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Determination of Abraham model solute descriptors and preferential solvation from measured solubilities for 4 nitropyrazole dissolved in binary
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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
Determination of Abraham model solute
descriptors and preferential solvation from
measured solubilities for 4-nitropyrazole dissolved
in 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 from
measured 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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3. 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 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 ek Á E þ sk Á S þ ak Á A þ bk Á B þ lk Á 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. 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 solvent
properties 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 units
of (cm3
mol−1
)/10, S quantifies the dipolarity/polarisability 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. Calculation of solute descriptors is relatively straightforward and involves setting up a
series of Abraham model expressions, Equations (1) and (2), to solve simultaneously where all of
the molar solubilities and solvent properties have been substituted into the respective Abraham
model expressions. In the present case, we will calculate the solute descriptors for 4-nitropyrazole
from the published solubility data reported by Wu and coworkers [14]. The authors measured the
solubility 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 representations
given by Wu et al. [14]:
ln XS;organic ¼ À5:584 þ 2:933 wmeoh þ 8:710 wmeoh
2
À 16:40 wmeoh
3
þ 7:636 wmeoh
4
; (3)
ln XS;organic ¼ À5:601 þ 8:537 wetoh À 4:749 wetoh
2
À 5:157 wetoh
3
þ 4:064 wetoh
4
; (4)
where wmeoh and wetoh are the mass fraction compositions of methanol and ethanol in the binary
solvent mixture calculated as if the solute were not present. The calculated mole fraction
solubilities are inverted into molar solubilities, CS,organic, by dividing XS,organic by the ideal
molar volume of the saturated solution:
CS;organic
exp
% XS;organic
exp
= XS;organic
exp
VSolute þ 1 À XS;organic
exp
À Á
VSolvent
 Ã
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 of
nitrobenzene − molar volume of benzene. Counting the solubilities of 4-nitropyrazole in neat
methanol, ethanol, and acetonitrile, we have 22 log CS,organic/CS,water mathematical equations to
use in the solute descriptor calculations. An experimental value of log CS,water = −0.687, calculated
from the mole fraction solubility determined by Wu et al., is used to compute the logarithm of the
molar solubility ratios of CS,organic/CS,water.
2 W. E. ACREE ET AL.
5. 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 are
not 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 as
part of the solute descriptor computations. 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; (6)
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; (7)
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):
log Kw ¼ À0:994 þ 0:577 E þ 2:549 S þ 3:813 A þ 4:841 B À 0:869 V; (8)
log Kw ¼ À1:271 þ 0:822 E þ 2:743 S þ 3:904 A þ 4:814 B À 0:213 L; (9)
are also available for use in the solute descriptor calculations. Abraham model correlations for
water-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 determined
by Wu and coworkers [14], and from a predicted water-to-1-octanol partition coefficients taken
from ChemSpider [15]. The number of mathematical expressions, and the chemical diversity of
the 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 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 = 0.7105
and E = 0.983. The 30 equations were solved simultaneously using Microsoft Solver software to
yield 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. Individual
standard 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 0.858
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
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.
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.
6. Unlike many of the strictly empirical mathematical correlations that are given in published
solubility studies the Abraham solvation parameter model does enable one to make solubility
predictions 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 equation
coefficients 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 known
values 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 experimental
measurements were not performed. Also included are the predictions for 4-nitropyrazole dissolved
in methanol, ethanol, acetonitrile, binary aqueous-methanol, and aqueous-ethanol solvent mixtures,
along with the experimental data expressed as log CS,organic. We elected to make predictions based only
on Equation (1) because our calculated values of L and log CS,gas were based on only experimental data
for pyrazole dissolved in three neat organic solvents (methanol, ethanol, and acetonitrile) and an
estimated 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 xL
1;3 À x1 ¼ Àδx2;3; (10)
where xL
1;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 of
4-nitropyrazole, CS,organic, in organic solvents and in binary
aqueous-methanol and aqueous-ethanol solvent mixtures at
298.15 K.
Organic solvent/solvent mixture log CS,organic
Methanol 0.193
Ethanol −0.034
Acetonitrile 0.006
10% Methanol + 90% Watera
−0.567
20% Methanol + 80% Water −0.419
30% Methanol + 70% Water −0.259
40% Methanol + 60% Water −0.105
50% Methanol + 50% Water −0.023
60% Methanol + 40% Water 0.125
70% Methanol + 30% Water 0.183
80% Methanol + 20% Water 0.202
90% Methanol + 10% Water 0.193
95% Methanol + 5% Water 0.178
10% Ethanol + 90% Waterb
−0.522
20% Ethanol + 80% Water −0.351
30% Ethanol + 70% Water −0.188
40% Ethanol + 60% Water −0.040
50% Ethanol + 50% Water 0.082
60% Ethanol + 40% Water 0.168
70% Ethanol + 30% Water 0.204
80% Ethanol + 20% Water 0.178
90% Ethanol + 10% Water 0.085
95% 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 mixtures
are expressed in terms of volume per cents.
