Experimental and Modeling Studies on the Solubility of 2-Chloro-N-(4

Article pubs.acs.org/jced

Experimental and Modeling Studies on the Solubility of 2‑Chloro-N-(4-methylphenyl)propanamide (S1) in Binary Ethyl Acetate + Hexane, Toluene + Hexane, Acetone + Hexane, and Butanone + Hexane Solvent Mixtures Using Polythermal Method Gladys Kate Pascual,† Philip Donnellan,† Brian Glennon,† Vamsi Krishna Kamaraju,‡ and Roderick C. Jones*,† †

Synthesis and Solid State Pharmaceutical Centre (SSPC), School of Chemical and Bioprocess Engineering, University College Dublin, Belfield, Dublin 4, Ireland ‡ APC Ltd, Cherrywood Business Park, Loughlinstown, Co Dublin, Ireland S Supporting Information *

ABSTRACT: The solubility of 2-chloro-N-(4-methylphenyl)propanamide (S1) in ethyl acetate + hexane mixtures between the temperatures of 273.43 to 327.67 K, in toluene + hexane mixtures from 273.24 to 331.62 K, in acetone + hexane mixtures from 269.81 to 318.8 butanone + hexane mixtures between 267.10 and 322.92 were determined using the polythermal method. In situ focused beam reflectance measurement (FBRM) was used to characterize the dissolution properties and to provide S1’s saturation temperature profile as a function of concentration. It was demonstrated that the solubility of S1 increases with increasing temperature at constant solvent composition. The experimental solubility data were correlated using Apelblat, λh, and phase equilibria with NRTL (nonrandom two liquid) model equations, and the predicted solubility data obtained agree sufficiently with the experimental data based on the relative deviation (RD%) and average relative deviation (ARD%) values. The Apelblat and λh model equation provides a convenient operational model of engineering interest to calculate the solubility of S1 quickly and easily, although it does not take the solvent composition into account, therefore needing separate parameters for each different solvent compositions. Therefore, the phase equilibria with NRTL model equation is used to provide a more comprehensive model that illustrates the effect of solvent composition on the solubility more apparently. One general set of NRTL parameters has the capability of describing all solvent compositions. Additionally, the melting temperature, Tm and the molar fusion enthalpy, ΔfusH, (394.83 K and 26.77 kJ mol−1 respectively) of S1 were determined by differential scanning calorimetry (DSC).

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Figure 1. Generalized structure of α-thio-β-chloroacrylamides.

such as reactIR and reactNMR.2 Such work has shown that due to the complex cascade nature of the overall reaction pathway, desired product purity profiles are highly dependent on starting material purity.1−3 Consequently, 2-chloro-N-(4-methylphenyl) propanamide (S1), a precursor in the multistep synthesis of (Z)-3-chloro-2-(phenylthio)-N-(p-tolyl)acrylamide (P1, an API of interest to this group, Scheme 1), requires extensive purification via crystallization before use in order to obtain clean product profiles. The solubility characteristics of a particular solute−solvent pair have considerable influence upon the design and optimization of any crystallization9−11 and therefore a detailed understanding of this solubility behavior based upon comprehensive

β-chloroacrylamides have complex synthetic pathways which have provided unique opportunities for developing novel mechanistic elucidation methods using real time monitoring techniques,

Received: March 22, 2017 Accepted: August 25, 2017 Published: September 8, 2017

INTRODUCTION Functionalized α-thio-β-chloroacrylamides derivatives are gaining increasing interest in the literature as synthetically viable advanced pharmaceutical intermediates1−3 (API) that can undergo transformations, such as Diels−Alder cycloadditions,4 1,3-dipolar cycloadditions,5 and sulfide group6,7 and nucleophilic substitutions (Figure 1).8

© 2017 American Chemical Society

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DOI: 10.1021/acs.jced.7b00288 J. Chem. Eng. Data 2017, 62, 3193−3205

Journal of Chemical & Engineering Data

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134.4, 134.0, 129.1, 119.7, 55.9, 22.4, 20.5. MS (EI) m/z 197 [M]+, [12C10H1235Cl14N16O 197]. HRMS (EI) m/z [M]+ 197.0604[C10H12ClNO]+ requires 197.0607. Materials used in this study with corresponding sources, purity (determined by chemical supplier), and analysis method are shown in Table 1. Experimental Methods. Melting Properties Measurements. The molar enthalpy of fusion (ΔfusH) and the melting temperature (Tm) of S1 were measured using differential scanning calorimetry (DCS 200 F3Maia, Netsch) under a nitrogen atmosphere, with a heating rate of 10 K·min−1 and temperature accuracy of 0.1 K. Approximately 7 mg of sample were weighed using an electronic analytic balance (type AX205, Mettler Toledo instrument Co. Ltd., uncertainty of ±0.01 mg) and placed on aluminum crucible pan. To ensure accuracy, measurement was conducted five times and the average result was taken. Solubility Measurements. The polythermal method, a widely used method to determine the metastable zone width,13−17 was used to measure the solubility of S1 in various solvent compositions. It has been reported in the literature that various factors such as cooling rate, initial composition, stirring rate and seed particles can affect the metastable zone width.18 This article examines only the effect of temperature upon S1’s solubility and therefore all other variables were kept constant. The experiments were conducted in an EasyMax (102, Mettler Toledo) reactor and in situ focused Beam reflectance measurement (FBRM ParticleTrack G400 series, Mettler Toledo) was used to characterize the nucleation and dissolution properties of S1.19

Scheme 1. Synthesis of (Z)-3-Chloro-2-(phenylthio)-N-(p-tolyl) acrylamide

experimental data is required. In this study, the polythermal method was used to obtain the solubility data, which involves cooling a saturated solution until nucleation occurs, and then subsequently heating the solution until it dissolves. This work quantifies the solubility behavior of the molecule S1 in ethyl acetate + hexane, toluene + hexane, acetone + hexane, and butanone + hexane solutions, as no such data is currently available in the literature. The experimental data were correlated with Apelblat, λh, and the phase equilibria with NRTL (nonrandom two liquid) model equations to enable both interpolation and extrapolation of the measured data.

