Abraham General Solvation Parameter Model: Predictive Expressions for Solute Transfer into Isobutyl Acetate

Abstract

Mole fraction of solubilities are reported for the: o-acetoacetanisidide, anthracene, benzoin, 4-tert-butylbenzoic acid, 3-chlorobenzoic acid, 3-chlorobenzoic acid, 2-chloro-5-nitrobenzoic acid, 4-chloro-3-nitrobenzoic acid, 3,4-dichlorobenzoic acid, 2,3-dimethoxybenzoic acid, 3,4-dimethoxybenzoic acid, 3,5-dimethoxybenzoic acid, 3,5-dinitrobenzoic acid, diphenyl sulfone, 2-ethylanthraquinone, 2-methoxybenzoic acid, 4-methoxybenzoic acid, 2-methylbenzoic acid, 3-methylbenzoic acid, 2-methyl-3-nitrobenzoic acid, 3-methyl-4-nitrobenzoic acid, 4-methyl-3-nitrobenzoic acid, 2-naphthoxyacetic acid, 3-nitrobenzoic acid, 4-nitrobenzoic acid, salicylamide, thioxanthene-9-one, 3,4,5-trimethoxybenzoic acid, and xanthene dissolved in isobutyl acetate at 298.15 K. The results of our experimental measurements, combined with the published literature data, were used to obtain Abraham model equations for isobutyl acetate. The mathematical correlations presented in the current study describe the observed molar solubility ratios of the solutes dissolved in isobutyl acetate to within an overall standard deviation of 0.12 log units or less.

1. Introduction

Several million tons of organic solvents are consumed annually by the chemical manufacturing sector. Organic solvents serve as the reaction media in the synthesis of new chemical products, as the mobile phase in high-performance liquid chromatographic separations, and as extractants in biphasic liquid–liquid partitioning systems. Considerable effort has been devoted to developing and revising guidelines to aid industrial workers in selecting the most appropriate organic solvent for a particular application. The guidelines are revised continually as compounds are added to or removed from the list of “acceptable” solvents for use in manufacturing processes. Workers are instructed to focus not only the safety and economic aspects, but to also consider the solvents’ polarity and hydrogen-bonding characteristics, as these are important items as well. Solute–solvent interactions that result from hydrogen-bond formation and from differences in dipole moments can not only increase a given solute’s solubility, but can also alter the thermodynamic states of chemical reactants, synthesized products, and reaction intermediates. Product yields and selectivity, as well as chemical reaction rates, can be controlled to some extent through the solvent selection process. Slight increases in product yield and reaction rates can make a manufacturing process significantly more profitable.

It is only natural that industrial researchers utilize all of the available resources at their disposal in designing synthetic processes. Design engineers ideally prefer to utilize actual experimental data whenever available, as this provides less uncertainty in the required input values/parameters. Experimental data are often unavailable for the many possible solute–solvent combinations currently encountered in the various manufacturing processes. This is particularly true in the case of more environmentally friendly organic mono-solvents and solvent mixtures that are now being suggested as possible solvent alternatives to replace the more toxic, hazardous compounds that have been traditionally used in industrial manufacturing processes. Increased environmental awareness and worker safety, combined with much larger disposal costs, have encouraged the manufacturing sector to reduce (and in certain cases to completely eliminate) the use of specific organic solvents. The disposal of toxic organic compounds in accordance with prevailing governmental regulations can represent a significant expenditure, which is then passed on to the consumer in the form of a higher product purchase price.

Over the last 50 years, a multitude of predictive methods have been developed to provide the scientific and manufacturing communities with the needed input values if measured data are unavailable. The expressions derived from such predictive methods can be used to prioritize potential organic solvent candidates for possible thermodynamic and solubility determinations. Predictive expressions must yield reasonably accurate estimates of the desired property to be of any real value. The more reliable of the proposed models have incorporated mathematical terms to account for the various molecular interactions believed to be present.

The objective of the current study is to develop Abraham model expressions [1,2,3], as follows:

log P or log (C_S,organic/C_S,water) = c_p + e_p × E + s_p × S + a_p × A + b_p × B + v_p × V

(1)

log K or log (C_S,organic/C_S,gas) = c_k + e_k × E + s_k × S + a_k × A + b_k × B + l_k × L

(2)

for estimating the logarithm water-to-isobutyl acetate partition coefficients, log P, the logarithm of gas-to-isobutyl acetate partition coefficients, log K, and the logarithm of molar solubility ratios, log (C_S,organic/C_S,water) and log (C_S,organic/C_S,gas), for solid nonelectrolyte organic compounds and inorganic gases dissolved in the isobutyl acetate mono-solvent. The subscripts “organic,” “water,” and “gas” are used to define the two solubility ratios that denote the phase to which each molar solute concentration pertains.

Each multiplicative term on the right-hand side of Equations (1) and (2) describes a different type of solute–solvent molecular interaction. Each interaction is quantified as the product of a solvent property (c_p, e_p, s_p, a_p, b_p, v_p, c_k, e_k, s_k, a_k, b_k, and l_k) times the complementary solute property (E, S, A, B, V, and L). The solvent properties are defined as follows: (e_p and e_k) give the tendency of the solvent to interact with solute molecules through polarizability-type interactions involving electron pairs; (s_p and s_k) are measures of the solvent phase’s dipolarity/polarity; (a_p and a_k) and (b_p and b_k) quantify the solvent’s ability to function as a hydrogen-bond acceptor and hydrogen-bond donor in its interactions with the surrounding solute molecules, respectively; and (v_p and l_k) represent the ease of breaking the solvent–solvent interaction in regards to the formation of a solvent cavity in which the dissolved solute will reside. The numerical values of the aforementioned properties are deduced by curve-fitting measured partition coefficient data and molar solubility ratios for a series of solutes with known solute descriptors (E, S, A, B, V, and L) in accordance with Equations (1) and (2). In the present study, we focus our attention on the lowercase solvent properties. A detailed discussion of the solute descriptors and their determination based on measured chromatographic retention times, partition coefficients, and molar solubilities is available in several published review articles [4,5,6,7,8] and research papers [2,3,9,10,11,12].