PHYSICS AND CHEMISTRY OF LIQUIDS 5
7. Table 3. Predicted molar solubilities of 4-nitropyrazole in organic solvents at 298.15 K based on the Abraham solvation
parameter model.
Solvent log Cexp
S;organic log ðCS;organic=CS;waterÞeq 1
log Ceq 1
S;organic
Hexane −2.824 −3.511
Heptane −2.835 −3.522
Octane −2.848 −3.535
Benzene −0.955 −1.642
Toluene −1.048 −1.735
p-Xylene −1.215 −1.902
Chlorobenzene −1.011 −1.698
Carbon Tetrachloride −1.906 −2.593
Chloroform −0.631 −1.318
Dichloromethane −0.416 −1.103
Methanol 0.193 0.939 0.252
Ethanol −0.034 0.705 0.018
1-Propanol 0.539 −0.148
1-Butanol 0.427 −0.260
1-Pentanol 0.333 −0.354
1-Hexanol 0.289 −0.398
1-Heptanol 0.226 −0.461
1-Octanol 0.229 −0.458
1-Decanol 0.023 −0.664
2-Propanol 0.526 −0.161
2-Butanol 0.444 −0.243
2-Methyl-1-propanol 0.311 −0.376
2-Methyl-2-propanol 0.526 −0.161
2-Pentanol 0.242 −0.445
3-Methyl-1-butanol 0.158 −0.529
Diisopropyl ether −0.341 −1.028
Tetrahydrofuran 1.110 0.423
1,4-Dioxane 1.098 0.411
Acetone 1.005 0.318
N,N-Dimethylformamide 1.716 1.029
Methyl acetate 0.733 0.046
Ethyl acetate 0.615 −0.072
Butyl acetate 0.393 −0.294
Acetonitrile 0.632 −0.055
Propylene carbonate 0.806 0.119
2-Methoxyethanol 1.296 0.609
2-Ethoxyethanol 1.116 0.429
2-Propoxyethanol 0.857 0.170
2-Isopropoxyethanol 0.923 0.236
2-Butoxyethanol 0.678 −0.009
10:90 MeOH + Watera
−0.567 0.072 −0.615
20:80 MeOH + Water −0.419 0.190 −0.497
30:70 MeOH + Water −0.259 0.325 −0.362
40:60 MeOH + Water −0.105 0.460 −0.227
50:50 MeOH +Water −0.023 0.596 −0.091
60:40 MeOH + Water 0.125 0.726 0.039
70:30 MeOH + Water 0.183 0.850 0.163
80:20 MeOH + Water 0.202 0.949 0.262
90:10 MeOH + Water 0.193 1.002 0.315
95:5 MeOH + Water 0.178 1.013 0.326
10:90 EtOH + Waterb
−0.522 0.026 −0.661
20:80 EtOH + Water −0.351 0.129 −0.558
30:70 EtOH + Water −0.188 0.278 −0.409
40:60 EtOH + Water −0.040 0.452 −0.235
50:50 EtOH +Water 0.082 0.612 −0.075
60:40 EtOH + Water 0.168 0.759 0.072
70:30 EtOH + Water 0.204 0.878 0.191
80:20 EtOH + Water 0.178 0.946 0.259
90:10 EtOH + Water 0.085 0.957 0.270
95:5 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.
