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Physics and Chemistry of LiquidsAn International Journal

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Determination of Abraham model solutedescriptors and preferential solvation frommeasured solubilities for 4-nitropyrazole dissolvedin binary aqueous-organic solvent mixtures

William E. Acree Jr., Ashley M. Ramirez, Sarah Cheeran & Fleming Martinez

To cite this article: William E. Acree Jr., Ashley M. Ramirez, Sarah Cheeran & Fleming Martinez(2016): Determination of Abraham model solute descriptors and preferential solvation frommeasured solubilities for 4-nitropyrazole dissolved in binary aqueous-organic solvent mixtures,Physics and Chemistry of Liquids, DOI: 10.1080/00319104.2016.1250272

To link to this article: http://dx.doi.org/10.1080/00319104.2016.1250272

Published online: 04 Nov 2016.

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Determination of Abraham model solute descriptors andpreferential solvation from measured solubilities for4-nitropyrazole dissolved in binary aqueous-organic solventmixturesWilliam E. Acree Jr.a, Ashley M. Ramireza, Sarah Cheerana and Fleming Martinez b

aDepartment of Chemistry, University of North Texas, Denton, TX, USA; bGrupo de Investigaciones Farmacéutico-Fisicoquímicas, Departamento de Farmacia, Facultad de Ciencias, Universidad Nacional de Colombia, Bogotá D.C.,Colombia

ABSTRACTAbraham model solute descriptors are determined for 4-nitropyrazolebased on published solubility data for 4-nitropyrazole dissolved in binaryaqueous-methanol and aqueous-ethanol solvent mixtures at 298.15 K.The calculated solute descriptors enable the solubility of 4-nitropyrazoleto be estimated in more than 80 different organic solvents. Also calcu-lated from the published solubility data are the preferential solvationparameters, obtained from the inverse Kirkwood–Buff integrals, fordescribing the solvent distribution around the dissolved 4-nitropyrazolesolute molecule.

ARTICLE HISTORYReceived 12 September 2016Accepted 16 October 2016

KEYWORDS4-Nitropyrazole solubility;Abraham model solutedescriptors; preferentialsolvation; inverse Kirkwood–Buff integrals

Introduction

Solubility studies can provide valuable information regarding preferential solvation and solute–solventinteractions that can exploited in designing new synthetic methods and chemical separations. Publishedstudies have focused for themost part onmeasuring the solubility of crystalline nonelectrolyte solutes ina few select organic solvents or binary aqueous-organic solvents at several temperatures for purposes ofproviding needed solubility data for commercial manufacturing processes. The range of organic solventsselected for study is often very limited in terms of chemical diversity, and there is very little rationalegiven for why the particular solvent sets were selected. The measured solubility data is described withmathematical expressions that allow journal readers to interpolate values at temperatures and/or binarysolvent compositions between experimental data points. The mathematical expressions may be semi-theoretical or strictly empirical in nature. Little discussion is provided regarding how readers mightutilise the measured data to make solubility predictions in additional organic solvents or ascertain thelocal solvent composition in the immediate vicinity of the dissolved non-electrolyte solute. In thepresent commentary, we give illustrational examples showing how to interpret the measured solubilitydata so that one can make solubility predictions in additional organic solvents and can calculate thepreferential solvation around the solute molecule.

Solute descriptor calculations and solubility predictions

The method that we are using to make additional solubility measurements is based on the Abrahamsolvation parameter model [1–5] which expresses the logarithms of molar solubility ratios, log CS,

CONTACT William E. Acree, Jr. acree@unt.edu© 2016 Informa UK Limited, trading as Taylor & Francis Group

PHYSICS AND CHEMISTRY OF LIQUIDS, 2016http://dx.doi.org/10.1080/00319104.2016.1250272

organic/CS,water and log CS,organic/CS,gas, in terms of products of solute properties (E, S, A, B, V, and L)and the complimentary solvent properties (cp, ep, sp, ap, bp, vp, ck, ek, sk, ak, bk, and lk):

logðCS;organic=CS;waterÞ ¼ cp þ ep � Eþ sp � Sþ ap � Aþ bp � B þ vp � V; (1)

logðCS;organic=CS;gasÞ ¼ ck þ ek � Eþ sk � Sþ ak � Aþ bk � Bþ lk � L; (2)

where CS,organic is the molar solubility of the solute in the organic solvent or binary solventmixture, CS,water is the solute’s molar solubility in water, and CS,gas is the solute’s gas phaseconcentration at the measurement temperature. The latter concentration can be calculated fromthe solute’s vapour pressure, or can be determined at the time that the solute descriptors arecalculated. Calculation of the solute descriptors is the key to making additional solubility predic-tions, as once the solute descriptors are known they can be combined with the known solventproperties that are readily available in several published papers. Numerical values of cp, ep, sp, ap,bp, vp, ck, ek, sk, ak, bk, and lk have been determined for more than 80 different organic solvents[2,6–10] and for both binary aqueous-methanol [11] and aqueous-ethanol solvent systems [12,13].We have tabulated in Table 1 the numerical values of the equation coefficients (solvent properties)that will be needed in the present study.