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EXPERIMENTAL SECTION Materials. As seen from Scheme 2, a modified procedure developed by Li,12 α-chloropropionyl chloride (1.16 mL, 12 mmol, Scheme 2. Synthesis of 2-Chloro-N-(4methylphenyl)propanamide (S1)

1.2 equiv) was added dropwise (with extreme caution) to a suspension of p-toluidine (1.07 g, 10 mmol) in toluene (20 mL) at 0 °C and the resulting solution was heated to reflux for 1 h with vigorous stirring. After cooling, the solvent was removed under vacuum and the resulting off white solid was collected by filtration and washed thoroughly with cold cyclohexane (1.89 g). Spectral data of the obtained product matched that reported in the literature.1 1 HNMR (300 MHz, CDCl3): δ 8.21 (s, 1H), 7.42 (d, J = 8.2 Hz, 2H), 7.15 (d, J = 8.2 Hz, 2H), 4.54 (q, J = 7.1 Hz, 1H) 2.13 (s, 3H), 1.83 (d, J = 7.1 Hz, 3H). 13C NMR (100 MHz, CDCl3): δ 166.9,

Figure 2. Schematic diagram of the experimental setup for solubility measurements.

Table 1. Sources and Mass Fraction Purity of Materials with Corresponding Analysis Method chemical name

CAS registry number

source

mass fraction purity

further purification method

analysis method

S1 ethyl acetate toluene acetone butanone hexane p-toluidine α-chloropropionyl chloride cyclohexane 4-acetaminophenol water

147372-41-6 141-78-6 108-88-3 67-64-1 78-93-3 110-54-3 106-49-0 7623-09-8 110-82-7 103-90-2 7732-18-5

synthesized Sigma-Aldrich Sigma-Aldrich Sigma-Aldrich Sigma-Aldrich Sigma-Aldrich Sigma-Aldrich Sigma-Aldrich Sigma-Aldrich Acros Organics Sigma-Aldrich

99% ≥99.5% 99.90% ≥99.8% ≥99.7% ≥97% 99% 99% 99% 98%

none none none none none none none none none none none

HNMR HPLC HPLC HPLC HPLC HPLC HPLC HPLC HPLC HPLC

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Table 2. Solubility of 4-Acetamidophenol in Water at Different Temperatures and p = 101.3 kPaa T/K

103 xpara

102RDtemp

102RDA

102RDB

288.24 293.62 298.66 302.88 307.94 312.88 318.20 322.99

1.32 1.53 1.81 2.10 2.47 2.93 3.45 4.08

−0.03 −0.16 −0.17 0.09 0.07 0.09 −0.02 0.05

−3.91 −5.47 −1.28 −1.44 0.01 0.30

−1.45 −0.86 −1.82 −1.27

102RDC

102RDD

102RDE

−1.96 −2.08 −0.56 −0.58 −0.89 −0.19 0.09

−1.63 −3.06 −5.17 −4.89 −5.53 −5.83 −4.48 −3.03

−12.84 −10.26 −7.53 −8.63 −4.51 −1.94

Standard uncertainties u are u(T) = 2 K, ur(p) = 0.05, ur(xpara) = 6 × 10−7. xpara is the measured mole fraction solubility of 4-acetaminophenol in water; RDA, RDB, RDC, RDD, and RDE are the relative deviations of the determined solubility with the literature data from Hojjati,30 Granberg,31 Fujiwara,32 Grant,33 and Shakeel,34 respectively, while RDtemp is relative deviation between the experimentally determined saturation temperatures using polythermal method and the saturation temperatures from the literatures.30−34 a

FBRM uses a focused beam of laser light that scans in a circular path to measure the chord length distribution (CLD) of a particle. For this study, total counts in the size range of 1−1000 μm were used to track the point of nucleation and saturation temperature of S1. The experimental set up is shown in Figure 2, and its operating procedure is as follows: (i) The solute and solvent mixture was dispensed from an electronic analytic balance (PA124, Ohaus Pioneer series) to the reactor. (ii) The solution was agitated at a constant rate of 200 rpm and temperature controlled at 60 °C (50 °C for acetone−hexane mixture) for at least 30 min to ensure full dissolution. (iii) To determine the temperature at which nucleation occurs, the solution was cooled at a constant rate of 0.5 K·min−1 until an excess of 1000 particles was detected in the size range 0−1000 μm. The solution would turn cloudy when this occurs. (iv) The saturation temperature (the temperature at which the particles dissolve once more) was determined by heating the solution at constant rate until the number of particles in the size range 0−1000 μm decreases below 50 counts and the solution becomes clear. It has been demonstrated in the literature20 that the rate at which the solution is heated to reach dissolution should be considerably slower than the cooling rate. Hence, the heating rate in this paper was maintained at a constant rate of 0.1 K·min−1. The procedure was repeated at different concentrations by using a dosing unit with 50 mL syringe (SP-50, Mettler Toledo), where a known amount of solvent mixture was added to the reactor to dilute the solution. To ensure accuracy, the saturation temperature at a specific concentration was measured twice, and the uncertainty of each saturated temperature was within ±0.05 K. The mole fraction solubility (x1) of S1 is defined as x1 =

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

Figure 3. Comparison between experimental solubility of 4-acetaminophenol in water with that reported in literature: □, literature data from Hojjati;30 ◇, literature data from Granberg;31 Δ, literature data from Fujiwara;32 × , literature data from Grant;33 + , literature data from Shakeel;34 ●, experimental data.

Apelblat Equation. The Apelblat equation is a commonly used semiempirical equation to correlate experimental solubility for mixed solvents.21−23 It is given as B + C ln T (2) T where x1 is the mole fraction solubility of S1, T is absolute temperature in Kelvin (K), and A, B, and C are empirical model parameters. λh Equation. Buchowski et al.24 introduced a semiempirical equation to report the relationship between the solubility data and temperature, which is given as ln x1 = A +

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

(1)

where m1 and M1 represents the mass and molecular weight of S1, m2, and M2 represents the mass and molecular weight of ethyl acetate in ethyl acetate + hexane solution, toluene in toluene + hexane solution, acetone in acetone + hexane solution, or butanone in butanone + hexane solution while m3 and M3 represents the mass and molecular weight of hexane, respectively.

(3)

where x1 is the mole fraction solubility of S1, T and Tm are the absolute temperature and melting temperature of S1 in Kelvin (K), and λ and h are the model parameters representing the nonideal properties of the system and excess mixture enthalpy of solution. Phase Equilibria Equations with Nonrandom Two Liquid Model (NRTL) Equation. Phase equilibria equations can also be used to predict the solubility of a solute in a solvent, which are derived based on the fact that the fugacities of all species must be equal in each phase at equilibrium. The ratio of a liquid’s fugacity to a stable solid’s fugacity (both at the same temperature) can be determined using eq 4 once the solid’s molar fusion enthalpy and melting point are known.25

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THERMODYNAMIC MODELS Modeling the experimental solubility data enables a more general quantification of the mixtures’ solubility profiles and hence a broader understanding of their behaviors. Moreover, such developed models enable both interpolation and extrapolation of the measured data. 3195



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Figure 4. DSC curve for S1.

