Solubility of caffeine in carbitol + ethanol mixture at different temperatures

Journal Pre-proof Solubility of caffeine in carbitol + ethanol mixture at different temperatures

Homa Rezaei, Elaheh Abolghasem Jouyban

Rahimpour,

Fleming

Martinez,

PII:

S0167-7322(19)37089-8

DOI:

https://doi.org/10.1016/j.molliq.2020.112465

Reference:

MOLLIQ 112465

To appear in:

Journal of Molecular Liquids

Received date:

24 December 2019

Accepted date:

4 January 2020

Please cite this article as: H. Rezaei, E. Rahimpour, F. Martinez, et al., Solubility of caffeine in carbitol + ethanol mixture at different temperatures, Journal of Molecular Liquids(2020), https://doi.org/10.1016/j.molliq.2020.112465

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© 2020 Published by Elsevier.

Journal Pre-proof

Solubility of caffeine in carbitol + ethanol mixture at different temperatures

Homa Rezaei a,b, Elaheh Rahimpour b,c,1, Fleming Martinez d, Abolghasem Jouyban b,e

a

Student Research Committee, Faculty of Pharmacy, Tabriz University of Medical Sciences, Tabriz, Iran Pharmaceutical Analysis Research Center and Faculty of Pharmacy, Tabriz University of Medical Sciences, Tabriz, Iran c Food and Drug Safety Research Center, Tabriz University of Medical Sciences, Tabriz, Iran d Grupo de Investigaciones Farmacéutico-Fisicoquímicas, Departamento de Farmacia, Facultad de Ciencias, Universidad Nacional de Colombia – Sede Bogotá, Cra. 30 No. 45-03, Bogotá, D.C., Colombia e Digestive Diseases Research Institute, Tehran University of Medical Sciences, Tehran, Iran.

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Corresponding author. E-mail: [email protected] .

Journal Pre-proof ABSTRACT The solubility of caffeine in non-aqueous mixed solutions of carbitol and ethanol at different temperatures are determined by a shake-flask method and fitted to some reported cosolvency models including the van’t Hoff, the double log-log, the mixture response surface, the Yalkowsky, the Jouyban-Acree, the Jouyban-Acree-van’t Hoff, and the modified Wilson models. Along with solubility, the densities of caffeine saturated mixtures are also measured and

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correlated with the Jouyban-Acree model. In order to study the accuracy of the employed

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models, the mean relative deviations (MRD%) of the back-calculated solubility and density data

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are calculated. Furthermore, the apparent thermodynamic properties of caffeine dissolution

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process in the mixed solutions of carbitol and ethanol are also calculated by using van’t Hoff and

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Gibbs equations.

Keywords: Solubility; Caffeine; Carbitol; Ethanol, Binary solvent mixtures; Cosolvency models.

Journal Pre-proof 1. Introduction Caffeine (3,7-dihydro-1,3,7-trimethyl-1H-purine-2,6-dione, Fig. 1) with two crystalline forms (anhydrous (C8H10N4O2) and hydrated (C8H10N4O2.H2O) is a natural compound from alkaloid family and considered as a mild stimulant among other psychoactive drugs [1]. Many antimigraine and pain-killer pharmaceutical formulations contain caffeine in a certain amount [2]. Some important physiological effects of caffeine are stimulation of the central nervous system,

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gastric acid secretion and blood pressure increase in the short term [3]. It is prescribed as a drug

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for patients with orthostatic hypotension and patients suffering from postdural puncture headache

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[1]. Caffeine is naturally found in cocoa beans, coffee, tea leaves, and cola nuts. So, caffeine

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extraction is an important industrial process that is commonly performed by using aqueous or

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non-aqueous mono-solvents or solvent mixtures. Therefore, knowing caffeine solubility behavior in aqueous and non-aqueous solvents provides useful information for its extraction and/or

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purification process design [4]. Solubility is reported to be an important property for immiscible solvent mixtures employed for extraction and anti-solvent/solvent systems employed for

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purification [5, 6]. Until now, the caffeine solubility has been reported in the neat solvents of

