Correlation and thermodynamic analysis of solubility of cefmetazole acid in three (alcohol + water) binary solvents at temperatures from 278.15 K to 303.15 K

J. Chem. Thermodynamics 103 (2016) 355–365

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Correlation and thermodynamic analysis of solubility of cefmetazole acid in three (alcohol + water) binary solvents at temperatures from 278.15 K to 303.15 K Mengmeng Sun, Kangli Li, Shichao Du, Yumin Liu, Dandan Han, Xiaona Li, Peng Yang, Shiyuan Liu, Junbo Gong ⇑ a b

School of Chemical Engineering and Technology, State Key Laboratory of Chemical Engineering, Tianjin University, Tianjin 300072, China The Co-Innovation Center of Chemistry and Chemical Engineering of Tianjin, Tianjin 300072, China

a r t i c l e

i n f o

Article history: Received 1 July 2016 Received in revised form 14 August 2016 Accepted 19 August 2016 Available online 21 August 2016 Keywords: Cefmetazole acid Solubility Activity coefficient Thermodynamic property

a b s t r a c t The solubility of cefmetazole acid in binary solvent mixtures, (methanol + water), (ethanol + water) and (isopropanol + water), was determined by UV spectroscopic method at temperatures from 278.15 to 303.15 K. The solubility of cefmetazole acid increased with the increase of temperature in all solvents. In (methanol + water) co-solvent mixture, the solubility of cefmetazole acid is maximal in neat methanol. In (ethanol + water) and (isopropanol + water) solvent mixtures, the solubility of cefmetazole acid reaches its maximum when the mole fraction of alcohol is 0.5 and 0.4, respectively. The modified Apelblat equation, the CNIBS/R-K model and the Jouyban–Acree model were applied to correlate the experimental solubility of cefmetazole acid. Moreover, the activity coefficients as well as the thermodynamic properties of mixing were calculated and discussed based on the NRTL model and experimental solubility values. Ó 2016 Elsevier Ltd.

1. Introduction Cefmetazole acid, (C15H17N7O5S3, CAS Registry No:56796-20-4), also known as (6R,7S)-7-({[(Cya-nomethyl)sulfanyl]acetyl}amino)7-methoxy-3-{[(1-methyl-1H-tetrazol-5-yl)sulfanyl]methyl}-8-ox o-5-thia-1-azabicyclo[4.2.0]oct-2-ene-2-carboxylic acid (Fig. 1), is an important cephalosporin antibiotics active component mainly prepared from 7-ACA or 7-MAC at present. Still, there are other ways to prepare cefmetazole acid: using 3-TZ [1] or cefmetazole benzyl ester [2] as the starting material, followed by the preparation of cefmetazole acid by a series of chemical reactions and crystallization. Because of its poor solubility in water, cefmetazole acid is usually transformed into cefmetazole sodium by reactive crystallization to improve its solubility and bioavailability. Recently, a research reports that cefmetazole acid can be prepared into aseptic powder with arginine which is much more stable than cefmetazole sodium [3] and can also overcome the poorly water-soluble problem of cefmetazole acid. Cefmetazole acid can produce an anti-bacterium composition with sodium citrate which makes the clinical application of cefmetazole acid more convenient [4]. ⇑ Corresponding author at: School of Chemical Engineering and Technology, State Key Laboratory of Chemical Engineering, Tianjin University, Tianjin 300072, China. E-mail address: [email protected] (J. Gong). http://dx.doi.org/10.1016/j.jct.2016.08.024 0021-9614/Ó 2016 Elsevier Ltd.

The knowledge of the solubility of cefmetazole acid in different solvents is of enormous significance to the aspects mentioned above, including the crystallization of cefmetazole acid, the preparation of cefmetazole sodium, etc. Moreover, although the theoretical and semi-empirical models can predict solubility of drugs in different solvent mixtures, experimental values are still fundamental for the pharmaceutical scientists [5]. The behaviour of drugs in co-solvent mixtures is frequently evaluated as a function of composition and temperature for the purification of raw materials, pre-formulation studies, and understanding the molecular mechanisms involved in the physical and chemical stability of pharmaceutical dissolutions [6]. The co-solvency considered as a solubilizing technique has been widely used in pharmaceutical dosage design [7]. In this work, the solubility of cefmetazole acid in the (alcohol + water) mixtures, (methanol + water), (ethanol + water) and (isopropanol + water), at temperatures ranging from 278.15 K to 303.15 K was determined by UV spectroscopic method. The experimental solubility of cefmetazole acid was correlated by the modified Apelblat equation, the CNIBS/R-K model and the Jouyban–Acree model. Furthermore, the mixing thermodynamic properties of the systems, including the Gibbs energy, the entropy and the enthalpy, were calculated and discussed for further understanding of the solubility.

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M. Sun et al. / J. Chem. Thermodynamics 103 (2016) 355–365

2.4. Solubility determination method

Fig. 1. The chemical structure of cefmetazole acid.

2. Experimental 2.1. Materials Cefmetazole acid was supplied by Yaoyou Pharmaceutical Co., Ltd of China. Distilled water was used in the preparation of solvent mixtures. Methanol, ethanol and isopropanol were purchased from Tianjin Kewei Chemical Reagent Co., Ltd of China. All of the organic solvents used for the experiments were of analytic reagent grade. Details of compounds (expressed in mass fraction) used in this work are summarized in Table 1. All chemicals were used without any further treatment. 2.2. Thermal analysis of cefmetazole acid The thermal analysis (TGA/DSC) of cefmetazole acid was carried out by TGA/DSC simultaneous thermal analyser (TGA/DSC 1, Mettler-Toledo, Switzerland) to estimate whether there was melting temperature of cefmetazole acid. There are two calibrating weights in the balance room of the TGA/DSC 1 with an automatic calibration function. The temperature and heat are calibrated by indium and zinc. A total of about (5–10) mg of cefmetazole acid was used and the thermal analyses were performed at a heating rate of 10 K
min1 under a dynamic nitrogen atmosphere. 2.3. Solvent mixtures preparation (Alcohol + water) mixtures were prepared by mixing appropriate masses of the solvents with analytical balance (type AB204, Mettler-Toledo, Switzerland) with the uncertainty of ±0.0001 g. The mole fraction of the alcohol ðx0B Þ in the binary solvent mixtures prepared, which is calculated by the Eq. (1), varied by 0.1.

mB =M B x0B ¼ mB =M B þ mC =M C

ð1Þ

where x0B is the mole fraction of the alcohol in the binary solvent mixtures, mB and mC are the masses of solvent B and solvent C. mB and MC are the corresponding molecular mass of solvent B and solvent C.