Table 3. Thermodynamic Properties of S1 at p = 101.3 kPaa

average STD a

Tm/K

ΔfusH/kJ·mol−1

394.75 394.65 394.75 395.15 394.85 394.83 0.192

27.11 26.64 27.47 26.60 26.05 26.77 0.542

Standard uncertainty u is ur(p) = 0.05.

⎡ ⎛ 1 ⎡ T ⎞ ⎢ΔfusH(T )⎜1 − f1L (T , P) = f1S (T , P)exp⎢ ⎟ Tm ⎠ ⎢⎣ RT ⎢⎣ ⎝ +

∫T

T

ΔCpdT − T

m

∫T

T

m

⎤⎤ dT ⎥⎥ ⎥⎦⎥⎦ T

ΔCp

(4) Figure 6. Three dimensional plot showing the relationship between number of particle counts and chord length distribution through a period of time, during an experimental run at x1exp = 0.00998 at w2 = 0.8, where w2 is the mass fraction of toluene in binary toluene + hexane mixtures.

Eq 4 is simplified to predict the saturation mole fraction of any solid in a liquid, which is given as ln x1γ1 = − +

ΔfusH ⎡ T ⎤ 1 ⎥− ⎢1 − R ⎣ Tm ⎦ RT 1 R

∫T

∫T

T

ΔCpdT

m

If heat capacity data is unavailable for both the solid and liquid, it is possible to assume that both values are approximately equal to each other, meaning that ΔCp ≈ 0. Therefore, eq 5 can be simplified to

T

m

ΔCpdT

(5)

Figure 5. FBRM trend during experimental run at x1exp = 9.98 × 10−3 when w2 = 0.8, where w2 is the mass fraction of toluene in binary toluene + hexane mixtures. 3196



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⎧Δ H ⎡ T ⎤⎫ ln x1 = −ln γ1 − ⎨ fus ⎢1 − ⎥⎬ Tm ⎦⎭ ⎩ RT ⎣ ⎪

⎪

⎪

⎪

⎡ 3 xjGij ln γi = 3 + ⎢∑ 3 ⎢ j=1 ∑ G x ∑k = 1 Gkixk ⎣ k = 1 kj k 3

∑ j = 1 τjiGjixj

(6)

where γ1, ΔfusH, and Tm are the activity coefficient, molar fusion enthalpy, and melting temperature of S1, respectively. Several thermodynamic models have been developed in the literature which attempt to predict or correlate activity coefficients.26 The nonrandom-two-liquid (NRTL) model is one such model and it is derived based on the assumption that a local composition exists around each molecule which is different to the bulk composition. In this article, the NRTL model is used to calculate the solute’s activity coefficient which enables the phase equilibria model to be used to estimate the solubility, given by eqs 7 and 8.27

3 ⎛ ∑k = 1 xkτkjGkj ⎞⎤ ⎜ ⎟⎥ × ⎜τij − 3 ∑k = 1 Gkjxk ⎟⎠⎥⎦ ⎝

τij = aij +

bij T

(7)

Gij = exp( −αijτij)αij = αjiτij ≠ τjiτii = 0

(8)

Subscript 1 represents S1, while subscript 2 represents ethyl acetate in ethyl acetate + hexane mixture, toluene in toluene + hexane mixture, acetone in acetone + hexane mixture, and

Table 4. Experimental and Predicted Mole Fraction Solubility of S1 (1) in Ethyl Acetate (2) + Hexane (3) at Different Temperatures and p = 101.3 kPaa,b,c,d,e λh

Apelblat

NRTL

w2

T/K

103 x1exp

103 x1cal

102RD

103 x1cal

102RD

103 x1cal

102RD

0.8

273.43 280.55 284.51 289.90 295.86 302.06 307.80 311.78 316.97 321.82 275.08 282.86 291.34 298.87 303.81 306.38 315.00 320.32 324.32 327.67 278.92 282.01 288.62 291.49 300.20 305.25 312.30 318.43 325.13 327.67 275.79 280.71 286.57 292.96 302.07 309.19 314.89 318.71 321.54 327.67

26.87 32.71 35.29 41.08 49.12 61.09 69.24 80.02 94.77 116.20 16.77 20.45 26.21 33.47 39.98 44.92 54.79 65.42 85.45 100.71 10.47 12.74 13.68 16.66 17.90 23.30 30.01 40.80 50.84 59.71 2.77 3.51 4.40 5.68 7.85 9.07 10.91 14.59 16.23 20.98

27.60 32.32 35.62 41.04 48.61 58.67 70.57 80.62 96.50 114.82 18.36 21.09 25.82 32.15 37.80 41.34 57.25 71.21 84.61 98.23 11.30 11.99 13.95 15.05 19.58 23.30 30.39 39.09 52.49 58.97 3.17 3.60 4.26 5.22 7.20 9.48 11.98 14.10 15.95 21.01

−2.72 1.18 −0.92 0.08 1.04 3.96 −1.92 −0.76 −1.83 1.19 −9.49 −3.13 1.50 3.96 5.47 7.96 −4.50 −8.84 0.98 2.45 −7.93 5.90 −2.03 9.66 −9.39 0.03 −1.26 4.19 −3.23 1.24 −14.32 −2.41 3.38 8.07 8.20 −4.60 −9.84 3.34 1.75 −0.15

23.23 30.01 34.49 41.41 50.39 61.29 73.52 82.83 96.62 110.57 12.39 17.39 24.71 33.29 40.19 44.20 60.92 73.67 83.83 93.52 8.55 9.77 12.93 14.53 20.66 25.07 32.70 40.84 52.06 56.75 2.43 3.04 3.94 5.17 7.52 9.99 12.48 14.42 16.07 20.25

13.53 8.25 2.28 −0.81 −2.58 −0.33 −6.18 −3.52 −1.94 4.85 26.15 14.99 5.72 0.54 −0.52 1.59 −11.20 −12.60 1.89 7.13 18.33 23.36 5.44 12.79 −15.40 −7.58 −8.95 −0.10 −2.39 4.96 12.29 13.39 10.58 8.83 4.10 −10.22 −14.41 1.10 1.03 3.44

