(4-Hydroxyphenyl)-2-butanone (Raspberry Ketone)

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J Solution Chem DOI 10.1007/s10953-017-0681-0

Solubility and Solution Thermodynamic Properties of 4-(4-Hydroxyphenyl)-2-butanone (Raspberry Ketone) in Different Pure Solvents Min Shu1 • Liang Zhu1 • Min Yuan2 • Liyu Wang1 • Yanfei Wang1 Libin Yang1 • Zuoliang Sha1 • Meng Zeng2



Received: 27 February 2017 / Accepted: 17 July 2017 Ó Springer Science+Business Media, LLC 2017

Abstract The solubility of 4-(4-hydroxyphenyl)-2-butanone (raspberry ketone) in six pure solvents was experimentally determined at temperatures ranging from 283.15 to 313.15 K under the pressure 0.10 MPa by employing a gravimetrical method. The experimental results indicate that the solubility of raspberry ketone in all studied solvents is temperature dependent, a rise in temperature brings about an increase in solubility. The experimental solubility data of raspberry ketone in six pure solvents (acetone, ethanol, ethyl acetate, npropyl alcohol, n-butyl alcohol, and distilled water) was correlated by using several commonly used thermodynamic models, including the Apelblat, van’t Hoff and kh equations. The results of the error analysis indicate that the van’t Hoff equation was able to give more accurate and reliable predictions of solubility with root-mean-square deviation less than 0.56%. Furthermore, the changes of dissolution enthalpies (DdissH°), dissolution entropies (DdissS°) and dissolution Gibbs energies (DdissG°) of raspberry ketone in the solvents studied were estimated by the van’t Hoff equation. The positive value of DdissH°, DdissS°, and DdissG° indicated that these dissolution processes of raspberry ketone in the solvents studied were all endothermic and enthalpy-driven. Keywords Raspberry ketone  Solubility  Pure solvent  Gravimetrical method  Dissolution thermodynamic properties

& Liang Zhu [email protected] & Min Yuan [email protected] 1

Tianjin Key Laboratory of Marine Resources and Chemistry, College of Material Science and Chemical Engineering, Tianjin University of Science & Technology, Tianjin 300457, People’s Republic of China

2

Tianjin Academy of Environmental Science, Tianjin 300191, People’s Republic of China

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J Solution Chem

1 Introduction Raspberry ketone {4-(4-hydroxyphenyl)-2-butanone, CAS Registry No. 5471-51-2}, as shown in Fig. 1, is a kind of perfume with fruity fragrance and is widely employed as a ingredient of edible flavor, cosmetic fragrance and an intermediate of medicine [1]. As a major aromatic compound contained in red raspberries, raspberry ketone also has a three times higher anti-obesity activity than capsaicin. Moreover, it can help increase the skin’s elasticity and promote hair growth by increasing dermal IGF-I production [2–4]. It has been reported that raspberry ketone is produced by the Claisen–Schmidt condensation reaction between p-hydroxy benzaldehyde and acetone [5, 6]. During the whole manufacturing process, crystallization is one of the most crucial operations that plays an important role in controlling the quality of the product raspberry ketone. Many studies about raspberry ketone had focused on the synthetic mechanism, but few works were reported to optimize the production process of raspberry ketone for obtaining a raspberry ketone product with high quality. It is commonly known that crystallization is universally applied in the field of chemical, pharmaceutical and food industries for the separation and purification of products. An appropriate crystallization solvent and optimized crystallization process are crucial to obtain a crystalline product with good particle size distribution [7], crystal form and morphology [8]. To choose the proper crystallization solvent and optimizing the crystallization process, it is necessary to know the corresponding thermodynamic data. However, to the best of our knowledge, there are few reports about the thermodynamic properties of raspberry ketone. Therefore, measuring the thermodynamic data of raspberry ketone including solubility and thermodynamic properties in different solvents is essential to develop a robust and explicit crystallization process. The most widely used measurement methods of solubility are the static method [9] and dynamic method [10]. Because the dissolution of the last solute can’t be observed exactly, the dynamic method could bring big errors into the experimental results, but the static method can solve this problem by determining the solubility data through analyzing the solid and liquid phase composition in the equilibrium saturated solution. Therefore, the static gravimetrical method was used to determine the solubility of raspberry ketone in different solvents. In this work, the solubility of raspberry ketone in six pure solvents from 283.15 to 313.15 K was determined by using a gravimetrical method. The Apelbat, van’t Hoff and kh equations were used to correlate the experimental data in the experimental solvents. Furthermore, the changes of dissolution enthalpy, dissolution entropy and dissolution molar Gibbs energy of raspberry ketone in all experimental solvents were evaluated by the van’t Hoff equation. These preliminary investigations should be useful for the development and optimization of the crystallization process for raspberry ketone.