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water, ethyl acetate, carbon tetrachloride, ethanol, methanol, chloroform, dichloromethane and acetone at different temperatures [7], in aqueous mixtures of ethanol, methanol, 1-propanol, acetone or ethyl acetate at different temperature [8], in the aqueous mixtures of dioxane [9], propylene glycol and polyethylene glycol 400 [9], and N, N-dimethylformamide at 298.2 K [10]. However, there is only one report of caffeine solubility profile in the non-aqueous systems [11]. In the current work, the solubilization profile of caffeine in a non-aqueous mixtures of carbitol and ethanol are investigated and reported. Carbitol with a chemical formula of C6H14O3 and ethanol with a chemical formula of C2H6O are considered the most commonly used non-aqueous

Journal Pre-proof solvents in the pharmaceutical industry for drug purification or pre-formulation [12]. To the best of our knowledge, there is no report on the study of caffeine solubility in the non-aqueous mixture of carbitol and ethanol. ***Fig. 1*** In order to extend caffeine solubility database in the cosolvency systems, the aims of the current

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work are to (1) measure the solubility and density of caffeine saturated solution in the nonaqueous mixed solutions of carbitol and ethanol at different temperatures; (2) correlate the

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measured data with some reported cosolvency models; and (3) compute the apparent

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thermodynamic parameters for caffeine dissolution process in carbitol and ethanol mixed

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solutions.

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2.1. Materials

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2. Materials and method

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Caffeine (mass fraction purity of 0.997, Dana Pharmaceutical Company, Iran), carbitol (mass fraction purity of 0.980, Merck, Germany), ethanol with mass fraction purity of 0.999 (Scharlau Chemie, Spain) are the materials used in the preparation of the saturated mixtures. Ethanol with mass fraction purity of 0.935 (Jahan Alcohol Teb, Arak, Iran) is employed for dilution purposes before spectrophotometric measurements.

2.2. Caffeine solubility measurement

Journal Pre-proof A traditional shake-flask method [13] is employed for the solid-liquid equilibrium of caffeine in the mixed solutions of carbitol and ethanol. Excess caffeine is dispersed into the flasks containing 10 grams of each investigated solvents or solvent mixtures in different mass ratios (w1=0.1-0.9). After tightly sealing, the flasks are placed in an incubator (Nabziran Industrial Group, Tabriz, Iran) at different temperatures (± 0.2 K) on a shaker (Behdad, Tehran, Iran). After 48 h, the saturated solutions are centrifuged, diluted with ethanol: water mixture (1:1 v/v), and

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their absorbances are measured at 273 nm by a spectrophotometer model UV-1800 (Shimadzu,

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Kyoto, Japan). Caffeine concentration in the solvent mixtures is calculated based on the

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constructed calibration curve. The given solubility data are the mean of measurements in three replications. The densities of the caffeine saturated solution at different temperatures are

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2.3. Thermodynamic parameters

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measured by a 5 mL pycnometer (uncertainty of 0.001 g∙cm-3).

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The caffeine dissolution process in the non-aqueous mixed solutions of carbitol and ethanol are

is reported as:

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investigated according to the van’t Hoff and Gibbs equations. The modified van’t Hoff equation

 ln x H   R 1 1      T Thm  p

(1)

Here x is mole fraction solubility of caffeine, T is the absolute temperature (K) and R is the ideal gas constant (J.mol-1.K-1), respectively [14]. Thm is the mean harmonic temperature computed as n

Thm  n /  (1/ T ) (n is the number of studied temperatures). H i 1

and G for saturated

Journal Pre-proof mixtures are obtained from the slope and the intercept of the plot of ln x against 1/T − 1/Thm, respectively [15], and Gibbs equation is employed to compute S . The relative contributions of entropy (TS) and enthalpy (H) to G of caffeine dissolution process in the mixtures of carbitol and ethanol are computed by the following equations [15].

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TS  ( H   TS  )

(3)

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 TS 

(2)

( H   TS  )

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H 

H 

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2.4. Mathematical models

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The measured solubility data for caffeine in the mixed solutions of carbitol and ethanol are fitted to some linear cosolvency models including the van’t Hoff, the double log-log, the mixture

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response surface, the Yalkowsky, the Jouyban-Acree, and the Jouyban-Acree-van’t Hoff models,

summarized here.