There are published experimental data for the following: hydrogen [13], nitrogen [13], carbon dioxide [13], carbon monoxide [13], naphthalene [14], fluorene [15], benzoic acid [16], acetylsalicylic acid [17], isophthalic acid [16], forchlorfenuron [18], metronidiazole benzoate [19], iminostilbene [20], isovanillin [21], lansoprazole [22], 2,2′-bis(2-hydroxyethoxy)-1,1′-binaphthalene [23], lovastatin [24], etodolac [25], simvastatin [26,27], 18β-glycyrrhetinic acid [28], and exo-5,6-dehydronorcantharidin [29] dissolved in isobutyl acetate. An experimental gas-to-liquid partition coefficient for isobutyl acetate dissolved in itself is also available from the vapor pressure measurements of Monton and coworkers [30]. Unfortunately, the number of experimental values is not sufficient for us to develop meaningful Abraham model expressions. To supplement the published literature values, we have determined the mole fraction of the solubilities of the following: o-acetoacetanisidide, anthracene, benzoin, 4-tert-butylbenzoic acid, 3-chlorobenzoic acid, 3-chlorobenzoic acid, 2-chloro-5-nitrobenzoic acid, 4-chloro-3-nitrobenzoic acid, 3,4-dichlorobenzoic acid, 2,3-dimethoxybenzoic acid, 3,4-dimethoxybenzoic acid, 3,5-dimethoxybenzoic acid, 3,5-dinitrobenzoic acid, diphenyl sulfone, 2-ethylanthraquinone, 2-methoxybenzoic acid, 4-methoxybenzoic acid, 2-methylbenzoic acid, 3-methylbenzoic acid, 2-methyl-3-nitrobenzoic acid, 3-methyl-4-nitrobenzoic acid, 4-methyl-3-nitrobenzoic acid, 2-naphthoxyacetic acid, 3-nitrobenzoic acid, 4-nitrobenzoic acid, salicylamide, thioxanthene-9-one, 3,4,5-trimethoxybenzoic acid, and xanthene dissolved in isobutyl acetate at 298.15 K based on UV/visible spectrophotometric measurements.

Our solute selection was based, in part, on the compounds’ availability within the laboratory from prior solubility studies, and the fact that their solute descriptor values were determined from large numbers of experimental measurements. Furthermore, our past studies have shown that these compounds are not prone to form solid solvates with alkyl acetates, and their solubilities can be readily determined by either UV/visible absorbance measurements or volumetric acid–base titrations. The senior author is also currently preparing a volume for the IUPAC-NIST Solubility Data Series (project number #2021-023-1-500) that will update his earlier volume on the solubility of benzoic acid and substituted benzoic acids dissolved in both neat organic solvents and organic solvent mixtures [31]. The solubility data from the current study will likely be part of the new volume. We further note that the carboxylic acid functional group is present in many medicinal compounds, such as nonsteroidal anti-inflammatory drugs (e.g., acetylsalicylic acid, salicylic acid, naproxen, ketoprofen, ibuprofen, etodolac, flurbiprofen, ketorolac, and tolfenamic acid), statins (e.g., atorvastatin, Lipitor^®, fluvastatin, pitavastatin, pravastatin, and cerivastatin) and β-lactam antibiotics (e.g., amoxicillin, oxacillin, flucloxacillin, and benzylpenicillin). The results of our experimental measurements, combined with the published literature data, were used to obtain Abraham model equations for isobutyl acetate. The derived Abraham model correlations reported in the current study are based on 49 experimental data points.

2. Chemical Materials and Experimental Methodology

The crystalline organic solutes selected for the solubility measurements include 21 carboxylic acids, as well as 8 noncarboxylic acid solutes of varying polarity and molecular sizes. All chemicals used in the current study were purchased from commercial sources in the highest purity available. Several of the noncarboxylic acid solutes were further purified by recrystallization from either acetone or anhydrous methanol prior to performing the solubility measurements. All solid compounds were dried for at least two days at 333 K to remove trace moisture. The purification details and chemical suppliers are given in

Table 1. Chemical sources and final mass fraction purities of chemicals used in the solubility studies.