Various solubility determination methods can be found in the literature [8]. The solubility of cefmetazole acid in binary solvent mixtures was determined using the saturation shake-flask method as reported in the literature [9]. The solubility of cefmetazole acid was determined by equilibrating an excess amount of the solid with the binary solvent mixtures using flasks placed in a thermostatic mechanical shaker (Tianjin Ounuo Instrument Co. Ltd., China) and shaken for 12 h, which had been confirmed long enough to reach equilibrium for the solutions. Then the suspensions were kept static at the original temperature to ensure that the undissolved solid precipitated to the bottom. Then the solubility measurement was performed, and the samples containing excess solid were equilibrated at the next higher temperature. The equilibrated solutions were filtered by a preheated (or precooled) organic membrane (0.22 lm, Tianjin Legg Technology Co., Ltd, Tianjin, China) and the filtrate was diluted with water and analysed by UVS. The absorbance of the diluted solutions was recorded at 272 nm. Then the concentrations of cefmetazole acid were calculated based on the Lambert-Beer law calibration curve (shown in Fig. S1) established from the measured absorbance of standard solutions. The influence of the original solvent mixtures taken from the saturated solution on absorbance Ab could be ignored since the amount of it was much less than the diluent [10] with the dilution ratio of solution being more than 160 in this work. Besides, it is noteworthy that at the very beginning of the dilution, it is unavoidable that a little precipitation may occur because the solubility of cefmetazole acid in water is lower than in the (alcohol + water) mixtures studied. However, when performing the experiment, we are sure that no precipitation occurred in the dilute solution because the amount of water is much more than the saturated mixtures which wold not influence the final concentration of the solution. The solubility measurement was carried out at least in triplicate at every test point. The solid phase of the suspension was separated and then identified to be cefmetazole acid by X-ray diffraction, and it was found that the PXRD pattern of all the samples used remained constant. Here we provide one as a sample to discuss (T = 303.15 K, water + alcohol ðx0B ¼ 0:5Þ, which is shown in Fig. S2. The mole fraction solubility of cefmetazole acid (xA ) was calculated by Eqs. (2) and (3) as reported in the literature [11].

mA ¼ xA ¼

Ab

ai

V

ð2Þ

mA =M A mA =M A þ mB =M B þ mC =M C

ð3Þ

where xA is the mole fraction solubility of cefmetazole acid, ai represents the slope of calibration curve with the value of 0.0241, V is the diluted volume, mA , mB and mC are the masses of cefmetazole acid, solvent B and solvent C, respectively. MA , MB and MC are the corresponding molecular mass of cefmetazole acid, solvent B and solvent C, respectively.

Table 1 Details of the compounds used in this work.

a b

Chemical name

Molar mass/(g
mol1)

Source

Purity in mass fraction

Analytical method

Cefmetazole acid Water Methanol Ethanol Isopropanol

471.52 18.02 32.04 46.07 60.06

Yaoyou Pharmaceutical Co., Ltd, China Lab made Tianjin Kewei Chemical Reagent Co., Ltd, China Tianjin Kewei Chemical Reagent Co., Ltd, China Tianjin Kewei Chemical Reagent Co., Ltd, China

>0.980 P0.998 >0.995 >0.995 >0.995

HPLCa None GCb GCb GCb

High performance liquid chromatography did by the supplier. Gas chromatography did by the supplier.

M. Sun et al. / J. Chem. Thermodynamics 103 (2016) 355–365

3. Thermodynamic models

357

ln ðxA ÞB;T ¼ a1 þ

b1 þ c1 lnðT=KÞ: T=K

ð8Þ

ln ðxA ÞC;T ¼ a1 þ

b2 þ c2 lnðT=KÞ: T=K

ð9Þ

3.1. Modified Apelblat equation The modified Apelblat equation, a widely used semi-empirical model with three parameters, can be applied to correlate the mole fraction solubility with the temperature [12] and can be expressed as

ln xA ¼ A þ

B þ C lnðT=KÞ: T=K

ð4Þ

where xA is the mole fraction solubility of solute, T is the absolute temperature of the solutions and A, B, C are the model parameters. The values of A, B are pertinent to the variation in solution activity coefficients and C indicates the effect of temperature on fusion enthalpy [13]. 3.2. CNIBS/R–K model

b1 x0 þ c1 ln T þ ða1  a2 Þx0B þ ðb1  b2 þ J 0  J 1 þ J2 Þ B T T  0 2  0 3  0 4 xB xB xB þ ð3J 1  J 0  5J 2 Þ þ ð8J 2  2J 1 Þ þ ð4J 2 Þ T T T 0 þ ðc1  c2 ÞxB ln T ð10Þ

ln xA ¼ a1 þ

Here, introducing several constant terms into the Eqs. (10) and (11) can be obtained as follows:

ln xA ¼ A1 þ

The Combined Nearly Ideal Binary Solvent (CNIBS)/Redlich–Kister model, suggested by Acree et al. [14], is considered to be one of the most appropriate models for binary solvent systems. This equation can be applied to correlate the mole fraction solubility with the initial mole fraction composition of the binary solvent mixtures and can be expressed as [15]

ln xA ¼ x0B ln ðxA ÞB;T þ x0C ln ðxA ÞC;T þ x0B x0C

N is equal to 2 in this work and x0C can be replaced by ð1  x0B Þ. Then the modified Jouyban-Acree model can be obtained as

