Mechanism of acid-catalysed decomposition of 3-alkyl-1,3-diphenyltriazenes by trichloroacetic acid in hexane

Article abstract of DOI:10.1002/poc.734

Eight 3-alkyl-1,3-diaryltriazenes with methyl, ethyl, propyl, butyl, pentyl, isopropyl, sec-butyl and cyclohexyl substituents were synthesized and their rate constants of decomposition by trichloroacetic acid (0.01-0.25 mol dm^-3) in hexane at 25°C were measured. The kinetic model and mechanism thereof were studied by modelling of the dependences of k _obs on the concentration of trichloracetic acid. On the basis of this kinetic model and the interpretation of solvent effects, a reaction mechanism was suggested according to which the triazene reacts with monomer and obviously also opens the dimer of trichloroacetic acid in a single reaction step. At the same time, a non-reactive associate between the N1 nitrogen of triazene and two molecules of trichloroacetic acid is formed in the reaction mixture. The equilibrium and rate constants depend on the addition of trichloroacetic acid as the co-solvent. Copyright

Full text of DOI:10.1002/poc.734

JOURNAL OF PHYSICAL ORGANIC CHEMISTRY
J. Phys. Org. Chem. 2004; 17: 343–349
Published online 6 February 2004 in Wiley InterScience (www.interscience.wiley.com). DOI: 10.1002/poc.734
Mechanism of acid-catalysed decomposition of
3-alkyl-1,3-diphenyltriazenes by trichloroacetic acid
in hexane
1
1
ˇ
´ ˇ2
´
´
Oldrich Pytela, * Roman Bednar and Jaromır Kavalek
1
ˇ
´
Faculty of Chemical Technology, University of Pardubice, Cs. Legiı 565, CZ-532 10 Pardubice, Czech Republic
2
´
´
IVAX-CR, Opava-Komarov, Ostravska 29, CZ-747 70 Opava, Czech Republic
Received 3 July 2003; revised 6 October 2003; accepted 12 November 2003
ABSTRACT: Eight 3-alkyl-1,3-diaryltriazenes with methyl, ethyl, propyl, butyl, pentyl, isopropyl, sec-butyl and
cyclohexyl substituents were synthesized and their rate constants of decomposition by trichloroacetic acid (0.01–
0.25 mol dmꢀ3) in hexane at 25 ꢁC were measured. The kinetic model and mechanism thereof were studied by
modelling of the dependences of kobs on the concentration of trichloracetic acid. On the basis of this kinetic model and
the interpretation of solvent effects, a reaction mechanism was suggested according to which the triazene reacts with
monomer and obviously also opens the dimer of trichloroacetic acid in a single reaction step. At the same time, a non-
reactive associate between the N1 nitrogen of triazene and two molecules of trichloroacetic acid is formed in the
reaction mixture. The equilibrium and rate constants depend on the addition of trichloroacetic acid as the co-solvent.
Copyright # 2004 John Wiley & Sons, Ltd.
KEYWORDS: triazenes; acid catalysis; kinetic model; mechanism
INTRODUCTION
triazene in an aqueous medium. The N3 atom of 1,3-
diphenyltriazene was estimated to be only a very weak
base,17 and the existence of a stable substrate protonated
at this centre in a specific acid catalysis is highly unlikely.
