

m 2 m3 + T

2

∑ Ji (m2 − m3)i i=0

(6)

⎛a ⎞ ⎛a ⎞ ln x1 = m2⎜ 1 + b1⎟ + m3⎜ 2 + b2⎟ ⎝T ⎠ ⎝T ⎠ mm + 2 3 T

(2)

where x1 is the mole fraction solubility of limonin; m1, m2, and m3 refer to the mass of limonin, ethyl acetate, and 2-propanol, respectively, and M1, M2, and M3 represent the molecular mass of limonin, ethyl acetate, and 2-propanol, respectively. 2.3. Thermal Analysis and Powder X-ray Diffraction (PXRD) Conditions. The thermochemical properties of limonin were determined by a thermogravimetry-differential scanning calorimetry (TG/DSC, type SDTQ600, American TA Co.). The sample was scanned at a heating rate of 10 °C min−1 with high-purity nitrogen at a constant flow rate of 100 mL min−1. The solid state samples in this study were identified by PXRD, and PXRD patterns were collected on a Bede D1 diffractometer (Bede, U.K.) with Cu Ka radiation (k = 0.154056).

2

∑ ji (m2 − m3)i i=0

(7)

⎛ ⎞ ⎛ ⎞ B B ln x1 = m2⎜A1 + 1 + C1 ln T ⎟ + m3⎜A 2 + 2 + C 2 ln T ⎟ ⎝ ⎠ ⎝ ⎠ T T +

m 2 m3 T

2

∑ ki(m2 − m3)i i=0

(8)

where x1, x2, and x3 are the mole fraction solubility of limonin in the binary solvent mixtures, ethyl acetate, and 2-propanol at temperature T (K), respectively; m2 and m3 represent the initial mass fractions of ethyl acetate and 2-propanol in the absence of limonin; and a1, a2, b1, b2, A1, B1, C1, A2, B2, C2, J0−J2, j0−j2, and k0−k2 represent model constants. The Ma model (eq 9)31 and Sun model (eq 10)31 were also used to correlate the solubility of solute in binary solvents at different temperatures. B



Article

m m 2 m3 D2 + D3m2 + D4 2 + D5 2 + D6 2 T T T T 4 m + D7 2 (9) T

average deviation (RAD) and root-mean-square deviation (RMSD) were employed, which are expressed as eqs 15 and 16, respectively.

ln x1 = D1 +

RAD =

E2 m m2 + E3 ln T + E4m2 + E5 2 + E6 2 T T T m23 m2 4 + E7 + E8 + E9m2 ln T (10) T T

ln x1 = E1 +

+

∑ j=1

Δmix M = ME + Δmix M id

n

(18)

i

Δmix H id = 0

Gijxj

⎡ ⎛ ⎞⎤ ⎞2 ⎛ G21 τ12G12 ln γi = x 2⎢τ21⎜ ⎟⎥ ⎟ +⎜ ⎢⎣ ⎝ x1 + G21x 2 ⎠ ⎝ (x 2 + G12x1) ⎠⎥⎦

(19) n

Δmix S id = −R ∑ xi ln xi

(12)

(20)

i

where xi represents the mole fraction of each component in the solution and n is equal to 2 and 3 for the solution with pure solvent and binary solvents, respectively. In addition, GE, HE, and SE can be calculated by the following eqs (eqs 21−23).

(13)

n

For a binary solvents the NRTL model is given by eq 14.

GE = RT ∑ xi ln γi

⎞ τ21G21x 2 + τ31G31x3 ⎛ x1 ⎜1 − ⎟ x1 + G21x 2 + G31x3 ⎝ x1 + G21x 2 + G31x3 ⎠

(21)

i n ⎛ ∂ln γi ⎞ HE = −RT ∑ xi⎜ ⎟ ⎝ ∂T ⎠ i

⎞ ⎛ G12x 2 τGx + τGx + ⎟ ⎜τ12 − G12x1 + x 2 + G32x3 ⎝ G12x1 + x 2 + G32x3 ⎠ +

(17)

Δmix Gid = RT ∑ xi ln xi

n ⎛ ∑m = 1 τmjGmjxm ⎞ ⎜ ⎟ τij − n n ∑k = 1 Gkjxk ⎟⎠ ∑k = 1 Gkjxk ⎜⎝

(16)

where M = G, H, or S; ΔmixG, ΔmixH, and ΔmixS are the apparent mixing Gibbs energy, mixing enthalpy, and mixing entropy, respectively; ME denotes the excess property in real solutions; and ΔmixMid is the mixing property of an ideal solution. The mixing properties of ideal solution can be obtained with eqs 18−20 as follows.