N X  i Si x0B  x0C

ð5Þ

i¼0

4

þ A8

ðx0B Þ þ A9 x0B ln T T

ð6Þ

where xA is the mole fraction solubility of the solute in the binary solvent mixtures, B0 , B1 , B2 , B3 and B4 are the model parameters and x0B refers to the initial mole fraction composition of the binary solvent mixtures. For the two models above, the modified Apelblat equation can only indicate the temperature dependence of the solubility and the CNIBS/R–K model can only indicate the mole fraction composition of the solvent mixtures dependence of the solid–liquid equilibrium. Therefore, it is necessary to introduce a model that can be applied to correlate the solubility of the solute with both the temperature and composition of solvent mixtures.

where A1 to A9 are the model parameters. This equation is also called a Hybrid model proposed by Zhou et al. [18]. The Hybrid model can describe temperature and initial mole fraction composition of binary solvent mixtures dependence of the solubility [19].

Based on the theory of solid–liquid phase equilibrium, the solubility of one compound in the solution can be calculated by the Eq. (12) [20].

ln xi ¼

      DH m 1 1 DC P T T    þ 1  ln ci ln Tm T Tm Tm R R

ln xi ¼

   DH m 1 1   ln ci Tm T R

The Jouyban–Acree model, proposed by Jouyban Gharamaleki and his co-workers in 1998 [16], can be applied to correlate the solubility with temperature and solvent composition of the solutions. The original equation form, obtained by modifying the CNIBS/R–K equation, can be expressed as [17] N X i Ji  0 xB  x0C : T i¼0

ð7Þ

where Ji is the model constant of the equation, the meaning of other symbols in Eq. (7) is the same with Eq. (5). ln ðxA ÞB;T and ln ðxA ÞC;T can be expressed by the modified Apelblat equation as

ð12Þ

where DHm , R, Tm and ci refer to the enthalpy of fusion, gas constant, melting temperature and activity coefficient of the solute, respectively. The DC P represents the molar heat capacity difference of the solute between its solid and liquid state at the melting temperature. Since the value of DC P is low at the melting temperature, a simplified equation can be obtained from Eq. (12):

3.3. Jouyban–Acree model

ln xA ¼ x0B ln ðxA ÞB;T þ x0B ln ðxA ÞC;T þ x0B x0C

ð11Þ

3.4. NRTL model

where xA is the mole fraction solubility of the solute in binary solvent mixtures, x0B ; x0C refer to the initial mole fraction composition of the binary solvent mixtures as if there is no solute. ðxA ÞB;T and ðxA ÞC;T refer to the saturated mole solubility of solute in pure solvent B and C respectively; Si is the model constant and N, equal to in this work, is the number of solvents. When N = 2 and introducing constant terms into Eq. (5), the CNIBS/R–K equation can be simplified into the General Single model as Eq. (6).

 2  3  4 ln xA ¼ B0 þ B1 x0B þ B2 x0B þ B3 x0B þ x0B

 0 2  0 3 x x A2 x0 þ A3 ln T þ A4 x0B þ A5 B þ A6 B þ A7 B T T T T

Fig. 2. Thermal analysis (TGA/DSC) of cefmetazole acid.

ð13Þ

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M. Sun et al. / J. Chem. Thermodynamics 103 (2016) 355–365

Table 2 Mole fraction solubility (xA ) of cefmetazole acid in the binary {methanol (B) + water (C)} solvent mixture at different temperatures from 278.15 to 303.15 K (P = 0.1 MPa).a

Table 3 Mole fraction solubility (xA ) of cefmetazole acid in the binary {ethanol (B) + water (C)} solvent mixture at different temperatures from 278.15 to 303.15 K (P = 0.1 MPa).a