Quantum-chemical calculations on triazene, on both
ab initio18,19 and PM3 semiempirical bases,20 indicated
that the protonation of triazene can take place at both the
N1 and N3 atoms. 1,3-Diphenyltriazene protonated at the
N3 nitrogen atom exhibits a weakening of the N2—N3
Studies on reactivity of triazene derivatives have so far
been focused especially on the kinetics and mechanism of
acid-catalysed splitting of the triazene chain. Earlier
workers preferred a mechanism of specific catalysis which
involves decomposition of 1,3-diaryltriazene protonated
at the N3 atom in the rate-limiting step,1–3 and the same
conclusions were drawn for 1,3-dialkyltriazenes and
1,3,3-trialkyltriazenes.4,5 However, a number of other
papers give arguments supporting the mechanism of
general acid catalysis for both 1,3,3-trialkyltriazenes6
and 3-alkyl-1-aryltriazenes.7–11 General acid catalysis
was demonstrated by studies of substitution effects in
the acid-catalysed decomposition of 1-aryl-3-methyl-3-
phenyltriazenes,12 in the reaction of 3-methyl-1,3-diphe-
nyltriazene with chloroacetic, formic and succinic acids in
40% aqueous ethanol13 and was indicated in a study of the
acid-catalysed decomposition of 1,3-bis(4-methylphe-
nyl)triazene in alcohols,14 aprotic solvents15 and water–
methanol mixtures of various methanol concentrations.16
The participation of general acid catalysis was also proven
in the thermal cis–trans isomerization of 1,3-diphenyl-
˚
bond (lengthened by about 0.2 A), while the decomposi-
tion products (i.e. the diazonium salt and aniline) become
more stable thermodynamically.20 Therefore, it can be
deduced that the protonated intermediate would rapidly
decompose to products if it were formed.
The physico-chemical properties and reactivity of 3-
alkyl derivatives of 1,3-diphenyltriazene with acids have
received little attention thus far: only the 3-methyl deriva-
tive has been described.12,13,21–23 This is surprising since
3-alkyl-1,3-diphenyltriazenes are suitable substrates for
verification of mechanisms of acid catalysis: in addition
to the inductive effect, steric effects can also participate
here. Another advantage is that the reaction can be studied
in a wide variety of solvents, including aprotic types.
The aim of this work was to study these substituent
effects for the purpose of verification of the mechanism
of acid catalysis in the acid-catalysed decomposition of
3-alkyl-1,3-diphenyltriazenes. For this purpose we chose
kinetic monitoring of the reactions of these compounds
with trichloroacetic acid (a bulky general acid) of varying
concentration in an inert medium of hexane.
*Correspondence to: O. Pytela, Faculty of Chemical Technology,
ˇ
´
University of Pardubice, Cs. Legiı 565, CZ-532 10 Pardubice, Czech
Republic.
E-mail: oldrich.pytela@upce.cz
Contract/grant sponsor: Ministry of Education, Youth and Sports of
the Czech Republic; Contract/grant number: CIMSM 253 100001.
Copyright # 2004 John Wiley & Sons, Ltd.
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O. PYTELA, R. BEDNAR AND J. KAVALEK
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344
EXPERIMENTAL
7.52, 8H (H-3,5; H-30,50; H-2,6 and H-20,60); 1.38, 6H
(CH3); 5.63, 1H (CH); 13C NMR (DMSO-d6), ꢀ 20.11, 2C
(CH3); 49.89, 1C (CH).
Synthesis of 3-alkyl-1,3-diphenyltriazenes. The 3-
alkyl-1,3-diphenyltriazenes of the general formula shown
were synthesized by azo coupling of a benzenediazonium
salt with the respective N-alkylanilines.12 Because of
their thermal instability,24 the products obtained were
purified by column chromatography on alumina with
tetrachloromethane as the mobile phase. Except for the
solid methyl derivative (m.p. 34–34.5 ꢁC), they are or-
ange oils. The identities of the compounds prepared were
1
3-sec-Butyl-1,3-diphenyltriazene. Yield 52%. H NMR
(DMSO-d6), ꢀ 7.15, 2H (H-4 and H-40); 7.25–7.61, 8H
(H-3,5; H-30,50; H-2,6 and H-20,60); 0.96, 3H (CH3); 1.18,
3H (CH3); 1.35–1.65, 2H (CH2); 5.30, 1H (CH); 13C
NMR (DMSO-d6), ꢀ 10.69, 1C (CH3); 20.10, 1C (CH3);
29.18, 1C (CH2); 49.02, 1C (CH).
