Hydrogen bonding Part 44 1Thermodynamics of complexation of 3,5-dichlorophenol with ketones and ethers in cyclohexane: The badger-Bauer relationship

Article abstract of DOI:10.1039/a708362i

Equilibrium constants for 1 : 1 hydrogen bond complexation between 3,5-dichioropheno' (DCP) and 17 ketones and 12 ethers in cyclohexane solution have been obtained by an FTIR method that takes into account both diiaerization of the acid and formation of 2 :1 complexes. Enthalpies of complexation for the same ketones and ethers have been determined by a calorimeiric method, leading to values of log K, AG, AH and AS0 for 1 :1 complexation in the 29 systems, as well as log K2 for the 2 :1 complexation between 2 mol of acid and 1 mol of base. For the ketone systems there is very little variation in the three thermodynamic parameters with alkyl substitution, but for the ethers there are systematic variations depending on the alkyl substituent or if the ethers are cyclic. Values of the OH stretching frequency in the DCP complexes with the ketones and ethers in cyclohexane have been obtained. The band shapes for the DCP-ketone complexes are very asymmetric, possibly due to the presence of stereoisomeric complexes, but the VOH band for DCP-ether complexes is symmetric and very suitable for the evaluation of any relationship between v()H and A/f. It is found that for the complexation of DCP with the 12 aliphatic ethers in cyclohexane, there is almost no connection between the calorimetrically determined AH° values and values of AvOH.

Full text of DOI:10.1039/a708362i

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Hydrogen bonding
Part 44¤ Thermodynamics of complexation of 3,5-dichlorophenol with ketones
and ethers in cyclohexane: the Badger–Bauer relationship
Michael H. Abraham,a* David V. Prior,b Ronald A. Schulz,c Je†rey J. Morrisd and
Peter J. Taylord
a Department of Chemistry, University College L ondon, 20 Gordon Street, L ondon, UK W C1H
OAJ
b Department of Chemistry, University of Surrey, Guildford, Surrey, UK GU2 5XH
c Department of Chemical and Process Engineering, University of Surrey, Guildford, Surrey, UK
GU2 5XH
d Zeneca Pharmaceuticals, Mereside Alderly Park, MacclesÐeld, Cheshire, UK SK10 5T G
Equilibrium constants for 1 : 1 hydrogen bond complexation between 3,5-dichlorophenol (DCP) and 17 ketones and 12 ethers in
cyclohexane solution have been obtained by an FTIR method that takes into account both dimerization of the acid and forma-
tion of 2 : 1 complexes. Enthalpies of complexation for the same ketones and ethers have been determined by a calorimetric
method, leading to values of log K, *G¡, *H¡ and *S¡ for 1 : 1 complexation in the 29 systems, as well as log K for the 2 : 1
2
complexation between 2 mol of acid and 1 mol of base. For the ketone systems there is very little variation in the three
thermodynamic parameters with alkyl substitution, but for the ethers there are systematic variations depending on the alkyl
substituent or if the ethers are cyclic.
Values of the OH stretching frequency in the DCP complexes with the ketones and ethers in cyclohexane have been obtained.
The band shapes for the DCPÈketone complexes are very asymmetric, possibly due to the presence of stereoisomeric complexes,
but the l band for DCPÈether complexes is symmetric and very suitable for the evaluation of any relationship between l and
OH
OH
*
H¡. It is found that for the complexation of DCP with the 12 aliphatic ethers in cyclohexane, there is almost no connection
between the calorimetrically determined *H¡ values and values of *lOH .
In 1937, Badger and Bauer1 studied the self-association of a
workers,5h12 but challenged by others,13h16 some of whom
number of compounds and suggested that there was a
maintain that the relationship is family dependent.14h16 In a
detailed study, Joesten and Schaad4 found that the BadgerÈ
Bauer relationship sometimes held reasonably well, but some-
times only very roughly. Kasende and Zeegers-Huyskens17,18
relationship between *l for self-association and the energy
OH
of self-association. The latter was found by indirect methods
such as a comparison of the enthalpy of vaporization of alco-
hols with that of alkanes. In a subsequent paper, the energies
of hydrogen bond formation for 2-chlorophenol and 2-
chloroethanol were obtained from di†erences in energy of the
two molecular conÐgurations, in one of which there is an
observed a linear relationship between *l and *H¡ for a
OH
series of phenols against a given base, although di†erent lines
were obtained when the base was varied, a clear example of
family dependent relationships. Similar observations were
made by Rao et al.19 in an earlier detailed study. More recent-
ly, Goralski20 found an approximate BadgerÈBauer relation-
ship for the complexation of cholesterol with a series of bases,
and suggested that the relationship could be used to estimate
intramolecular hydrogen bond.2 However, the plot of *l vs.
OH
hydrogen bond energy was shown as a curve, and not as a
straight line.2 Over the years, these observations of Badger
and Bauer have been elevated into what appears to be a
physicochemical rule. By 1971, Vinogradov and Linnell3
could state that “A direct relationship between the shift in the
IR stretching frequency *l caused by hydrogen bonding and
the magnitude of [*H¡ was Ðrst suggested by Badger and
BauerÏ, and Joesten and Schaad4 used a similar expression,
even though Badger and Bauer1,2 nowhere mention [*H¡,
and even though their observations were conÐned to self-
association and to intramolecular hydrogen bonds.
further *H¡ values. However, inspection of the *l vs. *H¡
OH
plot shows a small but signiÐcant family dependent relation-
ship. Borisenko et al.21 have shown that the BadgerÈBauer
relationship fails for a series of NH acids against a given base.