(11)

For a pure solvent system the NRTL model is given by eq 13.

ln γi =

(15)

where xi and represent the experimental mole fraction solubility and the calculated mole fraction solubility of limonin, respectively, and N is the number of experimental points. 3.5. Solution Mixing Thermodynamics. The thermodynamic property of a solute dissolved in a solvent can provide essential information for the dissolution procedure, and the mixing properties of solution can be obtained on the basis of the Lewis−Randall rule.32 For the nonideal solution, three thermodynamic properties can be calculated by eq 17.

n ∑ j = 1 τjiGjixj n ∑k = 1 Gkixk n

i=1

xic

where xi is the mole fraction of the component i, ΔfusHm is the fusion enthalpy, Tm is the melting temperature of limonin, and γi is the activity coefficient of limonin in the saturated solution. The NRTL model (eq 12) is widely applied to correlation and calculation of the fluid phase equilibrium. ln γi =

xic − xi xi

∑

⎡ ∑N (x c − x )2 ⎤1/2 i i ⎥ RMSD = ⎢ i = 1 ⎢⎣ ⎥⎦ N

where x1 is the mole fraction solubility of limonin in the binary solvents, m2 and m3 represent the initial mass fractions of ethyl acetate and 2-propanol in the absence of limonin, and D1−D7 and E1−E9 are the model parameters in eqs 9 and 10, respectively. 3.3. NRTL Model. According to the traditional theory of solid−liquid phase equilibrium, once a solid−liquid system reaches equilibrium at a certain temperature and pressure, the simplified equation describing the solubility of a solute in different solvents can be derived and expressed as eq 11. ⎞ Δ H ⎛T ln γixi = − fus m ⎜ m − 1⎟ ⎝ ⎠ RTm T

N

1 N

p,x

(22)

HE − GE (23) T where γi represents the activity coefficient of each component in the real solution. The activity coefficient (γi) can be obtained from the NRTL model.

⎛ G13x3 τ G x + τ23G23x 2 ⎞ ⎜τ13 − 13 13 1 ⎟ G13x1 + G23x 2 + x3 ⎝ G13x1 + G23x 2 + x3 ⎠

SE =

(14) gij − gjj

where Gij = exp(−aijτij), τij = , aij = aji, where τij refers to a RT constant related to the nonrandomness of the solution, Δgij represents the Gibbs energy of intermolecular interaction, and αij is an adjustable empirical constant ranging from 0 to 1,29,32 which describes the nonrandomness between components i and j. 3.4. Evaluation of Data Correlation by the Models. To evaluate the accuracy of the model correlations, the relative

4. RESULT AND DISCUSSION 4.1. Thermochemical Properties of Limonin. The thermochemical properties of limonin were determined by TGA/DSC. The DSC, TG, and DTG curves were presented in Figure S1 (Supporting Information). The melting point Tm of limonin was at 566.55 K, which was close to the value in ref C



Article

Table 2. Experimental Mole Fraction Solubility of Limonin (x) in Pure and Binary Solvents at Different Temperatures and Atmospheric Pressure (p = 101.1 kPa)a 104xc T/Kb

acetonitrile

ethyl acetate

283.2 288.2 293.2 298.2 303.2 308.2 313.2 318.2 323.2

27.25 ± 0.73d 31.35 ± 0.84 34.93 ± 0.93 38.5 ± 1.0 45.4 ± 1.2 52.3 ± 1.4 62.8 ± 1.7 73.9 ± 2.0 85.7 ± 2.3

7.46 ± 0.15 7.61 ± 0.16 8.01 ± 0.17 8.50 ± 0.18 9.40 ± 0.19 9.79 ± 0.20 10.11 ± 0.21 11.88 ± 0.25 12.75 ± 0.26

T/Kb 283.2 288.2 293.2 298.2 303.2 308.2 313.2 318.2 323.2

2-propanol 0.1079 0.1249 0.1560 0.1792 0.1874 0.2245 0.3031 0.3473 0.4524

± ± ± ± ± ± ± ± ±

0.0023 0.0027 0.0034 0.0039 0.0041 0.0049 0.0065 0.0075 0.0098

butyl acetate 3.230 3.487 3.747 4.126 4.84 5.30 6.16 6.46 6.80

± ± ± ± ± ± ± ± ±

± ± ± ± ± ± ± ± ±

42.5 43.3 44.7 45.8 47.9 51.2 53.1 57.0 59.9

xEA = 0.20e

n-butyl alcohol 0.1531 0.1937 0.2011 0.2638 0.2910 0.3538 0.4233 0.562 0.725

chloroform

0.064 0.072 0.078 0.086 0.10 0.11 0.13 0.13 0.14 104xc

0.0033 0.0042 0.0044 0.0057 0.0063 0.0077 0.0092 0.012 0.016

0.540 0.657 0.747 0.847 0.879 1.227 1.606 1.805 2.152

± ± ± ± ± ± ± ± ±

0.012 0.014 0.016 0.018 0.019 0.026 0.034 0.038 0.046

± ± ± ± ± ± ± ± ±

tetrahydrofuran

1.1 1.2 1.2 1.2 1.3 1.4 1.4 1.5 1.6

24.19 25.70 28.03 30.93 32.72 35.00 40.8 45.8 48.6 xEA = 0.50e 2.924 3.298 3.466 3.842 4.247 4.79 5.50 6.27 7.05

