ABHISHEK S1 APA LOG P advanced pharmaceutical analysis
Solubility of sorbic acid in organic mono solvents calculation of Abraham model solute descriptors from measured solubility data
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Solubility of sorbic acid in organic mono-solvents:
calculation of Abraham model solute descriptors
from measured solubility data
Maribel Barrera, Erin Hart, Melissa Y. Horton, Elizabeth Higgins, Sarah
Cheeran, Grace E. Little, Hunter Singleton, Donavyn Calhoon, Kyle Gillispie,
Febronia Khalil, Randall Williams, William E. Acree Jr. & Michael H. Abraham
To cite this article: Maribel Barrera, Erin Hart, Melissa Y. Horton, Elizabeth Higgins, Sarah
Cheeran, Grace E. Little, Hunter Singleton, Donavyn Calhoon, Kyle Gillispie, Febronia Khalil,
Randall Williams, William E. Acree Jr. & Michael H. Abraham (2016): Solubility of sorbic acid in
organic mono-solvents: calculation of Abraham model solute descriptors from measured solubility
data, Physics and Chemistry of Liquids, DOI: 10.1080/00319104.2016.1260715
To link to this article: http://dx.doi.org/10.1080/00319104.2016.1260715
Published online: 28 Nov 2016.
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3. solubility of several crystalline non-electrolyte solutes in organic monosolvents and binary solvent
mixtures, combined with the development of mathematical correlations that enable one to predict the
solubilities in additional organic solvents and solvent mixtures. Among the solutes studied we have
reported the solubility of pesticides (diuron [1,2] and monuron [1,3]), non-steroidal anti-inflammatory
drugs (aspirin [4,5], naproxen [5,6], ibuprofen [6,7], ketoprofen [5,8], and salicylic acid [5,9]) and several
substituted benzoic acid derivatives [10–14] in a wide range of organic solvents of varying polarity and
hydrogen-bonding character. We have calculated the solute descriptors of the studied organic com-
pounds by curve fitting the experimental molar solubility data in accordance to the Abraham equations,
logðCS;organic=CS;waterÞ ¼ cp þ ep Á E þ sp Á S þ ap Á A þ bp Á B þ vp Á V: (1)
logðCS;organic=CS;gasÞ ¼ ck þ ekÁ E þ skÁ S þ ak Á A þ bk ÁB þ lkÁ L; (2)
where CS,organic is the molar solubility of the solute in the organic solvent or binary solvent mixture,
CS,water is the solute’s molar solubility in water and CS,gas is the solute’s gas phase concentration at the
measurement temperature. The latter concentration can be calculated from the solute’s vapour pressure,
or can be determined at the time that the solute descriptors are calculated.
The Abraham model is a linear free energy model that describes solute transfer between two phases
based on molecular interactions. The terms on the right-hand side of Equations (1) and (2) represent
solute–solvent interactions that are described by the product of solute descriptors (the uppercase
alphabetical characters) and times the complementary solvent properties (the lowercase alphabetical
characters). The product represents a specific type of interaction that plays an important role in the
transfer process. For example, the ap · A and ak · A terms represent hydrogen-bonding interactions
between an H-bond donor solute molecule and the H-bond acceptor solubilising phase(s). Hydrogen-
bonding interactions between an H-bond acceptor molecule and H-bond donor solubilising phase(s)
are described by the bp · B and bk · B terms in Equations (1) and (2), respectively. The remaining solute
descriptors are defined as follows: E corresponds to the solute excess molar refractivity in units of
(cm3
mol−1
)/10, S quantifies the dipolarity/polarisability of the solute, 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. The complimentary solvent properties that 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 Equations
(1) and (2) also encode valuable chemical information pertaining the solvent or solubilising phase. In
the case of Equation (1) solute transfer occurs between two condensed phases, and the respective
lowercase equation coefficients represent differences in the receiving and originating solubilising
phase (or solvent) properties. Numerical values of the lowercase alphabetical characters are deter-
mined by regression analysis by curve-fitting solubility data of solutes with known solute descriptors
dissolved in the solvent (or solubilising phase) under consideration. Calculation of solvent equation
coefficients is described in greater detail elsewhere [15–18].
