Comment on Measurement and correlation of the solubility of p-coumaric acid in nine pure and

Comment on Measurement and correlation of the solubility of p-coumaric acid in nine pure and water + ethanol mixed solvents at temperatures from 293.15 to 333.15 K William E. Acree, Jr. a*, Maribel Barrera a and Michael H. Abraham b a Department of Chemistry, University of North Texas, 1155 Union Circle Drive #305070, Denton, TX 76203 (USA) b Department of Chemistry, University College London, 20 Gordon Street, London WC1H OAJ (UK) Abstract Experimental solubility measurements for p-coumaric acid dissolved in nine neat organic solvents and in binary aqueous-ethanol solvent mixtures are used to calculate solute descriptors for the monomeric form of the carboxylic acid based on the Abraham solvation parameter model. The solute descriptors once calculated are used to predict the solubility of p-coumaric acid in additional organic solvents in which the carboxylic acid is expected to exist predominantly in monomeric form. Key Words and Phrases: p-coumaric acid; Organic solvents; Binary aqueous-ethanol solvent mixtures; Solubility predictions *To whom correspondence should be addressed. (E-mail: acree@unt.edu); fax: 940-565-4318. 1

In a recent article published in This Journal Ji and coworkers 1 measured the solubility of p-coumaric acid in nine neat organic solvents (methanol, ethanol, 1-propanol, 2-propanol, 1- butanol, 2-methyl-1-propanol, acetone, methyl acetate and ethyl acetate) and in binary aqueousethanol solvent mixtures from 293.15 K to 333.15 K. Solubilities were determined by a gravimetric method of analysis that involved transferring weighed aliquots of the saturated solutions into pre-weighed evaporating dishes. The solvents were then removed in a vacuum drying oven. The concentrations of dissolved p-coumaric acid were calculated from the masses of the samples taken for analysis and the masses of the solid residues that remained after solvent evaporation. The authors analyzed their experimental mole fraction solubilities, x1, using several different solution models. The models selected described how the solubility varied with temperature (e.g., Apelblat equation, van t Hoff equation, Buchowski-Ksiazczak λh equation, nonrandom two-liquid (NRTL) equation, universal quasichemical (UNIQUAC) equation, and Wilson equation), or in the case of binary aqueous-ethanol mixtures how the solubility varied with both temperature and solvent composition (Jouyban-Acree model). Such models enable researchers to estimate the solubility of p-coumaric acid at other temperatures in the solvents studied, or in the case of the aqueous-ethanol system allow researchers to estimate the solubility of p-coumaric acid at other ethanol solvent compositions. The models do not allow one, however, to estimate solubilities in additional organic solvents which is often needed in the solvent selection. One of primary justifications given by researchers for conducting solubility studies is to select solvents for obtaining high-purity materials through recrystallization. 2

In this brief commentary we want to illustrate one additional method for analyzing experimental solubility data that does provide a convenient means to estimate solubilities in additional organic solvents. The method is based on the Abraham solvation parameter model 2-4 : log (P or CS,organic/CS,water) = cp + ep E + sp S + ap A + bp B + vp V (1) log (K or CS,organic/CS,gas) = ck + ek E + sk S + ak A + bk B + lk L (2) that describes solute transfer between two phases in terms of logarithms of molar solubility ratios, log (CS,organic/CS,water) and log (CS,organic/CS,gas), logarithms of water-to-organic solvent partition coefficients, log P, or logarithms of gas-to-organic solvent partition coefficients, log K. The molar solubility ratios are defined as the molar solubility of the solute in the organic solvent, CS,organic, divided by either the solute s molar solubility in water, CS,water, or molar concentration in the gas phase, CS,gas. The molar concentration of the solute in the gas phase is calculable from experimental vapor pressure data or can be treated as an adjustable parameter that is determined as part of the curve-fitting procedure used in computing the solute descriptors. The solution models used by Ji and coworkers 1 contained adjustable parameters that were determined by curve-fitting the measured solubility data in accordance with the respective model. The Abraham model 2-4 has similar parameters, called solute descriptors, which must be calculated using the experimental solubility data. Solute descriptors are denoted by the uppercase alphabetical characters are the right-hand side of eqs. 1 and 2, and are defined as follows: E corresponds to the solute excess molar refractivity in units of (cm 3 mol -1 )/10, S quantifies the dipolarity/polarizability of the solute, A and B measure the overall or total hydrogen-bond acidity and basicity, V refers to the McGowan volume in units of (cm 3 mol -1 )/100, and L is defined as the logarithm of the gas-to-hexadecane partition coefficient at 298 K. Solute descriptors encode valuable chemical information regarding the solute s ability to interact with surrounding solvent 3