On the other hand, Deng et al.22 have actually used a BadgerÈ
Bauer relationship to estimate enthalpies of interaction from
frequency shifts.
One difficulty in assessing the BadgerÈBauer relationship is
that some of the enthalpy data have been obtained through
the temperature variation of hydrogen bond equilibrium con-
stants, the so-called vanÏt Ho† method. This requires not only
very accurate equilibrium constants, but also accurate tem-
perature measurements as well, and it is doubtful if many
reported vanÏt Ho† *H¡ values have errors of less than 0.5
kcal mol~1. A major aim of the present work was to deter-
mine thermodynamic parameters for hydrogen bond complex-
ation, using FTIR methods to obtain equilibrium constants,
and calorimetry to obtain *H¡ values. With accurately mea-
sured *H¡ values, it should be possible to evaluate the
BadgerÈBauer relationship thoroughly. Since we would be in
possession of *H¡, *G¡ and *S¡ values for hydrogen bond
The use of the term “BadgerÈBauer relationshipÏ is now so
widespread, that we shall use this expression, not in the orig-
inal sense,1,2 but deÐned as a relationship between *l for a
OH
given acid in a series of hydrogen bond complexes with
various bases, and *H¡ for the complexation of the acid with
the bases, both in the same given solvent. The deÐnition can
also include the case of a series of OH acids with a given base,
and might possibly be extended to relationships between *l
for CxO shifts and *H¡ values. Used in these terms, the
BadgerÈBauer relationship has been supported by several
¤
Part 43: M. H. Abraham, F. Martins and R. C. Mitchell, J.
Pharm. Pharmacol., 1997, 49, 858.
J. Chem. Soc., Faraday T rans., 1998, 94(7), 879È885
879

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complexation, we could also study constitutional e†ects on
these thermodynamic parameters.
THAM to 50.0 ml of aqueous HCl. After correction for heat
of dilution and the heat of hydrolysis of THAM, the heat of
ionization was found to be [11.39 ^ 0.06 kcal mol~1 over 16
additions. This compares well with the value reported by
Ojelund and Wadso23 of [11.35 ^ 0.01 kcal mol~1 at the
same ionic strength.
The heat of ionization of water was also obtained, through
the incremental addition of aqueous perchloric acid to
aqueous sodium hydroxide. Over 16 additions a value of
13.40 ^ 0.10 kcal mol~1 was found, in good agreement with
reported values of 13.336,24 13.33525 and 13.331 kcal mol~1.26
The choice of acid, bases, and solvent may be quite critical,
and our selection was made as follows. First we chose cyclo-
hexane as a solvent because this precludes any speciÐc soluteÈ
solvent interactions. In addition, if various alkyl substituents
are introduced into the base, the relative permittivity in the
vicinity of the base functional group will not alter. Secondly, it
was necessary to choose an OH acid, and we selected 3,5-
dichlorophenol (DCP) because it is a solid, easy to handle,
and because with our selection of bases it would yield equi-
librium constants of the order of 102, a convenient and practi-
cal value. Thirdly, we chose a series of aliphatic ketones and
aliphatic ethers as the bases. Only aliphatic hydrocarbon sub-
stituents were allowed, so as to maintain a constant relative
permittivity around the base functional group.
Determination of equilibrium constants by FTIR
A calibration was Ðrst carried out of the absorbance, A, of the
OH fundamental stretching vibration of DCP at 3609 cm~1.
The DCP concentration, a , was varied between 0.001 M and
0
0
.02 M using 15 separately made-up solutions. A linear regres-
Materials and methods
sion analysis was carried out on eqn. (1), where e \ (molar
absorption coefficient) ] [cell path length (1 mm)].
Chemicals
A \ ea ] c
(1)
Cyclohexane was BDH Analar grade; DCP was the best
available commercial grade (Aldrich). The various bases used
were either the best available commercial grades, or were from
the ICI compound collection.
0
There was a deÐnite trend in both the slope and intercept, so
that eqn. (1) was not strictly obeyed. We concluded that
although the maximum DCP concentration was only 21 mM,
there was still some self-association of the phenol that had to
FTIR studies
be taken into account. The dimerization constant, K , is given
by,
d
All IR measurements were carried out on a Digilab FTS-20E
Fourier transform spectrophotometer. Spectra were recorded
at a resolution of 4 cm~1 and collected over 600 scans, unless
otherwise stated. A 1 mm cell with calcium Ñuoride windows
was used, and was placed in a water-jacketed cell holder
K \ d/a2
(2)
d
where d and a are the dimer and monomer concentrations, the
former being given by,
(
Specac) thermostated at 298 K to within 0.5 K using an LKB
d \ (a [ a)/2 \ (A [ A)/2e
(3)
0
0
Multitemp water circulator. At least 10 min was allowed for
the temperature to equilibrate, and the instrument was contin-
ually purged with dry nitrogen to remove traces of water and
carbon dioxide.