8. parameter is < 0 the solute is preferentially solvated by water (2). Values of δx1,3 are obtainable
from the inverse Kirkwood–Buff integrals for the individual solvent components analysed in
terms of some thermodynamic quantities as shown in the following equations [20–22]:
δx1;3 ¼
x1x2 G1;3 À G2;3
À Á
x1G1;3 þ x2G2;3 þ Vcor
; (11)
with,
G1;3 ¼ RTκT À V3 þ x2V2D=Q; (12)
G2;3 ¼ RTκT À V3 þ x1V1D=Q; (13)
Vcor ¼ 2522:5 r3 þ 0:1363 xL
1;3V1 þ xL
2;3V2
1=3
À 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 of
the solvents in the mixtures, similarly, V3 is the partial molar volume of 4-nitropyrazole in these
mixtures. The function D (Equation (15)) is the derivative of the standard molar Gibbs energies of
transfer of 4-nitropyrazole from neat water (1) to cosolvent (1) + water (2) mixtures with respect
to the solvent composition. The function Q (Equation (16)) involves the second derivative of the
excess molar Gibbs energy of mixing of the two solvents (GExc
1þ2) with respect to the water
proportion in the mixtures [7,8]. Vcor is the correlation volume and r3 is the molecular radius
of 4-nitropyrazole calculated by means of Equation (17) with NAv as the Avogadro’s number.
D ¼
@ΔtrGo
3;2!1þ2
@x1
T;p
; (15)
Q ¼ RT þ x1x2
@2
GExc
1þ2
@x2
2
T;p
; (16)
r3 ¼
3 Á 1021
V3
4πNAv
1=3
: (17)
Definitive correlation volume requires iteration because it depends on the local mole fractions
around the solute. It is done by replacing δx1,3 in the Equation (10) to calculate xL
1;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 the
mole fraction drug solubility data reported by Wu et al. [14], by using the following expression:
ΔtrGo
3;2!1þ2 ¼ RT ln
x3;2
x3;1þ2
; (18)
ΔtrGo
3;2!1þ2 values were correlated according to polynomial presented as Equation (19). The
obtained coefficients are presented in Table 4.
ΔtrGo
3;2!1þ2 ¼ a þ bx1 þ cx2
1 þ dx3
1 þ ex4
1: (19)
Thus, D values reported in Tables 5–7 were calculated from the first derivative of the
polynomial 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
9. literature [23]. On the other hand, for acetonitrile (1) + water (2) mixtures, the values of Q were
calculated from excess Gibbs energies (expressed in J mol−1
), which were in turn, calculated at
298.15 K, respectively, from Equation (20), as described by Marcus [20]:
GExc
1þ2 ¼ x1ð1 À x1Þ 5253 À 639ð1 À 2x1Þ þ 1316ð1 À 2x1Þ2Â Ã
: (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 0.9985
EtOH + W 0.00 −21.14 11.70 12.85 −10.09 0.9989
ACN + 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 at
298.15 K.
x1
a
D/kJ mol−1
G1,3/cm3
mol−1
G2,3/cm3
mol−1
Vcor/cm3
mol−1
100 δx1,3
0.00 −7.25 −126.4 −73.5 497 0.00
0.05 −9.12 −135.8 −80.1 511 −0.62
0.10 −10.43 −141.9 −89.1 526 −1.10
0.15 −11.25 −145.4 −100.0 541 −1.34
0.20 −11.63 −146.7 −112.2 557 −1.26
0.25 −11.63 −145.7 −125.2 575 −0.86
0.30 −11.29 −142.5 −138.1 594 −0.20
0.35 −10.70 −137.2 −149.7 613 0.61
0.40 −9.88 −129.9 −158.6 632 1.42
0.45 −8.92 −121.1 −163.5 652 2.07
0.50 −7.85 −111.6 −163.5 670 2.44
0.55 −6.74 −102.2 −158.6 687 2.49
0.60 −5.65 −93.7 −149.6 704 2.28
0.65 −4.63 −86.7 −138.4 720 1.91
0.70 −3.73 −81.5 −126.9 737 1.49
0.75 −3.03 −77.8 −117.0 753 1.10
0.80 −2.56 −75.6 −110.2 770 0.81
0.85 −2.39 −74.2 −107.9 787 0.61
0.90 −2.58 −73.3 −111.1 805 0.47
0.95 −3.18 −72.5 −121.5 823 0.31
1.00 −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.