x0B

104 xexp A

104 xcal;A A

104 xcal;C A

104 xcal;J A

x0B

104 xexp A

104 xcal;A A

104 xcal;C A

104 xcal;J A

0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00

0.775 1.610 3.114 5.275 7.994 10.10 12.09 13.89 16.32

T = 278.15 K 0.746 1.674 3.072 5.353 7.397 9.546 11.59 13.99 15.99

0.729 1.614 3.150 5.335 7.843 10.19 12.10 13.85 16.33

0.732 1.664 3.218 5.353 7.796 10.16 12.19 13.91 15.69

0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00

1.708 3.519 6.183 7.114 7.097 6.189 5.000 4.091 2.659

T = 278.15 K 1.704 3.498 6.005 6.938 6.906 6.256 4.957 3.916 2.623

1.528 3.769 6.018 7.159 7.063 6.223 5.099 3.914 2.742

1.652 3.634 5.745 7.067 7.209 6.406 5.130 3.770 2.560

0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00

1.118 2.418 4.098 7.267 8.802 12.21 14.33 17.28 18.75

T = 283.15 K 1.108 2.320 4.137 6.882 9.530 12.26 14.53 16.77 18.81

0.999 2.414 4.424 6.761 9.249 11.86 14.59 17.15 18.78

1.046 2.298 4.305 6.957 9.863 12.54 14.70 16.40 18.10

0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00

2.198 4.573 6.950 8.226 8.217 7.471 5.937 4.103 2.757

T = 283.15 K 2.217 4.559 7.186 8.438 8.478 7.586 6.005 4.422 2.889

2.213 4.580 6.902 8.241 8.306 7.374 5.891 4.237 2.689

2.165 4.618 7.121 8.581 8.604 7.532 5.954 4.331 2.911

0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00

1.498 3.063 5.609 8.896 12.25 14.86 17.77 20.40 22.18

T = 288.15 K 1.559 3.171 5.606 8.893 12.45 15.94 18.50 20.62 22.67

1.331 3.132 5.756 8.850 12.02 15.04 17.83 20.29 22.21

1.474 3.152 5.766 9.123 12.69 15.87 18.31 20.13 21.88

0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00

2.902 5.964 8.858 10.39 10.39 9.693 7.137 5.034 3.430

T = 288.15 K 2.981 6.110 9.063 10.65 10.64 9.371 7.347 5.132 3.333

2.995 5.890 8.771 10.50 10.58 9.298 7.300 5.176 3.313

2.949 6.093 9.155 10.80 10.63 9.154 7.133 5.122 3.403

0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00

2.087 4.460 7.581 11.80 16.69 20.95 23.89 25.07 27.33

T = 293.15 K 2.089 4.280 7.641 11.91 16.46 20.95 23.91 25.96 27.92

2.298 4.258 7.479 11.90 16.78 20.95 23.66 25.27 27.28

2.040 4.282 7.707 12.03 16.54 20.48 23.43 25.57 27.60

0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00

4.350 8.584 12.40 14.35 14.23 11.84 9.627 6.611 4.350

T = 293.15 K 4.133 8.401 12.00 13.89 13.64 11.78 9.074 6.110 4.015

4.338 8.578 12.44 14.37 14.05 12.13 9.440 6.634 4.131

4.149 8.301 12.14 14.00 13.52 11.45 8.783 6.219 4.080

0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00

2.729 5.551 10.55 16.44 22.25 28.82 32.09 34.43 36.36

T = 298.15 K 2.670 5.706 10.47 16.45 22.01 27.82 31.30 33.42 35.11

2.768 5.690 10.30 16.33 22.78 28.35 32.20 34.49 36.34

2.781 5.769 10.29 15.95 21.83 26.95 30.79 33.58 36.22

0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00

5.732 11.74 16.47 18.51 17.48 14.71 10.87 7.124 4.898

T = 298.15 K 5.896 11.83 16.63 18.71 17.81 15.04 11.30 7.447 5.033

5.880 11.54 16.52 18.60 17.54 14.50 10.84 7.446 4.705

6.021 11.66 16.60 18.70 17.69 14.71 11.10 7.743 5.010

0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00

3.243 7.565 14.83 23.60 29.59 36.89 41.15 43.63 44.55

T = 303.15 K 3.267 7.520 14.41 23.56 29.74 37.30 41.49 43.92 45.01

3.065 7.829 14.91 22.94 30.42 36.53 41.03 43.81 44.50

3.736 7.712 13.72 21.26 29.15 36.12 41.46 45.45 49.32

0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00

8.674 17.05 24.05 25.97 23.73 19.62 14.30 9.339 6.591

T = 303.15 K 8.635 17.03 24.04 25.95 23.67 19.50 14.19 9.278 6.551

8.730 17.05 23.89 26.13 23.91 19.28 14.22 9.797 6.341

8.994 16.85 23.33 25.66 23.76 19.40 14.38 9.868 6.291

a x0B is the initial mole fraction of methanol in the binary solvent mixture; xexp is A the experimentally determined solubility; xcal;A , xcal;C , and xcal;J are the calculated A A A solubility by Eqs. (4), (6) and (11), respectively; The standard uncertainty of temperature is u(T) = 0.05 K; The relative standard uncertainty of the solubility measurement is ur ðxA Þ ¼ 0:09; The relative standard uncertainty in mole fraction of methanol (B) in the solvent mixtures is ur (x0B ¼ 0:01); The relative uncertainty of pressure is ur(P) = 0.05.

a x0B is the initial mole fraction of ethanol in the binary solvent mixture; xexp A is the experimentally determined solubility; xcal;A , xcal;C , and xcal;J are the calculated solA A A ubility by Eqs. (4), (6) and (11), respectively; The standard uncertainty of temperature is u(T) = 0.05 K; The relative standard uncertainty of the solubility measurement is ur(xA) = 0.08; The relative standard uncertainty in mole fraction of ethanol (B) in the solvent mixtures is ur ðxB Þ ¼ 0:01; The relative uncertainty of pressure is ur(P) = 0.05.

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M. Sun et al. / J. Chem. Thermodynamics 103 (2016) 355–365 Table 4 Mole fraction solubility (xA ) of cefmetazole acid in the binary {isopropanol (B) + water (C)} solvent mixture at different temperatures from 278.15 to 303.15 K (P = 0.1 MPa).a x0B