Chemical	Supplier	Purification Method	Purity (Mass Fraction)
Isobutyl acetate	TCI America Chemical Company, Portland, OR, USA	Stored over activated molecular sieves and distilled	0.998
o-Acetoacetanisidide	Acros Organics, Morris Plains, NJ, USA	Dried for two days at 333 K	0.996
Anthracene	Aldrich Chemical Company, Milwaukee, WI, USA	Recrystallized from anhydrous acetone	0.997
Benzoin	Aldrich Chemical Company	Recrystallized from anhydrous methanol	0.997
Diphenyl sulfone	Aldrich Chemical Company	Recrystallized from anhydrous methanol	0.996
2-Ethylanthraquinone	Aldrich Chemical Company	Recrystallized from anhydrous methanol	0.996
Salicylamide	Aldrich Chemical Company	Recrystallized from anhydrous methanol	0.997
Thioxanthen-9-one	Aldrich Chemical Company	Recrystallized from anhydrous methanol	0.997
Xanthene	Aldrich Chemical Company	Recrystallized from anhydrous methanol	0.996
4-tert-Butylbenzoic acid	TCI America Chemical Company	Dried for two days at 333 K	0.998
3-Chlorobenzoic acid	Aldrich Chemical Company	Dried for two days at 333 K	0.997
4-Chlorobenzoic acid	Acros Organics	Dried for two days at 333 K	0.996
2-Chloro-5-nitrobenzoic acid	Acros Organics	Dried for two days at 333 K	0.998
4-Chloro-3-nitrobenzoic acid	Acros Organics	Dried for two days at 333 K	0.998
3,4-Dichlorobenzoic acid	Aldrich Chemical Company	Dried for two days at 333 K	0.998
2,3-Dimethoxybenzoic acid	Thermo Scientific, Ward Hill, MA, USA	Dried for two days at 333 K	0.997
3,4-Dimethoxybenzoic acid	Across Organics	Dried for two days at 333 K	0.998
3,5-Dimethoxybenzoic acid	Across Organics	Dried for two days at 333 K	0.995
3,5-Dinitrobenzoic acid	Aldrich Chemical Company	Dried for two days at 333 K	0.997
2-Methoxybenzoic acid	Aldrich Chemical Company	Dried for two days at 333 K	0.998
4-Methoxybenzoic acid	Aldrich Chemical Company	Dried for two days at 333 K	0.998
2-Methylbenzoic acid	Aldrich Chemical Company	Dried for two days at 333 K	0.998
3-Methylbenzoic acid	Aldrich Chemical Company	Dried for two days at 333 K	0.998
2-Methyl-3-nitrobenzoic acid	Aldrich Chemical Company	Dried for two days at 333 K	0.997
3-Methyl-4-nitrobenzoic acid	Aldrich Chemical Company	Dried for two days at 333 K	0.997
4-Methyl-3-nitrobenzoic acid	Aldrich Chemical Company	Dried for two days at 333 K	0.998
2-Naphthoxyacetic acid	Sigma-Aldrich Chemical Company, Milwaukee, WI, USA	Dried for two days at 333 K	0.995
3-Nitrobenzoic acid	Aldrich Chemical Company	Dried for two days at 333 K	0.996
4-Nitrobenzoic acid	Acros Organics	Dried for two days at 333 K	0.998
3,4,5-Trimethoxybenzoic acid	Aldrich Chemical Company	Dried for two days at 333 K	0.998
Toluene	Aldrich Chemical Company	None	0.998, anhydrous
Sodium methoxide, 25 mass % solution in methanol	Aldrich Chemical Company	None
2-Propanol	Aldrich Chemical Company	None	0.99

, along with the final purities, as determined by either gas–liquid chromatographic analysis (noncarboxylic acid solutes and flame ionization detector) or non-aqueous acid–base volumetric titration based on a modification of the published method used by Fritz and Lisicki [32]. Our modified titration procedure replaced benzene with toluene as a component in the titration solvent for health reasons.

The experimental mole fraction solubilities were determined using a spectrophotometric method of chemical analysis based on the Beer–Lambert law that establishes a mathematical relationship between the measured solution absorbance and the molar concentration of the dissolved solid solute. The saturated solutions were prepared by placing excess solid solute and approximately 20 mLs of isobutyl acetate into amber glass bottles. The resulting solutions were then equilibrated at 298.15 ± 0.05 in a constant-temperature water bath. The sealed solutions were periodically shaken to facilitate the mixing and dissolution of the solid solute. After a three-day equilibration period, weighed aliquots of the saturated solutions were transferred into tared volumetric flasks, and the transferred sample was diluted quantitatively with 2-propanol. The absorbances of the diluted solutions were recorded with a Milton Roy Spectronic 1000 Plus single-beam spectrophotometer (Milton Roy, Rochester, NY, USA). An additional dilution was sometimes required to ensure that the sample’s measured absorbance fell within the range of values determined for the standard solutions. Our earlier publications contain the analysis wavelength and concentration range for each solute considered in the current study. For the convenience of the reader, this information is summarized in

Table 2. Analysis wavelengths and concentration ranges of standard solutions used in the spectrophotometric determination of solubility.

Chemical	Analysis Wavelength	Molar Concentration Range
o-Acetoacetanisidide	282 (nm)	5.81 × 10−5 to 1.94 × 10−4
Anthracene	356 (nm)	6.86 × 10−5 to 2.28 × 10−4
Benzoin	313 (nm)	1.21 × 10−3 to 4.03 × 10−3
Diphenyl sulfone	267 (nm)	2.61 × 10−4 to 8.70 × 10−4
2-Ethylanthraquinone	325 (nm)	1.25 × 10−4 to 4.17 × 10−4
Salicylamide	300 (nm)	1.06 × 10−4 to 3.55 × 10−4
Thioxanthen-9-one	378 (nm)	6.05 × 10−5 to 2.02 × 10−4
Xanthene	280 (nm)	1.79 × 10−4 to 5.95 × 10−4
4-tert-Butylbenzoic acid	275 (nm)	2.81 × 10−4 to 9.37 × 10−4
3-Chlorobenzoic acid	280 (nm)	5.05 × 10−4 to 1.68 × 10−3
4-Chlorobenzoic acid	272 (nm)	4.63 × 10−4 to 1.54 × 10−3
2-Chloro-5-nitrobenzoic acid	280 (nm)	8.69 × 10−5 to 2.90 × 10−4
4-Chloro-3-nitrobenzoic acid	292 (nm)	3.55 × 10−4 to 1.18 × 10−3
3,4-Dichlorobenzoic acid	280 (nm)	4.66 × 10−4 to 1.55 × 10−3
2,3-Dimethoxybenzoic acid	293 (nm)	2.27 × 10−4 to 7.56 × 10−4
3,4-Dimethoxybenzoic acid	286 (nm)	9.25 × 10−5 to 3.08 × 10−4
3,5-Dimethoxybenzoic acid	305 (nm)	2.17 × 10−4 to 7.23 × 10−4
3,5-Dinitrobenzoic acid	267 (nm)	6.35 × 10−5 to 2.12 × 10−4
2-Methoxybenzoic acid	295 (nm)	1.69 × 10−4 to 5.63 × 10−4
4-Methoxybenzoic acid	273 (nm)	9.77 × 10−5 to 3.26 × 10−4
2-Methylbenzoic acid	279 (nm)	4.29 × 10−4 to 1.43 × 10−3
3-Methylbenzoic acid	280 (nm)	4.17 × 10−4 to 1.39 × 10−3
2-Methyl-3-nitrobenzoic acid	290 (nm)	3.36 × 10−4 to 1.12 × 10−3
3-Methyl-4-nitrobenzoic acid	295 (nm)	1.70 × 10−4 to 5.67 × 10−4
4-Methyl-3-nitrobenzoic acid	295 (nm)	3.29 × 10−4 to 1.10 × 10−3
2-Naphthoxyacetic acid	284 (nm)	1.35 × 10−4 to 6.74 × 10−4
3-Nitrobenzoic acid	280 (nm)	1.67 × 10−4 to 5.57 × 10−4
4-Nitrobenzoic acid	272 (nm)	4.75 × 10−5 to 1.58 × 10−4
3,4,5-Trimethoxybenzoic acid	289 (nm)	1.38 × 10−4 to 4.60 × 10−4