O

Fig. 1 Schematic diagram of the molecular structure of raspberry ketone

HO

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J Solution Chem

2 Experiments 2.1 Materials The raspberry ketone sample used in this work, with mass fraction purity higher than 99.6%, was kindly supplied by the Bestally Biological Technology Co., Ltd. (Zhangzhou, China). It was subsequently purified by recrystallization from a ethanol–water binary mixture and dried in vacuum to constant weight at 323.15 K. In the experiments, all organic solvents with purity higher than 99.7%, including ethanol, n-propyl alcohol, nbutyl alcohol, ethyl acetate, and acetone were purchased from Bolt Chemical Trade Co., Ltd. (Tianjin, China) and used without further purification. Detailed relevant information about the materials is listed in Table 1.

2.2 Apparatus and Experiment 2.2.1 Characterization of the Raspberry Ketone Sample The stability of raspberry ketone during all the experimental process was identified by X-ray powder diffraction (XRPD), which was conducted on a Puxi XD-3 automatic diffractometer system (Puxi, China) under the following experimental conditions: Cu Ka ˚ ) radiation, scan range 5° B 2h B 60°, scan step D2h = 0.02, and scan (k = 1.54187 A -1 speed 2 °min . The tube voltage and current were set at 40 kV and 40 mA respectively. The melting temperature and enthalpy of fusion of raspberry ketone were determined by differential scanning calorimetry (NETZSH DSC-200F3) with a heating rate of 10 Kmin-1 under the protection of nitrogen. All the measurement experiments were performed in triplicate in the temperature range from 293.15 to 393.15 K. Table 1 The descriptions of experimental materials used in this paper Chemical name

Source

Purification method

Final mass fraction purity

Analysis method

Raspberry ketone

Bestally Biological Technology Co., Ltd. (Zhangzhou, China)

Recrystallization

C 0.996

HPLCa

Acetone

Bolt Chemical Trade Co., Ltd. (Tianjin, China)

No further

C 0.997

GCa

Ethanol

Bolt Chemical Trade Co., Ltd. (Tianjin, China)

No further

C 0.997

GCa

n-Propyl alcohol

Bolt Chemical Trade Co., Ltd. (Tianjin, China)

No further

C 0.997

GCa

n-Butyl alcohol

Bolt Chemical Trade Co., Ltd. (Tianjin, China)

No further

C 0.997

GCa

Ethyl acetate

Bolt Chemical Trade Co., Ltd. (Tianjin, China)

No further

C 0.997

GCa

Water

Laboratory

Distillation

Distilleddeionized water



a

HPLC, high performance liquid chromatography; GC, gas–liquid chromatography

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2.3 Solubility Measurements of Raspberry Ketone The solubility of raspberry ketone was determined by the static analytical method. All the experiments were performed in the automated lab reactor (EasyMax 102, Mettler Toledo, Switzerland) as shown in Fig. 2, with a working volume of 50 mL. The metallic stirrer with four blades was controlled by an overhead motor. An excess amount of raspberry ketone was added into the glass crystallizer. After that, the crystallizer was maintained at the set temperature by the EasyMax with an precision of 0.05 K. The solution was continuously stirred for 12 h, which had been confirmed to be sufficient to ensure that it had reached solid–liquid equilibrium. Then, it was kept static for 10 h to allow the solid phase to settle out completely. After that, the supernatant liquid was withdrawn by a syringe with filter membrane (0.50 lm) and injected into a pre-weighed 10 mL evaporating dish with cover. The evaporating dish with the solution was weighed immediately and then placed in a vacuum oven at T = 323.15 K for 16 h until the weight remained constant. Meanwhile, the precipitated solutes, which were filtered and dried for all the above experiments, could be identified by X-ray powder diffraction (XRPD) to determine whether or not there was a polymorphic transformation during the experimental process. In all of the experiments, all of the masses of the raspberry ketone and solvents were weighed using an analytical balance (type AR2140, Ohaus Corp, Pine Brook, USA) with an uncertainty of ± 0.0001 g. Every experiment was repeated three times. The mole fraction (x) of the raspberry ketone in the pure solvents was calculated by the following equation [11]: x¼

m=M m=M þ ms =Ms

ð1Þ

where m and ms are the masses of raspberry ketone and experimental solvent, respectively; M and Ms represent the molar masses of solute and solvent, respectively.

