Comment on “Measurement and Correlation of the Solubility of p

Publication Date (Web): December 7, 2016. Copyright © 2016 American Chemical Society. *E-mail: [email protected]. Fax: 940-565-4318. Cite this:J. Chem...
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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.,*,† Maribel Barrera,† and Michael H. Abraham‡ †

Department of Chemistry, University of North Texas, 1155 Union Circle Drive #305070, Denton, Texas 76203, United States Department of Chemistry, University College London, 20 Gordon Street, London WC1H OAJ, U.K.

‡

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. n a recent article published in Journal of Chemical & Engineering Data Ji and co-workers1 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 aqueous-ethanol solvent mixtures from 293.15 to 333.15 K. Solubilities were determined by a gravimetric method of analysis that involved transferring weighed aliquots of the saturated solutions into preweighed 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 pcoumaric 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. 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

I

© XXXX American Chemical Society

log(P or CS,organic/CS,water) = c p + ep·E + sp·S + a p·A + bp·B + vp·V

(1)

log(K or CS,organic/CS,gas) = c k + ek · E + s k · S + a k · A + b k · B + l k · 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 co-workers1 contained adjustable parameters that were determined by curve-fitting the measured solubility data in accordance with the respective model. The Abraham model2−4 has similar parameters, called solute descriptors, which must be calculated using the experimental solubility data. Solute descriptors 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 (cm3 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 (cm3 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 Received: September 16, 2016 Accepted: November 22, 2016

A

DOI: 10.1021/acs.jced.6b00807 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

Journal of Chemical & Engineering Data

Comment/Reply

Table 1. Coefficients in Equation 1 and Equation 2 for Various Processes at 298.15 K process/solvent

c

1-octanol (wet) methanol (dry) ethanol (dry) 1-propanol (dry) 2-propanol (dry) 1-butanol (dry) 1-pentanol (dry) 1-hexanol (dry) 1-heptanol (dry) 1-octanol (dry) 1-decanol (dry) 2-butanol (dry) 2-methyl-1-propanol (dry) 2-methyl-2-propanol (dry) 2-pentanol (dry) 3-methyl-1-butanol (dry) diisopropyl ether (dry) tetrahydrofuran (dry) 1,4-dioxane (dry) acetone (dry) methyl acetate (dry) ethyl acetate (dry) butyl acetate (dry) acetonitrile (dry) propylene carbonate (dry) 2-methoxyethanol (dry) 2-rthoxyethanol (dry) 2-propoxyethanol (dry) 2-isopropoxyethanol (dry) 2-butoxyethanol (dry) 10% ethanol +90% waterb 20% ethanol +80% water 30% ethanol +70% water 40% ethanol +60% water 50% ethanol +50% Water 60% ethanol +40% water 70% ethanol +30% water 80% ethanol +20% water 90% ethanol +10% water 95% ethanol +5% water (gas to water)

0.088 0.276 0.222 0.139 0.099 0.165 0.150 0.115 0.035 −0.034 −0.058 0.127 0.188 0.211 0.115 0.073 0.181 0.223 0.123 0.313 0.351 0.328 0.248 0.413 0.004 0.175 0.133 0.053 0.107 −0.055 −0.173 −0.252 −0.269 −0.221 −0.142 −0.040 0.063 0.172 0.243 0.239 −0.994

1-octanol (wet) methanol (dry) ethanol (dry) 1-propanol (dry) 2-propanol (dry) 1-butanol (dry) 1-pentanol (dry) 1-hexanol (dry) 1-heptanol (dry) 1-octanol (dry) 1-decanol (dry) 2-butanol (dry) 2-methyl-1-propanol (dry) 2-methyl-2-propanol (dry) 2-pentanol (dry) 3-methyl-1-butanol (dry) diisopropyl ether (dry) tetrahydrofuran (dry)

−0.198 −0.039 0.017 −0.042 −0.048 −0.004 −0.002 −0.014 −0.056 −0.147 −0.139 −0.034 −0.003 0.053 −0.031 −0.052 0.139 0.193