molecules. The complimentary solvent properties are denoted by the lowercase alphabetical characters (cp, ep, sp, ap, bp, vp, ck, ek, sk, ak, bk, and lk) on the right-hand side of eqs 1 and 2, which when multiplied by a solute descriptor describes a particular type of solute-solvent interaction. Unlike the solution models used by Ji and coworkers 1, the Abraham model does enable one to estimate the solubility of the solute in additional organic solvents once the solute descriptors have been obtained. To date we have published equation coefficients for predicting molar solubilities in more than 80 different organic solvents 2,5-7, and in binary aqueous-ethanol 8,9 and aqueousmethanol 10 solvent mixtures. We have listed in Table 1 the equation coefficients for the solvents that will be used in the present study. Much larger listings of equation coefficients for organic solvents 2,5-7 and for ionic liquid solvents 11 can be found elsewhere. Calculation of the solute descriptors is the key to making solubility predictions in additional organic solvents. The solute descriptors are calculated by setting up a series of equations having the mathematical form of eqs 1 and 2 with the equation coefficients and molar solubilities inserted into the equations. The experimental solubility data in the paper by Ji and coworkers for p- coumaric acid dissolved in the nine neat organic solvents will provide us with a total of 18 mathematical expressions, nine log (CS,organic/CS,water) equations and nine log (CS,organic/CS,gas) equations. An additional ten log (CS,organic/CS,water) equations are available for the measured p- coumaric solubility data in binary aqueous-ethanol solvent mixtures. Two practical water-tooctanol partition coefficient equations: log P(wet octanol) = 0.088 + 0.562 E -1.054 S + 0.034 A - 3.460 B + 3.814 V (3) log K(wet octanol) = -0.198 + 0.002 E + 0.709 S + 3.519 A + 1.429 B + 0.858 L (4) where log K(wet octanol) = log P(wet octanol) + log CS,water - log CS,gas, and two more equations describing the logarithm of the gas-to-water partition coefficient (log Kw): 4

log Kw = -0.994 + 0.577 E + 2.549 S + 3.813 A + 4.841 B - 0.869 V (5) log Kw = -1.271 + 0.822 E + 2.743 S + 3.904 A + 4.814 B - 0.213 L (6) are also available for use in the solute descriptor calculations. In total we have been able to assemble 32 mathematical expressions from the solubility data determined by Ji and coworkers 1, and from the experimental water-to-1-octanol partition coefficients taken from BioLoom 14 The number of mathematical expressions, and the chemical diversity of the solvents studied, is more than sufficient for calculating the solute descriptors of p-coumaric acid. The mole fraction solubility data for p-coumaric acid dissolved in methanol, ethanol, 1- propanol, 2-propanol, 1-butanol, 2-methyl-1-propanol, acetone, methyl acetate and ethyl acetate are converted to molar solubilities by: CS exp XS exp /[XS exp VSolute + (1 XS exp ) VSolvent]) (7) dividing the measured mole fraction solubility be the ideal molar volume of the saturated solution. A numerical value of Vsolute = 127.9 cm 3 mol -1 was used for the molar volume of p-coumaric acid. The molar volume was estimated from fragment group values. Any errors resulting from our estimation of the p-coumaric acid s hypothetical subcooled liquid molar volume, VSolute, or the ideal molar volume approximation should have negligible effect of the calculated CS exp values as the measured mole fraction solubility is not very large. Calculation of molar solubilities in the binary aqueous-ethanol solvent mixtures is more involved as we have equation coefficients for specific compositions. Li et al. did describe the solubility behavior of p-coumaric acid in binary aqueous-ethanol mixtures with the following mathematical expression: ln 2 3 4 x1, T c3 w2 w w w3 c c w c c 2 c 2 1 2 2 4 5 6 c7 (8) T T T T T 5