104 xexp A

104 xcal;A A

104 xcal;C A

104 xcal;J A

0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90

0.792 2.459 3.680 4.072 3.907 3.359 2.611 1.916 1.018

T = 278.15 K 0.807 2.324 3.496 4.014 3.890 3.335 2.600 1.947 1.118

0.859 2.382 3.707 4.120 3.858 3.327 2.678 1.889 1.016

0.847 2.211 3.518 4.092 3.955 3.417 2.694 1.871 1.049

0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90

1.152 2.949 4.242 5.026 5.018 4.435 3.384 2.447 1.393

T = 283.15 K 1.135 3.028 4.474 5.142 5.048 4.419 3.367 2.372 1.343

1.238 2.822 4.313 5.053 4.987 4.378 3.469 2.417 1.238

1.141 2.908 4.557 5.251 5.043 4.340 3.412 2.369 1.332

0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90

1.615 3.852 5.712 6.725 6.560 5.771 4.344 2.852 1.803

T = 288.15 K 1.608 4.067 5.897 6.745 6.634 5.851 4.392 2.956 1.672

1.693 3.755 5.740 6.747 6.605 5.665 4.349 2.964 1.727

1.584 3.934 6.059 6.898 6.566 5.612 4.388 3.037 1.709

0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90

2.281 5.706 8.322 9.225 9.015 7.756 5.757 3.890 2.202

T = 293.15 K 2.290 5.616 7.987 9.041 8.819 7.739 5.766 3.763 2.150

2.410 5.565 8.312 9.391 8.942 7.617 5.871 3.946 2.122

2.256 5.448 8.229 9.234 8.691 7.357 5.707 3.927 2.204

0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90

3.277 8.005 10.98 12.23 11.70 10.27 7.662 4.795 2.645

T = 298.15 K 3.280 7.958 11.10 12.36 11.85 10.23 7.617 4.885 2.851

3.497 7.706 11.10 12.32 11.71 10.05 7.730 5.015 2.438

3.290 7.716 11.41 12.59 11.69 9.779 7.508 5.123 2.861

0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90

4.721 11.51 15.79 17.26 16.10 13.48 10.10 6.483 3.968

T = 303.15 K 4.719 11.55 15.78 17.23 16.07 13.50 10.11 6.460 3.890

5.006 11.12 15.97 17.40 16.03 13.31 10.11 6.793 3.729

4.909 11.16 16.12 17.46 15.96 13.16 9.979 6.737 3.735

a x0B is the initial mole fraction of isopropanol in the binary solvent mixture; xexp A is the experimentally determined solubility; xcal;A , xcal;C , and xcal;J are the calculated A A A solubility by Eqs. (4), (6) and (11), respectively; The standard uncertainty of temperature is u(T) = 0.05 K; The relative standard uncertainty of the solubility measurement is ur (xA ¼ 0:05); The relative standard uncertainty in mole fraction of isopropanol(B) in the solvent mixtures is ur ðxB Þ ¼ 0:01; The relative uncertainty of pressure is ur(P) = 0.05.

For real solutions, the activity coefficients which can be calculated by the NRTL model, one of the local composition models, have to be considered to calculate the thermodynamic properties. For the solution with pure solvent, the NRTL model can be expressed as

"

ln ci ¼

x2j

sji G2ji

ðxi þ Gji xj Þ2

where Gij ; Gji ; sij and

þ

sij Gij ðxj þ Gij xi Þ2

#

ð14Þ

sji are parameters of this model. And here,

Gij ¼ expðaij sij Þ

ð15Þ

sij ¼ ðg ij  g jj Þ=RT ¼ Dg ij =RT

ð16Þ

Fig. 3. Mole fraction solubility (xA ) of cefmetazole acid versus temperature T in {methanol (B) + water (C)} binary solvent mixtures at atmospheric pressure (P = 0.1 MPa). j, T = 278.15 K; , T = 283.15 K; , T = 288.15 K; , T = 293.15 K; , T = 298.15 K; , T = 303.15 K.

Fig. 4. Mole fraction solubility (xA ) of cefmetazole acid versus temperature T in {ethanol (B) + water (C)} binary solvent mixtures at atmospheric pressure (P = 0.1 MPa). j, T = 278.15 K; , T = 283.15 K; , T = 288.15 K; , T = 293.15 K; , T = 298.15 K; , T = 303.15 K.

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where s is a constant which is assumed for the non-randomness of the mixture; g represents the Gibbs energy of intermolecular interaction; a is an adjustable empirical constant. For the solution with binary solvent, the NRTL model can be expressed as

ln ci ¼

ðGji xj þ Gkj xk Þðsji Gji xj þ ski Gki xk Þ ðxi þ xj Gji þ xk Gki Þ2 þ þ

sij Gji x2j þ Gij Gkj xj xk ðsij  skj Þ ðxj þ xi Gij þ xk Gkj Þ2

sik Gki x2k þ Gik Gjk xj xk ðsik  sjk Þ ðxk þ xi Gik þ xj Gjk Þ2

ð17Þ

where Gij ; Gik ; Gji ; Gjk ; Gki ; Gkj ; sij ; sik ; sji ; sjk ; ski and skj are parameters of this model. The definition of these parameters is the same with the solution with pure solvent which is mentioned above.

4. Results and discussion 4.1. Melting properties of cefmetazole acid The thermal analysis (TGA/DSC) result of cefmetazole acid is shown in Fig. 2. It can be seen from the Fig. 2 that the cefmetazole acid sample shows a mass decline at the temperature 431.15 K and there is a sharp endothermic peak at the same temperature point, which indicates that cefmetazole acid decomposes before showing a melting characteristic. Therefore, the melting temperature and enthalpy of fusion of cefmetazole acid cannot be obtained by the thermal analysis directly. Thus, in this work, the group contribution method [21] was used to estimate the melting properties of cefmetazole acid. The average absolute error in estimating the melting points of organic compounds by this method is 33.2 K, which is a relatively low value considering the wide range of the relevant organic compounds. At the equilibrium, the free energy of transition is equal to zero. So the melting point of organic compounds can be calculated by the Eq. (18) as follows:

Tm ¼

DH m DSm

ð18Þ

where DHm is the enthalpy change of fusion of cefmetazole acid and the DSm is the corresponding entropy change and they can be estimated by the Eqs. (19) and (20).

DH m ¼

X

ni mi

ð19Þ

where ni is the number of times the group i appears in a compound, mi is the contribution of the group i to the enthalpy of melting.

DSm ¼ 50  R ln r þ R ln U

ð20Þ

where r represents the rotating positions of a molecule and U indicates the molecular flexibility which can be calculated by the Eq. (20-1).

U ¼ 2:435SP3þ0:5SP2þ0:5RING1 Fig. 5. Mole fraction solubility (xA ) of cefmetazole acid versus temperature T in {isopropanol (B) + water (C)} binary solvent mixtures at atmospheric pressure (P = 0.1 MPa). j, T = 278.15 K; , T = 283.15 K; , T = 288.15 K; , T = 293.15 K; , T = 298.15 K; , T = 303.15 K.

ð20-1Þ

where SP3 is the number of non-ring, nonterminal sp3 atoms, SP2 is the number of non-ring, nonterminal sp2 atoms and RING represents the number of independent single, fused, or conjugated ring systems [22].

Fig. 6. Experimental solubility (xA ) of cefmetazole acid in the {methanol (B) + water (C)} binary solvent mixtures at atmospheric pressure (P = 0.1 MPa) at various temperatures.