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and a non-linear model, i.e. the modified Wilson model, which details of each model are

2.4.1. van’t Hoff equation The relationship between the solubility values and the temperature can be demonstrated by using van’t Hoff equation written as [16]:

ln x  A 

B T

(4)

Journal Pre-proof where A and B are the model parameters.

2.4.2. The double log-log model The double log-log model is one of the first models reported for cosolvency systems which divides the solubility data to two parts and presents a model for each part [17].

ln[ln( xm / x2 )]  ln[ln(( xm )0.5 / x2 )]  B ln( w1 / w2 )

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for 0 < w2 ≤ 0.5

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ln[ln( x1 / xm )]  ln[ln( x1 /( xm )0.5 )]  b ln( w2 / 0.5)

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for 0 < w1 ≤ 0.5

(5)

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in which x1 and x2 are the mole fraction solubility in the mono solvents 1 and 2, ( xm )0.5 is the

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drug solubility in the mixed solutions with the cosolvent mass fraction of 0.5, w1 and w2 are the

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mass fractions of solvents 1 and 2 in the absence of solute, B and b are the equation parameters.

2.4.3. The mixture response surface (MRS) method MRS model is as:  1   1     5 w'1.w2 ln xm  1w'1   2 w2   3     4   w1   w2 

(7)

1  5 are equation parameters and w1' and w2' are obtained by using w1'  0.96 w1  0.02 and w2'  0.96 w2  0.02 [18].

Journal Pre-proof 2.4.4. Yalkowsky model The natural logarithmic solubility value in the cosolvency systems may be obtained by the Yalkowsky model as [19]:

ln xm  w1 ln x1  w2 ln x2

(8)

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The terms have the same meaning as those defined in the above models.

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2.4.5. Jouyban-Acree model

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The Jouyban-Acree model is another linear cosolvency model that relates the solubility values to

terms

are

the

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(9)

i 0

model

parameters

obtained

by

linear

regression

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w1 .w2 w1.w2 (w1  w2 ) w1 .w2 ( w1  w2 ) 2  w2 ln x2,T ) against , , and [21]. T T T

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(ln xm,T  w1 ln x1,T

 J i .(w1  w2 )i

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Ji

2

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ln xm,T  w1 ln x1,T  w2 ln x2,T

w .w  1 2 T

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both solvent composition and temperature. The general form of the model is as [20]:

The measured density values of caffeine in the mixture of carbitol and ethanol can be also correlated and back-calculated by the Jouyban-Acree model, where the solubility parameters in Eq. (9) are replaced by the density parameters for the studied mixtures.

2.4.6. Jouyban-Acree-van’t Hoff model

Journal Pre-proof The combination of the Jouyban-Acree model with the van’t Hoff equation provides a comprehensive model for fitting/predicting drug solubility data in the cosolvency systems. The Jouyban-Acree-van’t Hoff model is as [22]: ln xm,T  w1 ( A1 

B1 B w .w )  w2 ( A2  2 )  1 2 T T T

2

 J i .(w1  w2 )i

(10)

i 0

where A1, B1, A2, B2 and Ji are the model constants which are computed by simple linear

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regression.

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2.4.7. The modified Wilson model

In addition to linear models used for correlating / predicting the solubility data, non-linear

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models such as the modified Wilson, can be also used for the solubility data fitting at a given

w11  ln x1  w2 1  ln x2   w1  w2 12 w121  w2

(11)

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 ln xm  1 

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temperature. The general form of the modified Wilson model is as [23]:

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λ12 and λ21 are the equation parameters calculated by a simple nonlinear analysis.

2.4.8. Model accuracy The measured solubility data are correlated into the presented models and mean relative deviation (MRD%) (Eq. (12)) of the back-calculated solubility data are computed as a measure of the model.   100  Calculated Value  Observed Value  % MRD    N Observed Value    

(12)

Journal Pre-proof N is the number of data points.

