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

: 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.


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 hydrogenbonding 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 Liquids 2024, 4 471 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 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].
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.

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, along with the final purities, as determined by either gas-liquid chromatographic analysis (noncarboxylic acid solutes and flame ionization detector) or non-aqueous acidbase 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.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, show no indication of solid-solvate formation or polymorphism.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.
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-5,6dehydronorcantharidin 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, 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: 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, 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.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.
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  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, R 2 = 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, R 2 ; 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 Figures 1 and 2 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, R 2 ; 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 (CS,organic/CS,water) and log (CS,organic/CS,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 Figures 1 and 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, 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.Abraham model correlations have now been determined for eleven alkyl alkanoate mono-solvents.In Table 7, 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 aqueousalkyl 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.

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.

Figure 1 .
Figure 1.Comparison of experimental log (CS,organic/CS,water) data versus back-calculated values based on Equation (4) for organic compounds and inorganic gases dissolved in isobutyl acetate.

Figure 1 .
Figure 1.Comparison of experimental log (C S,organic /C S,water ) data versus back-calculated values based on Equation (4) for organic compounds and inorganic gases dissolved in isobutyl acetate.

Figure 2 .
Figure 2. Comparison of experimental log (CS,organic/CS,gas) data versus back-calculated values based on Equation (5) for organic compounds and inorganic gases dissolved in isobutyl acetate.

Figure 2 .
Figure 2. Comparison of experimental log (C S,organic /C S,gas ) data versus back-calculated values based on Equation (5) for organic compounds and inorganic gases dissolved in isobutyl acetate.

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

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

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 .

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

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

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.

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 C S,org /C S,water )