27.37 33.20 35.41 40.95 48.77 60.74 68.68 79.71 94.90 116.40 16.50 20.29 26.26 33.74 40.44 45.63 54.99 65.67 85.92 100.58 10.28 12.62 13.32 16.53 17.55 23.17 29.96 41.04 50.40 59.15 3.32 3.79 4.45 5.53 7.62 9.12 11.12 14.63 16.34 21.11

−1.85 −1.52 −0.33 0.30 0.71 0.57 0.80 0.39 −0.13 −0.17 1.62 0.78 −0.20 −0.78 −1.14 −1.58 −0.37 −0.37 −0.55 0.13 1.80 0.99 2.61 0.80 1.94 0.57 0.18 −0.59 0.87 0.95 −19.78 −7.92 −1.13 2.59 2.84 −0.56 −1.96 −0.30 −0.66 −0.65

0.6

0.4

0.2

Standard uncertainties u are u(T) = 2 K, ur(p) = 0.05, ur(x1) = 7 × 10−7, ur(w2) = 1 × 10−6. bw2 is the mass fraction of ethyl acetate (2) in binary ethyl acetate (2) + hexane (3) mixture. cx1exp is the mole fraction solubility of S1 (1) in ethyl acetate (2) + hexane (3) mixture. dx1cal represents the calculated solubility data using Apelblat, λh, and phase equilibria with NRTL model equations. eRD refers to the corresponding relative deviation. a

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butanone in butanone + hexane mixture, and subscript 3 represents hexane. In these equations, τ reflects the segment−segment interaction energies and α represents a predetermined nonrandomness factor. As recommended by Renon and Prausnitz,28 the selected value for αij is 0.3 during the optimization. The segment−segment interaction parameters are unique for each particular pair of species and are independent of composition and temperature. A detailed description of these parameters is provided by Tung et al.29 Modeling. Matlab (Mathwork, MA) was used to model the apelblat, λh and phase equilibria with NRTL equations and to provide a general quantification of the solute’s solubility profile. The function lsqcurvef it in Matlab’s optimization toolbox was used to estimate the required model parameters for the

experimental data. This function is based on the Levenberg− Marquardt algorithm, and uses the least-squares method to solve nonlinear curve-fitting problems. To evaluate the goodness of fit between the experimental and predicted solubility from the models, their relative deviation (RDi %) and average relative deviation (ARD %) were determined as cal x1,exp i − x1, i

RDi =

x1,exp i

ARD% =

100 N

(9) N

∑

cal x1,exp i − x1, i

x1,exp i

i=1

(10)

Table 5. Experimental and Predicted Mole Fraction Solubility of S1 (1) in Toluene (2) + Hexane (3) at Different Temperatures and p = 101.3 kPaa,b,c,d,e λh

Apelblat w2 1

0.8

0.6

0.4

T/K 273.24 278.33 285.50 290.93 297.29 301.24 307.73 312.06 315.66 321.66 278.26 286.03 292.31 297.02 302.36 308.95 313.74 316.55 321.18 326.46 278.51 281.86 285.78 289.67 296.39 308.14 311.71 315.29 320.67 324.07 285.35 293.53 297.25 304.24 307.91 313.39 318.25 321.77 326.94 331.62

3

10 x1

exp

5.17 7.19 9.29 12.51 16.75 20.00 27.85 35.58 41.30 57.94 4.07 5.39 6.75 9.98 12.97 17.98 21.75 26.24 33.05 44.68 2.50 2.95 3.63 4.63 6.12 8.69 9.95 11.64 14.02 18.45 1.56 2.92 3.92 5.79 6.67 7.69 8.40 9.85 13.13 15.50

10

3

x1cal

5.54 6.89 9.51 12.24 16.61 20.18 27.96 34.92 42.10 57.75 3.92 5.60 7.56 9.52 12.45 17.47 22.45 26.06 33.40 44.47 2.94 3.25 3.69 4.21 5.38 8.63 10.06 11.78 15.06 17.67 2.16 3.18 3.76 5.12 5.99 7.52 9.15 10.52 12.84 15.31

2

10 RD −7.18 4.08 −2.28 2.12 0.83 −0.92 −0.41 1.84 −1.92 0.32 3.64 −3.98 −12.02 4.63 4.03 2.85 −3.21 0.68 −1.04 0.47 −17.67 −10.30 −1.65 9.22 12.22 0.71 −1.11 −1.26 −7.43 4.24 −38.19 −8.85 4.13 11.54 10.23 2.22 −8.98 −6.76 2.19 1.23

10

3

x1cal

4.12 5.65 8.68 11.83 16.79 20.72 28.91 35.81 42.66 56.41 2.94 4.82 7.04 9.26 12.52 17.93 23.10 26.67 33.70 43.60 2.46 2.88 3.46 4.12 5.53 9.06 10.48 12.10 14.99 17.10 2.16 3.16 3.72 5.05 5.90 7.42 9.07 10.47 12.89 15.56

NRTL 2

3

cal

10 RD

10 x1

20.36 21.37 6.63 5.39 −0.19 −3.60 −3.81 −0.65 −3.30 2.63 27.77 10.58 −4.43 7.25 3.47 0.28 −6.20 −1.66 −1.95 2.41 1.40 2.15 4.71 11.17 9.72 −4.33 −5.37 −4.01 −6.96 7.28 −38.37 −8.10 5.11 12.79 11.55 3.50 −8.03 −6.26 1.83 −0.36

4.87 6.27 8.71 11.37 15.48 18.82 26.63 34.41 41.81 61.88 4.27 5.98 7.80 9.79 12.45 16.89 20.96 24.50 31.17 42.54 2.90 3.35 3.96 4.69 6.18 9.74 11.19 12.92 15.89 18.86 2.51 3.52 4.10 5.41 6.22 7.59 8.98 10.25 12.61 15.01

102RD 5.85 12.80 6.32 9.08 7.58 5.89 4.39 3.28 −1.22 −6.81 −4.89 −11.07 −15.56 1.90 4.05 6.06 3.65 6.62 5.69 4.78 −16.12 −13.72 −9.30 −1.12 −0.87 −12.07 −12.49 −10.99 −13.37 −2.22 −60.64 −20.47 −4.43 6.47 6.68 1.29 −6.90 −4.06 3.94 3.21

a Standard uncertainties u are u(T) = 2 K, ur(p) = 0.05, ur(x1) = 7 × 10−7, ur(w2) = 1 × 10−6. bw2 is the mass fraction of toluene (2) in binary toluene (2) + hexane (3) mixture. cx1exp is the mole fraction solubility of S1 (1) in toluene (2) + hexane (3) mixture. dx1cal represents the calculated solubility data using Apelblat, λh, and phase equilibria with NRTL model equations. eRD refers to the corresponding relative deviation.