2.4 Verification of the Solubility Data To ensure the reliability of the solubility of raspberry ketone in different solvents, verification experiments should be conducted. Using the measured solubility data, saturated raspberry ketone solutions at selected temperatures were prepared by the dynamic method combined with a laser monitoring system [12]. The deviation between the solubility data

Fig. 2 Experimental apparatus EasyMax: (1) controller of the automatic reactor; (2) temperature control unit; (3) metal stirrer; (4) thermometer

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measured by the dynamic method and static method can be used to validate the reliability of the solubility data measured by the static method as applied in this study.

2.5 The Thermodynamic Models Applied in Pure Solvents To extract more information from the solubility data in the temperature range from 283.15 to 313.15 K, the solubility data of raspberry ketone in the experimental pure solvents was correlated with three thermodynamic models, the modified Apelblat equation, van’t Hoff equation and kh equation.

2.5.1 The Apelblat Equation The Apelblat equation is based on solid–liquid equilibrium theory and widely applied to describe the relationship between the solubility and temperature in a solvent. It is a frequently used as a semi-empirical model and can be expressed as follow [13–15]: ln x ¼ A1 þ

B1 þ C1 ln T T

ð2Þ

where x denotes the mole fraction solubility of raspberry ketone in the solvent, T denotes the absolute temperature, and A1, B1 and C1 are the model constants which can be estimated by regression analysis of the experimental solubility data.

2.5.2 The van’t Hoff Equation In general, the van’t Hoff model provides a physical relationship between the solubility and temperature, which is expressed as the natural logarithm of the solubility upon the reciprocal of experimental temperature [16, 17]: ln x ¼ A2 þ

B2 T

ð3Þ

where x denotes the mole fraction solubility of the solute and T is the equilibrium temperature of the solution; A2 and B2 are the constant parameters of the van’t Hoff model.

2.5.3 The kh Equation The kh equation, which was first derived by Buchowski et al., is another empirical equation describing the relationship between mole fraction solubility and temperature. It can be used to fit the experimental solubility data for many systems with only two parameters. The equation is given as follows [18–20]:     kð1  xÞ 1 1 ¼ kh  ð4Þ ln 1 þ x T Tm where x denotes the mole fraction solubility, T and Tm are the experimental temperature and melting temperature of solute, respectively, while k and h are the model parameters.

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3 Results and Discussion 3.1 Characterization Results for the Raspberry Ketone Sample 3.1.1 XRPD Pattern of Raspberry Ketone Sample The XRPD pattern of raspberry ketone sample is shown in Fig. 3. The most characteristic radiation peaks are at 2h = 9.383°, 14.158°, 15.480°, 18.900°, 22.161°, 25.381°, 27.102°, 29.100°, 34.356°, 38.041°, 42.081° and 44.138°.

3.1.2 Melting Properties of Raspberry Ketone The melting temperature (Tm) and enthalpy of fusion (DfusH) of raspberry ketone were measured by DSC. As shown in Fig. 4, Tm and DfusH of raspberry ketone are 355.0 K (n = 3, n is the number of replicate experiments, the uncertainty is U = 0.5 K, 0.95 confidence interval) and 24.7 kJmol-1 (n = 3, the uncertainty is U = 0.1 kJmol-1, 0.95 confidence interval), respectively. The deviation is specified as the mean standard deviation of three experiments. The measured melting temperature is in good agreement with the reported data (355.15–356.15 K) [21, 22]. The value of the entropy of fusion (DfusS) was estimated to be 69.6 Jmol-1K-1 (n = 3, the uncertainty is U = 0.2 Jmol-1K-1, 0.95 confidence interval) by using the following equation: DSfus ¼