The solute properties, called solute descriptors, have been described in detail in earlier pub-lications and are defined as follows: E corresponds to the solute excess molar refractivity in unitsof (cm3 mol−1)/10, S quantifies the dipolarity/polarisability of the solute, A and B measure theoverall 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 coefficientat 298 K. Calculation of solute descriptors is relatively straightforward and involves setting up aseries of Abraham model expressions, Equations (1) and (2), to solve simultaneously where all ofthe molar solubilities and solvent properties have been substituted into the respective Abrahammodel expressions. In the present case, we will calculate the solute descriptors for 4-nitropyrazolefrom the published solubility data reported by Wu and coworkers [14]. The authors measured thesolubility of 4-nitropyrazole in binary aqueous-methanol, aqueous-ethanol, and aqueous-acetoni-trile solvent mixtures from 278.15 K to 318.15 K. We calculate the mole fraction solubilities of 4-nitropyrazole, XS,organic, in aqueous-methanol and aqueous-ethanol mixtures at the solvent com-positions for which we have Abraham model correlations using the mathematical representationsgiven by Wu et al. [14]:

ln XS;organic ¼ �5:584þ 2:933 wmeoh þ 8:710 wmeoh2 � 16:40 wmeoh

3 þ 7:636 wmeoh4; (3)

ln XS;organic ¼ �5:601þ 8:537 wetoh � 4:749 wetoh2 � 5:157 wetoh

3 þ 4:064 wetoh4; (4)

where wmeoh and wetoh are the mass fraction compositions of methanol and ethanol in the binarysolvent mixture calculated as if the solute were not present. The calculated mole fractionsolubilities are inverted into molar solubilities, CS,organic, by dividing XS,organic by the idealmolar volume of the saturated solution:

CS;organicexp � XS;organic

exp= XS;organicexp VSolute þ 1� XS;organic

exp� �

VSolvent� �Þ; (5)

where Vi refers to the molar volume of component i. The molar volume of 4-nitropyrazole,Vsolute = 75.7 cm3 mol−1, was estimated as the molar volume of pyrazole + molar volume ofnitrobenzene − molar volume of benzene. Counting the solubilities of 4-nitropyrazole in neatmethanol, ethanol, and acetonitrile, we have 22 log CS,organic/CS,water mathematical equations touse in the solute descriptor calculations. An experimental value of log CS,water = −0.687, calculatedfrom the mole fraction solubility determined by Wu et al., is used to compute the logarithm of themolar solubility ratios of CS,organic/CS,water.