The present study focusses on determining the solute descriptors of sorbic acid, which as noted
above is an important preservative found in food and cosmetic products. Solubilities have been
measured spectrophotometrically at 298.15 K for sorbic acid dissolved in methanol, ethanol, 1-
butanol, 1-pentanol, 1-hexanol, 2-propanol, 2-methyl-2-propanol, 2-pentanol, 1,4-dioxane, tetrahy-
drofuran, diisopropyl ether and methyl tert-butyl ether. Our experimental data, combined with a
published logarithmic water-to-partition coefficient of Log P = 1.33 [19] and recently published
solubility data of Fang and coworkers [20] for sorbic acid dissolved in acetone, acetonitrile and
ethyl acetate, were used to calculate the solute descriptor values for the monomeric form of sorbic acid.
Solubility data in carbon tetrachloride, and in nonpolar alkane and alkylbenzene solvents would be
needed to calculate the solute descriptors of the sorbic acid dimer [21]. The calculated solute
descriptors described the experimental values to within 0.10 log units, and can be used to predict
the solubility behaviour of sorbic acid in binary aqueous-methanol and binary aqueous-ethanol
solvent mixtures, and in those polar organic monosolvents for which sorbic acid is expected to exist
in monomeric form and for which we have solvent equation coefficients.
2 M. BARRERA ET AL.
4. 2. Experimental methodology
Sorbic acid (Sigma-Aldrich Chemical Company, 0.99 mass fraction) was used as received. Organic
solvents were purchased from commercial sources. The provenances and mass fraction chemical
purities (as supplied by the various manufacturers) are summarised in the last two columns of
Table 1. All solvents were stored over molecular sieves and distilled shortly before use. Gas
chromatographic analyses (with both a flame ionisation detector and thermal conductivity
detector) were used to verify the mass fraction purities stated by the manufacturers, and showed
all solvents to have a mass fraction purity of 0.997 or higher.
Mole fraction solubilities of sorbic acid dissolved in the nine alcohol and four alkyl ether solvents
were measured using a static equilibration method followed by spectrophotometric determination of
the concentration of the dissolved sorbic acid solute. The method involved equilibrating samples of
excess solute and organic solvent in sealed amber glass bottles in a constant temperature water bath at
298.2 ± 0.1 K for at least three days. Samples were periodically agitated to facilitate mixing. After
equilibration the samples were allowed to set undisturbed for several hours to allow any finely
dispersed solid particles to settle to the bottom of the container. Aliquots of the saturated sorbic
acid solutions were transferred through a coarse filter into a tared volumetric flask to determine the
amount of sample analysed, and then diluted quantitatively with 2-propanol for spectrophotometric
analysis at 257 nm on a Milton Roy Spectronic 1000. Concentrations of the diluted solutions were
determined from a Beer-Lambert law absorbance versus concentrations working curve for nine
standard solutions in the concentration range from 1.875 × 10–5
Molar to 6.250 × 10−5
Molar. The
calculated molar absorptivity, ɛ ≈ 24,500 L mol−1
cm−1
, remained constant over this concentration
range. Attainment of equilibrium was verified by repetitive measurements performed the following
day (or sometimes after two days) and by approaching equilibrium from super supersaturation by pre-
equilibrating the solutions at a slightly higher temperature.
The measured molar concentrations were converted to mass fraction solubilities by multipliying by
the molar mass of sorbic acid, by the volumes of the tarred volumetric flask(s) used and by any dilutions
required to place the measured absorbances on the Beer-Lambert Law absorbance versus concentration
working curve, and then dividing by the mass of the aliquot of the saturated sample taken for analysis.