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and literature data.30−34 Moreover, Figure 3 graphically shows the comparison between the experimental and literature data. From Table 2 and Figure 3 it can be seen that the measured experimental data is closely aligned with the published data, thus ensuring the assumption that the developed experimental method is sufficiently accurate. DSC Results. The thermal analysis of S1 is shown in Figure 4. The area under the curve represents the enthalpy of fusion, in J·g−1. To convert the value in J·mol−1, it was multiplied to the molecular mass of S1 (197.5 g·mol−1). ΔfusH and Tm are determined as 26.77 ± 0.542 kJ·mol−1 and 394.83 ± 0.192 K, respectively. These values are used to calculate the predicted mole fraction (x1cal) using the phase equilibria with NRTL model equations. The summary of results is listed in Table 3.

where N is the total amount of experimental values, xexp1,i and xcal1,i are the ith experimental and predicted solubility mole fractions.

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RESULTS AND DISCUSSION Validation of Experimental Technique. To confirm the accuracy of the polythermal method using in situ FBRM, the solubility of 4-acetamenophenol (paracetamol) in pure water were measured. Since the solubility data for S1 is not widely available in the literature, it was decided to use 4-acetaminophenol as its chemical structure is similar to S1 and its solubility data has been widely published in the literature. The experimental solubility data of 4-acetaminophenol in pure water is listed in Table 2, along with the relative deviation between experimental

Table 6. Experimental and Predicted Mole Fraction Solubility of S1 (1) in Acetone (2) + Hexane (3) at Different Temperatures and p = 101.3 kPaa,b,c,d,e λh

Apelblat w2 1

0.8

0.6

0.4

NRTL

T/K

103 x1exp

103 x1cal

102RD

103 x1cal

102RD

103 x1cal

102RD

271.96 283.37 287.02 290.81 294.37 300.04 302.89 307.95 310.94 315.55 269.81 279.02 285.52 287.18 292.69 300.27 306.06 308.65 313.31 318.18 276.51 284.73 286.58 290.72 294.67 298.49 302.48 307.52 313.50 318.38 276.47 279.77 282.54 292.79 299.00 300.62 306.58 312.23 315.07 318.80

61.58 76.73 81.13 86.08 91.66 105.33 113.81 135.68 150.09 155.07 50.17 61.04 68.45 77.93 81.92 101.98 122.72 135.06 142.53 172.03 42.51 55.89 57.83 64.59 73.15 84.31 99.49 121.35 155.14 191.87 19.51 20.43 26.92 37.29 45.85 54.31 63.29 75.82 87.35 103.02

61.07 74.90 80.63 87.39 94.59 108.03 115.79 131.59 142.24 160.98 49.90 60.95 70.99 73.90 84.82 103.37 120.99 129.99 148.29 170.63 43.37 54.06 57.14 65.10 74.38 85.23 98.96 120.79 155.06 192.03 19.86 22.55 25.08 37.24 47.33 50.37 63.38 78.79 87.88 101.39

0.82 2.39 0.62 −1.53 −3.20 −2.56 −1.73 3.01 5.23 −3.81 0.53 0.16 −3.71 5.16 −3.54 −1.37 1.41 3.75 −4.04 0.82 −2.02 3.26 1.19 −0.78 −1.69 −1.09 0.53 0.46 0.06 −0.08 −1.80 −10.35 6.82 0.12 −3.22 7.25 −0.15 −3.92 −0.61 1.58

54.94 73.83 81.00 89.07 97.24 111.14 118.58 132.05 140.42 157.66 44.48 58.89 71.34 74.25 87.21 106.66 123.40 131.17 148.93 165.75 33.55 49.31 53.70 64.57 76.55 89.62 104.89 127.04 157.05 183.83 18.54 21.56 24.27 37.53 48.23 51.08 64.42 79.57 87.85 99.86

10.78 3.78 0.16 −3.48 −6.08 −5.51 −4.19 2.68 6.44 −1.67 11.34 3.52 −4.23 4.72 −6.46 −4.59 −0.55 2.88 −4.49 3.65 21.07 11.77 7.14 0.03 −4.65 −6.30 −5.42 −4.69 −1.23 4.19 4.98 −5.50 9.85 −0.65 −5.18 5.94 −1.79 −4.95 −0.58 3.07

64.57 76.13 80.32 85.44 91.47 105.65 114.40 135.11 148.44 160.29 51.76 60.16 67.02 75.36 80.43 101.00 121.99 133.74 145.60 173.11 41.10 54.10 56.15 63.31 72.53 84.53 100.55 122.96 154.50 183.77 19.27 20.03 26.07 36.12 44.81 54.43 63.78 77.38 90.64 108.47

−4.87 0.78 1.00 0.74 0.21 −0.30 −0.52 0.42 1.10 −3.37 −3.17 1.45 2.09 3.29 1.81 0.96 0.59 0.98 −2.15 −0.63 3.32 3.19 2.91 1.98 0.85 −0.27 −1.06 −1.33 0.41 4.22 1.21 1.95 3.18 3.12 2.27 −0.23 −0.78 −2.05 −3.76 −5.29

a Standard uncertainties u are u(T) = 2 K, ur(p) = 0.05, ur(x1) = 7 × 10−7, ur(w2) = 1 × 10−6. bw2 is the mass fraction of acetone (2) in binary acetone (2) + hexane (3) mixture. cx1exp is the mole fraction solubility of S1 (1) in acetone (2) + hexane (3) mixture. dx1cal represents the calculated solubility data using Apelblat, λh, and phase equilibria with NRTL model equations. eRD refers to the corresponding relative deviation.