2 W. E. ACREE ET AL.

Table 1. Coefficients in Equations (1) and (2) for various processes.a

Process/solvent c e s a b v/l

A. Water to solvent: Equation (1)1-Octanol (wet) 0.088 0.562 −1.054 0.034 −3.460 3.814Hexane (wet/dry) 0.333 0.560 −1.710 −3.578 −4.939 4.463Heptane (wet/dry) 0.297 0.634 −1.755 −3.571 −4.946 4.488Octane (wet/dry) 0.241 0.690 −1.769 −3.545 −5.011 4.511Benzene (wet/dry) 0.142 0.464 −0.588 −3.099 −4.625 4.491Toluene (wet/dry) 0.125 0.431 −0.644 −3.002 −4.748 4.524p-Xylene (wet/dry) 0.166 0.477 −0.812 −2.939 −4.874 4.532Chlorobenzene (wet/dry) 0.065 0.831 −0.521 −3.183 −4.700 4.614Carbon tetrachloride (wet/dry) 0.199 0.523 −1.159 −3.560 −4.594 4.618Chloroform (wet/dry) 0.191 0.105 −0.403 −3.112 −3.514 4.395Dichloromethane (wet/dry) 0.319 0.102 −0.187 −3.058 −4.090 4.324Methanol (dry) 0.276 0.334 −0.714 0.243 −3.320 3.549Ethanol (dry) 0.222 0.471 −1.035 0.326 −3.596 3.8571-Propanol (dry) 0.139 0.405 −1.029 0.247 −3.767 3.9862-Propanol (dry) 0.099 0.344 −1.049 0.406 −3.827 4.0331-Butanol (dry) 0.165 0.401 −1.011 0.056 −3.958 4.0441-Pentanol (dry) 0.150 0.536 −1.229 0.141 −3.864 4.0771-Hexanol (dry) 0.115 0.492 −1.164 0.054 −3.978 4.1311-Heptanol (dry) 0.035 0.398 −1.063 0.002 −4.342 4.3171-Octanol (dry) −0.034 0.489 −1.044 −0.024 −4.235 4.2181-Decanol (dry) −0.058 0.616 −1.319 0.026 −4.153 4.2792-Butanol (dry) 0.127 0.253 −0.976 0.158 −3.882 4.1142-Methyl-1-propanol (dry) 0.188 0.354 −1.127 0.016 −3.568 3.9862-Methyl-2-propanol (dry) 0.211 0.171 −0.947 0.331 −4.085 4.1092-Pentanol (dry) 0.115 0.455 −1.331 0.206 −3.745 4.2013-Methyl-1-butanol (dry) 0.073 0.360 −1.273 0.090 −3.770 4.273Diisopropyl ether (dry) 0.181 0.285 −0.954 −0.956 −5.077 4.542Tetrahydrofuran (dry) 0.223 0.363 −0.384 −0.238 −4.932 4.4501,4-Dioxane (dry) 0.123 0.347 −0.033 −0.582 −4.810 4.110Acetone (dry) 0.313 0.312 −0.121 −0.608 −4.753 3.942Methyl acetate (dry) 0.351 0.223 −0.150 −1.035 −4.527 3.972Ethyl acetate (dry) 0.328 0.369 −0.446 −0.700 −4.904 4.150Butyl acetate (dry) 0.248 0.356 −0.501 −0.867 −4.973 4.281Acetonitrile (dry) 0.413 0.077 0.326 −1.566 −4.391 3.364Propylene carbonate (dry) 0.004 0.168 0.504 −1.283 −4.407 3.4212-Methoxyethanol (dry) 0.175 0.326 −0.140 0.000 −4.086 3.6302-Ethoxyethanol (dry) 0.133 0.392 −0.419 0.125 −4.200 3.8882-Propoxyethanol (dry) 0.053 0.419 −0.569 0.000 −4.327 4.0952-Isopropoxyethanol (dry) 0.107 0.391 −0.525 0.071 −4.439 4.0512-Butoxyethanol (dry) −0.055 0.377 −0.607 −0.080 −4.371 4.23410% Ethanol + 90% Waterb −0.173 −0.023 −0.001 0.065 −0.372 0.45420% Ethanol + 80% Water −0.252 0.043 −0.040 0.096 −0.823 0.91630% Ethanol + 70% Water −0.269 0.107 −0.098 0.133 −1.316 1.41440% Ethanol + 60% Water −0.221 0.131 −0.159 0.171 −1.809 1.91850% Ethanol + 50% Water −0.142 0.124 −0.252 0.251 −2.275 2.41560% Ethanol + 40% Water −0.040 0.138 −0.335 0.293 −2.675 2.81270% Ethanol + 30% Water 0.063 0.085 −0.368 0.311 −2.936 3.10280% Ethanol + 20% Water 0.172 0.175 −0.463 0.260 −3.212 3.32390% Ethanol + 10% Water 0.243 0.213 −0.575 0.262 −3.450 3.54595% Ethanol + 5% Water 0.239 0.328 −0.795 0.294 −3.514 3.69710% Methanol + 90% Waterc 0.012 0.072 −0.081 0.026 −0.249 0.26620% Methanol + 80% Water 0.022 0.142 −0.138 0.088 −0.574 0.55930% Methanol + 70% Water 0.016 0.187 −0.172 0.165 −0.953 0.89840% Methanol + 60% Water 0.020 0.222 −0.205 0.218 −1.329 1.25950% Methanol + 50% Water 0.023 0.223 −0.222 0.264 −1.747 1.66260% Methanol + 40% Water 0.053 0.207 −0.238 0.272 −2.157 2.07370% Methanol + 30% Water 0.098 0.192 −0.260 0.266 −2.558 2.47480% Methanol + 20% Water 0.172 0.197 −0.319 0.241 −2.912 2.84290% Methanol + 10% Water 0.258 0.250 −0.452 0.229 −3.206 3.17595% Methanol + 5% Water 0.270 0.278 −0.520 0.230 −3.368 3.365(Gas to water) −0.994 0.577 2.549 3.813 4.841 −0.869

(Continued )

PHYSICS AND CHEMISTRY OF LIQUIDS 3

An additional three log (CS,organic/CS,gas) equations are available from the solubility of 4-nitropyrazole in neat methanol, ethanol, and acetonitrile. Log (CS,organic/CS,gas) equations arenot available for the two binary aqueous-methanol and aqueous-ethanol solvent systems.Inclusion of the three log (CS,organic/CS,gas) equations introduces one additional solute descriptor,L, and the molar concentration of the solute in the gas phase, CS,gas, which must be calculated aspart of the solute descriptor computations. Two practical water-to-octanol partition coefficientequations:

log P wet octanolð Þ ¼ 0:088þ 0:562 E � 1:054 S þ 0:034 A� 3:460 B þ 3:814 V; (6)

log K wet octanolð Þ ¼ � 0:198þ 0:002 E þ 0:709 S þ 3:519 A þ 1:429 B þ 0:858 L; (7)

where log K(wet octanol) = log P(wet octanol) + log CS,water − log CS,gas, and two more equationsdescribing the logarithm of the gas-to-water partition coefficient (log Kw):

log Kw ¼ �0:994þ 0:577 E þ 2:549 Sþ 3:813 A þ 4:841 B � 0:869 V; (8)

log Kw ¼ �1:271 þ 0:822 E þ 2:743 Sþ 3:904 Aþ 4:814 B � 0:213 L; (9)

are also available for use in the solute descriptor calculations. Abraham model correlations forwater-to-organic solvent partition coefficients, P, and gas-to-organic solvent partition coefficients,K, have the same mathematical form as Abraham model correlations for solubility ratios. In total,we have been able to assemble 28 mathematical expressions from the solubility data determinedby Wu and coworkers [14], and from a predicted water-to-1-octanol partition coefficients takenfrom ChemSpider [15]. The number of mathematical expressions, and the chemical diversity ofthe solvents studied, is more sufficient for calculating the solute descriptors of 4-nitropyrazole.