However, if DCP forms a linear dimer, rather than a cyclic
dimer, the terminal OH of the dimer will be almost equivalent
to the OH of the monomer. The measured value of (A [ A)
for the linear dimer will then be only half that for a cyclic
0
dimer, and eqn. (3) is more correctly written as,
Calorimetric studies
d \ (A [ A)/e
(4)
The apparatus used was a modiÐed Hart ScientiÐc 5021 iso-
peribol titration calorimeter Ðtted with a burette of capacity
0
The same argument leads to
2.5 ml driven by a reversible stepper motor. The burette
a2 \ (A/e [ d)2
(5)
delivery rate could be varied from 0.01 to 999 steps per
second, and the delivery time could be controlled either manu-
ally or automatically from a Tronac CCP 930 calorimeter
computer programmer. The titrant outlet was Ðtted with a
pinched syringe needle in order to reduce the outlet area. This
modiÐcation was very important when working with non-
aqueous solvents as otherwise premature mixing of reactants
took place. The calorimeter was contained in a constant tem-
perature bath of 40 l capacity, Ðtted with a motor driven
stirrer, an auxiliary cooling system with a temperature 5È10 K
below the set point, and an electronic thermostat. Under
normal conditions the bath temperature could be maintained
at 298.15 K with a deviation of 0.003 K over a period of 24 h.
A Tronac CCP 930 calorimeter computer programmer com-
plete with a Texas Instruments Silent 700 data terminal was
interfaced to the burette motor, the electronic console and a
digital voltmeter. This enabled programmed control of both
the burette delivery rate and the calibration heating time,
together with programmed data processing of a thermogam.
The burette was calibrated by weighing water delivered, and a
delivery rate of 6.61 ll s~1 and a step volume of 0.1322 ll
were found. The calibration constant was found for both 50.0
ml water and 50.0 ml cyclohexane in the vessel, and was con-
stant to 0.6% with water, and to 0.5% with cyclohexane.
For dilute solutions A/e A d, and eqn. (2), (4) and (5) then gen-
erate a quadratic in A/e,
K (A/e)2 ] (A/e) [ a \ 0
(6)
d
0
which with incorporation of a possible intercept (c) leads to
A \ eM[[1 ] (1 ] 4K a )1@2]/2K N ] c
(7)
d 0
d
We then Ðtted our data to eqn. (7), with the results shown in
Table 1. Unlike the linear model, the non-linear Ðtting curve
passes through the origin, within the given standard error.
The dimerization constant of 2.27 l mol~1, when statistically
corrected to 1.14 l mol~1, compares favorably with the associ-
ation of DCP with the model compound 3,5-dichloroanisole,
viz. 1.2 l mol~1 as found in this work.
We can now take account of DCP dimerization to obtain
an expression for the equilibrium constant for a 1 : 1 DCPÈ
Table 1 Non-linear Ðtting of absorbanceÈconcentration data
95% conÐdence
parameter
estimate
error
interval
K
d
c
2.27 l mol~1
31.32 l mol~1
0.0007
0.45
0.27
0.0011
1.28È3.25
As
a
check,
the
heat
of
ionization
of
e
30.73È31.91
tris(hydroxymethyl)aminomethane (THAM) was obtained by
incremental addition of a 0.2512 M aqueous solution of
[0.0018È0.0032
880
J. Chem. Soc., Faraday T rans., 1998, V ol. 94

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Table 3 Reverse spectroscopic titration of DCP with cyclohexanone
base complex, reaction (I), as the expression in eqn. (8) where
in cyclohexane, at 298 K, assuming only a 1 : 1 complex
b is the initial base concentration.
0
a /mM
b /mM
A ] 100
K/l mol~1
K
0
0
DCP ] base A8B DCPÉ É Ébase
(I)
3
6
9.25
2.34
15.42
8.50
.08
.17
5.91
5.91
5.91
5.91
5.91
5.91
5.27
11.46
18.42
25.56
33.38
41.47
184
199
216
267
308
361
Note that the terms in K in eqn. (8) simply allow for the
d
non-linearity of the absorbanceÈconcentration data.
1
a [ A/e [ K (A/e)2
K \ [
0
d
(8)
1
A/e [ K (A/e)2]
d
]
[b [ a ] A/e ] K (A/e)2]
0
0
d
A titration experiment was conducted for the complexation of
DCP with cyclohexanone; solutions were made up with
various cyclohexanone initial concentrations and the same
initial concentration of DCP. Six solutions were studied, and
K values were calculated through eqn. (8); the value of K did
not remain constant, but decreased as the fraction of complexed
DCP increased. The most likely explanation is the formation
of a 2 : 1 complex as well as the 1 : 1 complex. There are two
possible forms of a 2 : 1 complex, see Fig. 1, for a ketone base.
The CxO band of cyclohexanone was monitored in the
presence of increasing concentrations of DCP; the Ðrst 1 : 1
bound band at 1706 cm~1 gradually broadened and shifted to
so that the reverse titration is a powerful method for deter-
mining the model to be used. We therefore use a model that
involves both 1 : 1 and 2 : 1 complexation, reaction (II), as well
as the non-linear absorbanceÈconcentration Ðt.