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specific mole fractions (x1exp). Figure 5 illustrates the FBRM trend obtained from the experimental run at a mole fraction

Solubility Data. The polythermal method with in situ FBRM was used to determine the saturation temperatures (T) at a

Table 7. Experimental and Predicted Mole Fraction Solubility of S1 (1) in Butanone (2) + Hexane (3) at Different Temperatures and p = 101.3 kPaa,b,c,d,e λh

Apelblat w2

T/K

1

10

271.23 275.52 280.90 285.45 291.46 296.73 302.41 307.63 313.15 319.11 267.10 275.61 282.71 288.74 294.84 296.95 303.07 309.04 316.09 321.41 274.60 281.33 286.43 291.08 294.49 300.32 306.78 311.37 315.91 322.92 274.95 284.12 294.62 302.86 305.01 306.80 309.25 312.40 315.87 320.50

0.8

0.6

0.4

3

x1exp

77.41 82.87 89.16 105.12 115.45 128.04 130.38 148.88 173.49 207.85 46.39 57.33 69.11 78.46 88.51 95.89 110.11 129.29 162.63 195.35 35.05 44.19 51.76 56.89 70.79 82.25 98.15 112.66 132.22 159.98 18.55 22.44 31.82 50.01 55.26 61.74 69.94 80.66 95.26 116.30

3

10 x1

2

cal

79.91 84.58 91.65 98.80 110.13 122.12 137.58 154.50 175.80 203.41 49.01 57.18 66.42 76.42 89.08 94.16 111.31 132.21 163.63 193.51 34.80 43.81 51.94 60.49 67.52 81.22 99.21 114.02 130.60 160.32 16.14 22.83 35.28 50.85 56.11 60.97 68.40 79.43 93.93 117.94

3

10 RD

10

x1cal

−3.22 −2.06 −2.79 6.02 4.61 4.62 −5.52 −3.77 −1.33 2.14 −5.65 0.25 3.90 2.60 −0.64 1.80 −1.08 −2.26 −0.62 0.94 0.71 0.86 −0.36 −6.33 4.62 1.26 −1.08 −1.21 1.23 −0.21 13.01 −1.75 −10.87 −1.67 −1.54 1.26 2.21 1.52 1.40 −1.41

73.24 80.70 91.05 99.54 113.21 126.17 143.66 158.91 175.91 194.63 39.28 51.90 64.73 77.72 93.10 98.59 117.11 137.45 163.72 185.02 33.96 43.31 51.76 60.78 67.51 81.57 99.85 114.62 130.50 159.64 11.39 19.44 34.37 51.87 57.55 62.55 70.08 80.89 94.24 114.92

NRTL 2

3

10 RD

10

x1cal

102RD

5.39 2.62 −2.11 5.31 1.94 1.46 −10.18 −6.74 −1.40 6.36 15.34 9.47 6.33 0.94 −5.18 −2.82 −6.36 −6.31 −0.67 5.29 3.11 1.98 −0.01 −6.84 4.64 0.83 −1.74 −1.74 1.30 0.22 38.62 13.37 −8.01 −3.73 −4.14 −1.31 −0.20 −0.28 1.07 1.19

80.88 84.95 91.56 96.76 107.67 119.19 137.18 154.05 175.29 202.41 45.31 58.42 70.19 80.97 93.39 97.71 113.97 134.16 164.53 192.58 36.18 43.03 50.00 57.91 64.01 77.46 96.02 111.76 129.22 163.02 19.10 22.00 33.46 50.95 56.93 62.27 70.25 81.57 95.03 114.95

−4.48 −2.51 −2.69 7.95 6.74 6.91 −5.214 −3.48 −1.04 2.62 2.33 −1.91 −1.56 −3.20 −5.51 −1.90 −3.50 −3.77 −1.17 1.41 −3.23 2.62 3.40 −1.80 9.58 5.83 2.17 0.80 2.27 −1.90 −2.96 1.98 −5.13 −1.87 −3.02 −0.85 −0.44 −1.12 0.24 1.16

a Standard uncertainties u are u(T) = 2 K, ur(p) = 0.05, ur(x1) = 7 × 10−7, ur(w2) = 1 × 10−6. bw2 is the mass fraction of butanone (2) in binary butanone (2) + hexane (3) mixture. cx1exp is the mole fraction solubility of S1 (1) in butanone (2) + hexane (3) mixture. dx1cal represents the calculated solubility data using Apelblat, λh, and phase equilibria with NRTL model equations. eRD refers to the corresponding relative deviation.

Table 9. Optimized Values for the Parameters of Apelblat and λh for Solubility of S1 (1) in Toluene (2) + Hexane (3)a

Table 8. Optimized Values for the Parameters of Apelblat and λh for Solubility of S1 (1) in Ethyl Acetate (2) + Hexane (3)a model

parameter

w2 = 0.8

w2 = 0.6

w2 = 0.4

w2 = 0.2

model

parameter

w2 = 1

w2 = 0.8

w2 = 0.6

w2 = 0.4

Apelblat

A B C λ h

−302.363 11051.2 46.0442 0.45224 5885.05

−470.904 18466.2 71.1718 0.48080 6919.00

−487.622 19133.6 73.6184 0.28081 11881.5

−389.956 14434.7 59.0538 0.10321 33408.6

Apelbat

A B C λ h

−315.699 10170.1 48.7106 0.85744 5524.05

−318.364 10196.7 49.0674 0.61397 8200.47

−391.296 14266.7 59.3736 0.11221 32341.1

−14.4476 −2983.89 3.31950 0.08089 46382.3

λh

λh

a

a

w2 is the mass fraction of ethyl acetate (2) in binary ethyl acetate (2) + hexane (3) mixture

w2 is the mass fraction of toluene (2) in binary toluene (2) + hexane (3) mixture 3200



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(x1exp) of 0.00998 for binary toluene + hexane mixtures at a composition of w2 = 0.8. The trend shows the steps involved to determine the saturation temperature where initially the solution is aged at 60 °C to ensure full dissolution, then cooled at a constant rate of 0.5 K·min−1 until the crystals start to crash out at the nucleation temperature, and finally heated at a constant rate of 0.1 K·min−1 to determine the saturation temperature (the temperature at which crystals are dissolved into the solution). Figure 6 illustrates the same trend while representing the relationship between the number of particle counts and the chord length distribution of the crystals throughout the experimental run. The measured saturation temperatures at various mole fractions of S1 in various solvent mixtures and the relative deviation between experimental and predicted solubility are listed in Tables 4, 5, 6, and 7, where x1 is the mole fraction solubility of S1 in the solvent mixtures and w2 is the mass fraction ethyl acetate in the binary ethyl acetate + hexane mixtures, toluene in binary toluene + hexane mixtures, acetone in binary acetone + hexane mixtures, and butanone in binary butanone + hexane mixtures. The experimental solubility data were correlated using Apelblat, λh, and phase equilibria with NRTL (nonrandom two liquid)