M. Sun et al. / J. Chem. Thermodynamics 103 (2016) 355–365

Here, substituting Eqs. (19) and (20) into Eq. (18), the melting point can be predicted by the Eq. (21) as follows:

Tm ¼

P DH m ni mi ¼ DSm 50  R ln r þ R ln

ð21Þ

In this work, the melting temperature and enthalpy of fusion of cefmetazole acid predicted by this method are 482 K and 54.373 kJ
mol1. 4.2. Solubility of cefmetazole acid in binary solvent mixtures The experimental mole fraction solubility of cefmetazole acid in binary solvent mixtures, (methanol + water), (ethanol + water) and (isopropanol + water), is listed in Tables 2–4 and shown graphically in Figs. 3–5 and Figs. 6–8. It is noteworthy that solubility of cefmetazole acid is low in neat water and neat isopropanol which makes the solubility determination in these solvents giving big

361

errors, therefore, the solubility data of cefmetazole acid in neat water and neat isopropanol as well as that in some solvent mixtures are not given here. From Figs. 3–5 and Figs. 6–8, it can be found that the mole fraction solubility of cefmetazole acid in the three solvent mixtures, (methanol + water), (ethanol + water) and (isopropanol + water), increases with the increase of temperature at a fixed composition of solvent mixtures, which indicates that cooling crystallization in the above solvents is appropriate for recrystallization of cefmetazole acid. Furthermore, the dissolving capacity of cefmetazole acid in the binary solvent mixtures at fixed temperature ranks as (methanol + water) > (ethanol + water) > (isopropanol + water) in general, which may be in agreement with the empirical rule ‘‘like dissolves like” [23] and hydrogen bonding interaction [24]. Moreover, in the (methanol + water) solvent mixture, the mole fraction solubility of cefmetazole acid increased with the increase of the initial mole fraction of methanol in the binary solvent. However, in (ethanol + water) and (isopropanol + water)

Fig. 7. Experimental solubility (xA ) of cefmetazole acid in the {ethanol (B) + water (C)} binary solvent mixtures at atmospheric pressure (P = 0.1 MPa) at various temperatures.

Fig. 8. Experimental solubility (xA ) of cefmetazole acid in the {isopropanol (B) + water (C)} binary solvent mixtures at atmospheric pressure (P = 0.1 MPa) at various temperatures.

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solvent mixtures, the solubility increased strongly with the increase of the initial mole fraction of alcohol at first, reaches a maximum, and then decreases to a low value. This phenomenon, described in previous studies [25,26], is also called co-solvency. Besides, the maximum composition point does not change with the temperature. The occurrence of these maxima has a complex thermodynamic basis, influencing by both enthalpy and entropy effects, and no definite explanation has been achieved [27]. Whereas, it may be due to the physico-chemical properties of the solvent, such as polarity, intermolecular interactions, and the ability of the solvents to form a hydrogen bond with the solute molecules [28]. On the other hand, ethanol and isopropanol act as overall waterstructure-breaker and disrupt the three-dimensional hydrogenbonded network around a certain mole fraction of water which enhances the ability of the solvents to form the hydrogen bond with the solute molecules [29]. However, for the water-rich solvent mixtures, water clusters are formed and for the alcohol-rich solvent mixtures, the effect of water-structure-breaker may decline or disappear, then the solubility is reduced. 4.3. Data correlation The modified Apelblat equation, the CNIBS/R-K model and the Jouyban–Acree model were used to correlate the experimental solubility of cefmetazole acid in the three solvent mixtures, (methanol + water), (ethanol + water) and (isopropanol + water). The parameters, together with the average relative deviation ARD%, of these three model were listed in Tables S1–S3, respectively. The average relative deviation ARD% is calculated by the Eq. (22):

  N  exp cal  100 X xi  xi  ARD% ¼    N i¼1  xcal i

ð22Þ

where N is the number of the experimental points, xexp is the deteri is the corresponding calmined solubility of the experiment and xcal i culated solubility by the selected solubility models. From the ARD% values listed in the Tables S1–S3, it can be found that the experimental solubility of cefmetazole acid shows a satisfactory agreement with that calculated by the modified Apelblat equation, the CNIBS/R-K model and the Jouyban–Acree model. 4.4. The thermodynamic properties of mixing The dissolution process contains two main stages: fusion and mixing. The detail of this process is considered to have four energetic steps [30,31]: Heating

Fusion

Solutesolid;T;P ! Solutesolid;T m ;Pe ! Soluteliquid;T m ;Pe Cooling

Mixing

! Soluteliquid;T;P ! Solutesolution;T;P where T and T m is the measurement temperature and the melting temperature, respectively. The symbols P and Pe represent the measurement pressure and the equilibrium pressure at the melting temperature point. The fusion properties are determined mainly by the crystal structure of cefmetazole acid. But the mixing properties are relevant to the solvents which can influence the solubility of cefmetazole acid. Therefore, the mixing properties of the solution should be determined to understand the dissolution process. The standard mixing Gibbs energy DGomix , mixing entropy DSomix and mixing enthalpy DHomix , can be calculated by E;o DMomix ¼ DM id;o mix þ M

ð23Þ

where M can be replaced by G, S and H. DM id;o mix is the mixing property of an ideal solution and ME;o is the excess property.

  id;o and The mixing Gibbs energy DGid;o mix , mixing entropy DSmix  id;o mixing enthalpy DHmix of the ideal solution can be calculated by the following equations [32].