K2
DCP ] DCPÉ É Ébase A8B DCPÉ É ÉDCPÉ É Ébase (II)
Previous workers have solved the problem of 1 : 1 and 2 : 1
complexation in a number of ways. Neel et al.27 introduced an
iterative graphical method, which is laborious but which has
been used quite successfully. A much easier method was
applied by Zeegers-Huyskens and co-workers28 who Ðrst cal-
1
701 cm~1 indicating the presence of a type II complex. A
very small concentration of a type I complex could just be
detected at 1678 cm~1. With the sterically hindered ketone,
di-tert-butylketone, only the 1 : 1 bound band and the type II
complex band could be detected.
We have, therefore, to take into account not only the non-
linear absorbanceÈconcentration data due to DCP dimer-
ization, but also the formation of 1 : 1 and 2 : 1 type II
complexes. Titration experiments usually take the form of a
constant initial concentration of acid, and a succession of
increased initial concentrations of base, see, for example Table
culated an apparent equilibrium constant, K , assuming
app
only a 1 : 1 complex, and then related K to K, K and the
app
2
free acid concentration. Although relatively quick, the method
has two main disadvantages: (i) the points which have the
greatest experimental error are those that have the greatest
weight in the calculation of K and K , and (ii) it is difficult to
2
evaluate the errors in K and K .
2
In our method we obtain an expression of the type K \
f (K ) as follows. At equilibrium, let the concentration of
2
monomer DCP be a, that of the 1 : 1 complex be x, that of the
2. In this procedure, the excess of base over acid towards the
2 : 1 complex be y and that of the dimer DCP be z. Then,
end of the titration prevents appreciable formation of 2 : 1
complexes. If a reverse titration is carried out with di†erent
initial concentrations of acid, and a Ðxed initial concentration
of base, 2 : 1 complexes will become more favoured towards
the end of the titration. At Ðrst sight, this seems not to be the
correct titration mode in order to obtain 1 : 1 complexation
constants. However, it has a considerable advantage in that
the procedure is very sensitive to the value of the second equi-
a \ a ] x ] 2y ] z
(9)
(10)
(11)
(12)
0
b \ b ] x ] y
0
K \ x/ab
K \ y/ax
2
and K is given by the expression,
librium constant, K , and it is much easier to check for 2 : 1
2
(
a [ a [ 2z)
complexes than with the normal mode of titration. This can
K \
0
(13)
be seen, Table 3, from a reverse titration of DCP with cyclo-
hexanone, using the non-linear absorbanceÈconcentration Ðt,
but assuming only a 1 : 1 complex. The apparent equilibrium
constant increases by a factor of two throughout the titration,
a[b (1 ] 2aK ) [ (a [ a [ 2z)(1 ] 2aK )]
0
2
0
2
If the identities (a ] z) \ A/e and z \ K (A/e)2 are substituted
d
into eqn. (13), the function K \ f(K ) contains only terms
2
which are experimentally obtainable. The Ðnal stage is non-
linear Ðtting of the data to the equation f (K ) [ K \ 0,
2
thereby generating the optimum values of the adjustable
parameters K and K . Except for a study of complexes of
2
acetic acid and amines,29 this seems to be the Ðrst method of
analysis that takes into account both acid self-association and
2
: 1 complex formation in the measurement of 1 : 1 equi-
librium constants. In Table 4 are summarized the results of
four independent reverse titration experiments; there is excel-
Fig. 1 Possible 2 : 1 complexes of DCP with ketones
lent reproducibility of both K and K .
2
Table 2 Spectroscopic titration of DCP with cyclohexanone in
cyclohexane at 298 K
Determination of DH for complexation by calorimetry
The titration curve for 1 : 1 complexation is described by the
equation,
a /mM
b /mM
A ] 100
K/l mol~1
0
0
1
1
1
1
1
1
0.09
0.09
0.09
0.09
0.09
0.09
0.00
3.54
7.08
14.16
21.24
28.32
30.98
23.92
18.83
12.17
8.60
È
Q \ *HV /2M(a ] b ] 1/K)
253
218
201
193
188
0
0
[
[(a ] b ] 1/K)2 [ 4a b ]1@2N
(14)
0
0
0 0
where Q is the heat due to hydrogen bonding and V is the
6.56
total volume of the calorimeter vessel contents in litres. The
J. Chem. Soc., Faraday T rans., 1998, V ol. 94
881

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Table 4 Results of the reverse titration procedure for the DCPÈcyclohexanone association in cyclohexane, at 298 K, assuming both 1 : 1 and
2
: 1 complexation
expt. K/l mol~1
p
95% conÐdence interval
K /l mol~1
p
95% conÐdence interval
2
(
(
(
(
i)
176.5
172.1
182.5
184.6
4.9
2.7
3.4
4.4
163.0
164.7
173.1
172.4
190.1
179.5
192.0
196.8
13.2
13.0
14.3
10.4
1.2
0.7
0.8
0.9
10.0
11.1
12.0
7.8
16.4
14.9
16.6
13.0
ii)
iii)
iv)
mean
178.9
È
È
È
12.7
È
È
È
various quantities in eqn. (14) are evaluated as,
*H is Ðnally calculated for each addition by substituting the
appropriate value of f into eqn. (19). It should be noted that K
in eqn. (21) is used only as a minor correction factor, so that
i/n
Q \ ; qHB
(15)
i
*
H is calculated e†ectively independently of K.