± ± ± ± ± ± ± ± ±

0.062 0.070 0.074 0.082 0.090 0.10 0.12 0.13 0.15

± ± ± ± ± ± ± ± ±

ethanol

0.50 0.69 0.76 0.84 0.88 0.95 1.1 1.2 1.3

0.2652 0.2928 0.3053 0.3531 0.427 0.548 0.671 0.849 1.011

± ± ± ± ± ± ± ± ±

0.0072 0.0063 0.0065 0.0075 0.012 0.015 0.014 0.018 0.022

xEA = 0.80e 4.96 5.46 5.66 6.22 6.69 7.28 7.79 8.49 9.68

± ± ± ± ± ± ± ± ±

0.11 0.12 0.12 0.13 0.14 0.15 0.17 0.18 0.21

a

Standard uncertainty u is u(p) = 10 hPa. bStandard uncertainties u is u(T) = 0.1 K. cx denotes the mole fraction solubility of limonin. dThe standard uncertainty (±) of solubility was calculated using combined standard uncertainty. exEA is the initial mole fraction of ethyl acetate in the ethyl acetate + 2-propanol binary solvent mixtures. The relative standard uncertainty ur is ur(xEA) = 0.06.

33,33 and a little difference was probably due to the different determination methods and operating conditions. In the DSC curve there was a small endothermic peak at around 530.96 K, and at almost the same temperature there was a small peak of weight loss in DTG curve. The phenomenon was maybe caused by the opening of the lactonic ring of limonin. Moreover, as shown in the TGA and DTG curves of limonin, decomposition of limonin began at almost the same time as melting. Therefore, the conventional calorimetric test could not obtain limonin’s fusion enthalpy because the fusion process was accompanied by decomposition. According to the literature,34−36 a group contribution method was used to estimate limonin’s fusion enthalpy. A semiempirical equation (eq 24) with two molecular descriptors, the molecular rotational symmetry number (σ) and the molecular flexibility number (Φ), was employed to estimate the total fusion entropy (ΔfusSm) of limonin. ΔfusSm = 50 − R ln σ + R ln Φ

where SP3 is the sum of Nonring(CH2, CH, C, NH, N, O, S), SP2 is the sum of Nonring(CH, C, N, CO), and Ring is the sum of independent single, fused, or conjugated ring systems, so the values of SP3, SP2, and Ring for limonin are 0, 0 and 7, respectively. According to eqs 25 and 26, Φ for limonin was 9.2523. Then, upon substitution of Φ (=9.2523) and σ (=1) into eq 24, ΔfusSm for limonin was estimated to be 68.4975 J K−1 mol−1. Finally, the molar fusion enthalpy (ΔfusHm) for limonin was 39.181 kJ mol−1 obtained by eq 27. ΔfusHm = ΔfusSmTm

4.2. PXRD Analysis. The representative PXRD patterns of limonin standard and precipitates in different solvents were showed in Figure S2. Compared with the PXRD pattern of limonin standard, the PXRD patterns of the precipitates in the solvents had the same characteristic peaks and exhibited no significant changes, indicating that limonin was stable and had no polymorphism transformation during the entire experiments. 4.3. Solubility Values. The mole fraction solubilities of limonin in the eight pure solvents (acetonitrile, ethyl acetate, butyl acetate, chloroform, tetrahydrofuran, ethanol, 2-propanol, 1-butanol) and ethyl acetate + 2-propanol binary solvents within the temperature range 283.2−323.2 K were presented in Table 2 and plotted in Figures 2 and 3. The mole fraction solubility of limonin in different solvents increased with the temperature. Moreover, the solubility increased with the initial composition of ethyl acetate in the ethyl acetate + 2-propanol binary solvents. At a given temperature within the range 283.2− 323.2 K, the order of the solubility of limonin was chloroform > tetrahydrofuran > ethyl acetate > butyl acetate > ethanol > 1butanol > 2-propanol. At a temperature below 303.2 K the

(24)

where R is the gas constant. The rotational symmetry number (σ) is the number of positions into which a molecule can be rotated and that are identical to a reference position. The σ value of limonin is 1, because the molecular structure of limonin has no symmetry. The molecular flexibility number (Φ) can be obtained by eq 25. Φ = 2.435τ

(25)

where the constant 2.435 is based on the literature37,38 and τ is the number of torsional angles or the flexibility count. The τ value can be calculated by the following semiempirical equation (eq 26).39 τ = SP3 + 0.5SP2 + 0.5Ring − 1

(27)