which was presumably obtained from the Jouyban-Acree model: n i J i ( w2 w3 ) ln x1, T w2 ln ( x1 ) 2, T w3 ln ( x1 ) 3, T w2w (9) T 3 i 0 in which x 1, T is the mole fraction solubility of p-coumaric acid in the mixed solvent at the temperature of interest, w2 and w3 are the mass fractions of ethanol and water in the initial binary solvent mixture calculated as if the solute were not present, ( x 1 ) 2, T and x 1 ) 3, T ( are the mole fraction solubility of p-coumaric acid in neat ethanol and water at T, and ci and Ji represent the calculated curve-fit parameters. The only way to obtain eq 8 from eq. 10 is to treat the mole fraction solubilities of p-coumaric acid in both ethanol and water as numerical constants whose values are independent of temperature. In other words, one has to assume that the solubility of p- coumaric acid in both co-solvents is independent of temperature, which is not in accord with the measured experimental data. While Li et al. 1 did tabulate curve-fit parameters (ci) for eq 8, we have elected to derive our mathematical representation based on the mass fraction version of the Combined Nearly Ideal Binary (NIBS)/Redlich-Kister model 12,13 : n i 1, t w2 ln ( x1) 2, T w3 ln ( x1) 2, T w2w3 J i ( w2 w3 ) i 0 ln x (10) as we need only to describe the experimental solubility data at 298.15 K. The authors did not measure the solubility of p-coumaric acid in water, so we have expanded eq. 10 into a polynomial expression in w2: ln x 1 0 1 2 2 2 2 3 3 2 4 4 2 c c w c w c w c w (11) 6

by assuming the summation extended to n=2 and by substituting w3 = 1 - w2. Our analysis of the x1 data at 298.15 in accordance with eq 11 gave: ln x 2 3 1 8.4878 9.2921w2 3.3408w2 1.4877 w2 2. 0149 w (12) (Average Absolute Relative Deviation = 0.0173) 4 2 which provides a very good mathematical description of the observed ln x1 data as shown in Table 2. The derived mathematical representation was then used to calculate the mole fraction solubility of p-coumaric acid at the needed volume fraction concentrations of ethanol. The calculated mole fraction solubilities were then converted to molar solubilities using the ideal molar volume approximation as discussed above. We have compiled in Table 3 our calculated molar solubilities of p-coumaric in the nine neat organic solvents and in the 10 binary aqueous-ethanol solvent mixtures for which we have Abraham model solvent equation coefficients. Also, included in Table 2 is the numerical value of the logarithm of the water-to-octanol, which represents the average of three experimental log P values in Bioloom (log P = 1.47, log P = 1.79, and log P = 2.20) 14. There are six solute descriptors, a log CS,water and a log CS,gas to be calculated from the experimental log CS,organic and log P values tabulated in Table 3. Two of the six solute descriptors can be calculated from molecular structure considerations. The McGowan characteristic volume, V, can be computed from the molecular structure, atomic sizes and number of bonds as described elsewhere 15. The E solute descriptor can be obtained using the PharmaAlgorithm software 16, which is based on molecular structure considerations using fragment group values 17,18, or estimated using a measured value (liquid solute) or an estimated value (solid solute) for the solute s refractive index. The refractive index of solid solutes can be estimated using the (free) ACD software 19. The values of V and E that we calculate are V = 1.2292 and E = 1.330. The 32 equations were solved simultaneously using Microsoft Solver software to yield numerical values of: E = 1.330; S = 1.453; 7

A = 0.841; B = 0.674; V = 1.2392; L = 6.795; log CS,water = -2.075; and log CS,gas = -10.949 with the overall standard error being SE = 0.094 log units. Individual standard errors are SE = 0.094 and SE = 0.097 for the 16 calculated and observed log (P or CS,organic/CS,water) values and the 26 calculated and observed log (K or CS,organic/CS,gas) values, respectively. Statistically there is no difference between the set of 16 log (P or CS,organic/CS,water) values and the total set of 32 log (P or CS,organic/CS,water) and log (K or CS,organic/CS,gas) values, thus suggesting that log CS,gas = -10.949 is a feasible value for p-coumaric acid. One of the major advantages in describing solubility data with the Abraham model is that once the solute descriptors have been calculated the numerical values can be used to predict the solubility of the solute in additional organic solvents. In the case of p-coumaric acid we can make solubility predictions in those organic solvents in which p-coumaric acid is expected to exist predominantly in monomeric form. The solute descriptors that we have calculated were based on solubility data in alcohol solvents, alkyl acetates, acetone, and binary aqueous-ethanol solvent mixtures. The fore-mentioned solvents are polar and capable of forming hydrogen bonds. p- Coumaric acid should exist predominantly in the monomeric form in these solvents. Solubility predictions cannot be made for p-coumaric acid dissolved in nonpolar hydrocarbon, alkylbenzene and chloroalkane solvents as dimerization is a major concern. In nonpolar solvents the measured solubility will include the solubility of both the monomeric and dimeric forms of the carboxylic acid. This is discussed in greater detail in an earlier publication where we illustrated the calculation of solute descriptors for the cinnamic acid dimer 20. In Table 4 we have tabulated the predicted log CS,organic values for p-coumaric acid in 30 different neat organic solvents and in several binary aqueous-ethanol solvent mixtures. Included in the tabulations are the predicted log CS,organic values for the nine neat organic solvents and binary 8