There are six solute descriptors and log CS,gas to be calculated from the experimental log CS,

organic and log P values tabulated in Table 2. Two of the six solute descriptors can be calculatedfrom molecular structure considerations. The McGowan characteristic volume, V, can becomputed from the molecular structure, atomic sizes and number of bonds as describedelsewhere [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 (solidsolute) for the solute’s refractive index. The refractive index of solid solutes can be estimatedusing the (free) ACD software [19]. The values of V and E that we calculate are V = 0.7105and E = 0.983. The 30 equations were solved simultaneously using Microsoft Solver software toyield numerical values of: E = 0.983; S = 1.507; A = 0.672; B = 0.384; V = 0.7105; L = 4.454;and log CS,gas = −7.900 with the overall standard error being SE = 0.119 log units. Individualstandard errors are SE = 0.122 and SE = 0.114 for the 25 calculated and observed log (P or CS,

organic/CS,water) values and the five calculated and observed log (K or CS,organic/CS,gas) values,respectively.

Table1. (Continued).

Process/solvent c e s a b v/l

B. Gas to solvent: Equation (2)1-Octanol (wet) −0.198 0.002 0.709 3.519 1.429 0.858Methanol (dry) −0.039 −0.338 1.317 3.826 1.396 0.973Ethanol (dry) 0.017 −0.232 0.867 3.894 1.192 0.846Acetonitrile (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 (CSsat/CW

sat) and log (CSsat/CG) for all of the correlations, except for the one water-to-octanol

partition coefficient.b The compositions in the binary aqueous-ethanol solvent mixtures are given in terms of volume per cents.c The compositions in the binary aqueous-methanol solvent mixtures are given in terms of volume per cents.

4 W. E. ACREE ET AL.

Unlike many of the strictly empirical mathematical correlations that are given in publishedsolubility studies the Abraham solvation parameter model does enable one to make solubilitypredictions for the solute in additional organic solvents. The calculated numerical values of E, S, A,B, V, and L of the solute are simply substituted into Equations (1) and (2) along with the equationcoefficients for any organic solvents that one wishes to consider. The predicted values log (P or CS,

organic/CS,water) and log (K or CS,organic/CS,gas) are converted into molar solubilities using the knownvalues of log CS,water and log CS,gas. We have given in Table 3 predicted values of log (CS,organic/CS,water)and log CS,organic for 4-nitropyrazole dissolved in 38 additional organic for which experimentalmeasurements were not performed. Also included are the predictions for 4-nitropyrazole dissolvedin methanol, ethanol, acetonitrile, binary aqueous-methanol, and aqueous-ethanol solvent mixtures,along with the experimental data expressed as log CS,organic. We elected tomake predictions based onlyon Equation (1) because our calculated values of L and log CS,gas were based on only experimental datafor pyrazole dissolved in three neat organic solvents (methanol, ethanol, and acetonitrile) and anestimated practical water-to-octanol partition coefficient taken from ChemSpider.

Preferential solvation computations

The preferential solvation parameter of 4-nitropyrazole (compound 3) by the cosolvent (com-pound 1) in cosolvent (1) + water (2) mixtures is defined as [20,21]:

δx1;3 ¼ xL1;3 � x1 ¼ �δx2;3; (10)

where xL1;3 is the local mole fraction of cosolvent (1) in the environment near to 4-nitropyrazole(3). If δx1,3 > 0 then the solute is preferentially solvated by cosolvent (1); on the contrary, if this

Table 2. Logarithms of the experimental molar solubilities of4-nitropyrazole, CS,organic, in organic solvents and in binaryaqueous-methanol and aqueous-ethanol solvent mixtures at298.15 K.

Organic solvent/solvent mixture log CS,organicMethanol 0.193Ethanol −0.034Acetonitrile 0.00610% Methanol + 90% Watera −0.56720% Methanol + 80% Water −0.41930% Methanol + 70% Water −0.25940% Methanol + 60% Water −0.10550% Methanol + 50% Water −0.02360% Methanol + 40% Water 0.12570% Methanol + 30% Water 0.18380% Methanol + 20% Water 0.20290% Methanol + 10% Water 0.19395% Methanol + 5% Water 0.17810% Ethanol + 90% Waterb −0.52220% Ethanol + 80% Water −0.35130% Ethanol + 70% Water −0.18840% Ethanol + 60% Water −0.04050% Ethanol + 50% Water 0.08260% Ethanol + 40% Water 0.16870% Ethanol + 30% Water 0.20480% Ethanol + 20% Water 0.17890% Ethanol + 10% Water 0.08595% Ethanol + 5% Water 0.022

a Compositions in the binary aqueous-methanol solvent mix-tures are expressed in terms of volume per cents.

b Compositions in the binary aqueous-ethanol solvent mixturesare expressed in terms of volume per cents.