Four independent experiments were carried out, in each of
i/1
i/n
V \ 0.05 ] ; v
(16)
(17)
(18)
which three additions of DCP were made to an excess of
cyclohexanone, leading to a value of *H¡ of [7.21 ^ 0.09
kcal mol~1. These results have been obtained using K \ 178.9
l mol~1, but they are insensitive to the exact value of K used;
the calculated *H¡ value is essentially constant (to within 0.03
kcal mol~1) over a range of K values from 160 to 200 l mol~1.
The f values are ca. 0.97, so that the K value is only used to
correct for a small fraction of uncomplexed DCP; hence *H¡
and *G¡ are essentially independent quantities.
i
i/1
a \ 0.05[DCP]/V
0
i/n
b \ ; v [base]/V
0
i
i/1
where qHB is the titration run heat less an equivalent dilution
i
run heat, v is the volume of the ith increment, [DCP] is the
i
initial concentration of DCP in the vessel, and [base] is the
titrant base concentration. Values of *H and K are then
Results and Discussion
Thermodynamics of hydrogen bond complexation
evaluated by Ðtting the titration data, eqn. (15)È(18), to eqn.
(
14). We found that there was a distinct trend in both *H and
K as the titration progresses. Experiments with other bases
also show this e†ect, which, from our spectroscopic work,
seems to be due to 2 : 1 complexation as well as 1 : 1 complex-
ation. If this so, a single titration experiment must be analysed
in such a way as to yield no less than four parameters, viz. K,
K , *H and *H . This is simply not practical, and so we
The FTIR method described above was used to obtain values
of K and K for the complexation of DCP with 17 aliphatic
2
ketones and 12 aliphatic ethers in cyclohexane at 298 K.
Results are summarized in Tables 5 and 6.
The K values for the ketones show only a small steric e†ect
of two secondary or two tertiary alkyl groups: cyclohexanone
(179), Me CO (119), Et CO (100), n-Pr CO (106), n-Bu CO
2
2
were forced to develop an alternative calorimetric procedure.
If a relatively dilute solution of DCP is added to a more
concentrated solution of the base in the calorimeter vessel, the
formation of 2 : 1 complexes (2 mol of acid and 1 mol of base)
will be avoided, and the titration heat will be due only to the
formation of the 1 : 1 complex (after correcting for the dilution
run). We refer to this procedure as the excess base method.
However, since the concentration of base is actually no more
than around 0.2 M, the results will still refer to cyclohexane
solution. Although most of the DCP will be in the complexed
form during the titration, a small quantity will be present as
the free acid. The spectroscopically determined K value is
used to correct for this, as follows. For each addition of DCP,
2
2
2
2
(112), n-Hexyl CO (124), i-Pr CO (100) and t-Bu CO (64).
2
2
2
This is to be expected because the R and R alkyl groups in
1
2
the ketones are some way away from the CxOÉ É ÉHO hydro-
gen bond. In agreement with this is the lack of any signiÐcant
steric e†ect of a single secondary or single tertiary group. The
K
values are all very nearly the same, from 10 to 16, as
2
would be expected for type II complexes but not for type I
complexes, Fig. 1.
Massat et al.30 have determined K values for the complex-
ation of 9 phenols with 23 aliphatic ketones at 301 K, but in
*H \ Q/Nf
(19)
Table 5 Values of K and K for complexation of DCP with ketones,
2
R1COR2, in cyclohexane at 298 K
where N is the total number of mol of DCP added during the
addition, and f is the fraction of DCP that is actually com-
plexed. For each of the triplicate additions in a single run, N
is constant and is given by
R1
R2
K/l mol~1
p
K /l mol~1
p
2
Me
Me
Et
n-Pr
i-Pr
n-Bu
i-Bu
t-Bu
n-Hept
Et
n-Bu
n-Pr
i-Pr
119.3
111.7
118.7
111.8
117.6
109.8
108.5
117.1
100.4
110.3
106.2
99.7
3.0
5.1
3.0
0.8
5.0
1.4
2.9
4.0
2.6
1.4
1.5
2.6
1.4
1.0
3.4
14.3
12.2
11.6
12.0
16.4
14.4
10.8
15.3
13.9
9.8
11.0
12.9
14.7
10.4
15.2
1.2
2.2
1.2
0.3
2.1
0.7
1.2
1.7
1.3
0.5
0.6
1.3
0.6
0.8
1.7
Me
Me
Me
Me
Me
Me
Me
Et
N \ 6.61 ] 10~4[DCP]
(20)
where [DCP] is the concentration of DCP in the burette. At
any point during the run, the total fraction of DCP complexed,
f T, may be calculated from the equation,
f T \ M(a ] b ] 1/K)
Et
0
0
n-Pr
i-Pr
n-Bu
t-Bu
n-Hex
[
[(a ] b ] 1/K)2 [ 4a b ]1@2N/2a
(21)
0
0
0 0 0
n-Bu
t-Bu
n-Hex
112.4
64.5
124.2
where a is the total concentration of DCP in the vessel. Then
0
if the total fraction of DCP complexed after i additions is f T, it
i
follows that the fraction complexed during the ith addition, f ,
is given by
cyclopentanone
cyclohexanonea
163.5
178.9
2.3
È
12.6
12.7
0.6
È
i
f \ if T [ (i [ 1) f T
i~1
(22)
a From Table 4.