aqueous-ethanol solvent mixtures used in the solute descriptor computations. The predictions were achieved by simply substituting the equation coefficients from Table 1 and the calculated solute descriptors into Eqns. 1 and 2. The calculated logarithms of the molar solubility ratios, log (CS,organic/CS,water) and log (CS,organic/CS,gas), are converted to log CS,organic values using the numerical values of log CS,water and log CS,gas from the respective solute descriptor computations. Comparison of the numerical entries in the second, fourth and sixth columns of Table 4 shows that the calculated solute descriptors do accurately predict the observed solubility data. For example, in the case of p-coumaric acid dissolved in methanol, the experimental value of log C = -0.049 exp S, organic in the second column of Table 4 compares very favorably the back-calculated values of log C eq 1 S, organic = -0.064 and log C eq 2 S, organic = -0.114 given in fourth and sixth columns of Table 3 for Eqns. 1 and 2, respectively. The predicted values pertain to 298.15 K. The calculated solute descriptors are independent of temperature; however, the equation coefficients that we have for the organic solvents and for the binary aqueous-ethanol solvent mixtures pertain only to 298.15 K. For some of the solvents one can extend the log (P or CS,organic/CS,water) and log (K or CS,organic/CS,gas) predictions to slightly lower or slightly higher temperatures using the predicted enthalpies of solvation for p-coumaric acid dissolved in the respective solvent. We have developed enthalpy of solvation equations 21,22 for several of the organic solvents listed in Table 1. Solubility predictions at other temperatures would require knowledge of log CS,water and log CS,gas at the new temperature. Log (P or CS,organic/CS,water) and log (K or CS,organic/CS,gas) at other temperatures are described in greater detail elsewhere. 21 As noted above many of the other solution models currently being used to mathematically describe experimental solubility are very good at predicting how the solubility in a given solvent varies with temperature. The models do not enable one, however, to predict 9

solubilities in additional organic solvents. We hope that our simple illustration will encourage other researchers to consider using the Abraham model when reporting the experimental results of their solubility studies. Acknowledgement Maribel Barrera thanks the University of North Texas and the U.S. Department of Education for support provided under the Ronald E. McNair Postbaccalaureate Achievement Program. 10

References (1) Ji, W.; Meng, Q.; Li, P.; Yang, B.; Wang, F.; Ding, L.; Wang, B. Measurement and correlation of the solubility of p-coumaric acid in nine pure and water + ethanol mixed solvents at temperatures from 293.15 to 333.15 K. J. Chem. Eng. Data 2016, 61, 3457-3465. (2) Abraham, M. H., Scales of solute hydrogen-bonding: their construction and application to physicochemical and biochemical processes. Chem. Soc. Reviews 1993, 22, 73-83. (3) Abraham, M. H.; Smith, R. E.; Luchtefeld, R.; Boorem, A. J.; Luo, R.; Acree, W. E. Jr. Prediction of solubility of drugs and other compounds in organic solvents. J. Pharm. Sci. 2010, 99, 1500-1515. (4) Abraham, M. H.; Acree, W. E. Analysis of the solubility of betaine: calculation of descriptors and physicochemical properties. Fluid Phase Equilib. 2015, 387, 1-4. (5) Abraham, M. H.; Acree, W. E., Jr.; Brumfield, M.; Hart, E.; Pipersburgh, L.; Mateja, K.; Dai, C.; Grover, D.; Zhang, S. Deduction of physicochemical properties from solubilities: 2,4-dihydroxybenzophenone, biotin, and caprolactam as examples. J. Chem. Eng. Data 2015, 60, 1440-1446. (6) Abraham, M. H.; Acree, W. E. Jr. Descriptors for the prediction of partition coefficients of 8-hydroxyquinoline and its derivatives. Sep. Sci. Technol. 2014, 49, 2135-2141. (7) Abraham, M. H.; Acree, W. E., Descriptors for the prediction of partition coefficients and solubilities of organophosphorus compounds. Sep. Sci. Technol. 2013, 48, 884-897. (8) Abraham, M. H.; Acree, W. E. Jr. Partition coefficients and solubilities of compounds in the water-ethanol solvent system. J. Solution Chem. 2011, 40, 1279-1290. 11