PHYSICS AND CHEMISTRY OF LIQUIDS 5

Table 3. Predicted molar solubilities of 4-nitropyrazole in organic solvents at 298.15 K based on the Abraham solvationparameter model.

Solvent log CexpS;organic log ðCS;organic=CS;waterÞeq 1 log Ceq 1S;organic

Hexane −2.824 −3.511Heptane −2.835 −3.522Octane −2.848 −3.535Benzene −0.955 −1.642Toluene −1.048 −1.735p-Xylene −1.215 −1.902Chlorobenzene −1.011 −1.698Carbon Tetrachloride −1.906 −2.593Chloroform −0.631 −1.318Dichloromethane −0.416 −1.103Methanol 0.193 0.939 0.252Ethanol −0.034 0.705 0.0181-Propanol 0.539 −0.1481-Butanol 0.427 −0.2601-Pentanol 0.333 −0.3541-Hexanol 0.289 −0.3981-Heptanol 0.226 −0.4611-Octanol 0.229 −0.4581-Decanol 0.023 −0.6642-Propanol 0.526 −0.1612-Butanol 0.444 −0.2432-Methyl-1-propanol 0.311 −0.3762-Methyl-2-propanol 0.526 −0.1612-Pentanol 0.242 −0.4453-Methyl-1-butanol 0.158 −0.529Diisopropyl ether −0.341 −1.028Tetrahydrofuran 1.110 0.4231,4-Dioxane 1.098 0.411Acetone 1.005 0.318N,N-Dimethylformamide 1.716 1.029Methyl acetate 0.733 0.046Ethyl acetate 0.615 −0.072Butyl acetate 0.393 −0.294Acetonitrile 0.632 −0.055Propylene carbonate 0.806 0.1192-Methoxyethanol 1.296 0.6092-Ethoxyethanol 1.116 0.4292-Propoxyethanol 0.857 0.1702-Isopropoxyethanol 0.923 0.2362-Butoxyethanol 0.678 −0.00910:90 MeOH + Watera −0.567 0.072 −0.61520:80 MeOH + Water −0.419 0.190 −0.49730:70 MeOH + Water −0.259 0.325 −0.36240:60 MeOH + Water −0.105 0.460 −0.22750:50 MeOH +Water −0.023 0.596 −0.09160:40 MeOH + Water 0.125 0.726 0.03970:30 MeOH + Water 0.183 0.850 0.16380:20 MeOH + Water 0.202 0.949 0.26290:10 MeOH + Water 0.193 1.002 0.31595:5 MeOH + Water 0.178 1.013 0.32610:90 EtOH + Waterb −0.522 0.026 −0.66120:80 EtOH + Water −0.351 0.129 −0.55830:70 EtOH + Water −0.188 0.278 −0.40940:60 EtOH + Water −0.040 0.452 −0.23550:50 EtOH +Water 0.082 0.612 −0.07560:40 EtOH + Water 0.168 0.759 0.07270:30 EtOH + Water 0.204 0.878 0.19180:20 EtOH + Water 0.178 0.946 0.25990:10 EtOH + Water 0.085 0.957 0.27095:5 EtOH + Water 0.022 0.840 0.153

a Compositions in the binary aqueous-methanol solvent mixtures are expressed in terms of volume per cents.b Compositions in the binary aqueous-ethanol solvent mixtures are expressed in terms of volume percents.

6 W. E. ACREE ET AL.

parameter is < 0 the solute is preferentially solvated by water (2). Values of δx1,3 are obtainablefrom the inverse Kirkwood–Buff integrals for the individual solvent components analysed interms of some thermodynamic quantities as shown in the following equations [20–22]:

δx1;3 ¼x1x2 G1;3 � G2;3

� �x1G1;3 þ x2G2;3 þ Vcor

; (11)

with,

G1;3 ¼ RTκT � V3 þ x2V2D=Q; (12)

G2;3 ¼ RTκT � V3 þ x1V1D=Q; (13)

Vcor ¼ 2522:5 r3 þ 0:1363 xL1;3V1 þ xL2;3V2

� �1=3� 0:085

� 3

: (14)

As has been previously described [20–22], in these equations κT is the isothermal compressi-bility of the cosolvent (1) + water (2) solvent mixtures, V1 and V2 are the partial molar volumes ofthe solvents in the mixtures, similarly, V3 is the partial molar volume of 4-nitropyrazole in thesemixtures. The function D (Equation (15)) is the derivative of the standard molar Gibbs energies oftransfer of 4-nitropyrazole from neat water (1) to cosolvent (1) + water (2) mixtures with respectto the solvent composition. The function Q (Equation (16)) involves the second derivative of theexcess molar Gibbs energy of mixing of the two solvents (GExc

1þ2) with respect to the waterproportion in the mixtures [7,8]. Vcor is the correlation volume and r3 is the molecular radiusof 4-nitropyrazole calculated by means of Equation (17) with NAv as the Avogadro’s number.