(26) D



E

1.8552 0.3753 0.1594 1.0971 1.0961 0.0341 0.0172 0.0274 0.0765 0.1593 0.1908 0.0412 0.0327 0.0245 0.0200 0.0241 0.0782 0.0794 0.0831 0.0678 0.0352 0.0239 0.9891 0.9475 0.98201 0.9600 0.9796 0.9791 0.9710 0.9730 0.9767 0.9838 0.9804

a

−2821.57 −1312.70 −1856.52 −839.19 −1715.40 −3673.77 −3535.17 −3916.51 −3463.27 −2135.01 −1520.06 acetonitrile ethyl acetate butyl acetate chloroform tetrahydrofuran ethanol 2-propanol n-butyl alcohol xEA = 0.20e xEA = 0.50e xEA = 0.80e

3.9502 −2.6391 −1.5194 −2.5426 −0.0270 2.1483 0.8818 2.5320 2.2651 −0.6760 −2.2776

10 RMSD RAD

R b a solvents

a, b, A, B, C, λ, and h are the parameters of the models. bR2 is the determinate coefficient. cRAD is the relative average deviation. dRMSD is the root-mean-square deviation. exEA is the mole fraction of ethyl acetate in the ethyl acetate + 2-propanol binary solvent mixtures. The relative standard uncertainty ur is ur(xEA) = 0.06.

1.8283 0.3531 0.1620 0.9333 1.0434 0.0339 0.0171 0.0273 0.0763 0.1522 0.1755 0.0406 0.0304 0.0253 0.0169 0.0227 0.0779 0.0789 0.0827 0.0674 0.0337 0.0216 0.9895 0.9535 0.9832 0.9710 0.9816 0.9713 0.9732 0.9713 0.9732 0.9852 0.9834 8278.1 282130.6 277566.2 100255.3 46415.2 287891.7 774040.7 318902.4 167708.3 212162.3 298404.9 0.3371 0.0037 0.0062 0.0034 0.0335 0.0127 0.0045 0.0122 0.0205 0.0096 0.0044 0.7223 0.2203 0.1594 0.3422 0.7621 0.0182 0.0100 0.0109 0.0671 0.0525 0.1007 0.0131 0.0147 0.0250 0.0057 0.0162 0.0391 0.0458 0.0337 0.0425 0.0111 0.0135 0.9981 0.9789 0.9797 0.9955 0.9885 0.9931 0.9886 0.9951 0.9792 0.9980 0.9936 46.4687 40.7158 −7.65461 26.5214 29.3787 79.2709 83.8561 102.301 44.5488 42.9553 30.1696 11414.2 11070.8 −4192.2 7210.6 2738.3 20714.2 22223.0 27558.9 10231.7 10981.1 7664.0

RAD R C B A

−308.576 −276.184 49.9318 −180.669 −197.464 −531.320 −563.289 −685.926 −297.500 −289.433 −204.995

104RMSD RAD R2 10 RMSD

λ

h

λh model

4 2

Modified Apelblat model

d

4 c

mole fraction solubility of limonin in acetonitrile was lower than that in chloroform, whereas at a temperature above 303.2 K the mole fraction solubility of limonin in acetonitrile was higher than that in chloroform. Therefore, the results showed that the solubility order was not completely consistent with the polarity order of the solvents. It was speculated that the hydrogen bond in the solution might also play an important role in making this difference.15 4.4. Correlation of Solubility of Limonin with Temperature. The experimental solubilities of limonin at various temperatures from 283.2 to 323.2 K were fitted by the van’t Hoff model, the modified Apelblat model, and the λh model with a nonlinear regression method to describe the solid−liquid equilibrium. The model parameters together with RAD and RMSD of the three models were listed in Table 3. All values of RAD and RMSD were acceptable, suggesting that the calculated solubilities using the models agreed very well with the experimental ones for all solvents, and all models could be used to describe the dissolution behavior of limonin in these solvents at various temperatures. Among the three models the modified Apelblat model had the highest R2 and lowest RMSD and gave the best correlation. The fitting plots of the modified Apelblat model were shown in Figure 2. The λ values of the λh model in Table 3 were all very small, indicating that there were no obvious association in the selected solvents, and the solutions were highly nonideal.40 4.5. Correlation of Solubility with Both Temperature and Initial Solvent Composition in the Ethyl Acetate + 2-Propanol Binary Solvents. As shown in Table 4, the fitting

2b

Figure 3. Mole fraction solubility (x) of limonin in the ethyl acetate + 2-propanol binary solvents with various initial mole fractions of ethyl acetate at different temperatures.

Van’t Hoff model

Figure 2. Mole fraction solubility profiles of limonin (x) correlated by the modified Apelblat model in various pure solvents at different temperatures (T).

a

Table 3. Parameters of the Van’t Hoff Model, Modified Apelblat Model, and λh Model Correlated from Experimental Data of Limonin in the Investigated Solvents