i
i
882
J. Chem. Soc., Faraday T rans., 1998, V ol. 94

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Table 6 Values of K and K for complexation of DCP with ethers,
hydrogen bond complexation with pyridine-N-oxide in cyclo-
hexane. Now it can be shown that for the complexation,
2
R1OR2 , in cyclohexane at 298 K
R1
R2
K/l mol~1
p
K /l mol~1
p
ROHÉ É ÉROH ] B H ROHÉ É ÉROHÉ É ÉB
(III)
2
Me
Et
n-Pr
i-Pr
n-Bu
i-Bu
n-Octyl
n-Decyl
t-Bu
90.8
62.1
40.6
88.6
40.4
18.9
48.6
50.3
0.6
1.2
0.9
3.1
1.1
1.8
1.0
1.4
12.4
8.7
6.6
10.9
10.3
7.1
0.4
0.9
1.1
1.5
1.5
4.9
1.0
1.4
the equilibrium constant is given by KK /K , where K refers
to reaction (II), written more conveniently as,
Et
2
d
2
n-Pr
i-Pr
n-Bu
i-Bu
n-Octyl
n-Decyl
ROH ] ROHÉ É Ébase H ROHÉ É ÉROHÉ É Ébase
(IV)
The average value of KK /K is 664 for the ketones and 377
2
d
9.2
10.7
for the ethers, as compared to average values for the complex-
ation of the monomeric ROH acid with bases of 116 for the
ketones and 80 for the ethers. Hence the dimer of DCP in
reaction (III) is a stronger hydrogen bond acid than the
monomer of DCP in reaction (I) by a factor of 5.7 or 4.7
towards ketones and ethers, respectively. These factors are in
general accord with the analysis of Frange et al.37
trimethylene oxide
terahydrofuran
tetrahydropyran
206.9
148.4
109.8
54.4
2.7
4.9
2.6
1.4
17.0
12.7
11.9
11.3
0.5
1.5
1.2
1.4
1
,4-dioxanea
a Not statistically corrected.
The K values obtained by the FTIR method may be com-
bined with the *H¡ values from the calorimetric method to
yield thermodynamic parameters for the 1 : 1 complexation of
DCP with ketones, Table 7, and ethers, Table 8. Taking into
account the error in K, and an average experimental error of
about 0.1 kcal mol~1 for *H¡, we estimate that the error in
*S¡ is ca. 0.4 cal K~1 mol~1.
tetrachloromethane solvent. In order to compare results we
have obtained aH and bH for these compounds as follows.
2
2
Some values of aH for the phenols were available,31 and the
2
others were calculated through32,33 eqn. (23),
log K \ 7.354aH bH [ 1.094
(23)
2
2
In the case of the ketones, none of the three thermodynamic
parameters varies very much; *S¡ varies by no more than 1.1
cal K~1 mol~1, even including the two cyclic ketones, and a
In eqn. (23), log K is the hydrogen bond complexation con-
stant in tetrachloromethane, and the 1 : 1 hydrogen bond
acidity and basicity parameters aH and bH refer to the particu-
2
2
lar reactants.33 For the ketones studied by Massat et al.,30 a
number of bH values were again available,32 and others were
calculated through eqn. (23). Our results are in agreement
2
Table 7 Thermodynamics of complexation of DCP with ketones,
R1COR2, in cyclohexane at 298 Ka
with those of Massat et al.,30 and show that steric e†ects
amongst alkyl substituted aliphatic ketones are small, unless
very bulky groups are present.
R1
Me
R2
Me
Et
n-Pr
i-Pr
n-Bu
i-Bu
t-Bu
n-Hept
Et
n-Bu
n-Pr
i-Pr
[*G¡
[*H¡
[*S¡
In the complexation of DCP with ethers, both polar and
2.83
2.79
2.83
2.79
2.82
2.78
2.78
2.82
2.73
2.79
2.76
2.73
2.80
2.47
2.86
7.02
7.01
6.86
6.98
6.94
6.82
6.95
6.82
6.97
6.86
6.86
6.91
6.82
6.76
6.83
14.0
14.1
13.5
14.0
13.8
13.5
14.0
13.4
14.2
13.7
13.7
14.0
13.5
14.4
13.3
Me
Me
Me
Me
Me
Me
Me
Et
steric e†ects can be seen: t-BuOMe (91) and i-Pr O (89) show
2
increased K values over those for the di-n-alkyl ethers, but
i-Bu O (19) has a much reduced K value. As for the ketones,
2
the range of K values suggests that type II complexes are
2
formed. Complexation constants for alkyl ethers against the
reference acid 4-chlorophenol in cyclohexane at 293 K have
been determined by Bellon et al.34 For 8 common ethers,
there is reasonable agreement between the two sets of results,
see Fig. 2. If all the data on ethers are considered, it seems as
though there is a polar e†ect of sec- and tert-alkyl groups that
increases log K, counterbalanced by a steric e†ect that
decreases log K, e.g. in di-tert-butyl ether.