D ¼ @ΔtrGo3;2!1þ2

@x1

� T;p

; (15)

Q ¼ RT þ x1x2@2GExc

1þ2

@x22

� T;p

; (16)

r3 ¼ 3 � 1021V3

4πNAv

� 1=3

: (17)

Definitive correlation volume requires iteration because it depends on the local mole fractionsaround the solute. It is done by replacing δx1,3 in the Equation (10) to calculate xL1;3 until a non-variant value of Vcor is obtained.

Figure 1 shows the Gibbs energy of transfer behaviour of 4-nitropyrazole (3) from neat water(2) to all cosolvent (1) + water (2) mixtures at 298.15 K. These values were calculated from themole fraction drug solubility data reported by Wu et al. [14], by using the following expression:

ΔtrGo3;2!1þ2 ¼ RT ln

x3;2x3;1þ2

� ; (18)

ΔtrGo3;2!1þ2 values were correlated according to polynomial presented as Equation (19). The

obtained coefficients are presented in Table 4.

ΔtrGo3;2!1þ2 ¼ aþ bx1 þ cx21 þ dx31 þ ex41: (19)

Thus, D values reported in Tables 5–7 were calculated from the first derivative of thepolynomial model, solved according to the cosolvent mixtures composition. For methanol (1) +water (2) and ethanol (1) + water (2) mixtures the Q, RTκT, V1 and V2 values were taken from the

PHYSICS AND CHEMISTRY OF LIQUIDS 7

literature [23]. On the other hand, for acetonitrile (1) + water (2) mixtures, the values of Q werecalculated from excess Gibbs energies (expressed in J mol−1), which were in turn, calculated at298.15 K, respectively, from Equation (20), as described by Marcus [20]:

GExc1þ2 ¼ x1ð1� x1Þ 5253� 639ð1� 2x1Þ þ 1316ð1� 2x1Þ2

� �: (20)

Figure 1. Gibbs energy of transfer of 4-nitropyrazole (3) from neat water (2) to cosolvent (1) + water (2) mixtures at 298.15 K.○: methanol (1) + water; □: ethanol (1) + water (2); Δ: acetonitrile (1) + water (2).

Table 4. Equation (19) parameters of 4-nitromethyzole (3) in cosolvent (1) + water (2) mixtures at 298.15 K.

System a a b c d e r2

MeOH + W −0.04 −7.25 −21.62 40.64 −18.92 0.9985EtOH + W 0.00 −21.14 11.70 12.85 −10.09 0.9989ACN + W −0.14 −37.20 64.16 −51.11 17.31 0.9986

a MeOH is methanol, EtOH is ethanol, ACN is acetonitrile, and W is water.

Table 5. Some properties associated to preferential solvation of 4-nitropyrazole (3) in methanol (1) + water (2) mixtures at298.15 K.

x1a D/kJ mol−1 G1,3/cm

3 mol−1 G2,3/cm3 mol−1 Vcor/cm

3 mol−1 100 δx1,30.00 −7.25 −126.4 −73.5 497 0.000.05 −9.12 −135.8 −80.1 511 −0.620.10 −10.43 −141.9 −89.1 526 −1.100.15 −11.25 −145.4 −100.0 541 −1.340.20 −11.63 −146.7 −112.2 557 −1.260.25 −11.63 −145.7 −125.2 575 −0.860.30 −11.29 −142.5 −138.1 594 −0.200.35 −10.70 −137.2 −149.7 613 0.610.40 −9.88 −129.9 −158.6 632 1.420.45 −8.92 −121.1 −163.5 652 2.070.50 −7.85 −111.6 −163.5 670 2.440.55 −6.74 −102.2 −158.6 687 2.490.60 −5.65 −93.7 −149.6 704 2.280.65 −4.63 −86.7 −138.4 720 1.910.70 −3.73 −81.5 −126.9 737 1.490.75 −3.03 −77.8 −117.0 753 1.100.80 −2.56 −75.6 −110.2 770 0.810.85 −2.39 −74.2 −107.9 787 0.610.90 −2.58 −73.3 −111.1 805 0.470.95 −3.18 −72.5 −121.5 823 0.311.00 −4.24 −71.5 −141.3 841 0.00

a x1 is the mole fraction of methanol (1) in the methanol (1) + water (2) mixtures free of 4-nitropyrazole (3).

8 W. E. ACREE ET AL.

For this binary system, the RTκT values were calculated by assuming additive mixing with thereported κT values for acetonitrile (1.070 GPa−1) and water (0.457 GPa−1) at 298.15 K [24].