.

We noted that isobutyl acetate is optically transparent at the analysis wavelengths listed in Table 2. We checked for possible interferences from the small amount of isobutyl acetate in the dilute samples that were subjected to absorbance measurements. We found that, to within experimental uncertainty, identical absorbances were obtained for standard solutions that contained no isobutyl acetate and for standard solutions that contained up to 5 percent isobutyl acetate by volume. We also checked for both solvate formation and solid-to-solid phase transitions by determining the melting point temperatures of the solid residue that remained in the amber glass bottles after the solubility measurements were complete. While there is no evidence for either phenomenon in the published literature for the organic solutes considered in the current study, we wanted to confirm that the solid phase remained the same during the initial equilibration period and during the additional equilibration time before the replicate follow-up set of solubility measurements. The attainment of equilibrium was verified by performing a second set of solubility measurements two (or three) days after the initial set of measurements. In all cases, the measured point temperature of the recovered solid material was within the experimental error of the melting point temperature of the purchased commercial sample or the recrystallized compound prior to being placed in contact with the isobutyl acetate mono-solvent. The measured melting point temperatures, given in

Table 3. Comparison of the melting point temperatures of the crystalline solutes prior to contact with isobutyl acetate, T_mp,initial ^a, and of the recovered crystalline solutes in equilibrium with the saturated solution, T_{mp,equilibrated} ^a at 101 kPa ^a.

Chemical Solute	Tmp,initial/K	Tmp,equilibrated/K	Tmp,literatuare/K
o-Acetoacetanisidide	359.7 ± 0.5	359.4 ± 0.5	359.2 b 355.2–357.2 [33]
Anthracene	490.7 ± 0.5	491.1 ± 0.4	488.9–491.3 [34]
Benzoin	408.6 ± 0.4	408.3 ± 0.5	408.2 [34]
Diphenyl sulfone	398.2 ± 0.4	398.0 ± 0.5	398.2 [34]
2-Ethylanthraquinone	383.8 ± 0.5	383.5 ± 0.5	382.9 [35] 384.2 [36]
Salicylamide	414.1 ± 0.5	413.9 ± 0.4	411.9–414.9 [37]
Thioxanthen-9-one	488.2 ± 0.5	488.0 ± 0.5	486.6–487.9 [34]
Xanthene	374.4 ± 0.5	374.1 ± 0.5	373.3–374.6 [34]
4-tert-Butylbenzoic acid	439.3 ± 0.4	439.1 ± 0.5	440 [34]
3-Chlorobenzoic acid	429.6 ± 0.5	429.2 ± 0.5	427.4–429.9 [37]
4-Chlorobenzoic acid	512.5 ± 0.3	512.7 ± 0.4	512.3–513.5 [37]
2-Chloro-5-nitrobenzoic acid	440.1 ± 0.5	440.4 ± 0.5	437.2–438.2 [38] 438.2–439.2 [39] 437–441 b
4-Chloro-3-nitrobenzoic acid	456.3 ± 0.5	456.5 ± 0.4	453.2–455.2 [39] 453–456 b
3,4-Dichlorobenzoic acid	480.7 ± 0.5	480.3 ± 0.5	478–481 b
2,3-Dimethoxybenzoic acid	394.9 ± 0.5	395.3 ± 0.5	393.1 [40] 394–397 b
3,4-Dimethoxybenzoic acid	452.9 ± 0.5	452.7 ± 0.5	453.1 [37]
3,5-Dimethoxybenzoic acid	455.9 ± 0.5	455.6 ± 0.5	454–458 b
3,5-Dinitrobenzoic acid	481.2 ± 0.5	481.0 ± 0.5	479.2–481.7 [37]
2-Methoxybenzoic acid	375.1 ± 0.5	374.9 ± 0.4	374.7 [37]
4-Methoxybenzoic acid	456.3 ± 0.5	456.5 ± 0.5	453–455.8 [37]
2-Methylbenzoic acid	377.2 ± 0.5	376.9 ± 0.5	376.5–376.9 [37]
3-Methylbenzoic acid	382.4 ± 0.4	382.8 ± 0.4	381.9 [36]
2-Methyl-3-nitrobenzoic acid	455.9 ± 0.5	455.7 ± 0.5	456.6 [41]
3-Methyl-4-nitrobenzoic acid	489.7 ± 0.5	489.4 ± 0.5	489.1 [41]
4-Methyl-3-nitrobenzoic acid	459.6 ± 0.5	459.2 ± 0.5	459.8 [41]
2-Naphthoxyacetic acid	424.6 ± 0.5	424.1 ± 0.5	424.3 [42]
3-Nitrobenzoic acid	414.7 ± 0.4	414.5 ± 0.4	408.7–414.3 [37]
4-Nitrobenzoic acid	512.2 ± 0.5	511.9 ± 0.5	512.4 [37]
3,4,5-Trimethoxybenzoic acid	443.9 ± 0.5	444.2 ± 0.5	444.5 [43]

^a standard uncertainties, u, u(T_mp) = 0.3 to 0.5 K, as stated, and u(P) = 3 kPa. ^b experimental melting point temperatures available on ChemSpider, Royal Society of Chemistry. database, accessed 2 May 2018.