10. For this binary system, the RTκT values were calculated by assuming additive mixing with the
reported 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 the
reported 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 at
298.15 K.
x1
a
D/kJ mol−1
G1,3/cm3
mol−1
G2,3/cm3
mol−1
Vcor/cm3
mol−1
100 δx1,3
0.00 −21.14 −227.6 −73.5 497 0.00
0.05 −19.88 −226.9 −97.4 518 −1.49
0.10 −18.45 −219.8 −122.5 543 −2.13
0.15 −16.90 −207.8 −146.3 574 −1.87
0.20 −15.24 −192.6 −166.7 609 −0.95
0.25 −13.51 −176.0 −182.5 646 0.26
0.30 −11.74 −159.4 −193.3 682 1.43
0.35 −9.96 −143.6 −198.9 717 2.34
0.40 −8.19 −129.1 −199.3 750 2.91
0.45 −6.48 −116.0 −194.2 780 3.11
0.50 −4.85 −104.2 −183.0 809 2.96
0.55 −3.32 −93.8 −164.6 835 2.47
0.60 −1.94 −84.5 −137.7 860 1.69
0.65 −0.73 −76.7 −101.7 884 0.71
0.70 0.28 −70.7 −59.0 907 −0.29
0.75 1.06 −67.3 −17.8 931 −1.06
0.80 1.58 −66.8 8.8 959 −1.33
0.85 1.81 −68.1 11.8 989 −1.09
0.90 1.72 −70.0 −5.6 1020 −0.61
0.95 1.27 −71.3 −33.0 1051 −0.19
1.00 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 at
298.15 K.
x1
a
D/kJ
mol−1
Q/kJ
mol−1
RT κT/cm3
mol−1
V1/cm3
mol−1
V2/cm3
mol−1
G1,3/cm3
mol−1
G2,3/cm3
mol−1
Vcor/cm3
mol−1
100
δx1,3
0.00 −37.20 2.479 1.133 49.46 18.07 −344.7 −73.5 497 0.00
0.05 −31.16 1.661 1.209 50.01 17.99 −394.0 −120.3 504 −3.52
0.10 −25.84 1.137 1.285 50.56 17.94 −440.4 −188.2 508 −7.70
0.15 −21.17 0.830 1.361 51.03 17.88 −460.6 −268.4 518 −11.09
0.20 −17.12 0.677 1.437 51.44 17.79 −432.8 −333.2 562 −7.63
0.25 −13.62 0.622 1.513 51.79 17.69 −363.9 −356.9 626 −0.49
0.30 −10.64 0.617 1.589 52.08 17.58 −285.3 −342.5 672 3.46
0.35 −8.11 0.626 1.665 52.32 17.46 −220.0 −310.1 705 4.81
0.40 −5.98 0.621 1.741 52.52 17.35 −173.0 −274.9 732 4.91
0.45 −4.20 0.586 1.817 52.67 17.24 −140.7 −242.7 756 4.51
0.50 −2.72 0.510 1.893 52.78 17.13 −118.4 −213.4 778 3.88
0.55 −1.49 0.396 1.969 52.86 17.04 −101.5 −182.0 799 3.01
0.60 −0.45 0.253 2.045 52.91 16.97 −84.7 −129.4 817 1.50
0.65 0.44 0.102 2.121 52.94 16.93 −47.2 74.6 818 −3.41
0.70 1.24 −0.027 2.196 52.95 16.91 −301.8 −1748.4 984 122.53
0.75 2.00 −0.097 2.272 52.95 16.92 −159.3 −888.7 985 21.27
0.80 2.77 −0.059 2.348 52.93 16.97 −232.5 −2072.1 1097 59.33
0.85 3.61 0.146 2.424 52.91 17.06 −9.0 1039.1 870 −13.13
0.90 4.56 0.584 2.500 52.89 17.20 −58.7 299.5 941 −3.51
0.95 5.68 1.333 2.576 52.88 17.39 −68.3 142.1 976 −1.09
1.00 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
11. V1 ¼ V þ x2
dV
dx1
; (21)
V2 ¼ V À x1
dV
dx1
: (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 this
communication (75.7 cm3
mol−1
). G1,3 and G2,3 values shown in Tables 5–7 are negative in
almost all cases indicating that 4-nitropyrazole exhibits affinity for both cosolvent and water in
the 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 using
Equations (10), (11), and (14) to obtain the values reported in Tables 5–7. These tables also
show 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 all
the 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 for
ethanol (1) + water (2), and x1 = 0.26 for acetonitrile (1) + water (2) mixtures. Maximum negative
values 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 (with
δx1,3 = −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 32.0
Ring closure, 5 atoms 1 1.05 16.0
Conj. double bond in ring 2 2 × 1.67 = 3.34 2 × −2.2 = −4.4
Σ ΔU° = 52.78 Σ V = 74.6
δ3 = (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.