DHfus Tm

ð5Þ

3.1.3 Stability of Raspberry Ketone Sample The XRPD patterns of the residual solutes in the solvents (acetone, ethanol, ethyl acetate, n-propyl alcohol, n-butyl alcohol, and distilled water) at temperatures ranging from 283.15 to 313.15 K are presented in Fig. 5. The most characteristic radiation peaks of the residual raspberry ketone are likely the same in all the experiments which indicates that the crystal form remains stable in each experimental solvent as well as over the whole experimental Fig. 3 XRPD pattern of raspberry ketone sample

3000

Intensity

2500 2000 1500 1000 500 0 10

20

30

2-Theta/ o

123

40

50

60

J Solution Chem 5

Fig. 4 DSC thermogram of raspberry ketone sample

Heat Flow/(mWmg-1)

4

3

Enthalpy of fusion: 24.7kJmol

-1

2

Onset melting point: 355.0 K

1

0 320

330

340

350

360

370

T/K

temperature range. Therefore, it is concluded that there was no polymorphic transformation under the experimental temperature conditions and the measured solubility data is reliable.

3.2 Solubility Data of Raspberry Ketone in Pure Solvents The measured and correlated solubility data of raspberry ketone in pure solvents from 283.15 to 313.15 K under 0.10 MPa are listed in Table 2, and the results of verification experiments are displayed in Table 3. The plots of mole fraction solubility (x) of raspberry ketone versus temperature (T) in different pure solvents correlated by three models along with error bars are demonstrated in Fig. 6. The solubility of raspberry ketone in all experimental solvents increases with temperature. The experimental results indicate that the solubility of raspberry ketone in the different solvents at a set temperature decreases in the order of acetone [ ethanol [ ethyl acetate [ n-propyl alcohol [ n-butyl alcohol [ distilled water. As acetone is toxic, ethanol could be chosen as a better solvent for wide applications. In addition, the raspberry ketone is slightly soluble in water. Therefore ethanol and water can be applied in the anti-solvent crystallization of raspberry ketone.

3.3 The Parameters and Error Analysis of the Models used for Solubility in the Pure Solvents The relative deviation (RD), relative average deviation (RAD), overall relative average deviation (ORAD), root-mean-square deviation (RMSD) and overall root-mean-square deviation (ORMSD) were calculated to assess the applicability of these models [12–14]. RD ¼

RAD ¼

xi  xcal i xi

 N  cal  1X xi  xi  N i¼1  xi 

ð6Þ

ð7Þ

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(a)

313.15 K

(b) 313.15 K

308.15 K 308.15 K 303.15 K 303.15 K

10

20

30

40

298.15 K

298.15 K

293.15 K

293.15 K

288.15 K

288.15 K

283.15 K

283.15 K

50

60

10

20

2-Theta/ o

30

40

50

60

2-Theta/ o

(d)

(c)

313.15 K

313.15 K

308.15 K 308.15 K 303.15 K

303.15 K

298.15 K

298.15 K

293.15 K 293.15 K 288.15 K

288.15 K 283.15 K

283.15 K

10

20

30

40

50

60

10

20

2-Theta/ o

30

40

50

60

2-Theta/ o

(e)

(f) 313.15 K 313.15 K

308.15 K 308.15 K 303.15 K

303.15 K 298.15 K 293.15 K

298.15 K 293.15 K

298.15 K

288.15 K 283.15 K

283.15 K

10

20

30

40

2-Theta/ o

50

60

10

20

30

40

50

60

2-Theta/ o

Fig. 5 XRPD patterns of the residual solids of raspberry ketone in different pure solvents from 283.15 to 313.15 K: a acetone, b ethanol, c ethyl acetate, d n-propyl alcohol, e n-butyl alcohol, and f distilled water

123

J Solution Chem Table 2 Experimental mole fraction solubility data (x) of raspberry ketone and calculated deviations of models from these values in different pure solvents from 283.15 to 313.15 K at 0.10 MPa T (K)