Mass fraction solubilities were converted to mole fraction solubilities using the molar masses of the
carboxylic acid solute and organic solvent. Experimental sorbic acid mole fraction solubilities, XS, in the
13 different organic monosolvents studied are reported in the second column of Table 2. Numerical
values represent the average of between four and eight independent experimental determinations, and
were reproducible to ±2.0%. Also listed in the next to last column of Table 2 are the mole fraction
solubilities determined by Fang and coworkers [20] for sorbic acid dissolved in methanol, ethanol, 1-
butanol, 2-propanol, and methyl tert-butyl ether. Except for the solubility in 1-butanol our measured
Table 1. Provenances and mass fraction purities of Sorbic acid and organic solvents.
Organic compounds Supplier Purity as specified by supplier
Sorbic acid Sigma-Aldrich Chemical Co. 0.99
Methanol Aldrich Chemical Co. 0.998, anhydrous
Ethanol Aaper Alcohol and Chemical Co. absolute
1-Propanol Aldrich Chemical Co. 0.99+, anhydrous
1-Butanol Aldrich Chemical Co. 0.998+, HPLC grade
1-Pentanol Aldrich Chemical Co. 0.99+
1-Hexanol Alfa Aesar Chemical Co. 0.99+
2-Propanol Aldrich Chemical Co. 0.99+, anhydrous
2-Methyl-2-propanol Arco Chemical Co. 0.99+
2-Pentanol Acros Chemical Co. 0.99+
Diisopropyl ether Aldrich Chemical Co. 0.99, anhydrous
Methyl tert-butyl ether Aldrich Chemical Co. 0.99+, anhydrous
Tetrahydrofuran Aldrich Chemical Co. 0.999, anhydrous
1,4-Dioxane Aldrich Chemical Co. 0.998, anhydrous
PHYSICS AND CHEMISTRY OF LIQUIDS 3
5. experimental mole fraction solubilities differ from the published literature values by an average absolute
deviation of 2.7%, which is less than the combined uncertainty associated with the given experimental
mole fraction solubilities. Differences in chemical purities and experimental methodologies can lead to
small differences in experimental values determined by independent research groups. The published
mole fraction solubility data for sorbic acid dissolved in 1-butanol is approximately 30% larger than the
value that we determined. We note that our measured value of XS
exp
= 0.0751 is more in line with the
experimental solubilities of sorbic acid in other alcohol solvents. The experimental mole fraction
solubility of XS
exp
= 0.09730 of Fang et al. [20]; however, appears to be too large when compared with
the alcohol solvent solubility data for sorbic acid (see Table 2).
3. Results and discussion
Calculation of solute descriptors is relatively straightforward and involves generating a series of
Abraham model equations that are solved simultaneously for the best of set of descriptor values
that describe the measured molar solubility ratios, (CS,organic/CS,water) and (CS,organic/CS,gas). In the
present study, we have solubility data for sorbic acid dissolved in 16 different organic solvents if
we combine our experimental values in Table 2 with the published data of Fang et al. [20] for
sorbic acid dissolved in acetone, acetonitrile and ethyl acetate. Sorbic acid is believed to exist
predominately in monomeric form in each organic solvent. The sorbic acid database includes
experimental solubilities in both polar protic organic solvents (alcohol solvents) and polar aprotic
organic solvents (ethers, alkanone, alkyl acetate, alkanenitrile). The chemical diversity of the
solvents should be more than sufficient for us to determine a meaningful set of solute descriptors
for sorbic acid. Numerical values of the Abraham model equation coefficients are tabulated in
Table 3 for each of the 16 organic solvents for experimental solubility data are available. A more
complete listing of equation coefficients can be found elsewhere [22–25].
The mole fraction solubilities in Table 2 are converted to molar solubilities by dividing XS
exp
, by the
ideal molar volume of the saturated solution (i.e. CS
exp
≈ XS
exp
/[XS
exp
VSolute + (1 – XS
exp
) VSolvent]). A
value of VSolute = 124.0 cm3
mol−1
was used for the molar volume of the hypothetical subcooled liquid
sorbic acid. Any errors resulting from our estimation of the sorbic acid’s hypothetical subcooled liquid
molar volume, VSolute, or the ideal molar volume approximation should have negligible effect of the
calculated CS
exp
values. The mole fraction solubility data of Fang et al. [20] were converted to molar
solubilities in similar fashion. Once the mole fraction solubilities have been converted into molar
solubilities, the solubility ratio, (CS,organic/CS,water), is calculated for each measured solubility datum
point using a value of log CS,water = −1.77 [26–28] for the logarithm of aqueous molar solubility of
molecular, monomeric sorbic acid. This gives us 16 log (CS,organic/CS,water) equations to solve simulta-
neously and five solute descriptors (E, S, A, B and V) to be determined. Two of the five solute descriptors
can be calculated from molecular structure considerations. The McGowan characteristic volume, V, can
Table 2. Experimental mole fraction solubilities, XS
exp
, of sorbic acid at 298.2 K.