3. Results and discussions 3.1. Caffeine solubility behavior in the non-aqueous mixed solutions of carbitol and ethanol The measured mole fraction caffeine solubility in the non-aqueous mixed solutions of carbitol

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and ethanol at different temperatures along with the standard deviation of the three replicated

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measurements are given in Table 1. The lowest caffeine solubility data in the mixtures of carbitol

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and ethanol is measured for neat ethanol at 293.2 K (C = 1.63 × 10-2 mol∙L–1), and the highest

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one is reported for neat carbitol at 313.2 K (C = 7.14 × 10–2 mol∙L-1). The caffeine solubility

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values increase proportionally to the increase in both carbitol mass fraction and temperature.

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***Table 1***

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3.2. Thermodynamic parameters calculation for caffeine dissolution process

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Table 2 presents the apparent thermodynamic parameters including: H , S , and G for caffeine dissolution in the non-aqueous mixed solutions of carbitol and ethanol, calculated according to the van’t Hoff and Gibbs equations at Thm. The highest and lowest value obtained for H of caffeine dissolution in the studied mixtures is 17.70 kJ.mol−1 and 11.98 kJ.mol−1, in neat ethanol and w1 = 0.9, respectively. S values are positive in the interval of 0.0 ≤ w1 ≤ 0.5 and neat carbitol but negative in the interval of 0.6 ≤ w1 ≤ 0.9. It is noteworthy that these values are relatively low in magnitude if compared with dissolution entropy of other drugs in other nonaqueous systems. G values calculated for caffeine in the investigated mixtures are in the range

Journal Pre-proof of 16.90 – 12.04 kJ.mol−1 with the lowest value for neat carbitol which indicates that caffeine solubility and dissolution are more favorable in this solvent. According to calculated thermodynamic parameters, it is concluded that the caffeine dissolution in the non-aqueous mixed solutions of carbitol and ethanol is endothermicin all cases, and entropically-driven in ethanol-rich mixtures and neat carbitol. H and TS are also given in Table 2 which shows that in

0.87 in all mixtures).

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***Table 2***

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the caffeine dissolution processes, the enthalpy is the main contributor of G (H > TS and H >

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The H against G plot is used to investigate the co-solvency mechanism of caffeine in the

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non-aqueous mixed solutions of carbitol and ethanol [24]. Fig. 2 presents a non-linear behavior

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with a region with a positive slope (0.0 ≤ w1 ≤ 0.9) indicating an enthalpy-driven mechanism of transfer between different polarities and a region with a negative slope in the range of 0.9 ≤ w1 ≤

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1.0 indicating entropy-driven mechanism in this transfer process.

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***Fig. 2***

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3.3. Computational modeling of caffeine solubility The measured data for caffeine solubility in the non-aqueous mixtures of carbitol and ethanol are fitted to some linear and non-linear cosolvency models including the van’t Hoff, the Yalkowsky, the Jouyban-Acree, the Jouyban-Acree-van’t Hoff, the modified Wilson, the double log-log and the MRS models. The model parameters and MRDs% of predicted solubility data are summarized in Tables 3-8. Although all investigated models presented low MRDs% (< 15%) for back-calculated caffeine solubility data, it should be said that the error level from different equations is not comparable with each other. Because the van’t Hoff model predicts solubility at various temperatures in the same solvent mixture, and Yalkowsky, the double log-log and the

Journal Pre-proof MRS and the modified Wilson models predict solubility in different solvent compositions at the same temperature. Whereas, the Jouyban-Acree and the Jouyban-Acree-van’t Hoff models predict solubility data at different temperatures as well as different solvent mixtures. The prediction capability of Jouyban-Acree-van’t Hoff model is also studied by using the minimum number of data fitted to model (i.e. solubility data in mono-solvents at 293.2 and 313.2 K and in solvent composition with carbitol mass fractions of 0.3, 0.5 and 0.7 at 298.2 K).

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Jouyban-Acree-van’t Hoff model is trained by employing these data and then the solubility data

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in other carbitol mass fractions are calculated by employing the trained model. The MRDs% for

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predicted solubility data are 1.4%, 1.6%, 1.0%, 2.9% and 1.3% for 293.2, 298.2, 303.2, 308.2

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and 313.2 K, respectively (overall MRD is 1.7 %).

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***Tables 3- 8*** In another computational analysis, caffeine solubility data in carbitol and ethanol mixture are

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fitted to a recently modified version of the Jouyban-Acree model [25].

