REACTION OF CARBOXYLIC ACIDS WITH DIAZODIPHENYLMETHANE
257
terms of the contribution of the initial and the transi-
ln(k/T ) = −ꢀH#/RT + ln(kb/h) + ꢀS#/R
ꢀG# = ꢀH# − T ꢀS#
(5)
(6)
tion state. Solvation models of all the examined acids
are suggested [3–5]. To obtain a complete overview of
the mechanism of the examined reaction in the present
study, the activation parameters were determined and
the solvent influence on them was given quantitatively
by means of the Kamlet–Taft equation, which has not
been tried before to the best of our knowledge. The
carboxylic acids chosen to react with DDM for this
study were representatives of different structures, such
as cyclohex-1-enecarboylic acid, 2-methylcyclohex-1-
enecarboylic acid, cyclohex-1-eneacetic acid, pheny-
lacetic acid, benzoic acid, and 2-methylbenzoic acid.
The reaction rate constants were determined at 30, 33,
37, 40, and 45◦C in a set of 12 solvents of different
structures and properties, which have various effects
on the examined reaction: Some of them accelerate it,
whereas some of them slow it down. As expected with
the increase of temperature, the reaction rate is also in-
creased in proportion with the reaction conditions and
reactant properties.
This paper demonstrates how the linear solvation
energy relationship method can be used to explain and
present multiple interacting effects of the solvent on
the activation energy and the standard Gibbs energy of
the activation for each examined carboxylic acids.
EXPERIMENTAL
Cyclohex-1-enecarboxylic and 2-methylcyclohex-1-
enecarboxylic acids were prepared by the method
of Wheeler and Lerner [10] from the correspond-
ing cycloalkanone cyanohydrine, which was dehy-
drated to cyanoalkene. The nitrile was hydrolyzed with
phosphoric acid to the corresponding cycloalkenecar-
boxylic acid. Cyclohex-1-eneacetic acid was prepared
by the method of Sugasawa and Saito [11] from the
corresponding ketone with ammonium acetate, and
the resulting cycloalkenylacetonitrile was hydrolyzed
to the corresponding acid with potassium hydroxide.
Phenylacetic, benzoic and 2-methylbenzoic acid were
commercial product (Fluka; Sigma–Aldrich, St. Louis,
MO).
The chemical structure and the purity of the ob-
tained compounds were confirmed by melting or boil-
ing points and 1H NMR, FTIR, and UV spectra.
DDM was prepared by the method of Smith and
Howard [12], and stock solutions were stored in a re-
frigerator and diluted before use. Solvents were puri-
fied as described in previous papers [13,14]. All the sol-
vents used in kinetic studies were analytical grade. Rate
constants for the reaction of examined acids with DDM
were determined as reported previously, by the spec-
troscopic method of Roberts and his co-workers [15],
using a Shimadzu UV-1700 spectrophotometer. Opti-
cal density measurements were performed at 525 nm
with 1-cm cells at 30 0.05◦C, 33 0.05◦C, 37
0.05◦C, 40 0.05oC, and 45 0.05◦C. The second-
order rate constants for all acids were obtained by di-
viding the pseudo–first-order rate constants by the acid
concentration (the concentration of acid was 0.06 mol
dm−3 and of DDM 0.006 mol dm−3). The correlation
analysis was carried out using Origin and Microsoft
Excel computer software. The goodness of fit is dis-
cussed using correlation coefficient (R) and standard
deviation (SD).
As is well known, based on the Arrhenius equation
kr = A e−E /RT
the following correlation can be derived:
ln kr = −Ea/RT + ln A
(1)
a
(2)
and so the activation energy can be calculated from the
slope of a straight line obtained by the kinetic data on
different temperatures.
To analyze the solvent effect on the activation en-
ergy, the obtained values were correlated using the
Kamlet–Taft total solvatochromic equation (3):
A = A0 + sπ∗ + aα + bβ
(3)
In Eq. (3), A is the examined property and A0 its ref-
erence value (in cyclohexane, the solvent where all
the solvent parameters are taken to have 0 value). The
parameter π* is the measure of the solvent dipolar-
ity/polarizability, whereas the other two represent the
effects of the solvent proton-donor and proton-acceptor
ability, expressed by the parameters α and β, respec-
tively.
Using the values for the activation energy, Eyring
parameters, such as the standard enthalpy (Eq. (4)),
the standard entropy (Eq. (5)), and the standard Gibbs
energy of activation (Eq. (6)), were calculated at 30◦C
and also correlated with the Kamlet–Taft equation:
The reported conformations and the corresponding
heats of formation of the examined molecules were
obtained by the semiempirical MO PM6 method, us-
ing the MOPAC 2007 program package, as reported
ꢀH# = Ea# − RT
(4)
International Journal of Chemical Kinetics DOI 10.1002/kin.20762