102 xa

D (102 xcal) Apelblatb

van’t Hoffc

khd

Raspberry ketone–acetone 283.15

20.11

0.18

0.13

288.15

22.75

0.14

0.13

0.13 0.07

293.15

26.17

- 0.43

- 0.41

- 0.50

298.15

29.23

- 0.39

- 0.35

- 0.43

303.15

32.01

0.22

0.26

0.26

308.15

35.20

0.70

0.72

0.89

313.15

40.34

- 0.44

- 0.48

- 0.03

Raspberry ketone–ethanol 283.15

11.14

0.69

0.63

0.09

288.15

14.09

0.34

0.31

- 0.02

293.15

17.96

- 0.35

- 0.35

- 0.52

298.15

21.50

- 0.38

- 0.36

- 0.13

303.15

25.82

- 0.07

- 0.05

0.07

308.15

30.01

1.17

1.17

1.01

313.15

35.70

0.27

0.20

1.05

Raspberry ketone–ethyl acetate 283.15

10.20

0.79

0.79

0.23

288.15

13.68

- 0.30

- 0.29

- 0.68

293.15

15.86

0.31

0.31

0.18

298.15

19.66

- 0.22

- 0.22

- 0.06 - 0.31

303.15

24.04

- 0.82

- 0.82

308.15

27.75

- 0.19

- 0.19

0.70

313.15

31.98

0.56

0.57

1.80

Raspberry ketone–n-propyl alcohol 283.15

9.43

- 0.02

0.02

- 0.13

288.15

11.26

0.42

0.42

0.34

293.15

14.26

0.12

0.13

0.08

298.15

17.79

- 0.19

- 0.19

- 0.21

303.15

21.54

- 0.16

- 0.15

- 0.18

308.15

26.43

- 0.60

- 0.59

- 0.69

313.15

30.51

0.50

0.50

0.24

Raspberry ketone–n-butyl alcohol 283.15

7.04

0.41

0.32

- 0.01

288.15

9.12

0.31

0.27

0.03

293.15

11.77

0.09

0.11

0.00

298.15

15.03

- 0.18

- 0.12

- 0.07

303.15

19.05

- 0.55

- 0.48

- 0.26

308.15

23.41

- 0.49

- 0.45

- 0.07

313.15

27.67

0.60

0.54

0.98

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J Solution Chem Table 2 continued T (K)

102 xa

D (102 xcal) Apelblatb

van’t Hoffc

khd

Raspberry ketone–distilled water 283.15

0.05

- 0.001

0.000

- 0.001

288.15

0.07

0.001

0.002

0.002

293.15

0.09

0.000

0.000

0.001

298.15

0.11

- 0.003

- 0.003

- 0.002

303.15

0.14

0.003

0.002

0.002

308.15

0.17

0.001

0.000

- 0.002

313.15

0.21

- 0.001

0.000

- 0.010

Standard uncertainties u are u(T) = 0.05 K and u(p) = 0.01 MPa (0.68 level of confidence) and combined expanded uncertainty Uc is Uc(x) = 0.0005 (0.95 level of confidence) a

Measured in the experiment

b

Deviation calculated by using the Apelblat model

c

The deviation calculated by using the van’t Hoff model

d

The deviation calculated by using the kh model

ORAD ¼ "

M 1X RAD M i¼1

N 1X 2 RMSD ¼ ðxi  xcal i Þ N i¼1

ORMSD ¼

ð8Þ #1=2

M 1X RMSD M i¼1

ð9Þ

ð10Þ

where xi denotes the experimental solubility data and xcal i the calculated solubility data, and i stands for the solubility data measured in one pure solvent at one temperature; N is the number of experimental points and M is the number of the pure solvents. The parameters of three basic thermodynamic models including modified Apelblat, van’t Hoff and kh equations for the pure solvents are listed in Table 4. They indicate that these thermodynamic models all satisfactorily correlated the experimental solubility data of raspberry ketone: the values of 102 ORAD and 102 ORMSD are both less than 2.00 and 0.50, respectively. And, the van’t Hoff equation has better results from the error analysis with its lower value of 102 ORAD (1.86) and 102 ORMSD (0.37), thus it can be used to correlate and predict the solubility of raspberry ketone.

3.4 Dissolution Thermodynamic Properties of Raspberry Ketone in Pure Solvents It was essential to study the dissolution properties of raspberry ketone in different solvents. The change of dissolution enthalpy, dissolution entropy, dissolution Gibbs energy and equilibrium constants of raspberry ketone were estimated in this study.