Article



Article

Table 4. Parameters of the Jouyban−Acree Model, van’t Hoff−Jouyban−Acree Model, Apelblat−Jouyban−Acree Model and Ma, Sun, and NRTL Models Correlated from the Experimental Values for Limonin in the Binary Solvents Ethyl Acetate + 2Propanol Jouyban−Acree model parameters

value

van’t Hoff−Jouyban− Acree model parameters

Apelblat−Jouyban− Acree model

value

parameters

value

J0a J1 J2

1076.83 −216.012 −730.303

a1b b1 a2 b2 J0 J1 J2

−1282.62 −2.7372 −3937.36 2.1630 1092.14 −222.107 −724.755

R2 g RADh 104RMSDi

0.9989 0.0376 0.1212

R2 RAD 104RMSD

0.9962 0.0537 0.2094

A1c B1 C1 A2 B2 C2 J0 J1 J2 R2 RAD 104RMSD

−241.801 9538.81 35.5841 −153.709 3184.41 23.1642 1091.08 −221.924 −725.814 0.9985 0.0424 0.1268

Sun model parameters

Ma model

NRTL model

value

parameters

value

parameters

value

D1d D2 D3 D4 D5 D6 D7

2.1383 −3925.96 −4.87378 3200.28 1908.10 −5469.82 2944.28

R2 RAD 104RMSD

0.9962 0.0568 0.2152

E1e E2 E3 E4 E5 E6 E7 E8 E9 R2 RAD 104RMSD

−253.371 7755.48 37.9773 −2.3428 2808.88 2482.05 −6049.07 3170.40 −0.32186 0.9986 0.0418 0.1256

α1f α2 α3 g21 − g11/R g31 − g11/R g12 − g22/R g32 − g22/R g13 − g33/R g23 − g33/R R2 RAD 104RMSD

−0.05117 0.00065 0.3 893.198 −3198.19 −1060.75 −11.7717 35676.9 −129.119 0.9918 0.3379 0.4157

a

J0, J1, and J2 are the parameters of the Jouyban−Acree model. ba1, b1, a2, b2, j0, j1, and j2 are the parameters of van’t Hoff−Jouyban−Acree model. A1, B1, C1, A2, B2, C2, k0, k1, and k2 are the parameters of the Apelblat−Jouyban−Acree model. dD1, D2, D3, D4, D5, D6, and D7 are the parameters of the Sun model. eE1, E2, E3, E4,E5, E6, E7, E8, and E9 are the parameters of the Ma model. fα1, α2, α3, g21 − g11/R, g31 − g11/R, g12 − g22/R, g32 − g22/R, g13 − g33/R, and g23 − g33/R are the parameters of the NRTL model. gR2 is the determinate coefficient. hRAD is the relative average deviation. i RMSD is the root-mean-square deviation. c

Table 5. Parameters of the NRTL Model Correlated from Experimental Data of Limonin in the Pure Solvents NRTL model

a

solvents

g21 − g11/Ra

g12 − g22/R

α

R2 b

RADc

104RMSDd

acetonitrile ethyl acetate butyl acetate chloroform tetrahydrofuran ethanol 2-propanol n-butyl alcohol

1657.775 3235.069 3408.014 3373.273 2693.731 3528.587 3672.241 3590.046

−678.976 −996.047 −828.515 −1536.45 −1074.98 −690.859 −652.737 −675.514

0.496 0.345 0.449 0.179 0.288 0.560 0.601 0.575

0.9989 0.9984 0.9958 0.9994 0.9982 0.9929 0.9748 0.9916

0.0085 0.0217 0.0307 0.0167 0.0173 0.0148 0.0360 0.0170

0.4539 0.2068 0.1404 0.5316 0.5875 0.1002 0.0096 0.0045

g21 − g11/R, g12 − g22/R, and α are the parameters of the NRTL model. bR2 is the determinate coefficient. cRAD is the relative average deviation. RMSD is the root-mean-square deviation.

d

were presented in Table 6. All values of ΔGmix were negative and decreased with the temperature, indicating that the mixing process of limonin in the selected solvents was a spontaneous and favorable process. The values of ΔHmix were all negative in eight pure solvents, which meant that the mixing process was exothermic, whereas in the binary ethyl acetate + 2-propanol solvent systems, ΔHmix was endothermic on the basis of the positive values of ΔHmix.

solubility data using the Jouyban−Acree model, van’t Hoff− Jouyban−Acree model, Apelblat−Jouyban−Acree model, and Ma, Sun, and NRTL models showed good agreement with the experimental values, which indicated that all selected models had acceptable accuracy. Among these six models, the Jouyban−Acree model showed the best correlation results due to the highest regression coefficient and the lowest RAD and RMSD, suggesting that Jouyban−Acree model was the most suitable model to describe the dissolution behavior of limonin in the binary mixture solvents ethyl acetate + 2propanol and could predict the solubilities of limonin at temperatures not studied. 4.6. Correlation of Solubility Data by the NRTL Model. The fitting results of the NRTL model for the binary solvents and pure solvent were presented in Tables 4 and 5, respectively. The NRTL model gave good fitting results of the solubility data of limonin in all investigated solvents, indicating that the NRTL model could be used to predict the solubilities in both pure and mixture solvents at various temperatures. On the basis of this consideration, the NRTL model was better than other models. 4.7. Mixing Thermodynamic Properties. In terms of the regressed parameters in the NRTL model and the experimental solubility data, the calculated mixing thermodynamic properties