In similar way, the partial molar volumes of both solvents in the mixtures were calculated from thereported density values of acetonitrile (1) + water (2) mixtures at 298.15 K [25], by using Equations(21) and (22). In these equations, V is the molar volume of the mixtures calculated as V = (x1·M1 +x2·M2)/ρ. Here, M1 is 41.05 g mol−1 for acetonitrile and M2 is 18.02 g mol−1 for water [26].

Table 6. Some properties associated to preferential solvation of 4-nitropyrazole (3) in ethanol (1) + water (2) mixtures at298.15 K.

x1a D/kJ mol−1 G1,3/cm

3 mol−1 G2,3/cm3 mol−1 Vcor/cm

3 mol−1 100 δx1,30.00 −21.14 −227.6 −73.5 497 0.000.05 −19.88 −226.9 −97.4 518 −1.490.10 −18.45 −219.8 −122.5 543 −2.130.15 −16.90 −207.8 −146.3 574 −1.870.20 −15.24 −192.6 −166.7 609 −0.950.25 −13.51 −176.0 −182.5 646 0.260.30 −11.74 −159.4 −193.3 682 1.430.35 −9.96 −143.6 −198.9 717 2.340.40 −8.19 −129.1 −199.3 750 2.910.45 −6.48 −116.0 −194.2 780 3.110.50 −4.85 −104.2 −183.0 809 2.960.55 −3.32 −93.8 −164.6 835 2.470.60 −1.94 −84.5 −137.7 860 1.690.65 −0.73 −76.7 −101.7 884 0.710.70 0.28 −70.7 −59.0 907 −0.290.75 1.06 −67.3 −17.8 931 −1.060.80 1.58 −66.8 8.8 959 −1.330.85 1.81 −68.1 11.8 989 −1.090.90 1.72 −70.0 −5.6 1020 −0.610.95 1.27 −71.3 −33.0 1051 −0.191.00 0.44 −71.7 −61.3 1080 0.00

a x1 is the mole fraction of ethanol (1) in the ethanol (1) + water (2) mixtures free of 4-nitropyrazole (3).

Table 7. Some properties associated to preferential solvation of 4-nitropyrazole (3) in acetonitrile (1) + water (2) mixtures at298.15 K.

x1a

D/kJmol−1

Q/kJmol−1

RT κT/cm3

mol−1V1/cm

3

mol−1V2/cm

3

mol−1G1,3/cm

3

mol−1G2,3/cm

3

mol−1Vcor/cm

3

mol−1100δx1,3

0.00 −37.20 2.479 1.133 49.46 18.07 −344.7 −73.5 497 0.000.05 −31.16 1.661 1.209 50.01 17.99 −394.0 −120.3 504 −3.520.10 −25.84 1.137 1.285 50.56 17.94 −440.4 −188.2 508 −7.700.15 −21.17 0.830 1.361 51.03 17.88 −460.6 −268.4 518 −11.090.20 −17.12 0.677 1.437 51.44 17.79 −432.8 −333.2 562 −7.630.25 −13.62 0.622 1.513 51.79 17.69 −363.9 −356.9 626 −0.490.30 −10.64 0.617 1.589 52.08 17.58 −285.3 −342.5 672 3.460.35 −8.11 0.626 1.665 52.32 17.46 −220.0 −310.1 705 4.810.40 −5.98 0.621 1.741 52.52 17.35 −173.0 −274.9 732 4.910.45 −4.20 0.586 1.817 52.67 17.24 −140.7 −242.7 756 4.510.50 −2.72 0.510 1.893 52.78 17.13 −118.4 −213.4 778 3.880.55 −1.49 0.396 1.969 52.86 17.04 −101.5 −182.0 799 3.010.60 −0.45 0.253 2.045 52.91 16.97 −84.7 −129.4 817 1.500.65 0.44 0.102 2.121 52.94 16.93 −47.2 74.6 818 −3.410.70 1.24 −0.027 2.196 52.95 16.91 −301.8 −1748.4 984 122.530.75 2.00 −0.097 2.272 52.95 16.92 −159.3 −888.7 985 21.270.80 2.77 −0.059 2.348 52.93 16.97 −232.5 −2072.1 1097 59.330.85 3.61 0.146 2.424 52.91 17.06 −9.0 1039.1 870 −13.130.90 4.56 0.584 2.500 52.89 17.20 −58.7 299.5 941 −3.510.95 5.68 1.333 2.576 52.88 17.39 −68.3 142.1 976 −1.091.00 7.03 2.479 2.652 52.87 17.63 −71.9 77.9 1005 0.00

a x1 is the mole fraction of acetonitrile (1) in the acetonitrile (1) + water (2) mixtures free of 4-nitropyrazole (3).