1
1
checked by H and 13C NMR spectroscopy (N-alkylani-
3-Cyclohexyl-1,3-diphenyltriazene. Yield 33%, H NMR
lines in CDCl3, 3-alkyl-1,3-diphenyltriazenes in DMSO-
d6, Bruker AMX 360 spectrometer).
(DMSO-d6), ꢀ 7.08, 2H (H-4 and H-40); 7.35–7.50, 8H
(H-3,5; H-30,50; H-2,6 and H-20,60); 1.12–1.97, 10H
(CH2); 5.37, 1H (CH); 13C NMR (DMSO-d6), ꢀ 27.4,
1C (CH2); 24.44, 2C (CH2); 32.72, 2C (CH2); 50.55,
1C (CH).
The starting N-alkylanilines were synthesized by
the reduction of acylanilides with bis(2-methoxyethoxy)-
aluminium hydride in toluene (ethyl and propyl), by
alkylation of aniline according to Hickinbottom and co-
workers25,26 with subsequent separation of the mixture
(butyl, isopropyl, sec-butyl), by reductive amination of 1-
pentan-ol with aniline27 in the presence of Raney nickel
catalyst (pentyl) and by the reduction of alkylideneaniline
with lithium tetrahydridoalanate (cyclohexyl). The N-
methyl derivative was a commercial product.
3-Methyl-1,3-diphenyltriazene. Yield 76%. 1H NMR
(DMSO-d6), ꢀ 7.19, 1H, (H-40); 7.31, 1H (H-4); 7.43–
7.51, 4H (H-3,5 and H-30,50); 7.56–7.62, 4H (H-2,6 and
H-20, 60); 3.61, 1H (CH3); 13C NMR (DMSO-d6), ꢀ 32.14,
1C (CH3).
3-Ethyl-1,3-diphenyltriazene. Yield 67%. 1H NMR
(DMSO-d6), ꢀ 7.18, 1H (H-40); 7.30, 1H (H-4); 7.44–
7.49, 4H (H-3,5 and H-30,50); 7.55–7.62, 4H (H-2,6 and
H-20,60); 1.23, 3H (CH3); 4.34, 2H (CH2); 13C NMR
(DMSO-d6), ꢀ 10.94, 1C (CH3); 40.29, 1C (CH2).
Kinetic measurements. The kinetic measurements
were based on spectrophotometric monitoring of the
decrease in the absorbance of the respective triazene at
359 nm in hexane 25.5 ꢁC using a Durrum D-110 stoped-
flow spectrophotometer. One reservoir of the apparatus
contained a solution of trichloroacetic acid in hexane
(0.02–0.50 mol dmꢀ3) and the other reservoir (of the same
capacity) contained a solution of triazene in hexane of
concentration such as to obtain a resulting absorbance of
the reaction mixture after the rapid mixing of solutions
from both reservoirs in the range 0.5–1.0 units. The
solutions of the components and the cell compartment
were kept at 25.5 ꢂ 0.2 ꢁC. The concentration of trichlor-
oacetic acid was determined by reverse titration of the
reaction mixture after its extraction in a double volume of
aqueous sodium hydroxide of suitable concentration.
Altogether 61–92 measurements were carried out for
each derivative in the given concentration range of
3-Propyl-1,3-diphenyltriazene. Yield 65%. 1H NMR
(DMSO-d6), ꢀ 7.17, 1H (H-40); 7.30, 1H (H-4); 7.43–
7.49, 4H (H-3,5 and H-30,50); 7.55–7.61, 4H (H-2,6 and
H-20,60); 0.94, 3H (CH3); 1.68, 2H (CH2); 4.25, 2H
(CH2); 13C NMR (DMSO-d6), ꢀ 11.28, 1C (CH3);
18.87, 1C (CH2); 45.38, 1C (CH2).