5. CONCLUSION In this work, the solubility of limonin in pure and binary solvents within the temperature range 283.2−323.2 K was determined by the HPLC method. The solubility of limonin increased with the temperature and the initial mole fraction of ethyl acetate in the binary systems of ethyl acetate + 2propanol. In all selected monosolvent systems except acetonitrile, the solubility values at a given temperature ranked as chloroform > tetrahydrofuran > ethyl acetate > butyl acetate > ethanol > 1-butanol > 2-propanol. Besides, the solubility in acetonitrile was more sensitive to temperature than in other solvents. The solubility order was not completely consistent with the polarity order of the solvents, which maybe resulted from the difference of the hydrogen bond interaction between F


G

−77.972 −0.0929 −81.872 −0.0964 −84.900 −0.0915 −95.931 −0.1102 −105.015 −0.1297 −99.993 −0.1000 −107.503 −0.0909 −136.763 −0.1562 −156.977 −0.2042 xEA = 0.20d

ΔHmix/J mol−1

−365.379 −290.445 −205.716 −213.812 −177.777 −126.085 −148.944 −155.022 −134.329

−51.667 −54.093 −58.071 −63.061 −65.692 −69.163 −79.032 −87.056 −90.981

ΔGmixc/J mol−1

−1366.28 −1410.03 −1431.06 −1452.17 −1472.83 −1495.55 −1518.45 −1540.18 −1562.85

283.2 288.2 293.2 298.2 303.2 308.2 313.2 318.2 323.2

Tb/K

283.2 288.2 293.2 298.2 303.2 308.2 313.2 318.2 323.2

−0.5613 −0.6113 −0.6297 −0.7167 −0.8521 −1.0687 −1.2826 −1.5857 −1.8494

ΔGmix/ J mol−1

3.5342 3.8847 4.1792 4.1528 4.2713 4.4434 4.3726 4.3531 4.4199

ΔSmix/J mol−1 K−1

ΔSmix/ J mol−1 K−1

−15.730 −15.826 −16.422 −17.169 −18.674 −19.167 −19.516 −22.482 −23.697

−1973.59 −2000.81 −2030.68 −2062.36 −2094.26 −2127.33 −2161.81 −2196.81 −2231.86

ΔGmix/J mol−1

−0.7445 −0.8711 −0.8679 −0.8427 −0.9267 −1.1649 −1.6124 −2.0867 −2.5969

ΔHmix/ J mol−1

−25.180 −25.609 −26.141 −26.639 −29.517 −32.671 −30.354 −33.345 −41.230 ethanol

−460.751 −384.28 −253.827 −204.832 −170.820 −106.673 −57.351 −42.181 −41.9612

ΔHmix/J mol−1

−0.0007 −0.0009 −0.0008 −0.0004 −0.0002 −0.0003 −0.0011 −0.0016 −0.0023 xEA = 0.50d


−0.0334 −0.0339 −0.0332 −0.0318 −0.0358 −0.0438 −0.0346 −0.0341 −0.0543


5.3420 5.6091 6.0602 6.2291 6.3438 6.5563 6.7192 6.7713 6.7757


−0.2288 −0.2608 −0.3201 −0.3619 −0.3740 −0.4401 −0.5803 −0.6536 −0.7336

ΔGmix/ J mol−1

−6.529 −6.951 −7.367 −7.981 −9.159 −9.857 −11.210 −11.586 −12.029

ΔGmix/ J mol−1

−1403.77 −1424.66 −1446.48 −1470.47 −1493.86 −1517.95 −1541.56 −1566.23 −1592.18

xEA

−266.919 −230.492 −143.247 −109.705 −108.701 −103.061 −90.084 −35.222 −6.8241

−0.3195 −0.4800 −0.5098 −0.5502 −0.7239 −0.7691 −0.9222 --1.1492 −1.4246

ΔHmix/ J mol−1

−150.327 −153.807 −157.821 −159.020 −156.661 −168.179 −172.983 −180.761 −198.519 n-butyl alcohol

ΔHmix/ J mol−1

chloroform

4.0143 4.1435 4.4449 4.5632 4.5685 4.5908 4.6343 4.8115 4.9052


−0.2641 −0.3335 −0.4165 −0.4753 −0.5817 −0.6942 −0.8154 −1.0560 −1.3293 = 0.80d

ΔGmix/ J mol−1

−90.813 −91.237 −92.846 −93.889 −96.689 −101.711 −103.831 −109.633 −113.314

ΔGmix/ J mol−1

ΔHmix/J mol−1

−0.00016 −0.00013 −0.00013 −0.00045 −0.00027 −0.00034 −0.00029 −0.00033 −0.00030


−0.0142 −0.0157 −0.0176 −0.0231 −0.0255 −0.0308 −0.0312 −0.0289 −0.0317


ΔGmix/J mol−1

−0.2735 −0.2992 −0.3582 −0.4954 −0.4572 −0.5436 −0.6721 −0.7583 −0.8293

ΔHmix/ J mol−1

−10.550 −11.485 −12.532 −14.876 −16.890 −19.354 −20.997 −20.779 −22.285 2-propanol