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xm,T  x1w,T1  x2w,2T  e

w1 .w2 2  J i ( w1  w2 ) i T i 0

(13)

in which e is the Euler's number (e = 2.718). The trained model with measured solubility data is as:

xm,T 

x1w,T1

 x2w,2T

{317.308.

e

w1 .w2 w .w ( w  w ) w .w ( w  w ) 2  34.304. 1 2 1 2  34.655. 1 2 1 2 } T T T

The back-calculated MRD% for Eq. (14) in the arithmetic scale is 1.3 % (N=55).

(14).

Journal Pre-proof 3.4. Density data and mathematical modeling The measured density data for caffeine in the saturated mixtures at different temperatures may also be correlated with the Jouyban-Acree model [26]. The trained model for caffeine in the nonaqueous mixtures of carbitol and ethanol (Table 9) is as:

ln m,T  w1. ln 1,T  w2 . ln 2,T  1.575

w1.w2 T

(15)

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 m ,T is the density of caffeine saturated solutions and 1,T , and  2,T are the density of caffeine saturated neat solvents at temperature T. The back-calculated MRD% is reported to be 0.1 %

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demonstrating that the Jouyban-Acree model presents good capability for the density prediction

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at different temperatures.

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***Table 9***

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4. Conclusions

The caffeine solubility profile in the non-aqueous mixtures of carbitol and ethanol at different

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temperatures are measured by commonly used shake-flask method and fitted into six linear

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cosolvency models including the van’t Hoff, the double log-log, the MRS, the Yalkowsky, the Jouyban-Acree, the Jouyban-Acree-van’t Hoff models, and a non-linear model (i.e. the modified Wilson model). The accuracy of investigated models is studied by computing MRDs% of backcalculated data. According to obtained results, it can be concluded that the investigated cosolvency models could calculate caffeine solubility in the carbitol and ethanol mixtures at different temperatures with a low %MRDs (<15 %). Furthermore, the apparent thermodynamic parameters of caffeine dissolution process are also calculated and discussed.

Journal Pre-proof Acknowledgements The research reported in this publication was supported by the Student Research Committee under

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grant number 64737, Faculty of Pharmacy, Tabriz University of Medical Sciences, Tabriz, Iran.

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Fig. 1. Molecular structure of caffeine

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Fig. 2. Enthalpy-entropy compensation plot for caffeine in the non-aqueous mixtures of carbitol and ethanol at 303.0 K. The points represent the mass fraction of carbitol in carbitol and ethanol mixtures in the absence of solute.

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Table 1 Experimental mole fraction solubility ( x m ,T ) values as the mean of three experiments (± standard deviation) measured for caffeine in the nonaqueous mixtures of carbitol and ethanol at different temperatures.

w1a 0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00 a

293.2 K 9.56 (±0.75) × 10–4 1.32 (±0.02) × 10–3 1.74 (±0.16) × 10–3 2.16 (±0.26) × 10–3 2.81 (±0.01) × 10–3 3.45 (±0.07) × 10–3 4.13 (±0.00) × 10–3 4.91 (±0.28) × 10–3 5.68 (±0.22) × 10–3 6.64 (±0.06) × 10–3 7.13 (0.01) × 10–3

298.2 K 1.09 (±0.03) × 10–3 1.43 (±0.11) × 10-3 1.71 (±0.04) × 10–3 2.44 (±0.07) × 10–3 3.07 (±0.13) × 10–3 3.76 (±0.16) × 10–3 4.50 (±0.17) × 10–3 5.33 (±0.08) × 10–3 6.10 (±0.10) × 10–3 6.92 (±0.03) × 10–3 7.62 (±0.02) × 10–3

303.2 K 1.23 (±0.05) × 10–3 1.63 (±0.09) × 10–3 2.16 (±0.12) × 10–3 2.77 (±0.14) × 10–3 3.45 (±0.06) × 10–3 4.13 (±0.05) × 10–3 4.96 (±0.16) × 10–3 5.77 (±0.07) × 10–3 6.62 (±0.30) × 10–3 7.55 (±0.22) × 10–3 8.44 (±0.04) × 10–3

n r u

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w1 is mass fraction of carbitol in carbitol and ethanol mixtures in the absence of caffeine.