e

s

A. Water to Solvent: eq (1)a 0.562 −1.054 0.334 −0.714 0.471 −1.035 0.405 −1.029 0.344 −1.049 0.401 −1.011 0.536 −1.229 0.492 −1.164 0.398 −1.063 0.489 −1.044 0.616 −1.319 0.253 −0.976 0.354 −1.127 0.171 −0.947 0.455 −1.331 0.360 −1.273 0.285 −0.954 0.363 −0.384 0.347 −0.033 0.312 −0.121 0.223 −0.150 0.369 −0.446 0.356 −0.501 0.077 0.326 0.168 0.504 0.326 −0.140 0.392 −0.419 0.419 −0.569 0.391 −0.525 0.377 −0.607 −0.023 −0.001 0.043 −0.040 0.107 −0.098 0.131 −0.159 0.124 −0.252 0.138 −0.335 0.085 −0.368 0.175 −0.463 0.213 −0.575 0.328 −0.795 0.577 2.549 B. Gas to Solvent: eq (2)a 0.002 0.709 −0.338 1.317 −0.232 0.867 −0.246 0.749 −0.324 0.713 −0.285 0.768 −0.161 0.535 −0.205 0.583 −0.216 0.554 −0.214 0.561 −0.090 0.356 −0.387 0.719 −0.357 0.699 −0.443 0.699 −0.325 0.496 −0.430 0.628 −0.473 0.610 −0.391 1.244 B

a

b

v/l

0.034 0.243 0.326 0.247 0.406 0.056 0.141 0.054 0.002 −0.024 0.026 0.158 0.016 0.331 0.206 0.090 −0.956 −0.238 −0.582 −0.608 −1.035 −0.700 −0.867 −1.566 −1.283 0.000 0.125 0.000 0.071 −0.080 0.065 0.096 0.133 0.171 0.251 0.293 0.311 0.260 0.262 0.294 3.813

−3.460 −3.320 −3.596 −3.767 −3.827 −3.958 −3.864 −3.978 −4.342 −4.235 −4.153 −3.882 −3.568 −4.085 −3.745 −3.770 −5.077 −4.932 −4.810 −4.753 −4.527 −4.904 −4.973 −4.391 −4.407 −4.086 −4.200 −4.327 −4.439 −4.371 −0.372 −0.823 −1.316 −1.809 −2.275 −2.675 −2.936 −3.212 −3.450 −3.514 4.841

3.814 3.549 3.857 3.986 4.033 4.044 4.077 4.131 4.317 4.218 4.279 4.114 3.986 4.109 4.201 4.273 4.542 4.450 4.110 3.942 3.972 4.150 4.281 3.364 3.421 3.630 3.888 4.095 4.051 4.234 0.454 0.916 1.414 1.918 2.415 2.812 3.102 3.323 3.545 3.697 −0.869

3.519 3.826 3.894 3.888 4.036 3.705 3.778 3.621 3.596 3.507 3.547 3.736 3.595 4.026 3.792 3.661 2.568 3.256

1.429 1.396 1.192 1.076 1.055 0.879 0.960 0.891 0.803 0.749 0.727 1.088 1.247 0.882 1.024 0.932 0.000 0.000

0.858 0.973 0.846 0.874 0.884 0.890 0.900 0.913 0.933 0.943 0.958 0.905 0.881 0.907 0.934 0.937 1.016 0.994

DOI: 10.1021/acs.jced.6b00807 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

Journal of Chemical & Engineering Data

Comment/Reply

Table 1. continued process/solvent 1,4-dioxane (dry) acetone (dry) N,N-dimethylformamide (dry) methyl acetate (dry) ethyl acetate (dry) butyl acetate (dry) acetonitrile (dry) propylene carbonate (dry) 2-methoxyethanol (dry) 2-ethoxyethanol (dry) 2-propoxyethanol (dry) 2-isopropoxyethanol (dry) 2-butoxyethanol (dry) (gas to water)

c −0.034 0.127 −0.391 0.134 0.182 0.147 −0.007 −0.356 −0.141 −0.064 −0.091 −0.045 −0.109 −1.271

e

s

B. Gas to Solvent: eq (2)a −0.389 1.724 −0.387 1.733 −0.869 2.107 −0.477 1.749 −0.352 1.316 −0.414 1.212 −0.595 2.461 −0.413 2.587 −0.265 1.810 −0.257 1.452 −0.288 1.265 −0.264 1.296 −0.304 1.126 0.822 2.743

a

b

2.989 3.060 3.774 2.678 2.891 2.623 2.085 2.207 3.641 3.672 3.566 3.046 3.407 3.904

0.000 0.000 0.000 0.000 0.000 0.000 0.418 0.455 0.590 0.662 0.390 0.352 0.660 4.814

v/l 0.922 0.866 1.011 0.876 0.916 0.954 0.738 0.719 0.790 0.843 0.902 0.880 0.914 −0.213

a

The dependent variable is log (CS,organicsat/CS,watersat) and log (CS,organicsat/CS,gas) for all of the correlations, except for the one water-to-octanol partition coefficient. bThe compositions in the binary aqueous-ethanol solvent mixtures are given in terms of volume percents.

