Abraham et al.
JOCArticle
other, they formed 45 straight lines that intersected at a point
where all the log K values are -1.1 (with the K values on the
molar scale). This enabled a general hydrogen bond acidity
scale, KHA, to be defined through eq 2, where LB and DB are
coefficients that refer to a given base. The log KHA values were
then converted into a more practical scale through eq 3; addi-
tion of 1.1 ensures that the origin of the scale is now at zero
instead of -1.1, and the factor 4.636 simply gives a convenient
spread of values. Equation 3 represents the definition of the
term RH2, which now forms a scale of solute hydrogen bonding
in 1:1 complexes.
TABLE 1. Coefficients in eq 7 for 1:1 Hydrogen Bond Complexation in
Solvents and the Gas Phasea
solvent
c
m
N
R2
SD
ref
gas phase
-0.870 9.130
-1.100 8.560
-1.252 7.967
-1.120 8.010
-0.954 7.674 430 0.975 0.174
-1.094 7.354 1312 0.991 0.093
23
14
65
12
0.974 0.200 10
0.288 this work
0.878 0.337 this work
perfluorohexane
hexane/heptane
carbon disulfide
cyclohexane
0.982 0.130
12
12
8
tetrachloromethane
tetrachloroethene
o-dichlorobenzene
-1.087 7.382
-1.215 7.204
79
32
94
14
6
0.993 0.107 this work
0.962 0.171 this work
0.957 0.164 this work
0.971 0.145 this work
0.098 this work
1,1,1-trichloroethane -1.098 6.763
log Kiðseries of acids against base BÞ ¼ LB log KH þ DB
chlorobenzene
bromobenzene
1,2-dichloroethane
dichloromethane
benzene
-1.110 6.860
-1.100 6.730
-1.270 6.260
-1.364 6.288
-0.582 5.624
-1.100 4.697
-1.100 4.480
-0.710 2.860
A
ð2Þ
70
97
83
27
14
27
0.940 0.140
12
0.895 0.251 this work
0.905 0.226 this work
0.374 this work
RH ¼ ð1:1 þ log KHAÞ=4:636
ð3Þ
2
chloroform
benzonitrile
octan-1-ol
In exactly the same way,6,7 when various series of log K
values for hydrogen bond bases against 34 hydrogen bond
acids were plotted against each other, all the lines intersected
again at -1.1, and a general scale of solute 1:1 hydrogen
bond basicity was defined through eqs 4 and 5.
0.171 this work
0.948 0.103 this work
aWhere c is fixed at -1.100, no value of R2 can be given.
were available as follows: perfluorohexane,13 hexane or hep-
tane,1,14-18 benzene,1,14-22 benzonitrile,23 chlorobenzene,1,24,25
bromobenzene,1,26 and an updated equation for 1,1,1-trichloro-
ethane.11,27 The coefficients in eq 7 are given in Table 1.
log Kiðseries of bases against acid AÞ ¼ LA log KH þ DA
B
ð4Þ
log K ¼ c þ mRH βH
ð7Þ
2
2
βH ¼ ð1:1 þ log KHBÞ=4:636
3
ð5Þ
2
Finally, the entire series of 1312 equilibrium constants
used to construct eqs 2-5 could be used to obtain an
equation, eq 6, from which it was possible to predict thou-
sands of log K values in tetrachloromethane at 298 K for
various combinations of hydrogen bond acids and hydrogen
bond bases.8
These solvents, such as dichloromethane, trichloro-
methane, tetrachloroethene, and benzene, are all rather
nonpolar. Cook et al.28 have recently obtained values of
the 1:1 equilibrium constant for hydrogen bonding between
the strong hydrogen bond acid, perfluoro-tert-butanol, and
the strong hydrogen bond base, tri-n-butylphosphine oxide,
in a variety of solvents including polar solvents such as
dimethyl sulfoxide and decan-1-ol. Values of K decrease very
considerably from 105 in cyclohexane to 0.68 in DMSO and
to 0.16 in decan-1-ol. Of course, it is impossible to obtain the
coefficients in eq 7 with data on only one acid-base pair, but
the results show that hydrogen bonding becomes increas-
ingly unfavorable as the solvent becomes more polar.
log K ¼ - 1:094ð0:007Þ þ 7:354ð0:019ÞRH βH
ð6Þ
2
2
3
N ¼ 1312, R2 ¼ 0:991, SD ¼ 0:093
In eq 6, N is the number of data points, R is the correlation
coefficient, and SD is the standard deviation. Some time
later, Raevsky et al.9 devised an equivalent scale, but in terms
of Gibbs energies rather than log K values.
Marco et al.10 have obtained an equation of the general type
of eq 6, that is eq 7, for 1:1 complexation in the gas phase, an
equation is known for complexation in 1,1,1-trichloroethane,11
and Abraham and Berthelot12 have used literature data to ob-
tain coefficients in eq 7 for the solvents carbon disulfide, cyclo-
hexane, and 1,2-dichloroethane and we have obtained coeffi-
cients for a number of solvents for which equilibrium constants
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