123

J Solution Chem Table 3 Verification experiments of the solubility data of raspberry ketone in six pure solvents from 283.15 K to 313.15 K at 0.10 MPa T (K)

102 xa Gravimetrical method

D (102 x)b Verification (dynamic method)

Raspberry ketone–acetone 283.15

20.11

20.12

- 0.01

288.15

22.75

23.02

- 0.27

293.15

26.17

26.55

- 0.38

298.15

29.23

29.45

- 0.22

303.15

32.01

32.13

- 0.12

308.15

35.20

35.05

0.15

313.15

40.34

40.24

0.10

Raspberry ketone–ethanol 283.15

11.14

11.41

- 0.27

288.15

14.09

13.89

0.20

293.15

18.00

17.66

0.34

298.15

21.50

20.98

0.52

303.15

25.82

25.97

- 0.15

308.15

30.01

29.89

0.12

313.15

35.70

35.25

0.45

Raspberry ketone–ethyl acetate 283.15

10.20

10.52

- 0.32

288.15

13.68

14.01

- 0.33

293.15

15.86

15.38

0.48

298.15

19.66

20.04

- 0.38

303.15

24.04

24.12

- 0.08

308.15

27.75

28.05

- 0.30

313.15

31.98

31.66

0.32

Raspberry ketone–n-propyl alcohol 283.15

9.43

9.49

- 0.06

288.15

11.26

11.73

- 0.47 - 0.25

293.15

14.26

14.51

298.15

17.79

17.77

0.02

303.15

21.54

22.05

- 0.51

308.15

26.43

26.84

- 0.41

313.15

30.51

31.00

- 0.49

Raspberry ketone–n-butyl alcohol 283.15

7.04

6.84

0.20

288.15

9.12

9.18

- 0.06

293.15

11.77

12.01

- 0.24

298.15

15.03

14.77

0.26

303.15

19.05

18.75

0.30

308.15

23.41

23.88

- 0.47

313.15

27.67

28.15

- 0.48

123

J Solution Chem Table 3 continued T (K)

102 xa

D (102 x)b

Gravimetrical method

Verification (dynamic method)

Raspberry ketone–Distilled water 283.15

0.05

0.05

288.15

0.07

0.06

0.00 0.01

293.15

0.09

0.08

- 0.01

298.15

0.11

0.10

0.01

303.15

0.14

0.14

0.00

308.15

0.17

0.18

- 0.01

313.15

0.21

0.22

- 0.01

Standard uncertainties u are u(T) = 0.05 K and u(p) = 0.01 MPa (0.68 level of confidence) and combined expanded uncertainty Uc is Uc(x) = 0.0005 (0.95 level of confidence) a

Measured by gravimetrical method and verification solubility in pure solvents

b

The deviation between solubility data in pure solvents determined by the gravimetrical method and verification experiments

Deduced from the van’t Hoff equation, the molar enthalpy, entropy and Gibbs energy change of solution can be evaluated from a plot of lnx versus 1/T. To minimize the error, the harmonic average temperature is defined as follow [23]: XN ð1=TÞ ð11Þ Tmean ¼ N= i¼1 where N denotes the number of experimental points and i stands for an experimental value of T. Thus in this study, Tmean = 297.81 K was used to calculated the thermodynamic functions. Assuming that the heat capacity of a solution can be considered constant in a short range of temperature, the change of molar enthalpy of solution can be derived from van’t Hoff equation as follows [23]:     o ln x o ln x o ¼ R ð12Þ Ddiss H ¼ R oð1=TÞ oð1=T  1=Tmean Þ where R is the universal gas constant, 8.314 Jmol-1K-1. For the pure solvents, the lnx versus 104(1/T - 1/Tmean) plots with error bars are shown in Fig. 7, and they can be used to calculate the molar enthalpy change of solution. This figure demonstrates a linear relationship between the solubility values and the reciprocal of temperature. The value of the slope, intercept and R2 of each plot are listed in Table 5. All the correlation coefficient are higher than 0.99, which indicates that the van’t Hoff equation can be used to accurately estimate the thermodynamic data of raspberry ketone. In general, the change of dissolution Gibbs energy of the solution can be deduced by the following equation [24]: Ddiss G ¼ RTmean  intercept where the intercept in Eq. 13 is the value of intercept of the plot. Then the dissolution entropy change can be calculated as follows [25]:

123

ð13Þ

J Solution Chem

40

(a)