Organic solvent XS
exp
XS
lit
[Reference]
Methanol 0.0572 0.05526 [20]
Ethanol 0.0615 0.06432 [20]
1-Propanol 0.0520
1-Butanol 0.0751 0.09730 [20]
1-Pentanol 0.0683
1-Hexanol 0.0651
2-Propanol 0.0622 0.06131 [20]
2-Methyl-2-propanol 0.0758
2-Pentanol 0.0672
Diisopropyl ether 0.0306
Methyl tert-butyl ether 0.0571 0.05772 [20]
Tetrahydrofuran 0.1379
1,4-Dioxane 0.1174
4 M. BARRERA ET AL.
6. be computed from the molecular structure, atomic sizes and number of bonds as described elsewhere
[29]. The E solute descriptor can be obtained using the PharmaAlgorithm software [30], which is based
on molecular structure considerations using fragment group values [31,32], 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 [33]. The values of V
and E that we calculate are V = 0.9424 and E = 0.480.
Calculation of the (CS,organic/CS,gas) solubility ratios is a bit more difficult as we are missing an
experimental value for log CS,gas. We will treat the value of log CS,gas as an additional adjustable curve-
fit parameter and its numerical value will be calculated as part of the solute descriptor determinations.
This computation has been described in detail in several earlier papers [1,4,6,11–14,22]. Two practical
water-to-octanol partition coefficient equations:
log P wet octanolð Þ ¼ 0:088 þ 0:562 E À 1:054 S þ 0:034 A À 3:460 B þ 3:814 V:
(3)
log K wet octanolð Þ ¼ À 0:198 þ 0:002 E þ 0:709 S þ 3:519 A þ 1:429 B þ 0:858 L;
(4)
Table 3. Coefficients in Equations (1) and (2) for various processes.
Process/solvent c e s a b v/l
A. Water to solvent: Equation (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
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
Diisopropyl ether (dry) 0.181 0.285 −0.954 −0.956 −5.077 4.542
Methyl tert-butyl ether (dry) 0.341 0.307 −0.817 −0.618 −5.097 4.425
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
Ethyl acetate (dry) 0.328 0.369 −0.446 −0.700 −4.904 4.150
Acetonitrile (dry) 0.413 0.077 0.326 −1.566 −4.391 3.364
(Gas to water) −0.994 0.577 2.549 3.813 4.841 −0.869
B. Gas to solvent: Equation (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
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
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
Diisopropyl ether (dry) 0.139 −0.473 0.610 2.568 0.000 1.016
Methyl tert-butyl ether (dry) 0.231 −0.536 0.890 2.623 0.000 0.999
Tetrahydrofuran (dry) 0.193 −0.391 1.244 3.256 0.000 0.994
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
Ethyl acetate (dry) 0.182 −0.352 1.316 2.891 0.000 0.916
Acetonitrile (dry) −0.007 −0.595 2.461 2.085 0.418 0.738
(Gas to water) −1.271 0.822 2.743 3.904 4.814 −0.213
a
The dependent variable is log (CS
sat
/CW
sat
) and log (CS
sat
/CG) for all of the correlations, except for the one water-to-octanol
partition coefficient.