Et
n-Pr
i-Pr
n-Bu
t-Bu
n-Hex
n-Bu
t-Bu
n-Hex
The ratio K/K for the 17 ketones studied is 8.9, and for the
2 ethers is 7.5. Previous workers28,35,36 have obtained a
variety of values for this ratio, but in general the larger the
cyclopentanone
cyclohexanone
3.02
3.07
7.08
7.21
13.6
13.9
2
1
a *G¡ and *H¡ in kcal mol~1; *S¡ in cal K~1 mol~1.
value of K the greater is the ratio of K/K . Frange et al.37
2
showed that alcohol dimers (type II) are about an order of
magnitude more acidic than the corresponding monomers in
Table 8 Thermodynamics of complexation and values of *l for
OH
complexation of DCP with ethers, R1OR2, in cyclohexane at 298 Ka
R1
R2
[*G¡
[*H¡
[*S¡
*l /cm~1
OH
Me
Et
n-Pr
i-Pr
n-Bu
i-Bu
n-Octyl
n-Decyl
t-Bu
2.67
2.45
2.19
2.66
2.19
1.74
2.30
2.32
7.65
7.06
6.77
7.54
6.79
6.65
6.94
7.01
16.7
15.5
15.3
16.4
15.4
16.5
15.6
15.7
374
342
351
362
357
353
359
359
Et
n-Pr
i-Pr
n-Bu
i-Bu
n-Octyl
n-Decyl
trimethylene oxide
terahydrofuran
tetrahydropyran
3.16
2.96
2.78
2.37
7.55
7.28
7.17
5.97
14.7
14.5
14.7
12.1
330
340
347
295
1
,4-dioxaneb
Fig. 2 A plot of log K for ethers against 4-chlorophenol vs. log K
for ethers against 3,5-dichlorophenol
a *G¡ and *H¡ in kcal mol~1; *S¡ in cal K~1 mol~1. b Not sta-
tistically corrected.
J. Chem. Soc., Faraday T rans., 1998, V ol. 94
883

View Article Online
plot of *H¡ against *G¡ (not shown) is a scatter diagram
except for the two cyclic ketones. It should be pointed out
that since there are two stereoisomeric complexes formed from
a phenol and a ketone, the observed *H¡ will be a weighted
sum of the two individual *H¡ values. This will also be the
case for *G¡, although the weights will be di†erent to those
for *H¡. Under these conditions, a plot of *H¡ against *G¡
may have little meaning, anyway.
particular, steric e†ects increase the contribution of the linear
geometrical form, i.e. the high frequency component. Our
results are in line with those of Laurence et al.40 The marked
asymmetry of the OH band in the complexes of DCP with
ketones, as well as the very small variation in *H¡, no more
than 0.45 kcal mol~1 over all the ketones studied, suggests
that the DCPÈketone system in cyclohexane is not at all suit-
able for any analysis of the BadgerÈBauer relationship.
For the ethers, there is considerably more variation in *H¡,
Fritzsche38 recognized that in contrast to carbonyl bases,
the complexed OH band of phenol associated with 1,4-
dioxane or tetrahydrofuran was essentially symmetrical. We
Ðnd this also for the complexed OH band of DCP with the
*
G¡ and *S¡ with structure. In order to compare 1,4-dioxane
with the mono-ethers, we can make a statistical correction for
the two ether sites, giving corrected values of [*G¡ \ 1.96
kcal mol~1 and [*S¡ \ 13.5 cal K~1 mol~1. A plot of
various ethers we have studied; in Table 8 are values of *l
OH
[
*H¡ against [*G¡ with the corrected value for 1,4-dioxane,
for the complexed band, as di†erences from l for free DCP
OH
at 3609 cm~1. A plot of *l against *H¡ is shown in Fig. 4.
OH
is shown in Fig. 3. There seem to be three separate lines for
the n-alkyl ethers, the branched chain ethers, and the cyclic
ethers. We note that the displacement of the two outermost
lines from the central line in Fig. 3 amounts to only 0.3 and
Apart from the point for 1,4-dioxane, there is complete scatter.
Even for the acyclic ethers there is a very poor relationship
between *l and *H¡,
OH
0
.5 kcal mol~1, and it is doubtful if the [*H¡ against [*G¡
*l
\ 238.5 ] 16.8 *H¡
(24)
plot could be resolved into three lines if the *H¡ values had
been obtained by the vanÏt Ho† method. It should also be
noted that the problem of stereoisomeric forms does not occur
for the DCPÈether complexes we have studied (see the dis-
cussions below).
OH
n \ 7, p \ 7.5, r2 \ 0.4349, F \ 4.6, where n is the number of
results, p is the population standard deviation, r is the corre-
lation coefficient and F is the F-test value. Our conclusion is
quite deÐnite: when values of *H¡ for complexation of DCP
with ethers in cyclohexane are determined by a calorimetric
The Badger–Bauer relationship
method, there is only a very poor relationship between *l
OH
and *H¡. Even for a restricted set of acyclic ethers, the
Spectra of the complexed OH bands for the ketone adducts of
DCP were obtained in cyclohexane using an excess of the
ketone base to avoid 2 : 1 complexation. In all cases, the
bonded OH band was made up of a high frequency and a low
frequency component, with the high frequency contribution
increasing as the ketone becomes more sterically hindered.