30

10 2 x

Fig. 6 The figures show deviations with error bars between the experimental data and the values calculated by a the van’t Hoff model; b the modified Apelblat model; c the kh model for the solvents: (filled square) acetone, (filled circle) ethanol, (filled triangle) ethyl acetate, (filled inverse triangle) n-propyl alcohol, (filled diamond) n-butyl alcohol, and (filled left pointed triangle) distilled water

20 acetone ethanol ethyl acetate n-propyl alcohol n-butyl alcohol distilled water

10

0 285

290

295

300

305

310

315

T/K 40

(b)

10 2 x

30

20 acetone ethanol ethyl acetate n-propyl alcohol n-butyl alcohol distilled water

10

0 285

290

295

300

305

310

315

T/K 40

(c)

10 2 x

30

20 acetone ethanol ethyl acetate n-propyl alcohol n-butyl alcohol distilled water

10

0 285

290

295

300

T/K

305

310

315

Ddiss G ¼ Ddiss H   Tmean Ddiss S

ð14Þ

Ddiss S ¼ ðDdiss H   Ddiss G Þ=Tmean

ð15Þ

123

123 - 3208.41

1.18 1.97 0.40 0.38 0.9941 5.48

- 2003.03

102 RADb

102 ORADc

102 RMSDd

102 ORMSDe

R2

Af2 1.15 1.86 0.40 0.37 0.9954

102 RADb

102 ORADc

102 RMSDd

102 ORMSDe

R2

Bf2

9.50

8.59

Ca1

van’t Hoff

567.97

0.9971

0.56

2.43

0.9958

0.59

2.43

3.15

- 2352.08

- 11.59

- 52.09

Aa1

Ba1

Ethanol

Modified Apelblat

Acetone

Parameters

Model

0.9938

0.52

2.69

- 3208.44

9.12

0.9905

0.52

2.69

7.48

- 961.78

- 41.03

Ethyl acetate

0.9972

0.35

1.50

- 3525.42

10.09

0.9962

0.35

1.51

2.99

- 2626.24

- 9.97

n-Propyl alcohol

0.9968

0.37

2.25

- 3970.13

11.41

0.9947

0.42

2.63

8.47

- 1421.42

- 45.38

n-Butyl alcohol

Table 4 Parameters of three thermodynamic models correlated to the solubility data of raspberry ketone in six pure solvents with the error analysis

0.9988

0.00

1.15

- 4027.62

6.69

0.9984

0.00

1.40

12.53

- 255.59

- 77.34

Distilled water

J Solution Chem

0.44 0.43 0.9962

102 RMSDd

102 ORMSDe

R2

RAD is the relative average deviation

RMSD is the root mean square deviation

g

k, h are the parameters of the kh equation

A2, B2 are the parameters of the van’t Hoff equation

ORMSD is the overall root mean square deviation

e

d

ORAD is the overall relative average deviation

c

b

f

1.87

A1, B1, C1 are the parameters of the Apelblat equation

a

1.11

102 ORADc

hg

102 RADb

0.62

2781.32

kg

kh

Acetone

Parameters

Model

Table 4 continued

0.9979

0.59

1.57

1987.04

1.98

Ethanol

0.9914

0.80

2.60

2357.21

1.59

Ethyl acetate

0.9970

0.33

1.49

2732.12

1.36

n-Propyl alcohol

0.9997

0.39

1.87

2544.14

1.75

n-Butyl alcohol

0.9971

0.01

2.59

588670.05

0.01

Distilled water

J Solution Chem

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J Solution Chem Fig. 7 The van’t Hoff plots with error bars of logarithm mole fraction solubility (x) of raspberry ketone versus 104(1/ T - 1/Tmean) in pure solvents: (filled square) acetone, (filled circle) ethanol, (filled triangle) ethyl acetate, (filled inverse triangle) n-propyl alcohol, (filled diamond) n-butyl alcohol, and (filled left pointed triangle) distilled water

-1 -2

lnx

-3 acetone ethanol ethyl acetate n-propyl alcohol n-butyl alcohol distilled water

-4 -5 -6 -7 -1.5

-1.0

-0.5

0.0

0.5

1.0

1.5

2.0

104(1/T-1/Tmean)

Table 5 Slope and intercept of the ln x versus 104(1/T - 1/ Tmean) plot for the six pure solvents