Table 5 The activity coefficients and thermodynamic properties of mixing for solution with the binary {methanol (B) + water (C)} solvent mixture from 278.15 to 303.15 K (P = 0.1 MPa).a x0B

DGomix =ðkJ
mol1 Þ

DSomix =ðJ
K1
mol1 Þ

DHomix =ðkJ
mol1 Þ

cA

0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00

0.277 0.307 0.344 0.388 0.434 0.466 0.466 0.390 0.040

T = 278.15 K 3.165 3.671 3.947 4.062 4.019 3.775 3.241 2.240 0.028

0.603 0.714 0.754 0.742 0.684 0.584 0.435 0.233 0.033

0.651 0.277 0.146 0.091 0.064 0.050 0.042 0.039 0.037

0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00

0.297 0.331 0.369 0.416 0.458 0.492 0.488 0.409 0.046

T = 283.15 K 3.189 3.706 3.986 4.103 4.055 3.806 3.265 2.256 0.034

0.606 0.718 0.759 0.746 0.690 0.586 0.436 0.229 0.036

0.692 0.303 0.163 0.103 0.073 0.058 0.049 0.045 0.043

0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00

0.316 0.354 0.396 0.443 0.489 0.518 0.513 0.428 0.054

T = 288.15 K 3.214 3.739 4.025 4.142 4.093 3.839 3.291 2.272 0.042

0.609 0.723 0.764 0.750 0.691 0.588 0.435 0.227 0.042

0.731 0.329 0.181 0.116 0.083 0.066 0.057 0.052 0.050

0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00

0.337 0.380 0.424 0.474 0.521 0.552 0.544 0.449 0.065

T = 293.15 K 3.237 3.772 4.063 4.181 4.131 3.872 3.318 2.290 0.052

0.612 0.726 0.767 0.752 0.690 0.583 0.429 0.222 0.050

0.770 0.356 0.199 0.129 0.094 0.075 0.065 0.059 0.057

0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00

0.357 0.404 0.454 0.507 0.556 0.589 0.578 0.481 0.084

T = 298.15 K 3.260 3.804 4.102 4.222 4.170 3.908 3.346 2.312 0.067

0.615 0.730 0.769 0.751 0.687 0.576 0.420 0.209 0.065

0.808 0.382 0.218 0.143 0.105 0.085 0.074 0.068 0.066

0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00

0.377 0.431 0.487 0.546 0.594 0.627 0.614 0.511 0.101

T = 303.15 K 3.281 3.837 4.142 4.264 4.209 3.943 3.376 2.334 0.081

0.618 0.732 0.769 0.747 0.682 0.569 0.410 0.197 0.077

0.844 0.409 0.237 0.159 0.118 0.096 0.083 0.077 0.075

a cA is the activity coefficient of cefmatazole acid; The expanded uncertainties are UðDSomix Þ ¼ 0:065DSomix , UðDGomix Þ ¼ 0:044DGomix (0.95 level of confidence).

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DGid;o mix ¼ RT

n X xi ln xi

ð24Þ

i¼1

DSid;o mix

DHid;o mix ¼ 0

ð26Þ

where xi is the mole fraction of every component in the solution.

n X ¼ R xi ln xi

ð25Þ

i¼1

Table 6 The activity coefficients and thermodynamic properties of mixing for solution with the binary {ethanol (B) + water (C)} solvent mixture from 278.15 to 303.15 K (P = 0.1 MPa).a

The excess mixing Gibbs energy ðDGE;o Þ, excess mixing entropy ðDSE;o Þ and excess mixing enthalpy ðDHE;o Þ can be calculated by the Eqs. (27), (28) and (29), respectively. Table 7 The activity coefficients and thermodynamic properties of mixing for solution with the binary {isopropanol (B) + water (C)} solvent mixture from 278.15 to 303.15 K (P = 0.1 MPa).a