(9) Abraham, M. H.; Acree, W. E. Jr. Equations for the partition of neutral molecules, ions and ionic species from water to water-ethanol mixtures. J. Solution Chem. 2012, 41, 730-740. (10) Abraham, M. H.; Acree, W. E. Jr. Equations for the partition of neutral molecules, ions and ionic species from water to water-methanol mixtures. J. Solution Chem. 2016, 45, 861-874. (11) Jiang, B.; Horton, M. Y.; Acree, W. E. Jr.; Abraham, M. H. Ion-specific equation coefficient version of the Abraham model for ionic liquid solvents: determination of coefficients for tributylethylphosphonium, 1-butyl-1-methylmorpholinium, 1-allyl-3- methylimidazolium and octyltriethylammonium cations. Phys. Chem. Liq. 2016, Ahead of Print, DOI: 10.1080/00319104.2016.1218009. (12) Acree, W. E. Jr.; McCargar, J. W.; Zvaigzne, A. I.; Teng, I. L. Mathematical representation of thermodynamic properties. Carbazole solubilities in binary alkane + dibutyl ether and alkane + tetrahydropyran solvent mixtures. Phys. Chem. Liq. 1991, 23, 27-35. (13) Acree, W. E. Jr. Mathematical representation of thermodynamic properties. Part 2. Derivation of the combined nearly ideal binary solvent (NIBS)/Redlich-Kister mathematical representation from a two-body and three-body interactional mixing model. Thermochim. Acta 1992, 198, 71-79. (14) BioLoom, BioByte Corp, 201W. 4th Street, #204 Claremont, CA 91711 4707, USA. (15) Abraham, M. H.; McGowan, J. C. The use of characteristic volumes to measure cavity terms in reversed phase liquid chromatography. Chromatographia 1987, 23, 243-246. (16) PharmaAlgorithms, ADME Boxes, Version 3.0, PharmaAlgorithms Inc., 591 Indian Road, Toronto, Ontario M6P 2C4, Canada. 12

(17) Platts, J. A.; Butina, D.; Abraham, M. H.; Hersey, A. Estimation of molecular linear free energy relation descriptors using a group contribution approach. J. Chem. Inf. Comp. Sci. 1999, 39, 835-845. (18) Platts, J. A.; Abraham, M.H.; Butina, D.; Hersey, A. Estimation of molecular linear free energy relationship descriptors by a group contribution approach. 2. Prediction of partition coefficients. J. Chem. Inf. Comp. Sci. 2000, 40, 71-80. (19) Advanced Chemistry Development, 110 Yonge St., 14 th Floor, Toronto, Ontario M5C 1T4, Canada. The ACD Freeware can be accessed at http://www.acdlabs.com/. (Accessed on August 11, 2016). (20) Bradley, J.-C.; Abraham, M. H.; Acree, W. E. Jr.; Lang, A. S.; Beck, S. N.; Bulger, D. A.; Clark, E. A.; Condron, L. N.; Costa, S. T.; Curtin, E. M.; Kurtu, S. B.; Mangir, M. I.; McBride, M. J. Determination of Abraham model solute descriptors for the monomeric and dimeric forms of trans-cinnamic acid using measured solubilities from the Open Notebook Science Challenge. Chem. Central J. 2015, 9, 11/1. (21) Mintz, C.; Clark, M.; Acree, W. E., Jr.; Abraham, M. H. Enthalpy of solvation correlations for gaseous solutes dissolved in water and in 1-octanol based on the Abraham model. J. Chem. Inf. Model. 2007, 47, 115-121. (22) Schmidt, A.; Zad, M.; Acree, W. E., Jr.; Abraham, M. H. Development of Abraham model correlations for predicting enthalpies of solvation of nonionic solutes dissolved in formamide. Phys. Chem. Liq. 2016, 54, 313-324. 13