PHYSICS AND CHEMISTRY OF LIQUIDS 9

V1 ¼ V þ x2dVdx1

; (21)

V2 ¼ V � x1dVdx1

: (22)

The Q, RTκT, V1 and V2 values for acetonitrile (1) + water (2) mixtures are shown in Table 7.Molar volume of 4-nitropyrazole (3) was calculated by following the Fedors’ method as

74.6 cm3 mol−1 (Table 8) [27]. This calculated value is similar to that mentioned earlier in thiscommunication (75.7 cm3 mol−1). G1,3 and G2,3 values shown in Tables 5–7 are negative inalmost all cases indicating that 4-nitropyrazole exhibits affinity for both cosolvent and water inthe mixtures. The main exception is with G2,3 in acetonitrile-rich mixtures. Solute radius value(r3) was calculated as 0.309 nm. The correlation volume was iterated three times by usingEquations (10), (11), and (14) to obtain the values reported in Tables 5–7. These tables alsoshow the preferential solvation parameters of 4-nitropyrazole (3) by all the cosolvents (1),δx1,3.

Figure 2 shows that the values of δx1,3 vary non-linearly with the cosolvent (1) proportion in allthe aqueous mixtures. Addition of cosolvent (1) makes negative the δx1,3 values of 4-nitropyrazole(3) from the pure water to the mixture x1 = 0.31 for methanol (1) + water (2), x1 = 0.24 forethanol (1) + water (2), and x1 = 0.26 for acetonitrile (1) + water (2) mixtures. Maximum negativevalues are obtained in the mixture x1 = 0.15 (with δx1,3 = −1.34 × 10−2) for methanol (1) + water(2), x1 = 0.10 (with δx1,3 = −2.13 × 10−2) for ethanol (1) + water (2), and x1 = 0.15 (withδx1,3 = −0.111) for acetonitrile (1) + water (2) mixtures, respectively.

Table 8. Estimation of internal energy, molar volume, and Hildebrand solubility parameter of 4-nitropyrazole by the Fedors’method.

Group or atom Group number ΔU°/kJ mol−1 V/cm3 mol−1

–CH= 2 2 × 4.31 = 8.62 2 × 13.5 = 27.0>C= 1 4.31 −5.5–NH– 1 8.4 4.5–N= 1 11.7 5.0–NO2 aromatic 1 15.36 32.0Ring closure, 5 atoms 1 1.05 16.0Conj. double bond in ring 2 2 × 1.67 = 3.34 2 × −2.2 = −4.4

Σ ΔU° = 52.78 Σ V = 74.6δ3 = (52,780/74.6)1/2 = 26.6 MPa1/2

Figure 2. δx1,3 values of 4-nitropyrazole (3) in cosolvent (1) + water (2) mixtures at 298.15 K. ○: methanol (1) + water; □:ethanol (1) + water (2); Δ: acetonitrile (1) + water (2).

10 W. E. ACREE ET AL.

In methanol (1) + water (2) mixtures with composition 0.31 < x1 < 1.00, the δx1,3 values arepositive indicating preferential solvation of 4-nitropyrazole by this alcohol. The cosolvent actionto increase the solute solubility could be associated to the breaking of the ordered structure ofwater around the non-polar moieties of 4-nitropyrazole which increases the solvation of thissolute exhibiting maximum value in x1 = 0.55 (δx1,3 = 2.49 × 10−2. It is conjecturable that in0.31 < x1 < 1.00 region this solute is acting as Lewis acid with methanol molecules because thiscosolvent is more basic than water as described by their Kamlet–Taft hydrogen bond acceptorparameters: β = 0.66 and 0.47 for water [24,28]. In ethanol (1) + water (2) mixtures with0.24 < x1 < 0.68 positive δx1,3 values are observed but with 0.68 < x1 < 1.00 negative δx1,3 valuesare observed again. This is because the maximum solubility of 4-nitropyrazole is observed in amixture instead of neat ethanol. In this last region (0.68 < x1 < 1.00), where the solute ispreferentially solvated by water, this compound could be acting mainly as a Lewis base in frontto water because the Kamlet–Taft hydrogen bond donor parameters are, α = 1.17 for water and0.86 for ethanol, respectively [24,29], being water more acidic than ethanol.

In the case of acetonitrile (1) + water (2) mixtures, the exhibited behaviour in acetonitrile-richmixtures is erratic because some extreme positive-negative-positive jumps are observed evenreaching δx1,3 values higher than 1.22 which is not coherent. This anomalous behaviour couldbe a consequence of the negative Q values observed in these mixtures regarding the highly positiveexcess Gibbs energy of mixing. Similar behaviours have been reported with other compounds indifferent aqueous solvent mixtures also exhibiting high positive excess Gibbs energies of mixing[30, 31]. However, as a qualitative result for acetonitrile (1) + water (2) mixtures in the region0.62 < x1 < 1.00, the δx1,3 negative values could also be attributed to acid behaviour of this solutein front to water as described previously for ethanol (1) + water (2) mixtures.

In conclusion, further numerical analyses for modelling the solubility and preferential solvation of4-nitropyrazole (3) in several cosolvent (1) + water (2) mixtures were provided. As it is well known,all these analyses are required to understand the molecular events involved in dissolution processes.

Disclosure statement

No potential conflict of interest was reported by the authors.

ORCIDFleming Martinez http://orcid.org/0000-0002-4008-7273

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