PHYSICS AND CHEMISTRY OF LIQUIDS 5
7. where log P(wet octanol) = 1.33 [19] and 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):
log Kw ¼ À 0:994 þ 0:577 E þ 2:549 S þ 3:813 A þ 4:841 B À 0:869 V: (5)
log Kw ¼ À 1:271 þ 0:822 E þ 2:743 S þ 3:904 A þ 4:814 B À 0:213 L: (6)
are available for use in the solute descriptor calculations. Inclusion of the 16 additional log
(CS,organic/CS,gas) equations in the solute descriptor computations allows us to obtain a numer-
ical value for the L solute descriptor that can be used in predicting gas-to-organic solvent
transfer properties, such as the enthalpy of solvation of organic solutes dissolved in water and in
organic monosolvents [34–38]. Enthalpy of solvation data can be used to extrapolate solubility
ratios and partition coefficients measured at 298.15 K to slightly higher or slightly lower
temperatures.
The 36 Abraham model equations that we have constructed based on measured solubility and
partition coefficient data at 298.15 K were solved simultaneously using Microsoft Solver software
to yield numerical values of: E = 0.480; S = 0.904; A = 0.528; B = 0.432; V = 0.9424; L = 4.047 and
log CS,gas = −6.681 with the overall standard error being SE = 0.086 log units. Individual standard
errors are SE = 0.079 and SE = 0.094 for the 18 calculated and observed log (P or CS,organic/CS,water)
values and the 18 calculated and observed log (K or CS,organic/CS,gas) values, respectively.
Statistically there is no difference between the set of 18 log (P or CS,organic/CS,water) values and
the total set of 36 log (P or CS,organic/CS,water) and log (K or CS,organic/CS,gas) values, thus suggesting
that log CS,gas = −6.681 is a feasible value for sorbic acid. We note that our calculated descriptor
values are in reasonably good agreement with the numerical values of E = 0.480, S = 0.830,
A = 0.550, B = 0.510, V = 0.9424 and L = 3.817 that are found in the UFZ-LSER database [39].
The values in the UFZ-LSER database are our earlier experimental values obtained with only few
data. Our present descriptors are based on a very large data set of 36 equations. Table 4 provides a
summarised comparison of the experimental molar solubility data and back-calculated values
using the solute descriptors that we have determined.
Table 4. Comparison between observed and back-calculated molar solubilities of sorbic acid based upon Equation (1) and
Equation (2) and calculated values for molecular solute descriptorsa
.
Equation (1) Equation (2)
Solvent log CS
exp
log (CS/CW)exp
log (CS/CW)calc
log CS
calc
log (CS/CG)exp
log (CS/CG)calc
log CS
calc
1-Octanol (wet) 1.330b
1.522 6.241 6.393
Methanol (dry) 0.091 1.861 1.829 0.059 6.772 6.742 0.061
Ethanol (dry) 0.014 1.784 1.766 −0.004 6.695 6.686 0.005
1-Propanol (dry) −0.171 1.599 1.663 −0.107 6.510 6.573 −0.108
2-Propanol (dry) −0.141 1.659 1.678 −0.092 6.570 6.607 −0.074
1-Butanol (dry) −0.096 1.674 1.574 −0.196 6.585 6.493 −0.188
1-Pentanol (dry) −0.203 1.567 1.543 −0.227 6.478 6.458 −0.223
1-Hexanol (dry) −0.258 1.512 1.502 −0.268 6.423 6.408 −0.273
2-Methyl-2-propanol (dry) −0.102 1.668 1.719 −0.051 6.579 6.571 −0.110
2-Pentanol (dry) −0.214 1.556 1.580 −0.190 6.467 6.487 −0.194
Diisopropyl ether (dry) −0.667 1.103 1.037 −0.733 6.017 5.932 −0.749
Methyl tert-butyl ether (dry) −0.313 1.457 1.391 −0.379 6.368 6.207 −0.474
Tetrahydrofuran (dry) 0.205 1.975 1.987 0.217 6.886 6.873 0.193
1,4-Dioxane (dry) 0.119 1.889 1.748 −0.022 6.800 6.649 −0.032
Acetone (dry) −0.040 1.730 1.694 −0.076 6.641 6.630 −0.051
Ethyl acetate (dry) −0.341 1.429 1.524 −0.246 6.340 6.437 −0.244
Acetonitrile (dry) −0.679 1.091 1.191 −0.579 6.002 6.201 −0.480
Gas-to-Water 4.911 4.874 4.911 4.911
a
Numerical values of the descriptors used in these calculations are: E = 0.480, S = 0.904, A = 0.528, B = 0.432, V = 0.9424 and
L = 4.047.
b
Value is the logarithm of a water-to-1-octanol partition coefficient.