Fritzsche,38 examined the shape of the hydrogen-bonded OH
band for complexes of phenol in tetrachloromethane. For car-
bonyl complexes, he interpreted the asymmetry of the OH
band as due to the superposition of two symmetrical bands
originating from two stereoisomeric complexes. The lower fre-
quency component was attributed to an angular complex
where the hydrogen bond forms in the direction of the lone
pair, and the high frequency component to either a bidendate
complex or a p-complex. This two-component model was sup-
ported by Korppi-Tommola and Shurvell.39 Laurence et al.40
have made a very thorough study of the complex OH band
resulting from the interaction of methanol and of 2,6-
diisopropyl-4-nitrophenol (DINP) with carbonyl compounds.
They concluded that there exists two planar stereoisomers; a
low frequency angular complex as proposed by Fritzsche,38
and a high frequency linear complex where the hydrogen
bond forms along the axis of the CxO bond. Laurence et
al.40 further suggested that the contribution of the two forms
was linked to both steric repulsion and electronic e†ects. In
BadgerÈBauer relationship (as deÐned above) does not hold. It
should be noted that the complexation of DCP with ethers
has been chosen to provide very good conditions as regards
the BadgerÈBauer relationship. First, the variables are the
same as those used in many studies, viz. *l and *H¡. Sec-
OH
ondly, the values of *H¡ have been obtained by a rigorous
calorimetric method. Thirdly, the OH bands in the DCPÈ
ether complexes are symmetric and do not su†er from the
complications seen with the DCPÈketone complexes.
Fourthly, the bases are all within a family, so that there is no
possibility of any relationship between *l and *H¡ being
OH
family dependent. If, under these conditions, there is almost
no connection between *l and *H¡, we can conclude that
OH
the BadgerÈBauer relationship is not general and that such a
relationship cannot be assumed even within a family of bases.
It has been suggested that steric e†ects in the aliphatic ether
series may render the BadgerÈBauer relationship questionable.
Certainly, steric e†ects on hydrogen bond complexation may
be one reason why the BadgerÈBauer relationship does not
generally hold. But this cannot be the entire reason for the
collapse of the relationship in the present case. Even if methyl
tert-butyl ether and diisopropyl ether are omitted, and only
the Ðve acyclic ethers with primary alkyl groups are con-
sidered, there is still no relationship between *l and *H¡. A
OH
fundamental reason for lack of such a relationship is that
Fig. 3 A plot of [*H¡ for ethers against DCP vs. [*G¡ for ethers
Fig. 4 The BadgerÈBauer relationship: a plot of *l
against DCP vs. [*H¡ for ethers against DCP
OH for ethers
against DCP
884
J. Chem. Soc., Faraday T rans., 1998, V ol. 94

View Article Online
*
l
is not a thermodynamic quantity at all, but because of
the FranckÈCondon principle, refers to a situation in which
18 O. Kasende and Th. Zeegers-Huyskens, J. Phys. Chem., 1984, 88,
OH
2
132; 2636.
1
9
C. N. R. Rao, P. C. Davivedi, H. Ratajczak and W. J. Orville-
Thomas, J. Chem. Soc., Faraday T rans. 2, 1975, 71, 955.
P. Goralski, J. Chem. Soc., Faraday T rans., 1993, 89, 2433.
the solvent around an excited state is not in equilibrium with
the excited state. A relationship between *l and *H¡ thus
involves a comparison of structural e†ects on (i) the di†erence
2
0
OH
21 V. E. Borisenko, G. Y. Blinkova, L. L. Osipova and Y. A. Zavja-
in spectroscopic energy between an excited complex that is
not in equilibrium with the solvent and a ground state
complex that is in equilibrium with the solvent, and (ii) the
di†erence in enthalpy between a complex that is in equi-
librium with the solvent, and the reactants that are in equi-
librium with the solvent. There is therefore no fundamental
reason why such a relationship should hold.
lova, J. Mol. L iq., 1996, 70, 31.
2
2
H. Deng, J. Zheng, A. Clarke, J. J. Holbrook, R. Callender and
J. W. Burgner, Biochemistry, 1994, 33, 2297.
2
2
3
4
G. Ojelund and I. Wadso, Acta Chem. Scand., 1968, 22, 2691.
C. E. Vanderzee and J. A. Swanson, J. Phys. Chem., 1963, 67,
2
608.
25 J. D. Hale, R. M. Izatt and J. J. Christensen, J. Phys. Chem., 1963,
67, 2605.
2
2
6
7
L. D. Hansen and E. A. Lewis, J. Chem. T hermodyn., 1971, 3, 35.
J. Neel, P. Pineau and C. Quivoron, J. Chim. Phys. Phys.-Chim.
Biol., 1965, 62, 37.
We thank the SERC for a CASE award (to D.V.P.) and Dr
Michel Berthelot for helpful comments.
2
2
3
3
8
9
0
1
D. Clotman, D. Van Lerberghe and T. Zeegers-Huyskens,
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Paper 7/08362I; Received 19th November, 1997
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885