TABLE 1. Coefficients in Eqn. (1) and Eqn. (2) for Various Processes at 298.15 K Process/solvent c e s a b v/l A. Water to solvent: Eqn. (1) a 1-Octanol (wet) 0.088 0.562-1.054 0.034-3.460 3.814 Methanol (dry) 0.276 0.334-0.714 0.243-3.320 3.549 Ethanol (dry) 0.222 0.471-1.035 0.326-3.596 3.857 1-Propanol (dry) 0.139 0.405-1.029 0.247-3.767 3.986 2-Propanol (dry) 0.099 0.344-1.049 0.406-3.827 4.033 1-Butanol (dry) 0.165 0.401-1.011 0.056-3.958 4.044 1-Pentanol (dry) 0.150 0.536-1.229 0.141-3.864 4.077 1-Hexanol (dry) 0.115 0.492-1.164 0.054-3.978 4.131 1-Heptanol (dry) 0.035 0.398-1.063 0.002-4.342 4.317 1-Octanol (dry) -0.034 0.489-1.044-0.024-4.235 4.218 1-Decanol (dry) -0.058 0.616-1.319 0.026-4.153 4.279 2-Butanol (dry) 0.127 0.253-0.976 0.158-3.882 4.114 14

TABLE 1. (Continued) Process/solvent c e s a b v/l 2-Methyl-1-propanol (dry) 0.188 0.354-1.127 0.016-3.568 3.986 2-Methyl-2-propanol (dry) 0.211 0.171-0.947 0.331-4.085 4.109 2-Pentanol (dry) 0.115 0.455-1.331 0.206-3.745 4.201 3-Methyl-1-butanol (dry) 0.073 0.360-1.273 0.090-3.770 4.273 Diisopropyl ether (dry) 0.181 0.285-0.954-0.956-5.077 4.542 Tetrahydrofuran (dry) 0.223 0.363-0.384-0.238-4.932 4.450 1,4-Dioxane (dry) 0.123 0.347-0.033-0.582-4.810 4.110 Acetone (dry) 0.313 0.312-0.121-0.608-4.753 3.942 Methyl acetate (dry) 0.351 0.223-0.150-1.035-4.527 3.972 Ethyl acetate (dry) 0.328 0.369-0.446-0.700-4.904 4.150 Butyl acetate (dry) 0.248 0.356-0.501-0.867-4.973 4.281 Acetonitrile (dry) 0.413 0.077 0.326-1.566-4.391 3.364 Propylene carbonate (dry) 0.004 0.168 0.504-1.283-4.407 3.421 2-Methoxyethanol (dry) 0.175 0.326-0.140 0.000-4.086 3.630 2-Ethoxyethanol (dry) 0.133 0.392-0.419 0.125-4.200 3.888 2-Propoxyethanol (dry) 0.053 0.419-0.569 0.000-4.327 4.095 15

TABLE 1. (Continued) Process/solvent c e s a b v/l 2-Isopropoxyethanol (dry) 0.107 0.391-0.525 0.071-4.439 4.051 2-Butoxyethanol (dry) -0.055 0.377-0.607-0.080-4.371 4.234 10 % Ethanol + 90 % Water b -0.173-0.023-0.001 0.065-0.372 0.454 20 % Ethanol + 80 % Water -0.252 0.043-0.040 0.096-0.823 0.916 30 % Ethanol + 70 % Water -0.269 0.107-0.098 0.133-1.316 1.414 40 % Ethanol + 60 % Water -0.221 0.131-0.159 0.171-1.809 1.918 50 % Ethanol + 50 % Water -0.142 0.124-0.252 0.251-2.275 2.415 60 % Ethanol + 40 % Water -0.040 0.138-0.335 0.293-2.675 2.812 70 % Ethanol + 30 % Water 0.063 0.085-0.368 0.311-2.936 3.102 80 % Ethanol + 20 % Water 0.172 0.175-0.463 0.260-3.212 3.323 90 % Ethanol + 10 % Water 0.243 0.213-0.575 0.262-3.450 3.545 95 % Ethanol + 5 % Water 0.239 0.328-0.795 0.294-3.514 3.697 (Gas to water) -0.994 0.577 2.549 3.813 4.841-0.869 B. Gas to solvent: Eqn. (2) a 1-Octanol (wet) -0.198 0.002 0.709 3.519 1.429 0.858 Methanol (dry) -0.039-0.338 1.317 3.826 1.396 0.973 16