6 M. BARRERA ET AL.
8. 4. Conclusion
The Abraham solvation parameter model has been found to provide a reasonably accurate
mathematical description of the observed solubility behaviour of sorbic acid dissolved in metha-
nol, ethanol, 1-propanol, 1-butanol, 1-pentanol, 1-hexanol, 2-propanol, 2-methyl-2-propanol, 2-
pentanol, diisopropyl ether, methyl tert-butyl ether, tetrahydrofuran, 1,4-dioxane, acetone, ethyl
acetate and acetonitrile. Differences between the experimental and back-calculated solubilities
based on the Abraham model were for the most part less than 0.09 log units. Solute descriptors
determined in the present study are for the monomeric form of the sorbic acid solute and are
expected to provide reasonably accurate predictions of the solubility behaviour of sorbic acid in
organic solvents in which dimerisation is negligible/minimal. Of the possible organic solvents,
Abraham model equation coefficients are available for 2-butanol [40], 2-methyl-1-propanol [40],
3-methyl-1-butanol [40], 1-heptanol [41], 1-octanol [22], 1-decanol [41], diethyl ether [42],
ethylene glycol [43], 1,2-propylene glycol [17], tributyl phosphate [16], butanone [44], cyclohex-
anone [44], propylene carbonate [43], methyl acetate [45], butyl acetate [45], 2-methoxyethanol
[25], 2-ethoxyethanol [46], 2-propoxyethanol [47], 2-isopropoxyethanol [47] and 2-butyoxyetha-
nol [48]. Calculated solute descriptors can also be used to estimate log P values for sorbic acid in
both water-polar organic solvent and water-non-polar solvent partitioning systems, which might
be needed to design practical extraction processes. While carboxylic acids do dimerise in non-
polar alkane and alkylbenzene solvents, it might be possible to perform extractions at sufficiently
low sorbic acid concentrations where dimerisation is minimal.
Acknowledgements
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. Melissa Y. Horton and
Elizabeth Higgins thank the University of North Texas’s Texas Academy of Math and Science (TAMS) program
for a summer research award. Donavyn Calhoon, Kyle Gillispie, Febronia Khalil, and Randall Williams thank
the US Department of Education for support provided to them under the Upward Bound Math and Science
Program.
Disclosure statement
No potential conflict of interest was reported by the authors.
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molliq.2015.05.037
PHYSICS AND CHEMISTRY OF LIQUIDS 9
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Physics and Chemistry of Liquids
An International Journal
ISSN: 0031-9104 (Print) 1029-0451 (Online) Journal homepage: http://www.tandfonline.com/loi/gpch20
Solubility of sorbic acid in organic mono-solvents:
calculation of Abraham model solute descriptors
from measured solubility data
Maribel Barrera, Erin Hart, Melissa Y. Horton, Elizabeth Higgins, Sarah
Cheeran, Grace E. Little, Hunter Singleton, Donavyn Calhoon, Kyle Gillispie,
Febronia Khalil, Randall Williams, William E. Acree Jr. & Michael H. Abraham
To cite this article: Maribel Barrera, Erin Hart, Melissa Y. Horton, Elizabeth Higgins, Sarah
Cheeran, Grace E. Little, Hunter Singleton, Donavyn Calhoon, Kyle Gillispie, Febronia Khalil,
Randall Williams, William E. Acree Jr. & Michael H. Abraham (2016): Solubility of sorbic acid in
organic mono-solvents: calculation of Abraham model solute descriptors from measured solubility
data, Physics and Chemistry of Liquids, DOI: 10.1080/00319104.2016.1260715
To link to this article: http://dx.doi.org/10.1080/00319104.2016.1260715
Published online: 28 Nov 2016.
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