model equations and the optimized parameter values for all the equations were obtained using Matlab’s lsqcurvef it function. It should be noted that the Apelblat and λh model equation does not take the solvent composition into consideration, and thus Table 13. Optimized Values for Parameters of Phase Equilibria with NRTL Model Equations for Solubility of S1 (1) in Toluene (2) + Hexane (3)a

model

parameter

w2 = 1

w2 = 0.8

w2 = 0.6

w2 = 0.4

A B C λ h

−230.722 8382.98 35.1612 0.39822 4508.12

−195.042 6583.05 29.9488 0.55460 3922.13

−420.481 15854.8 64.0321 1.98605 1883.76

−143.827 3347.95 22.7314 0.79282 4373.39

λh

parameter

values

NRTL

a12 a13 a21 a23 a31 a32 b12 b13 b21 b23 b31 b32

−1.42222 1.09929 3.96221 0.41662 2.96684 0.01718 0.12828 −19.8879 2.77062 19.6612 10.7332 −3.23033

a w2 is the mass fraction of toluene (2) in binary toluene (2) + hexane (3) mixture

Table 10. Optimized Values for the Parameters of Apelblat and λh for Solubility of S1 (1) in Acetone (2) + Hexane (3)a Apelblat

model

Table 14. Optimized Values for the Parameters of Phase Equilibria with NRTL Model Equations for Solubility of S1 (1) in Acetone (2) + Hexane (3)a model

parameter

values

NRTL

a12 a13 a21 a23 a31 a32 b12 b13 b21 b23 b31 b32

2.62402 13.5277 −3.58803 20.8426 3.39349 −12.4812 −1387.01 −4765.35 2614.35 −6770.75 1267.73 4057.14

a

w2 is the mass fraction of acetone (2) in binary acetone (2) + hexane (3) mixture

Table 11. Optimized Values for the Parameters of Apelblat and λh for Solubility of S1 (1) in Butanone (2) + Hexane (3)a model

parameter

w2 = 1

w2 = 0.8

w2 = 0.6

w2 = 0.4

Apelblat

A B C λ h

−224.424 8337.06 34.1174 0.33571 4268.89

−257.651 9333.04 39.3178 0.66155 3540.49

−48.5390 −343.620 8.26880 0.70405 3899.82

−340.136 11655.3 52.2771 1.75288 2595.60

λh

a w2 is the mass fraction of acetone (2) in binary acetone (2) + hexane (3) mixture

a

w2 is the mass fraction of butanone (2) in binary butanone (2) + hexane (3) mixture

Table 15. Optimized Values for the Parameters of Phase Equilibria with NRTL Model Equations for Solubility of S1 (1) in Butanone (2) + Hexane (3)a

Table 12. Optimized Values for Parameters of Phase Equilibria with NRTL Model Equations for Solubility of S1 (1) in Ethyl Acetate (2) + Hexane (3)a model

parameter

values

NRTL

a12 a13 a21 a23 a31 a32 b12 b13 b21 b23 b31 b32

3.4999 2.79327 −6.18745 −20.9361 −6.21239 26.8731 −1631.48 −1550.07 3507.13 5540.44 4502.81 −7325.74

a

model

parameter

values

NRTL

a12 a13 a21 a23 a31 a32 b12 b13 b21 b23 b31 b32

−8.31736 12.3799 15.2292 58.7989 −34.5934 44.3644 2257.48 −2863.69 −4495.72 −17738.7 11795.9 −12449.5

a

w2 is the mass fraction of ethyl acetate (2) in binary ethyl acetate (2) + hexane (3) mixture

w2 is the mass fraction of butanone (2) in binary butanone (2) + hexane (3) mixture 3201



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more apparently. One general set of NRTL parameters has the capability of describing all solvent compositions, which are listed in Tables 12, 13, 14, and 15. Moreover, the average relative deviations for various mixture compositions are shown in Tables 16, 17, 18, and 19. Figures 7, 8, 9, 10, 11, 12, 13, and 14 present the model equations that give the best ARD% in each solvent mixture (graphs for the remaining models can be found in the Supporting Information). The general trend in Figures 7 to 10 is that the solubility of S1 increases significantly with an increase in temperature. To further illustrate the effect of solvent composition on the solubility of S1, the experimental solubility data of ethyl acetate + hexane between 280 and 320 K, toluene + hexane between 300

require separate parameters for each different solvent compositions, which are shown in Tables 8, 9, 10, and 11. The use of Apelblat and λh model equation provide a convenient operational model of engineering interest to calculate the solubility of S1 quickly and easily. The Phase Equilibria with NRTL model equation is used to provide a more comprehensive model that illustrates the effect of solvent composition on the solubility Table 16. ARD% of Various Models in Ethyl Acetate (2) + Hexane (3)a model

w2 = 0.8

w2 = 0.6

w2 = 0.4

w2 = 0.2

Apelblat λh NRTL

0.06965 1.35524 0.12226

0.36539 3.36917 0.24689

0.28333 3.04558 1.01189

0.65907 3.01381 2.75246

a w2 is the mass fraction of ethyl acetate (2) in binary ethyl acetate (2) + hexane (3) mixture

Table 17. ARD% of Various Models in Toluene (2) + Hexane (3)a model

w2 = 1

w2 = 0.8

w2 = 0.6

w2 = 0.4

Apelbat λh NRTL

0.35242 4.48437 4.71545

0.39533 3.75347 0.12447

1.30175 1.57710 9.22668

3.12349 2.63524 7.49120

a

w2 is the mass fraction of toluene (2) in binary toluene (2) + hexane (3) mixture

Figure 8. Solubility data of S1 (1) in toluene (2) + hexane (3) mixtures: *, w2 = 1; + , w2 = 0.8; ◇, w2 = 0.6; □, w2 = 0.4; −, apelblat equation calculated. w2 is the mass fraction of toluene (2) in binary toluene (2) + hexane (3) mixtures.