interact with surrounding solvent molecules. The complementary 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−ethanol8,9 and aqueous−methanol10 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 solvents2,5−7 and for ionic liquid solvents11 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 10 log (CS,organic/ CS,water) equations are available for the measured p-coumaric solubility data in binary aqueous−ethanol solvent mixtures. Two practical water-to-octanol partition coefficient equations:

log K w = − 1.271 + 0.822E + 2.743S + 3.904A + 4.814B

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 BioLoom14 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, 1butanol, 2-methyl-1-propanol, acetone, methyl acetate, and ethyl acetate are converted to molar solubilities by CSexp ≈ XSexp/[XSexpVSolute + (1 − XSexp)VSolvent])

(3)

ln x1, T = c1 + c 2w2 +

log K (wet octanol) = −0.198 + 0.002E + 0.709S + 3.519A + 1.429B + 0.858L

c3 w4 w w2 w3 + c4 2 + c5 2 + c6 2 + c 7 3 T T T T T (8)

(4)

which was presumably obtained from the Jouyban−Acree model:

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):

ln x1, T = w2 ln(x1)2, T + w3 ln(x1)3, T n

log K w = − 0.994 + 0.577E + 2.549S + 3.813A + 4.841B − 0.869V

(7)

dividing the measured mole fraction solubility by the ideal molar volume of the saturated solution. A numerical value of Vsolute = 127.9 cm3 mol−1 was used for the molar volume of pcoumaric acid. The molar volume was estimated from fragment group values. Any errors resulting from our estimation of the pcoumaric acid’s hypothetical subcooled liquid molar volume, VSolute, or the ideal molar volume approximation should have a negligible effect of the calculated CSexp 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:

log P (wet octanol) = 0.088 + 0.562E − 1.054S + 0.034A − 3.460B + 3.814V

(6)

− 0.213L

+ w2w3 ∑

(5)

i=0

C

Ji (w2 − w3)i T

(9) DOI: 10.1021/acs.jced.6b00807 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

Journal of Chemical & Engineering Data

Comment/Reply

in which x1,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, (x1)2,T and (x1)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 pcoumaric acid in both ethanol and water as numerical constants, the values of which are independent of temperature. In other words, one has to assume that the solubility of pcoumaric acid in both cosolvents 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

We have compiled in Table 3 our calculated molar solubilities of p-coumaric in the nine neat organic solvents and in the 10 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

n

ln x1, t = w2 ln(x1)2, T + w3 ln(x1)2, T + w2w 3 ∑ Ji (w2 − w3)i i=0

(10)

as we need only to describe the experimental solubility data at 298.15 K. The authors did not measure the solubility of pcoumaric acid in water, so we have expanded eq 10 into a polynomial expression in w2: ln x1 = c0 + c1w2 + c 2w2 2 + c3w2 3 + c4w2 4

(11)

ln x1 = −8.4878 + 9.2921w2 − 3.3408w2 + 1.4877w2

(12)

(Average Absolute Relative Deviation = 0.0173)

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. Table 2. Comparison of the Experimental ln x1 Data and Back-Calculated Values Based on eq 12 for p-Coumaric Acid Dissolved in Binary Ethanol (2) + Water (3) Mixtures at 298.15 K

a

mass fraction of ethanol

ln xexp 1

12 ln xeq 1

% Rel. Dev.a

0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00

−7.601 −6.725 −5.991 −5.279 −4.625 −4.023 −3.616 −3.268 −3.090 −3.088

−7.591 −6.754 −5.977 −5.262 −4.617 −4.055 −3.594 −3.256 −3.068 −3.064

1.01 −2.86 1.01 1.02 0.80 −3.15 2.22 1.21 2.22 2.43

methanol ethanol 1-propanol 2-propanol 1-butanol 2-methyl-1-propanol acetone ethyl acetate methyl acetate 10% ethanol + 90% watera 20% ethanol + 80% water 30% ethanol + 70% water 40% ethanol + 60% water 50% ethanol + 50% water 60% ethanol + 40% water 70% ethanol + 30% water 80% ethanol + 20% water 90% ethanol + 10% water 95% ethanol + 5% water 1-octanol (wet)

−0.049 −0.132 −0.315 −0.376 −0.401 −0.617 −0.251 −0.888 −0.661 −1.748 −1.543 −1.329 −1.105 −0.874 −0.640 −0.414 −0.219 −0.096 −0.086 1.82

binary aqueous−ethanol solvent mixtures for which we have Abraham model solvent equation coefficients. Also, included in Table 3 is the numerical value of the logarithm of the water-tooctanol, 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; 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.