x0B

DGomix =ðkJ
mol1 Þ

DSomix =ðJ
K1
mol1 Þ

DHomix =ðkJ
mol1 Þ

cA

x0B

DGomix =ðkJ
mol1 Þ

DSomix =ðJ
K1
mol1 Þ

DHomix =ðkJ
mol1 Þ

cA

0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00

0.792 0.953 1.052 1.092 1.077 1.000 0.848 0.582 0.007

T = 278.15 K 3.577 4.272 4.660 4.811 4.731 4.386 3.690 2.470 0.002

0.203 0.235 0.244 0.246 0.239 0.219 0.179 0.104 0.006

0.274 0.138 0.087 0.073 0.073 0.084 0.110 0.160 0.261

0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90

0.367 0.585 0.738 0.830 0.864 0.844 0.769 0.639 0.435

T = 278.15 K 1.901 2.593 3.010 3.266 3.389 3.378 3.216 2.836 2.057

0.162 0.136 0.099 0.078 0.078 0.096 0.125 0.150 0.138

0.496 0.193 0.138 0.127 0.132 0.151 0.193 0.292 0.609

0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00

0.813 0.979 1.079 1.121 1.105 1.026 0.869 0.595 0.007

T = 283.15 K 3.591 4.289 4.680 4.829 4.747 4.397 3.698 2.477 0.003

0.204 0.235 0.244 0.246 0.239 0.219 0.179 0.104 0.006

0.314 0.160 0.106 0.089 0.089 0.102 0.133 0.192 0.307

0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90

0.376 0.596 0.751 0.845 0.881 0.861 0.786 0.653 0.445

T = 283.15 K 1.914 2.610 3.026 3.282 3.404 3.396 3.234 2.852 2.065

0.166 0.143 0.106 0.084 0.083 0.101 0.130 0.154 0.139

0.566 0.224 0.161 0.146 0.151 0.172 0.220 0.332 0.678

0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00

0.834 1.005 1.109 1.151 1.135 1.054 0.891 0.610 0.008

T = 288.15 K 3.604 4.305 4.695 4.843 4.759 4.403 3.705 2.479 0.005

0.205 0.235 0.244 0.244 0.236 0.215 0.177 0.105 0.007

0.351 0.181 0.122 0.103 0.104 0.119 0.157 0.225 0.353

0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90

0.386 0.609 0.766 0.862 0.898 0.878 0.802 0.668 0.457

T = 288.15 K 1.928 2.628 3.042 3.297 3.421 3.414 3.252 2.869 2.075

0.170 0.148 0.110 0.088 0.088 0.105 0.135 0.159 0.141

0.637 0.253 0.180 0.163 0.169 0.194 0.249 0.375 0.748

0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00

0.856 1.034 1.141 1.186 1.168 1.082 0.915 0.626 0.010

T = 293.15 K 3.617 4.316 4.704 4.848 4.761 4.411 3.706 2.481 0.005

0.204 0.231 0.238 0.236 0.228 0.212 0.171 0.101 0.008

0.372 0.194 0.132 0.114 0.117 0.138 0.179 0.257 0.402

0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90

0.395 0.623 0.784 0.881 0.918 0.897 0.820 0.683 0.467

T = 293.15 K 1.941 2.644 3.058 3.313 3.438 3.432 3.271 2.885 2.083

0.174 0.152 0.112 0.090 0.090 0.109 0.139 0.162 0.143

0.704 0.275 0.194 0.177 0.185 0.214 0.276 0.416 0.819

0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00

0.878 1.064 1.175 1.220 1.200 1.110 0.937 0.639 0.011

T = 298.15 K 3.629 4.328 4.711 4.853 4.768 4.417 3.714 2.486 0.009

0.204 0.226 0.230 0.227 0.222 0.206 0.171 0.102 0.009

0.397 0.203 0.142 0.125 0.132 0.157 0.207 0.296 0.453

0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90

0.406 0.639 0.802 0.901 0.938 0.918 0.839 0.699 0.479

T = 298.15 K 1.945 2.660 3.075 3.329 3.456 3.451 3.290 2.901 2.092

0.176 0.154 0.115 0.092 0.092 0.111 0.142 0.166 0.145

0.763 0.295 0.209 0.190 0.200 0.232 0.302 0.458 0.890

0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00

0.904 1.098 1.215 1.261 1.237 1.143 0.963 0.657 0.015

T = 303.15 K 3.641 4.332 4.703 4.844 4.762 4.414 3.713 2.485 0.011

0.200 0.216 0.211 0.208 0.206 0.195 0.163 0.097 0.012

0.389 0.200 0.140 0.129 0.141 0.172 0.231 0.331 0.501

0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90

0.491 0.716 0.859 0.940 0.962 0.925 0.824 0.658 0.418

T = 303.15 K 2.101 2.917 3.308 3.469 3.472 3.344 3.089 2.677 1.967

0.145 0.168 0.144 0.112 0.091 0.089 0.112 0.154 0.179

0.810 0.305 0.214 0.196 0.210 0.249 0.327 0.495 0.948

a cA is the activity coefficient of cefmatazole acid; The expanded uncertainties are UðDSomix Þ ¼ 0:065DSomix , UðDGomix Þ ¼ 0:044DGomix (0.95 level of confidence).

a cA is the activity coefficient of cefmatazole acid; The expanded uncertainties are UðDSomix Þ ¼ 0:065DSomix , UðDGomix Þ ¼ 0:044DGomix (0.95 level of confidence).

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DGE;o ¼ RT

n X

xi ln ci

ð27Þ

i¼1

DSE;o ¼ 

  n n X X @GE @ ln ci ¼ R xi ln ci  RT xi @T @T p;x i¼1 i¼1

DHE;o ¼ RT 2

  n X @ ln ci xi @T p;x i¼1

the practical crystallization, purification and application of cefmetazole acid. Acknowledgements

ð28Þ

ð29Þ

where ci is the activity coefficient of every component in the solution. The calculated thermodynamic properties of mixing are listed in Tables 5–7. It can be found from the Tables 5–7 that DGomix is negative and positive values of DSmix indicate that the mixing process in the selected solvents is entropically favorable. What’s more, the mixing process in pure solvent is exothermic while the mixing process in binary solvent is endothermic. 4.5. The enthalpy–entropy compensation analysis The enthalpy–entropy compensation analysis is employed by using plots of DHomix versus DGomix (Figs. S3–S5) to help rationalize the mechanism of the co-solvent action [33]. For each of the three binary solvent systems, the curve of DHomix versus DGomix is nonlinear throughout the composition range of the solvent mixture [34]. Fig. S3 shows that cefmetazole acid in the (methanol + water) solvent mixture presents a non-linear DHomix versus DGomix curve with a variable negative slope in methanol (B) mole fraction interval from 0.2 to 0.4, and then up to x0B ¼ 0:7 a variable but positive slope is obtained and from this solvent mixture to neat methanol again a negative slope is obtained. Fig. S4 shows that cefmetazole acid in the (ethanol + water) solvent mixture presents a nonlinear DHomix versus DGomix curve which is similar with the phenomenon in (methanol + water) solvent mixture. Fig. S5 shows that cefmetazole acid in the (isopropanol + water) solvent mixture presents a non-linear DHomix versus DGomix curve with a variable positive slope in isopropanol (B) mole fraction interval from 0.1 to 0.8, and then up to x0B ¼ 0:9 negative slope is obtained. Accordingly, the driving mechanism for the dissolution of cefmetazole acid is entropy in the case with a negative slope probably implying water-structure loosening [33], whereas in the case with a positive slope the driving mechanism is enthalpy. 5. Conclusions In this work, the solubility of cefmetazole acid in the (alcohol + water) solvent mixtures, (methanol + water), (ethanol + water) and (isopropanol + water), at temperatures ranging from 278.15 K to 303.15 K was determined by the UV spectroscopic method. The mole fraction solubility of cefmetazole acid in the three solvent mixtures increases with the increase of temperature at a fixed composition of solvent mixture. In (methanol + water) solvent mixture, the mole fraction solubility of cefmetazole acid increases with the increase of the initial mole fraction of methanol in the binary solvent. And in mixtures of (ethanol + water) and (isopropanol + water), there is co-solvency phenomenon of cefmetazole acid. Three models, the modified Apelblat equation, CNIBS/R-K model and Jouyban–Acree model, were applied to correlate the values of experimental solubility of cefmetazole acid and it was found that all the thermodynamic models selected in this paper showed satisfactory correlation results. The NRTL model was applied to calculate the activity coefficients and the thermodynamic properties of mixing. On the basis of the above results, the experimental solubility and equations presented in this paper can be used to optimize

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JCT 16-531