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308.2 K 1.38 (±0.01) × 10–3 1.90 (±0.07) × 10–3 2.46 (±0.01) × 10–3 3.08 (±0.19) × 10–3 3.91 (±0.18) × 10–3 4.76 (±0.06) × 10–3 5.47 (±0.30) × 10–3 6.48 (±0.08) × 10–3 7.31 (±0.57) × 10–3 8.50 (±0.22) × 10–3 9.28 (±0.18) × 10–3

313.2 K 1.52 (±0.01) × 10–3 2.04 (±0.09) × 10–3 2.56 (±0.01) × 10–3 3.39 (±0.30) × 10–3 4.15 (±0.24) × 10–3 4.90 (±0.46) × 10–3 5.78 (±0.12) × 10–3 6.75 (±0.23) × 10–3 7.77 (±0.45) × 10–3 8.89 (±0.47) × 10–3 9.84 (±0.33) × 10–3

Journal Pre-proof Table 2 Apparent thermodynamic parameters for dissolution behavior of caffeine in the non-aqueous mixtures of carbitol and ethanol at Thm. TΔS° (kJ.mol–1) 0.79 1.36 1.76 2.43 1.32 0.53 -0.14 -0.24 -0.36 -0.29 0.80

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ΔS° (J.K–1.mol–1) 2.61 4.48 5.82 8.01 4.34 1.75 -0.47 -0.78 -1.17 -0.97 2.64

H

TS

0.957 0.928 0.908 0.877 0.922 0.964 0.989 0.982 0.972 0.976 0.941

0.043 0.072 0.092 0.123 0.078 0.036 0.011 0.018 0.028 0.024 0.059

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ΔH° (kJ.mol–1) 17.70 17.51 17.30 17.30 15.60 14.34 13.24 12.73 12.27 11.98 12.84

ro

0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00

ΔG° (kJ.mol–1) 16.90 16.15 15.54 14.87 14.29 13.81 13.38 12.97 12.63 12.28 12.04

-p

w1a

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Table 3 The van’t Hoff model parameters and the corresponding MRD% for caffeine in the non-aqueous mixtures of carbitol and ethanol w1 A B MRD% -2128.424 0.7 0.00 0.314 0.539 -2106.106 1.9 0.10 0.700 -2080.609 4.8 0.20 0.964 -2080.768 0.6 0.30 0.522 -1876.908 1.2 0.40 0.211 -1725.083 1.7 0.50 -0.560 -1592.780 0.7 0.60 -0.940 -1531.601 1.0 0.70 -0.141 -1476.182 0.8 0.80 -0.117 -1441.162 1.7 0.90 -0.317 -1544.495 0.9 1.00 Overall 1.4

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Journal Pre-proof Table 4

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Calculated ln x values of caffeine obtained by Yalkowsky model in the non-aqueous mixtures of carbitol and ethanol at different temperatures. ln x w1 293.2 K 298.2 K 303.2 K 308.2 K 313.2 K 0.00 -6.95 -6.82 -6.7 -6.58 -6.49 -6.75 -6.62 -6.51 -6.39 -6.3 0.10 -6.55 -6.43 -6.32 -6.2 -6.12 0.20 -6.35 -6.24 -6.12 -6.01 -5.93 0.30 -6.15 -6.04 -5.93 -5.82 -5.74 0.40 -5.95 -5.85 -5.74 -5.63 -5.56 0.50 -5.75 -5.65 -5.55 -5.44 -5.37 0.60 -5.55 -5.46 -5.35 -5.25 -5.18 0.70 -5.35 -5.27 -5.16 -5.06 -5 0.80 -5.14 -5.07 -4.97 -4.87 -4.81 0.90 -4.94 -4.88 -4.77 -4.68 -4.62 1.00 MRD% 15.4 13.3 13.8 14.8 13.4 Overall MRD% 14.1

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Journal Pre-proof Table 5 Parameters calculated for the Jouyban-Acree, and Jouyban-Acree-van’t Hoff model for caffeine solubility in the non-aqueous mixtures of carbitol and ethanol.