ΔHmix/ J mol−1

butyl acetate

−0.0002 −0.0005 −0.0003 −0.0002 −0.0004 −0.0002 −0.0003 −0.0029 −0.0029


−0.2102 −0.2171 −0.2216 −0.2184 −0.1978 −0.2157 −0.2208 −0.2235 −0.2636


Standard uncertainty u is u(p) = 10 hPa. bStandard uncertainties u is u(T) = 0.1 K. cΔGmix, ΔHmix, and ΔSmix denote the mixing Gibbs energy, mixing enthalpy, and mixing entropy, respectively. The relative standard uncertainties of ΔurGmix, ΔurHmix, and ΔurSmix are 0.034, 0.060, and 0.053, respectively. dxEA is the initial mole fraction of ethyl acetate in the ethyl acetate + 2-propanol binary solvent mixtures. The relative standard uncertainty ur is ur(xEA)=0.06.

a

ΔHmix/ J mol−1

ΔGmixc/ J mol−1

−0.0371 −0.0617 −0.0924 −0.0723 −0.0553 −0.0665 −0.0658 −0.1239 −0.1588

Tb/K

−69.076 −84.131 −99.816 −100.490 −108.134 −123.913 −142.499 −180.047 −211.107 tetrahydrofuran

−58.563 −66.326 −72.709 −78.902 −91.345 −103.400 −121.872 −140.617 −159.781

283.2 288.2 293.2 298.2 303.2 308.2 313.2 318.2 323.2

ΔGmix/ J mol−1

ΔHmix/ J mol−1


ΔHmix/ J mol−1

ΔGmix / J mol−1

c

Tb/K

ethyl acetate

acetonitrile

Table 6. Mixing Thermodynamic Properties of Limonin (x) in the Pure and Mixed Solvents at Different Temperatures and Atmospheric Pressure (p = 101.1 kPa)a