Solvent

Slope

R2

Intercept

Acetone

- 0.2004

- 1.2495

0.9963

Ethanol

- 0.3407

- 1.5710

0.9958

Ethyl acetate

- 0.3338

- 1.6550

0.9921

n-Propyl alcohol

- 0.3576

- 1.7534

0.9978

n-Butyl alcohol

- 0.4107

- 1.9256

0.9981

Distilled water

- 0.4014

- 6.8337

0.9985

As the solubility of raspberry ketone was determined in the solution at the equilibrium state, the equilibrium constants can calculated be from Eqs. 16 and 17. H Ddiss G ¼ RT ln Kdiss

ð16Þ

Table 6 Thermodynamic functions (DdissH°, DdissS°, DdissG°, KH diss) related to dissolution process of raspberry ketone at Tmean = 297.81 K in the six pure solvents KH diss

%nH

%nTS

3.10

0.29

55.12

44.88

3.89

0.21

53.69

46.31

79.42

4.10

0.19

53.99

46.01

29.73

85.25

4.34

0.17

53.94

46.06

n-Butyl alcohol

34.15

98.66

4.77

0.15

53.75

46.25

Distilled water

33.37

55.23

16.92

0.01

66.98

33.02

DdissH° (kJmol-1)

DdissS° (Jmol-1K-1)

Acetone

16.66

45.57

Ethanol

28.33

82.05

Ethyl acetate

27.75

n-Propyl alcohol

Solvent

DdissG° (kJmol-1)

Tmean = 297.81 K

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J Solution Chem

H Kdiss



Ddiss G ¼ exp  RT

 ð17Þ

H The estimated values of DdissH°, DdissS°, DdissG° and Kdiss in various pure solvents are listed in Table 6. From this table, it can be seen that all the changes of the dissolution enthalpy and Gibbs energy of raspberry ketone are positive, which demonstrates that these dissolutions are endothermic. Also, in this work, as the solubility of raspberry ketone increases with temperature in the temperature range of the measurements, the value of o ln x oð1=TÞ is always negative. Based on the Eq. 12, the value of DdissH° is always positive. Moreover, according to Eq. 14, the values of DdissH°, TDdissS° and DdissG° are all positive, which means the value of DdissH° is bigger than TDdissS°. Therefore, the change of dissolution enthalpy is the main contributor to the positive dissolution Gibbs energy change in all of the investigated solvents. Furthermore, to compare the relative contributions of enthalpy and entropy to the Gibbs energy change, %nH and %nTS, which represent contributions of enthalpy and entropy respectively, were calculated by following equations [26, 27]:    DH    100 ð18Þ %nH ¼    diss  DH þ T  DS  diss

%nTS

diss

  T  DS  ¼     diss    100 DHdiss þ TDSdiss

ð19Þ

The values of %nH and %nTS in the pure solvents are reported in Table 6. They can give a more convincing conclusion that the main contributor to the dissolution Gibbs energy is the dissolution enthalpy during the dissolution of raspberry ketone as the %nH value are all more than 50%.

4 Conclusions In the present study, the solubility data of raspberry ketone was measured by the static method in six pure solvents (ethanol, n-propyl alcohol, n-butyl alcohol, ethyl acetate, acetone and distilled water) over the temperature range 283.15–313.15 K under standard atmospheric pressure 0.1 MPa. The results generally reveal that the temperature has a direct effect on the solubility of raspberry ketone in all the experimental solvents. The solubility data increases with rising temperature in the experimental pure solvents and is well correlated by using the Apelblat equation, van’t Hoff equation and kh equation. From the error analysis results of three thermodynamic models, the van’t Hoff equation is best able to correlate and predict the solubility of raspberry ketone with its lower value of 102 ORAD (1.86) and 102 ORMSD (0.37). Dissolution thermodynamic studies indicate endothermic and enthalpy-driven dissolution of raspberry ketone in all of the selected solvents. And, the equilibrium constants increase with the rising solubility. In addition, the change of dissolution enthalpy is the main contributor to the positive value of the molar Gibbs energy of the dissolving process. Acknowledgements The financial supports of the Tianjin Research Program of Application Foundation and Advanced Technology (No. 14JCZDJC40900), The Training Program for Changjiang Scholars and

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J Solution Chem Innovative Research Team in University ([2013]373) and the Innovative Research Team of Tianjin Municipal Education Commission (TD12-5004) are gratefully acknowledged.

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