3-Butyl-1,3-diphenyltriazene. Yield 54%. 1H NMR
(DMSO-d6), ꢀ 7.17, 1H (H-40); 7.29, 1H (H-4); 7.40–
7.48, 4H (H-3,5 and H-30,50); 7.55–7.59, 4H (H-2,6 and
H-20,60); 0.94, 3H (CH3); 1.38, 2H (CH2); 1.65, 2H
(CH2); 4.32, 2H (CH2); 13C NMR (DMSO-d6), ꢀ 13.72,
1C (CH3); 19.83, 1C (CH2); 27.63, 1C (CH2); 43.56, 1C
(CH2).
3-Pentyl-1,3-diphenyltriazene. Yield 60%. 1H NMR
spectrum (DMSO-d6), 7.16, 1H (H-40); 7.28, 1H (H-4);
7.41–7.46, 4H (H-3,5 and H-30,50); 7.53–7.57, 4H (H-2,6
and H-20,60); 0.87, 3H (CH3); 1.32, 2H (CH2); 1.34, 2H
(CH2); 1.61, 2H (CH2); 4.27, 2H (CH2); 13C NMR
(DMSO-d6), ꢀ 13.98, 1C (CH3); 22.10, 1C (CH2);
25.04, 1C (CH2); 28.65, 1C (CH2); 43.78, 1C (CH2).
trichloroacetic acid. The observed rate constants, kobs
,
were calculated from the reaction half-time read on the
apparatus display. A reaction order of unity was verified
for 3-propyl-1,3-diphenyltriazene by the method of initial
concentrations.
Evaluation of experimental data. The mathemati-
cal–statistical modelling of the dependence of the ob-
served rate constant, kobs, on the concentration of
trichloroacetic acid, c, was carried out by non-linear
1
3-Isopropyl-1,3-diphenyltriazene. Yield 62%. H NMR
(DMSO-d6), ꢀ 7.24, 1H (H-40); 7.35, 1H (H-4); 7.39–
Copyright # 2004 John Wiley & Sons, Ltd.
J. Phys. Org. Chem. 2004; 17: 343–349

ACID-CATALYSED DECOMPOSITION OF 3-ALKYL-1,3-DIPHENYLTRIAZENES
345
regression using efficient optimization methods (genetic
algorithm, simplex method, Levenberg–Marquardt
method). The results were evaluated statistically, the statis-
tically insignificant rate constants were omitted from the
modelsandthecalculationwasrepeated.Thecriteriaforthe
selection of the most suitable model were the residual
standard deviation and positive values of rate and equili-
brium constants as the optimized parameters.
RESULTS AND DISCUSSION
Figures 1 and 2 present typical dependences of the
observed rate constant, kobs, of reaction of 3-alkyl-1,3-
diphenyltriazenes on the concentration of trichloroacetic
acid in hexane for the methyl and sec-butyl derivatives,
respectively. The dependences of the observed rate
Figure 2. Dependence of observed rate constant, kobs (sꢀ1),
on concentration of trichloroacetic acid, c (mol dmꢀ3), for
3-sec-butyl-1,3-diphenyltriazene
constant on concentration of trichloroacetic acid for ethyl,
propyl, butyl and pentyl substituents are of identical type
to those of the methyl derivative, whereas those of the
isopropyl and cyclohexyl substituents are identical with
those of the sec-butyl derivative. In the case of the
cyclohexyl substituent, we failed to record experimentally
the starting section of the curve. As can clearly be seen
from the figures, the dependences have non-trivial courses.
Proposed kinetic model
Scheme 1 was the starting point for suggesting possible
regression functions: it was derived from the known
pieces of information concerning the reaction system,
including the products (see Introduction). With regard to
the non-polar medium, we assume the formation of less
polar associates instead of polar ion pairs.
Figure 1. Dependence of observed rate constant, kobs (sꢀ1),
on concentration of trichloroacetic acid, c (mol dmꢀ3), for 3-
methyl-1,3-diphenyltriazene
Scheme 1
Copyright # 2004 John Wiley & Sons, Ltd.
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O. PYTELA, R. BEDNAR AND J. KAVALEK
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346
The suggestion was based upon the presumption of
or higher associates of trichloroacetic acid can be taken in
to account as the catalyst particles.
identical reaction mechanisms for all the compounds
studied, and the presumption of three basic factors
affecting the experimental dependence of observed rate
constant on trichloroacetic acid concentration, viz. the
solvent, the substrate and the acid catalyst.