TABLE 1. (Continued) Process/solvent c e s a b v/l Ethanol (dry) 0.017-0.232 0.867 3.894 1.192 0.846 1-Propanol (dry) -0.042-0.246 0.749 3.888 1.076 0.874 2-Propanol (dry) -0.048-0.324 0.713 4.036 1.055 0.884 1-Butanol (dry) -0.004-0.285 0.768 3.705 0.879 0.890 1-Pentanol (dry) -0.002-0.161 0.535 3.778 0.960 0.900 1-Hexanol (dry) -0.014-0.205 0.583 3.621 0.891 0.913 1-Heptanol (dry) -0.056-0.216 0.554 3.596 0.803 0.933 1-Octanol (dry) -0.147-0.214 0.561 3.507 0.749 0.943 1-Decanol (dry) -0.139-0.090 0.356 3.547 0.727 0.958 2-Butanol (dry) -0.034-0.387 0.719 3.736 1.088 0.905 2-Methyl-1-propanol (dry) -0.003-0.357 0.699 3.595 1.247 0.881 2-Methyl-2-propanol (dry) 0.053-0.443 0.699 4.026 0.882 0.907 2-Pentanol (dry) -0.031-0.325 0.496 3.792 1.024 0.934 3-Methyl-1-butanol (dry) -0.052-0.430 0.628 3.661 0.932 0.937 Diisopropyl ether (dry) 0.139-0.473 0.610 2.568 0.000 1.016 Tetrahydrofuran (dry) 0.193-0.391 1.244 3.256 0.000 0.994 17

TABLE 1. (Continued) Process/solvent c e s a b v/l 1,4-Dioxane (dry) -0.034-0.389 1.724 2.989 0.000 0.922 Acetone (dry) 0.127-0.387 1.733 3.060 0.000 0.866 N,N-Dimethylformamide (dry) -0.391-0.869 2.107 3.774 0.000 1.011 Methyl acetate (dry) 0.134-0.477 1.749 2.678 0.000 0.876 Ethyl acetate (dry) 0.182-0.352 1.316 2.891 0.000 0.916 Butyl acetate (dry) 0.147-0.414 1.212 2.623 0.000 0.954 Acetonitrile (dry) -0.007-0.595 2.461 2.085 0.418 0.738 Propylene carbonate (dry) -0.356-0.413 2.587 2.207 0.455 0.719 2-Methoxyethanol (dry) -0.141-0.265 1.810 3.641 0.590 0.790 2-Ethoxyethanol (dry) -0.064-0.257 1.452 3.672 0.662 0.843 2-Propoxyethanol (dry) -0.091-0.288 1.265 3.566 0.390 0.902 2-Isopropoxyethanol (dry) -0.045-0.264 1.296 3.046 0.352 0.880 2-Butoxyethanol (dry) -0.109-0.304 1.126 3.407 0.660 0.914 (Gas to water) -1.271 0.822 2.743 3.904 4.814-0.213 18

a The dependent variable is log (CS,organic sat /CS,water sat ) and log (CS,organic sat /CS,gas) for all of the correlations, except for the one water-tooctanol partition coefficient. b The compositions in the binary aqueous-ethanol solvent mixtures are given in terms of volume percents. 19

TABLE 2. Comparison of the Experimental ln x1 Data and Back-Calculated Values Based on Eqn. 12 for p-coumaric Acid Dissolved in Binary Ethanol (2) + Water (3) Mixtures at 298.15 K exp 12 Mass fraction of ethanol ln x 1 ln x eq 1 % Rel. Dev. a 0.10-7.601-7.591 1.01 0.20-6.725-6.754-2.86 0.30-5.991-5.977 1.01 0.40-5.279-5.262 1.02 0.50-4.625-4.617 0.80 0.60-4.023-4.055-3.15 0.70-3.616-3.594 2.22 0.80-3.268-3.256 1.21 0.90-3.090-3.068 2.22 1.00-3.088-3.064 2.43 a % Rel. Dev. = 100 x [ exp x 1 - x ]/ x. eq 12 1 exp 1 20