3

− 2.0149w2 4

log CS,organic

a Compositions in the binary aqueous−ethanol solvent mixtures are expressed in terms of volume percents.

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 2

organic solvent/solvent mixture

eq12 exp % Rel. Dev. = 100x[xexp 1 − x1 ]/x1 .

D

DOI: 10.1021/acs.jced.6b00807 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

Journal of Chemical & Engineering Data

Comment/Reply

Table 4. Predicted Molar Solubilities of p-Coumaric Acid in Organic Solvents at 298.15 K Based on the Abraham Solvation Parameter Model

a

solvent

log Cexp S,organic

log (CS,organic/CS,water)eq1

1 log Ceq S,organic

log (CS,organic/CS,water)eq 2

2 log Ceq S,organic

methanol ethanol 1-propanol 1-butanol 1-pentanol 1-hexanol 1-heptanol 1-octanol 1-decanol 2-propanol 2-butanol 2-methyl-1-propanol 2-methyl-2-propanol 2-pentanol 3-methyl-1-butanol diisopropyl ether tetrahydrofuran 1,4-dioxane acetone N,N-dimethylformamide methyl acetate ethyl acetate butyl acetate acetonitrile propylene carbonate 2-methoxyethanol 2-ethoxyethanol 2-propoxyethanol 2-isopropoxyethanol 2-butoxyethanol 10:90 EtOH + watera 20:80 EtOH + Water 30:70 EtOH + water 40:60 EtOH + water 50:50 EtOH + water 60:40 EtOH + water 70:30 EtOH + water 80:20 EtOH + water 90:10 EtOH + water 95:5 EtOH + water

−0.049 −0.132 −0.315 −0.401

2.011 1.935 1.750 1.579 1.602 1.519 1.400 1.408 1.326 1.751 1.618 1.529 1.637 1.598 1.488 0.530 2.092 1.855 1.681 2.650 1.389 1.376 1.173 0.846 1.114 2.112 2.088 1.901 1.910 1.754 0.157 0.397 0.693 1.004 1.302 1.556 1.736 1.866 1.942 1.943

−0.064 −0.140 −0.325 −0.496 −0.473 −0.556 −0.675 −0.667 −0.749 −0.324 −0.457 −0.546 −0.438 −0.477 −0.587 −1.545 0.017 −0.220 −0.394 0.575 −0.686 −0.699 −0.902 −1.229 −0.961 0.037 0.013 −0.174 −0.165 −0.321 −1.921 −1.678 −1.382 −1.071 −0.773 −0.519 −0.339 −0.209 −0.133 −0.132

10.835 10.798 10.652 10.488 10.501 10.410 10.366 10.245 10.241 10.669 10.520 10.388 10.622 10.362 10.483 9.459 10.972 10.731 10.587 11.557 10.244 10.281 10.045 9.826 9.901 10.963 10.965 10.754 10.265 10.643

−0.114 −0.151 −0.297 −0.461 −0.448 −0.539 −0.583 −0.704 −0.708 −0.280 −0.429 −0.561 −0.327 −0.587 −0.466 −1.490 0.023 −0.218 −0.362 0.608 −0.705 −0.668 −0.904 −1.123 −1.048 0.014 0.016 −0.195 −0.684 −0.306

−0.376 −0.617

−0.251 −0.661 −0.888

−1.748 −1.543 −1.329 −1.105 −0.874 −0.640 −0.414 −0.219 −0.096 −0.086

Compositions in the binary aqueous−ethanol solvent mixtures are expressed in units of volume percents.

forms of the carboxylic acid. This is discussed in greater detail in an earlier publication in which 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 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 eqs 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

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. pCoumaric 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 E

DOI: 10.1021/acs.jced.6b00807 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

Journal of Chemical & Engineering Data

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(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. (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 watermethanol mixtures. J. Solution Chem. 2016, 45, 861−874. (11) Jiang, B.; Horton, M. Y.; Acree, W. E., Jr.; Abraham, M. H. Ionspecific 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: Claremont, CA, 2016. (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., Toronto, Ontario, Canada. (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, 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. Cent. J. 2015, 9, 11. (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.

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 Cexp S,organic = −0.049 in the second column of Table 4 compares very favorably the back-calculated eq2 values of log Ceq1 S,organic = −0.064 and log CS,organic = −0.114 given in fourth and sixth columns of Table 3 for eqs 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 equations21,22 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 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.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Fax: 940-565-4318. Funding

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. Notes

The authors declare no competing financial interest.

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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. Rev. 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. F

DOI: 10.1021/acs.jced.6b00807 J. Chem. Eng. Data XXXX, XXX, XXX−XXX