, show no indication of solid–solvate formation or polymorphism.

3. Results and Discussion

The experimental mole fraction solubilities, X_S,organic, of the 29 different crystalline organic solutes dissolved in isobutyl acetate are tabulated in the second and fourth columns of

Table 4. Mole fraction solubilities, X_S,organic, of select crystalline nonelectrolyte organic compounds dissolved in isobutyl acetate at a temperature of 298.15 K and an ambient atmospheric pressure of 101 kPa ^a.

Chemical Name	XS,organic	Chemical Name	XS,organic
o-Acetoacetanisidide	0.0464	3,4-Dimethoxybenzoic acid	0.00461
Anthracene	0.00506	3,5-Dimethoxybenzoic acid	0.00432
Benzoin	0.00882	3,5-Dinitrobenzoic acid	0.0309
Diphenyl sulfone	0.0302	2-Methoxybenzoic acid	0.0353
2-Ethylanthraquinone	0.0341	4-Methoxybenzoic acid	0.00789
Salicylamide	0.0500	2-Methylbenzoic acid	0.1222
Thioxanthen-9-one	0.00306	3-Methylbenzoic acid	0.1265
Xanthene	0.1057	2-Methyl-3-nitrobenzoic acid	0.0247
4-tert-Butylbenzoic acid	0.0750	3-Methyl-4-nitrobenzoic acid	0.0111
3-Chlorobenzoic acid	0.0541	4-Methyl-3-nitrobenzoic acid	0.0183
4-Chlorobenzoic acid	0.00825	2-Naphthoxyacetic acid	0.0148
2-Chloro-5-nitrobenzoic acid	0.0517	3-Nitrobenzoic acid	0.0967
4-Chloro-3-nitrobenzoic acid	0.0246	4-Nitrobenzoic acid	0.00682
3,4-Dichlorobenzoic acid	0.0133	3,4,5-Trimethoxybenzoic acid	0.00825
2,3-Dimethoxybenzoic acid	0.0206

^a Standard uncertainties and relative uncertainties are: u(T) = 0.05 K; u(p) = 5 kPa; and u_r(x) = 0.025.

. The numerical values represent the average of 6 to 10 independent experimental determinations, including the follow-up measurements that were performed after the initial three-day equilibration time. The follow-up studies confirmed that, in all cases, equilibrium was achieved after three days. The tabulated X_S,organic values were reproducible to within ±2.5% (relative error). We were not able to find in the published chemical and engineering literature solubility data for these organic solutes in isobutyl acetate that we could compare our experimental values against. This was not unexpected, in that it was only until recently that researchers started performing solubility measurements in isobutyl acetate.

The published experimental solubility data that we found were for the following: hydrogen [13], nitrogen [13], carbon dioxide [13], carbon monoxide [13], naphthalene [14], fluorene [15], benzoic acid [16], acetylsalicylic acid [17], isophthalic acid [16], forchlorfenuron [18], metronidiazole benzoate [19], iminostilbene [20], isovanillin [21], lansoprazole [22], 2,2′-bis(2-hydroxyethoxy)-1,1′-binaphthalene [23], lovastatin [24], etodolac [25], simvastatin [26,27], 18β-glycyrrhetinic acid [28], and exo-5,6-dehydronorcantharidin [29] dissolved in isobutyl acetate. Our Abraham model solute descriptor database contains solute descriptors for 13 of the 20 aforementioned solutes. As part of the current study, descriptor values were determined for forchlorfenuron, metronidiazole benzoate, iminostilbene, 2,2′-bis(2-hydroxyethoxy)-1,1′-binaphthalene, etodolac, and 18β-glycyrrhetinic acid using the published solubility data taken from the published chemical literature [18,19,20,23,25,28]. In calculating the solute descriptors of etodolac we eliminated the solubility data reported by Rathi and Deshpande [44] from our computations. The authors reported the solubility of etodolac in 1,4-dioxane and in water in terms of mole fraction and molar solubilities. The reported mole fraction solubilities are not internally consistent with the solubility data expressed in units of molarity [45].

As an informational note, we attempted to calculate the solute descriptors for the remaining two solutes without success. The database for exo-5,6-dehydronorcantharidin contained only a single solvent capable of acting as hydrogen-bond donors (no alcohol solvents), which prevented the calculation of a meaningful set of solute descriptor values. The two lone pairs of electrons on each of the four oxygen atoms on exo-5,6-dehydronorcantharidin can serve as H-bond acceptor sites. In calculating the molecule’s solute descriptors, it is imperative that the database contains solvent molecules capable of acting as H-bond donors. In

Table 5. Solute descriptors of the compounds used in the regression analysis for determining the Abraham model correlations for isobutyl acetate.