TABLE 3. Logarithms of the Experimental Molar Solubilities of p-coumaric Acid, CS,organic, in Organic Solvents and in Binary Aqueous-Ethanol Solvent Mixtures at 298.15 K Organic Solvent/Solvent Mixture log CS,organic Methanol -0.049 Ethanol -0.132 1-Propanol -0.315 2-Propanol -0.376 1-Butanol -0.401 2-Methyl-1-propanol -0.617 Acetone -0.251 Ethyl acetate -0.888 Methyl acetate -0.661 10 % Ethanol + 90 % Water a -1.748 20 % Ethanol + 80 % Water -1.543 30 % Ethanol + 70 % Water -1.329 40 % Ethanol + 60 % Water -1.105 50 % Ethanol + 50 % Water -0.874 60 % Ethanol + 40 % Water -0.640 70 % Ethanol + 30 % Water -0.414 80 % Ethanol + 20 % Water -0.219 90 % Ethanol + 10 % Water -0.096 95 % Ethanol + 5 % Water -0.086 a Compositions in the binary aqueous-ethanol solvent mixtures are expressed in terms of volume percents. 21

TABLE 4. Predicted Molar Solubilities of p-coumaric Acid in Organic Solvents at 298.15 K Based on the Abraham Solvation Parameter Model Solvent log C exp S, organic log ( C eq 1 S, organic/ CS, water) log C eq 1 S, organic log( C eq 2 S, organic/ CS, water) log C eq 2 S, organic Methanol -0.049 2.011-0.064 10.835-0.114 Ethanol -0.132 1.935-0.140 10.798-0.151 1-Propanol -0.315 1.750-0.325 10.652-0.297 1-Butanol -0.401 1.579-0.496 10.488-0.461 1-Pentanol 1.602-0.473 10.501-0.448 1-Hexanol 1.519-0.556 10.410-0.539 1-Heptanol 1.400-0.675 10.366-0.583 1-Octanol 1.408-0.667 10.245-0.704 1-Decanol 1.326-0.749 10.241-0.708 2-Propanol -0.376 1.751-0.324 10.669-0.280 2-Butanol 1.618-0.457 10.520-0.429 2-Methyl-1-propanol -0.617 1.529-0.546 10.388-0.561 2-Methyl-2-propanol 1.637-0.438 10.622-0.327 2-Pentanol 1.598-0.477 10.362-0.587 3-Methyl-1-butanol 1.488-0.587 10.483-0.466 Diisopropyl ether 0.530-1.545 9.459-1.490 Tetrahydrofuran 2.092 0.017 10.972 0.023 22

TABLE 4. (Continued) Solvent log C exp S, organic log ( C eq 1 S, organic/ CS, water) log C eq 1 S, organic log ( C eq 2 S, organic/ CS, water) log C eq 2 S, organic 1,4-Dioxane 1.855-0.220 10.731-0.218 Acetone -0.251 1.681-0.394 10.587-0.362 N,N-Dimethylformamide 2.650 0.575 11.557 0.608 Methyl acetate -0.661 1.389-0.686 10.244-0.705 Ethyl acetate -0.888 1.376-0.699 10.281-0.668 Butyl acetate 1.173-0.902 10.045-0.904 Acetonitrile 0.846-1.229 9.826-1.123 Propylene carbonate 1.114-0.961 9.901-1.048 2-Methoxyethanol 2.112 0.037 10.963 0.014 2-Ethoxyethanol 2.088 0.013 10.965 0.016 2-Propoxyethanol 1.901-0.174 10.754-0.195 2-Isopropoxyethanol 1.910-0.165 10.265-0.684 2-Butoxyethanol 1.754-0.321 10.643-0.306 10:90 EtOH + Water a -1.748 0.157-1.921 20:80 EtOH + Water -1.543 0.397-1.678 30:70 EtOH + Water -1.329 0.693-1.382 40:60 EtOH + Water -1.105 1.004-1.071 50:50 EtOH +Water -0.874 1.302-0.773 60:40 EtOH + Water -0.640 1.556-0.519 23

TABLE 4. (Continued) Solvent log C exp S, organic log ( C eq 1 S, organic/ CS, water) log C eq 1 S, organic log( C eq 2 S, organic/ CS, water) log C eq 2 S, organic 70:30 EtOH + Water -0.414 1.736-0.339 80:20 EtOH + Water -0.219 1.866-0.209 90:10 EtOH + Water -0.096 1.942-0.133 95:5 EtOH + Water -0.086 1.943-0.132 a Compositions in the binary aqueous-ethanol solvent mixtures are expressed in units of volume percents. 24