MRD%

1.4

9.2

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Not statistically significant (p-value >0.05)

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Jouyban-Acree-van’t Hoff A1 -0.317 B1 -1544.495 A2 0.314 B2 -2128.424 J0 667.294 J1 617.878 J2 868.679

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Jouyban-Acree J0 315.554 J1 0a J2 0a

Carbitol + ethanol

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Journal Pre-proof Table 6 The modified Wilson model parameters at the investigated temperatures and the MRD% for backcalculated caffeine solubility in the non-aqueous mixtures of carbitol and ethanol. λ12 1.102 1.415 0.880 0.798 0.799

T (K) 293.2 298.2 303.2 308.2 313.2 Overall

λ21 1.132 0.944 1.303 1.411 1.389

MRD% 1.1 1.7 0.5 0.9 0.9

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1.0

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Table 7 The double log-log model constants at investigated temperatures and the MRD% for back-calculated caffeine solubility in the non-aqueous mixtures of carbitol and ethanol. b MRD%

for 0 < w2 ≤ 0.5

MRD%

4.1 5.9 6.4 4.0 5.0 5.1

1.397 1.256 1.168 1.221 1.193

1.6 0.7 0.9 1.2 0.2 0.9

0.592 0.678 0.613 0.585 0.593

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293.2 298.2 303.2 308.2 313.2 Overall MRD%

of

T (K)

B

for 0 < w1 ≤ 0.5

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Journal Pre-proof Table 8 The MRS model constants at the investigated temperatures and the MRD% for back-calculated caffeine solubility in the non-aqueous mixtures of carbitol and ethanol. T (K)

β1

293.2 -4.913 298.2 -4.851 303.2 -4.771 308.2 -4.674 313.2 -4.616 Overall MRD%

β3

β4

β5

MRD%

-7.003 -6.912 -6.756 -6.622 -6.536

0a 0a 0a 0a 0a

0a 0a 0a 0a 0a

1.148 1.145 1.127 1.143 1.056

1.2 1.8 1.0 1.5 1.4 1.4

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Not statistically significant (p-value >0.05)

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β2

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308.2 K 0.771 ± 0.001 0.790 ± 0.002 0.809 ± 0.001 0.831 ± 0.030 0.843 ± 0.001 0.860 ± 0.001 0.883 ± 0.000 0.901 ± 0.001 0.924 ± 0.001 0.943 ± 0.002 0.967 ± 0.001

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303.2 K 0.791 ± 0.001 0.805 ± 0.002 0.824 ± 0.002 0.842 ± 0.001 0.862 ± 0.001 0.880 ± 0.001 0.900 ± 0.001 0.920 ± 0.001 0.942 ± 0.001 0.962 ± 0.001 0.985 ± 0.002

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solutions in the non-aqueous mixtures of carbitol and

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Table 9 Measured density (g.cm–3) of caffeine saturated ethanol at different temperatures. a w1 293.2 K 298.2 K 0.00 0.789 ± 0.001 0.789 ± 0.001 0.10 0.809 ± 0.002 0.807 ± 0.002 0.20 0.826 ± 0.001 0.828 ± 0.001 0.30 0.846 ± 0.001 0.843 ± 0.001 0.40 0.864 ± 0.001 0.862 ± 0.001 0.50 0.883 ± 0.002 0.883 ± 0.001 0.60 0.903 ± 0.002 0.903 ± 0.001 0.70 0.925 ± 0.001 0.921 ± 0.000 0.80 0.949 ± 0.001 0.944 ± 0.001 0.90 0.969 ± 0.002 0.966 ± 0.000 1.00 0.991 ± 0.001 0.987 ± 0.000

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313.2 K 0.785 ± 0.002 0.803 ± 0.002 0.819 ± 0.001 0.830 ± 0.001 0.856 ± 0.001 0.877 ± 0.002 0.895 ± 0.001 0.917 ± 0.001 0.937 ± 0.001 0.955 ± 0.001 0.978 ± 0.001

Journal Pre-proof Declaration of competing interest

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The authors declare no conflict of interest.

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Journal Pre-proof Highlights

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Solubility of caffeine in carbitol/ethanol mixtures at different temperatures. Correlation/back-calculation of the solubility data by some cosolvency models. Calculation of thermodynamic parameters by using the van’t Hoff and Gibbs equations.

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