Solute	E	S	A	B	L	V
Hydrogen	0.000	0.000	0.000	0.000	−1.200	0.1086
Nitrogen	0.000	0.000	0.000	0.000	−0.978	0.2222
Carbon monoxide	0.000	0.000	0.000	0.040	−0.836	0.2220
Carbon dioxide	0.000	0.280	0.050	0.100	0.058	0.2809
Isobutyl acetate	0.520	0.570	0.000	0.470	3.161	1.0284
Naphthalene	1.340	0.920	0.000	0.200	5.161	1.0854
Anthracene	2.290	1.340	0.000	0.280	7.568	1.4544
Xanthene	1.502	1.070	0.000	0.230	7.153	1.4152
Fluorene	1.588	1.060	0.000	0.250	6.922	1.3565
Benzoic acid	0.730	0.900	0.590	0.400	4.657	0.9317
4-tert-Butylbenzoic acid	0.730	1.111	0.551	0.443	6.547	1.4953
3-Chlorobenzoic acid	0.840	0.950	0.630	0.320	5.197	1.0541
4-Chlorobenzoic acid	0.840	1.020	0.630	0.270	4.947	1.0541
3,4-Dichlorobenzoic acid	0.950	0.920	0.670	0.260	5.623	1.1766
2,3-Dimethoxybenzoic acid	0.890	1.636	0.564	0.703	6.612	1.3309
3,4-Dimethoxybenzoic acid	0.950	1.646	0.570	0.755	6.746	1.3309
3,5-Dimethoxybenzoic acid	0.950	1.531	0.684	0.564	6.699	1.3309
3,4,5-Trimethoxybenzoic acid	1.001	1.760	0.603	0.850	7.711	1.5309
2-Methoxybenzoic acid	0.899	1.410	0.450	0.620	5.636	1.1313
4-Methoxybenzoic acid	0.899	1.250	0.620	0.520	5.741	1.1313
2-Methylbenzoic acid	0.730	0.840	0.420	0.440	4.677	1.0726
3-Methylbenzoic acid	0.730	0.890	0.600	0.400	4.819	1.0726
2-Methyl-3-nitrobenzoic acid	1.040	1.396	0.541	0.532	6.332	1.2468
3-Methyl-4-nitrobenzoic acid	1.040	1.336	0.525	0.500	6.266	1.2468
4-Methyl-3-nitrobenzoic acid	1.040	1.461	0.659	0.521	6.434	1.2468
3-Nitrobenzoic acid	0.990	1.180	0.730	0.520	5.601	1.1059
4-Nitrobenzoic acid	0.990	1.520	0.680	0.400	5.770	1.1059
3,5-Dinitrobenzoic acid	1.250	1.630	0.700	0.590	6.984	1.2801
2-Chloro-5-nitrobenzoic acid	1.250	1.400	0.670	0.460	6.513	1.2283
4-Chloro-3-nitrobenzoic acid	1.250	1.470	0.700	0.440	6.685	1.2283
Isophthalic acid	1.100	1.360	1.055	0.585	6.144	1.1470
2-Naphthoxyacetic acid	1.610	1.940	0.690	0.764	8.553	1.5003
2-Ethylanthraquinone	1.410	1.545	0.000	0.557	8.781	1.8106
Thioxanthen-9-one	1.940	1.441	0.000	0.557	8.436	1.5357
Diphenylsulfone	1.570	2.150	0.000	0.700	8.902	1.6051
Acetylsalicylic acid	0.781	1.690	0.710	0.670	6.279	1.2879
o-Acetoacetanisidide	1.190	2.333	0.264	1.025	8.563	1.6108
Salicylamide	1.160	1.650	0.630	0.480	5.910	1.0315
Benzoin	1.587	2.115	0.196	0.847	9.159	1.6804
Forchlorfenuron	1.870	1.928	1.186	0.702	9.986	1.7617
Metronidazole benzoate	1.430	2.452	0.000	1.077	10.171	1.9563
Iminostilbene	2.000	1.801	0.246	0.401	9.013	1.5542
Isovanillin	1.040	1.477	0.308	0.681	5.868	1.1313
Lansoprazole	2.300	2.652	0.607	1.514	13.187	2.3700
2,2′-bis(2-Hydroxyethoxy)-1,1′-binaphthalene	3.610	3.377	0.491	1.633	17.398	2.8606
Lovastatin	1.230	2.730	0.310	1.760	15.459	3.2853
18β-Glycyrrhetinic acid	1.800	2.809	0.823	2.220	18.246	3.8984
Etodolac	1.610	1.860	0.455	1.170	11.019	2.2390

, we have compiled our newly calculated solute descriptors, as well as the numerical values for all of the solutes that will be considered in the current study. Readers interested in learning about how the Abraham model solute descriptors are calculated from published solubility data can refer to earlier papers [12,46,47] that describe the computational method in detail.

The Abraham model correlations that we have derived thus far for describing the solubilizing properties of organic mono-solvents have used the two molar solubility ratios, log (C_S,organic/C_S,water) and log (C_S,organic/C_S,gas), as the independent solute property that appears on the left-hand side of Equations (1) and (2), respectively. Published solubility data are often reported in the published literature as mole fraction solubilities, and this is how we have elected to report our measured solubility data in Table 3 for the 29 crystalline organic compounds for which solubility measurements were performed. The conversion of mole fraction solubilities to molar solubilities is relatively straightforward and involves dividing X_S,organic by the ideal molar volume of the saturated solution, as follows:

C_S,organic ≈ X_S,organic/[X_S,organic V_Solute + (1 − X_S,organic) V_Solvent]

(3)

A numerical value of V_solvent = 0.1341 liter mol⁻¹ was used for the molar volume of the isobutyl acetate solvent. Mole fraction solubility data taken from the published chemical literature [14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29] were converted into molar solubilities in a similar fashion. The estimated values of V_solute, taken from the Chemspider website [48], were used for the solid organic solutes. In

Table 6. Experimental logarithms of molar solubility ratios, log (C_S,organic/C_S,gas) and log (C_S,organic/C_S,water), for solutes dissolved in isobutyl acetate at 298.15 K, as well as the logarithms of solute’s molar gas phase concentration, log C_S,gas, and the solute’s molar solubility in water, log C_S,water, at 298.15 K.