12. In methanol (1) + water (2) mixtures with composition 0.31 x1 1.00, the δx1,3 values are
positive indicating preferential solvation of 4-nitropyrazole by this alcohol. The cosolvent action
to increase the solute solubility could be associated to the breaking of the ordered structure of
water around the non-polar moieties of 4-nitropyrazole which increases the solvation of this
solute exhibiting maximum value in x1 = 0.55 (δx1,3 = 2.49 × 10−2
. It is conjecturable that in
0.31 x1 1.00 region this solute is acting as Lewis acid with methanol molecules because this
cosolvent is more basic than water as described by their Kamlet–Taft hydrogen bond acceptor
parameters: β = 0.66 and 0.47 for water [24,28]. In ethanol (1) + water (2) mixtures with
0.24 x1 0.68 positive δx1,3 values are observed but with 0.68 x1 1.00 negative δx1,3 values
are observed again. This is because the maximum solubility of 4-nitropyrazole is observed in a
mixture instead of neat ethanol. In this last region (0.68 x1 1.00), where the solute is
preferentially solvated by water, this compound could be acting mainly as a Lewis base in front
to water because the Kamlet–Taft hydrogen bond donor parameters are, α = 1.17 for water and
0.86 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-rich
mixtures is erratic because some extreme positive-negative-positive jumps are observed even
reaching δx1,3 values higher than 1.22 which is not coherent. This anomalous behaviour could
be a consequence of the negative Q values observed in these mixtures regarding the highly positive
excess Gibbs energy of mixing. Similar behaviours have been reported with other compounds in
different 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 region
0.62 x1 1.00, the δx1,3 negative values could also be attributed to acid behaviour of this solute
in front to water as described previously for ethanol (1) + water (2) mixtures.
In conclusion, further numerical analyses for modelling the solubility and preferential solvation of
4-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.
ORCID
Fleming Martinez http://orcid.org/0000-0002-4008-7273
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12 W. E. ACREE ET AL.
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Determination of Abraham model solute
descriptors and preferential solvation from
measured solubilities for 4-nitropyrazole dissolved
in 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 from
measured 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 and
preferential solvation from measured solubilities for
4-nitropyrazole dissolved in binary aqueous-organic solvent
mixtures
William E. Acree Jr.a
, Ashley M. Ramireza
, Sarah Cheerana
and Fleming Martinez b
a
Department of Chemistry, University of North Texas, Denton, TX, USA; b
Grupo de Investigaciones Farmacéutico-
Fisicoquímicas, Departamento de Farmacia, Facultad de Ciencias, Universidad Nacional de Colombia, Bogotá D.C.,
Colombia
ABSTRACT
Abraham model solute descriptors are determined for 4-nitropyrazole
based on published solubility data for 4-nitropyrazole dissolved in binary
aqueous-methanol and aqueous-ethanol solvent mixtures at 298.15 K.
The calculated solute descriptors enable the solubility of 4-nitropyrazole
to be estimated in more than 80 different organic solvents. Also calcu-
lated from the published solubility data are the preferential solvation
parameters, obtained from the inverse Kirkwood–Buff integrals, for
describing the solvent distribution around the dissolved 4-nitropyrazole
solute molecule.
ARTICLE HISTORY
Received 12 September 2016
Accepted 16 October 2016
KEYWORDS
4-Nitropyrazole solubility;
Abraham model solute
descriptors; preferential
solvation; inverse Kirkwood–
Buff integrals
Introduction
Solubility studies can provide valuable information regarding preferential solvation and solute–solvent
interactions that can exploited in designing new synthetic methods and chemical separations. Published
studies have focused for the most part on measuring the solubility of crystalline nonelectrolyte solutes in
a few select organic solvents or binary aqueous-organic solvents at several temperatures for purposes of
providing needed solubility data for commercial manufacturing processes. The range of organic solvents
selected for study is often very limited in terms of chemical diversity, and there is very little rationale
given for why the particular solvent sets were selected. The measured solubility data is described with
mathematical expressions that allow journal readers to interpolate values at temperatures and/or binary
solvent compositions between experimental data points. The mathematical expressions may be semi-
theoretical or strictly empirical in nature. Little discussion is provided regarding how readers might
utilise the measured data to make solubility predictions in additional organic solvents or ascertain the
local solvent composition in the immediate vicinity of the dissolved non-electrolyte solute. In the
present commentary, we give illustrational examples showing how to interpret the measured solubility
data so that one can make solubility predictions in additional organic solvents and can calculate the
preferential 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 Abraham
solvation 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, 2016
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