Table 18. ARD% of Various Models in Acetone (2) + Hexane (3)a model

w2 = 1

w2 = 0.8

w2 = 0.6

w2 = 0.4

Apelblat λh NRTL

0.07655 0.29049 0.48095

0.08331 0.57776 0.52205

0.01619 2.19151 1.42412

0.42694 0.52111 0.03861

a

w2 is the mass fraction of acetone (2) in binary acetone (2) + hexane (3) mixture

Table 19. ARD% of Various Models in Butanone (2) + Hexane (3)a model

w2 = 1

w2 = 0.8

w2 = 0.6

w2 = 0.4

Apelblat λh NRTL

0.13099 0.26558 0.48160

0.07493 1.60388 1.87610

0.05066 0.17478 1.97470

0.21541 3.65769 1.20150

a w2 is the mass fraction of butanone (2) in binary butanone (2) + hexane (3) mixture

Figure 9. Solubility data of S1 (1) in acetone (2) + hexane mixtures (3): *, w2 = 1; + , w2 = 0.8; ◇, w2 = 0.6; □, w2 = 0.4; −, apelblat equation calculated. w2 is the mass fraction of acetone (2) in binary acetone (2) + hexane (3) mixtures.

Figure 7. Solubility data of S1 (1) in ethyl acetate (2) + hexane (3) mixtures: *, w2 = 0.8; + , w2 = 0.6; ◇, w2 = 0.4; □, w2 = 0.2; −, apelblat equation calculated. w2 is the mass fraction of ethyl acetate (2) in binary ethyl acetate (2) + hexane (2) mixtures.

Figure 10. Solubility data of S1 (1) in butanone (2) + hexane (3) mixtures: *, w2 = 1; + , w2 = 0.8; ◇, w2 = 0.6; □, w2 = 0.4; −, apelblat equation calculated. w2 is the mass fraction of butanone (2) in binary butanone (2) + hexane (3) mixtures. 3202



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and 320 K, acetone + hexane between 285 and 305 K, and butanone + hexane between 275 and 315 K were correlated using the regressed model parameters for apelblat, λh, and phase equilibria with NRTL model equations listed in Tables 8 to 15. It can be clearly seen from Figures 11 to 14 that the change of solvent composition has a great effect on the solubility of S1, as the presence of hexane in the solvent mixtures decreases the solubility of S1.

■

CONCLUSION

The polythermal method using in situ focused beam reflectance measurement (FBRM) was used to characterize the solubility

Figure 14. Solubility data of S1 (1) in butanone (2) + hexane (3) mixtures: ○, T = 275 K; *, T = 285 K; + , T = 295 K; ◇, T = 305 K; □, T = 315 K; −, apelblat equation calculated. w2 is the mass fraction of butanone (2) in binary butanone (2) + hexane (3) mixtures.

properties of 2-chloro-N-(4-methylphenyl)propanamide (S1) in ethyl acetate + hexane, toluene + hexane, acetone + hexane and butanone + hexane mixtures in various temperatures. To provide a general quantification of the solubility profiles, the experimental data was correlated using the Apelblat, λh, and phase equilibria with NRTL model equations. The Apelblat and λh model equation provides a convenient operational model of engineering interest to calculate the solubility of S1 quickly and easily, although it does not take the solvent composition into account, therefore needing separate parameters for each different solvent compositions. Therefore, the phase equilibria with NRTL model equation is used to provide a more comprehensive model that illustrates the effect of solvent composition on the solubility more apparently. One general set of NRTL parameters has the capability of describing all solvent compositions. The predicted solubility data obtained using the Apelblat, λh, and phase equilibria with NRTL model equations agrees well with the experimental solubility data, as shown by the RD% and ARD% values.

Figure 11. Solubility data of S1 (1) in ethyl acetate (2) + hexane (3) mixtures: ○, T = 280 K; *, T = 290 K; + , T = 300 K; ◇, T = 310 K; □, T = 320 K; −, apelblat equation calculated. w2 is the mass fraction of ethyl acetate (2) in binary ethyl acetate (2) + hexane (3) mixtures.

■

ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jced.7b00288. Graphs showing the solubility data of S1 in ethyl acetate + hexane, toluene + hexane, acetone + hexane, and butanone + hexane solvent mixtures, correlated using the Apelblat, λh, and phase equilibria with NRTL model equations (PDF)

■

Figure 12. Solubility data of S1 (1) in toluene (2) + hexane (3) mixtures: ○, T = 300 K; *, T = 305 K; + , T = 310 K; ◇, T = 315 K; □, T = 320 K; −, λh equation calculated. w2 is the mass fraction of toluene (2) in binary toluene (2) + hexane (3) mixtures.

AUTHOR INFORMATION

Corresponding Author

*Tel.: +353 1 7162815; Fax: +353 1 7161177; E-mail: [email protected]. ORCID

Philip Donnellan: 0000-0001-8576-7857 Roderick C. Jones: 0000-0002-2884-4884 Funding

The financial support of the Synthesis and Solid State Pharmaceutical center (SSPC) and Science Foundation Ireland (SFI, 12/RC/2275) are gratefully acknowledged. Notes

The authors declare no competing financial interest.

■

Figure 13. Solubility data of S1 (1) in acetone (2) + hexane (3) mixtures: ○, T = 285 K; *, T = 290 K; + , T = 295 K; ◇, T = 300 K; □, T = 305 K; −, apelblat equation calculated. w2 is the mass fraction of acetone (2) in binary acetone (2) + hexane (3) mixtures. 3203

NOMENCLATURE A, B, C empirical model parameters for Apelblat equation API advanced pharmaceutical intermediates DOI: 10.1021/acs.jced.7b00288 J. Chem. Eng. Data 2017, 62, 3193−3205


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ARD average relative deviation CLD chord length distribution CSD crystal size distribution DSC differential scanning calorimetry FBRM focused beam reflectance measurement h model parameter for λh equation representing excess mixture enthalpy of solution m mass (g) M molecular mass (g mol−1) NRTL nonrandom two liquid model R universal gas constant (J mol−1K−1) RD relative deviation S1 2-chloro-N-(4-methylphenyl)propanamide STD standard deviation T absolute temperature (K) Tm melting temperature of S1 (K) w solvent mixture compositions x1 mole fraction solubility of S1 (mol) x1cal predicted mole fraction solubility of S1 (mol) xpara mole fraction solubility of 4-acetaminophenol (paracetamol) (mol) Greek Symbols

ΔCp change of heat capacity at constant pressure ΔfusH molar fusion enthalpy ΔHd dissolution enthalpy ΔSd dissolution entropy ΔHfus molar enthalpy of fusion ΔSfus molar entropy of fusion λ model parameter for λh equation representing nonideal properties of the system γ1 activity coefficient of S1 τ segment−segment interaction energies α nonrandomness factor Subscripts

1 S1 2 ethyl acetate, toluene, acetone, or butanone 3 hexane

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REFERENCES

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Experimental and Modeling Studies on the Solubility of 2-Chloro-N-(4

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