Solute	log (CS,organic/CS,gas)	log (CS,organic/CS,water)	log CS,gas	log CS,water
Hydrogen	−1.073 a	0.647 b
Nitrogen	−0.761 a	1.039 b
Carbon monoxide	−0.628 a	0.992 b
Carbon dioxide	0.660 a	0.740 b
Isobutyl acetate	3.880 a	2.161 b
Naphthalene	5.709	3.979	−5.35	−3.62
Anthracene	8.036	5.006	−9.46	−6.43
Xanthene	7.601	5.101	−7.71	−5.21
Fluorene	7.280	4.830	−7.45	−5.00
Benzoic acid	6.706	1.566	−6.69	−1.55
4-tert-Butylbenzoic acid	8.862	3.638	−9.123	−3.899
3-Chlorobenzoic acid	7.408	2.258	−7.80	−2.65
4-Chlorobenzoic acid	7.149	2.349	−8.36	−3.56
3,4-Dichlorobenzoic acid	7.715	2.975	−8.72	−3.98
2,3-Dimethoxybenzoic acid	9.432	1.347	−10.245	−2.16
3,4-Dimethoxybenzoic acid	9.478	1.031	−10.942	−2.495
3,5-Dimethoxybenzoic acid	9.678	1.984	−11.170	−3.476
3,4,5-Trimethoxybenzoic acid	10.593	1.338	−11.805	−2.55
2-Methoxybenzoic acid	7.776	0.976	−8.354	−1.554
4-Methoxybenzoic acid	8.270	1.570	−9.50	−2.80
2-Methylbenzoic acid	6.325	2.025	−6.36	−2.06
3-Methylbenzoic acid	7.100	2.120	−7.12	−2.14
2-Methyl-3-nitrobenzoic acid	8.713	1.976	−9.447	−2.71
3-Methyl-4-nitrobenzoic acid	8.510	2.146	−9.594	−3.23
4-Methyl-3-nitrobenzoic acid	9.104	1.819	−9.97	−2.685
3-Nitrobenzoic acid	8.473	1.543	−8.61	−1.68
4-Nitrobenzoic acid	8.587	1.687	−9.88	−2.98
3,5-Dinitrobenzoic acid	10.080	1.780	−10.717	−2.417
2-Chloro-5-nitrobenzoic acid	9.125	2.175	−9.538	−2.588
4-Chloro-3-nitrobenzoic acid	9.474	2.264	−10.21	−3.00
Isophthalic acid	9.457	0.484	−12.083	−3.11
2-Naphthoxyacetic acid	11.584	1.665	−12.543	−2.624
2-Ethylanthraquinone	9.744	4.930	−10.344	−5.530
Thioxanthen-9-one	8.965	3.897	−10.608	−5.54
Diphenyl sulfone	10.380	2.990	−11.03	−3.64
Acetylsalicylic acid	9.411	0.911	−10.18	−1.68
o-Acetoacetanisidide	11.307	1.073	−11.775	−1.541
Salicylamide	9.011	1.326	−9.439	−1.754
Benzoin	11.218	2.487	−12.401	−3.67
Forchlorfenuron	14.174	2.755	−15.369	−3.95
Metronidazole benzoate	12.143	2.521	−12.697	−3.075
Iminostilbene	10.670	4.389	−11.592	−5.311
Isovanillin	7.661	0.823	−8.390	−1.552
Lansoprazole	16.370	1.677	−18.364	−3.671
2,2′-bis(2-Hydroxyethoxy)-2,2′-binaphthalene	20.307	3.298	−21.965	−4.956
Lovastatin	18.159	4.177	−19.597	−5.585
Simvastatin	17.932	4.282	−18.68	−5.03
18β-Glycyrrhetinic acid	22.179	4.349	−23.917	−6.087
Etodolac	13.451	3.267	−13.790	−3.606

^a Tabulated value pertains to the logarithm of the solute’s gas-to-isobutyl acetate partition coefficient. ^b Tabulated value pertains to the logarithm of the solute’s water-to-isobutyl acetate transfer coefficient.

, we have assembled the calculated molar solubility ratios for the 44 solid organic compounds that will be used in the regression analyses for obtaining Abraham model correlations for isobutyl acetate. Also included in Table 6 are the logarithms of the gas-to-isobutyl acetate partition coefficients, log K, and logarithms of the water-to-isobutyl acetate transfer coefficients, log P, for the four inorganic gases (hydrogen, nitrogen, carbon monoxide, and carbon dioxide) and for isobutyl acetate, as well as the log C_S,gas and log C_S,water values used in calculating the individual molar solubility ratios.

While most of the experimental data points compiled in Table 6 pertain to solid organic compounds, the range of values spanned by the individual solute descriptors are as follows: from E = 0.000 to E = 3.610; from S = 0.000 to S = 3.377; from A = 0.000 to A = 1.186; from B = 0.000 to B = 1.860; from V = 0.1086 to V = 3.4628; and L= −1.200 to L = 17.398, which is sufficiently large enough to allow for the development of meaningful Abraham model correlations for predicting the molar solubilities of many organic compounds commonly encountered in industrial manufacturing processes. The range of solute descriptors covered determines the area of predictive chemical space over which the correlation can be used. An analysis of the experimental data points in Table 6 yielded the following two Abraham model expressions:

log P or log (C_S,organic/C_S,water) = 0.234(0.055) + 0.351(0.053) E − 0.471(0.080) S − 1.050(0.060) A − 4.982(0.142) B + 4.212(0.081) V
(with N = 49, SD = 0.112, SEE = 0.119; R² = 0.992, F = 1099)

(4)

log K or log (C_S,organic/C_S,gas) = 0.173(0.044) − 0.353(0.047) E + 1.183(0.073) S + 2.463(0.058) A
+ 0.936(0.015) L
(with N = 49, SD = 0.112, SEE = 0.117, R² = 0.999, F = 15753)

(5)

where the numerical value enclosed within the parentheses following each coefficient represents the standard error in the respective coefficient. The statistical information associated with correlation includes the following: the number of experimental data points used in determining the equation coefficients, N; the standard deviation, SD; the squared correlation coefficient, R²; the standard error of the estimate, SEE; and the Fisher F-statistic, F. As an informational note, the b × B term was not included in the Equation (5) regression analysis because isobutyl acetate lacks acidic hydrogen, and thus cannot act as an H-bond donor. Both correlations were obtained using the IBM SPSS Statistical 22 commercial software.