Journal of Chemical & Engineering Data Article



Article

disease and inflammation in overweight human adults. J. Funct. Foods 2015, 12, 271−281. (4) Bao, Y.; Yuan, F.; Zhao, X.; Liu, Q.; Gao, Y. Equilibrium and kinetic studies on the adsorption debittering process of ponkan (Citrus reticulata Blanco) juice using macroporous resins. Food Bioprod. Process. 2015, 94, 199−207. (5) Gualdani, R.; Cavalluzzi, M. M.; Lentini, G.; Habtemariam, S. The chemistry and pharmacology of Citrus limonoids. Molecules 2016, 21, 1530−1568. (6) Tan, Q. G.; Luo, X. D. Meliaceous limonoids: chemistry and biological activities. Chem. Rev. 2011, 111, 7437−7522. (7) Zou, Z.; Xi, W.; Hu, Y.; Nie, C.; Zhou, Z. Antioxidant activity of citrus fruits. Food Chem. 2016, 196, 885−896. (8) Castillo-Herrera, G. A.; Farías-Á lvarez, L. J.; García-Fajardo, J. A.; Delgado-Saucedo, J. I.; Puebla-Pérez, A. M.; Lugo-Cervantes, E. Bioactive extracts of citrus aurantifolia swingle, seeds obtained by supercritical CO2, and organic solvents comparing its cytotoxic activity against L5178y leukemia lymphoblasts. J. Supercrit. Fluids 2015, 101, 81−86. (9) Lee, D. H.; Jeon, E. J.; Ahn, J.; Hwang, J. T.; Hur, J.; Ha, T. Y.; Jung, C. H.; Sung, M. J. Limonin enhances osteoblastogenesis and prevents ovariectomy-induced bone loss. J. Funct. Foods 2016, 23, 105−114. (10) Fan, J. P.; Liao, D. D.; Xie, Y. L.; Zheng, B.; Yu, J. X.; Cao, Y. H.; Zhang, X. H.; Peng, H. L. A molecular imprinted polymer on the surface of superparamagneticFe3O4−graphene oxide (MIP@Fe3O4@ GO) for simultaneous recognition and enrichment of evodiamine and rutaecarpine in evodiae fructus. J. Appl. Polym. Sci. 2017, 134, 44465. (11) Chandler, B. V.; Robertson, G. L. The solubility of limonin, the bitter principle of orange juice. J. Sci. Food Agric. 1983, 34, 1272−1284. (12) Luo, X.; Ren, R.; Qian, Z.; Yang, J. HPLC determination of equilibrium solubility and apparent oil /water partition coefficient of limonin. Chin. J. Pharm. Anal. 2013, 33, 1711−1714. (13) Fan, J. P.; Zheng, B.; Liao, D. D.; Yu, J. X.; Cao, Y. H.; Zhang, X. H.; Zhu, J. H. Determination and modeling of the solubility of (limonin in methanol or acetone + water) binary solvent mixtures at T = 283.2 to 318.2 K. J. Chem. Thermodyn. 2016, 98, 353−360. (14) Fan, J. P.; Liao, D. D.; Zheng, B.; Xu, X. K.; Zhang, X. H. Measurement and modeling of the Solubility of genistin in water + (ethanol or acetone) binary solvent mixtures at T = 278.2−313.2 K. Ind. Eng. Chem. Res. 2015, 54, 12981−12986. (15) Fan, J. P.; Xu, X. K.; Shen, G. L.; Zhang, X. H. Measurement and correlation of the solubility of genistin in eleven organic solvents from T = (283.2 to 323.2) K. J. Chem. Thermodyn. 2015, 89, 142−147. (16) Fan, J. P.; Yang, D.; Xu, X. K.; Guo, X. J.; Zhang, X. H. Solubility of daidzin in different organic solvents and (ethyl alcohol + water) mixed solvents. J. Chem. Thermodyn. 2015, 88, 85−89. (17) Fan, J. P.; Kong, T.; Zhang, X.-H.; Zhang, L.; Tong, S.; Tian, Z.Y.; Zhu, J.-H. Solubilities of oleanolic acid and ursolic acid in ethanol + water mixed solvents from (292.2 to 328.2) K. J. Chem. Thermodyn. 2012, 47, 372−375. (18) Fan, J. P.; Kong, T.; Zhang, L.; Tong, S.; Tian, Z.-Y.; Duan, Y.H.; Zhang, X.-H. Solubilities of ursolic acid and oleanolic acid in four solvents from (283.2 to 329.7) K. J. Chem. Eng. Data 2011, 56, 2723− 2725. (19) Aniya, V.; De, D.; Mohammed, A. M.; Thella, P. K.; Satyavathi, B. Measurement and modeling of solubility of para-tert-butylbenzoic acid in pure and mixed organic solvents at different temperatures. J. Chem. Eng. Data 2017, 62, 1411−1421. (20) Wu, G.; Hu, Y.; Gu, P.; Yang, W.; Ding, Z.; Wang, C.; Qian, Y. Solubility and solution thermodynamics of Gibberellin A4 in different organic solvents from 278.15 to 333.15 K. J. Chem. Eng. Data 2015, 60, 2104−2109. (21) Nam, K.; Ha, E. S.; Kim, J. S.; Kuk, D. H.; Ha, D. H.; Kim, M. S.; Cho, C. W.; Hwang, S. J. Solubility of oxcarbazepine in eight solvents within the temperature range T = (288.15−308.15) K. J. Chem. Thermodyn. 2017, 104, 45−49. (22) Jiang, S.; Qin, Y.; Wu, S.; Xu, S.; Li, K.; Yang, P.; Zhao, K.; Lin, L.; Gong, J. Solubility correlation and thermodynamic analysis of

the solute and the solvent. The experimental solubilities of limonin in eight pure solvents were correlated with the van’t Hoff model, the modified Apelblat equation, the λh equation, and the NRTL equation. The dependence of the solubility of limonin in ethyl acetate + 2-propanol binary solvents upon temperature and initial solvent composition was correlated with the Jouyban−Acree model, van’t Hoff−Jouyban−Acree model, Apelblat−Jouyban−Acree model, Ma model, Sun model, and NRTL model. As a whole, all the models gave good correlation results, and the modified Apelblat model and the Jouyban− Acree model showed better correlation results than the others. In addition, the thermodynamic properties of the mixing process in all selected solvents, including mixing Gibbs energy, mixing enthalpy, and mixing entropy, were calculated. The results showed that the mixing processes in all studied solvent systems were spontaneous.

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jced.7b00851. DTG, TG, and DSC curves of limonin (Figure S1) and the representative PXRD patterns of limonin standard and precipitates in different solvents at 293.2 K (Figure S2) (PDF)

■

AUTHOR INFORMATION

Corresponding Author

*J.-P. Fan. E-mail: [email protected]. Tel: 086-79183968583. Fax: 086-791-83968594. ORCID

Jie-Ping Fan: 0000-0002-9410-3670 Funding

Financial support from the National Natural Science Foundation of China (Nos. 21366019, 20806037 and 20876131), Jiangxi Province Academic and Technical Leaders of Major Academic Disciplines (20162BCB22010), Key Laboratory of Coa1Gasification and Energy Chemical Engineering of Ministry of Education (2016KY11-049), Jiangxi Province Young Scientists (Jinggang Star) Cultivation Plan (20112BCB23002), Jiangxi Province Higher School Science and Technology Landing Plan Projects (No. KJLD13012), Special Funds for Graduate Student Innovation in Jiangxi Province (No. YC2014-S013), and Jiangxi Province Undergraduate Innovation and Entrepreneurship Training Program (No. 201310403040) are gratefully acknowledged. Notes

The authors declare no competing financial interest.

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Determination and Thermodynamic Analysis of the Solubility of

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