Careful examination of the statistical information reveals that both mathematical expressions provide a reasonably accurate description of the observed log (C_S,organic/C_S,water) and log (C_S,organic/C_S,gas) values, as documented by the small standard deviations (SD = 0.112 log units for both equations) and small standard errors of the estimate (SEE = 0.117 and SEE = 0.119 log units for Equations (4) and (5), respectively). The descriptive ability of both equations is depicted graphically in Figure 1 and Figure 2, which compare the logarithms of the observed molar solubility ratios to the back-calculated values based on our derived Abraham model correlations. As expected from the near-unity squared correlation coefficients, the back-calculated and observed values are in very good agreement.

Abraham model correlations have now been determined for eleven alkyl alkanoate mono-solvents. In

Table 7. Abraham model correlations for predicting log (C_S,organic/C_S,water) and log (C_S,organic/C_S,gas) molar solubility ratios into select alkyl alkanoate mono-solvents.

Log (P or CS,org/CS,water)	cp	ep	sp	ap	bp	vp
Methyl acetate	0.351	0.223	−0.150	−1.035	−4.527	3.972
Ethyl acetate	0.328	0.314	−0.348	−0.847	−4.899	4.142
Propyl acetate	0.362	0.280	−0.390	−0.975	−4.928	4.183
Isopropyl acetate	0.307	0.314	−0.481	−0.952	−4.779	4.159
Butyl acetate	0.289	0.336	−0.501	−0.913	−4.964	4.262
Isobutyl acetate	0.234	0.351	−0.471	−1.050	−4.982	4.212
tert-Butyl acetate	0.456	0.324	−0.661	−1.068	−4.680	4.101
Pentyl acetate	0.182	0.261	−0.474	−1.017	−4.952	4.388
Methyl butyrate	0.238	0.368	−0.538	−1.031	−4.623	4.253
Isopropyl myristate	−0.605	0.930	−1.153	−1.682	−4.093	4.249
Dimethyl adipate	0.128	0.546	−0.404	−1.001	−4.481	3.987
Log (K or CS,org/CS,gas)	ck	ek	sk	ak	bk	lk
Methyl acetate	0.134	−0.477	1.749	2.678	0.000	0.876
Ethyl acetate	0.171	−0.403	1.428	2.726	0.000	0.914
Propyl acetate	0.246	−0.346	1.318	2.537	0.000	0.916
Isopropyl acetate	0.233	−0.495	1.324	2.550	0.000	0.928
Butyl acetate	0.154	−0.439	1.223	2.586	0.000	0.953
Isobutyl acetate	0.173	−0.353	1.183	2.463	0.000	0.936
tert-Butyl acetate	0.178	−0.444	1.045	2.522	0.000	0.964
Pentyl acetate	0.154	−0.424	1.172	2.506	0.000	0.962
Methyl butyrate	0.201	−0.502	1.290	2.469	0.000	0.958
Dimethyl adipate	0.051	−0.248	1.579	2.513	0.000	0.877

, we have summarized the equation coefficients for the following: methyl acetate, ethyl acetate, propyl acetate, isopropyl acetate, butyl acetate, isobutyl acetate, tert-butyl acetate, pentyl acetate, methyl butanoate, isopropyl myristate, and dimethyl adipate [49,50,51,52]. The tabulated equation coefficients pertain to the ‘dry, anhydrous’ organic solvents. The words ‘dry, anhydrous’ indicate that the organic solvent was not in direct contact with water, as would be the case for practical partitioning processes involving the removal of the solute from water with, for example, either ethyl acetate or butyl acetate as the extracting organic solvent. Abraham model correlations have been published for ‘wet’ ethyl acetate and ‘wet’ butyl acetate in an earlier paper [53]; however, there has not been sufficient practical partition coefficient data for the other biphasic aqueous-alkyl alkanoate extraction systems to develop meaningful Abraham model correlations.

An examination of the numerical entries in Table 7 reveals that the equation coefficients for isobutyl acetate are very similar to those of butyl acetate. There should be very little difference in the solubilizing characteristics of these two alkyl acetate solvents. The sign and the magnitude of the c_p, e_p, s_p, a_p, b_p, and v_p coefficients determine whether or not a given solute–solvent interaction increases or decreases the solute’s solubility in the organic solvent relative to the solute’s solubility in water. For example, the negative a_p and b_p equation coefficients for isobutyl acetate, when substituted into Equation (1), would result in negative a_p × A and b_p × B terms, and thus decrease the calculated log (C_S,organic/C_S,water) value. In other words, a solute capable of hydrogen-bond formation is expected to be more soluble in water than in isobutyl acetate when all other solute–solvent interactions are ignored. Large solute molecules, on the other hand, would have a positive v_p × V term, which would increase the calculated log (C_S,organic/C_S,water) value. Large solute molecules would tend to be more soluble in isobutyl acetate when all other solute–solvent interactions are ignored. It is the sum of the five interaction terms, however, that determines the molar solubility ratio.

4. Summary

Mathematical equations based on the Abraham solvation parameter model have been determined by performing multi-linear regression analyses on a chemically diverse set containing 49 organic solutes dissolved in isobutyl acetate. The derived Abraham model expressions were found to accurately predict the observed solubility data to within an overall standard deviation of 0.12 log units or less. Based on prior experience using the Abraham model, we expect that the derived correlations reported in the current study will provide accurate solubility predictions for additional organic compounds dissolved in isobutyl acetate, provided that one does not venture outside of the range of the predictive area of chemical space defined by the 49 solute data sets used in deriving Equations (4) and (5). Moreover, the derived Abraham model correlations will allow us to use experimental solubility data determined in isobutyl acetate in our future solute descriptor calculations. As noted previously in the manuscript, several research groups have started measuring the solubility of drug molecules dissolved in isobutyl acetate.