On the basis of the above considerations, we have
created a systematic series of possible kinetic models and
the respective regression functions for the interpretation
of the measured dependences of the observed rate con-
stant, kobs, on the concentration of trichloroacetic acid, c.
The models start from Scheme 1 and involve catalysis by
monomeric and dimeric trichloroacetic acid, the potential
formation of associates of trichloroacetic acid with the
N1 and N3 atoms of triazene and a possible dependence
of rate and equilibrium constants on the changes in
properties of the reaction medium due to added trichlor-
oacetic acid.
Hexane as a non-polar ("r ¼ 1.91) aprotic solvent28
does not stabilize either polar transition states or polar
products of an ionic nature. However, the properties
of this medium can be changed by the addition of
trichloroacetic acid (monomer, ꢁ ¼ 3.0, Ref. 29) as a
co-solvent. Experimental measurements in binary mix-
tures composed of a non-polar and a polar solvent
showed30 that the reacting system is preferably solvated
by the more polar component, and the logarithm of the
observed rate constant is a linear function of concentra-
tion over a broad concentration interval.31 Measure-
ments32 of the acid-catalysed decomposition of 1,3-
bis(4-methylphenyl)triazene by various organic acids in
mixtures of hexane and the organic acid revealed an
exponential increase in the observed rate constant at
low concentrations of the organic acid used as the co-
solvent. Therefore, it can be deduced for the system
studied that the values of the logarithm of rate and
equilibrium constants in Scheme 1 can depend on the
trichloroacetic acid concentration in the reaction mix-
ture,33 especially at lower concentrations of the acid.
The properties the substrate in the series adopted are
predominantly due to the distribution of electron density
in nitrogen atoms of the triazene chain, and to inductive
and steric effects of the alkyl groups. From quantum-
chemical calculations,18–20 it can be presumed that the
N1 and N3 atoms will be protonated (or, as the case may
be, will form associates with the acid), which stands
in accordance with the resonance formula given in
Scheme 1. From configurational studies it is known that
triazenes possess a trans configuration, and the cis–trans
isomerization is subject to general acid and general base
catalyses.17 The barrier to rotation around the N2—N3
bond of 1-phenyl-3,3-dialkyltriazenes in a non-polar
solvent34 depends little on the bulkiness of the alkyl
substituent, and the molecule is almost planar. The
mutual steric interaction between alkyl and phenyl
groups in the 3-alkyl-1,3-diphenyltriazenes studied can,
in principle, cause a deviation of the benzene ring from
the common plane of the N1, N2, and N3 atoms. This can
restrict or even prevent the delocalization of free electron
pairs from the N3 atom into the benzene ring (steric
hindrance to resonance), while the electron density of this
atom can be contrastingly increased.
With the use of the criterion of the minimum residual
standard deviation, the model in Eqn (1) was selected.
2
K1ðkHA½HAꢃ þ kHA2½HAꢃ Þegc
kobs
¼
ð1Þ
2
ð1 þ K1½HAꢃ egcÞ
where kHA is the rate constant of reaction with participa-
tion of one molecule of trichloroacetic acid, kHA2 is the
rate constant of reaction with participation of two mole-
cules of trichloroacetic acid, K1 is the dissociation con-
stant of associates of two molecules of trichloroacetic
acid with N1 of triazene (A1-2 in Scheme 1) and g is the
slope of the dependence describing changes in pro-
perties of the reacting system caused by the addition of
trichloroacetic acid as a co-solvent. The introduction of
an exponential term into the regression model was
inevitable for a proper description of the onset part of
the dependence at low concentrations of acid. The calcu-
lation with separate constants g for the individual rate and
equilibrium constants in Eqn (1) proved that they are
identical for a given substrate.
According to the literature,33,35 the dimer D is a
dominating form of trichloroacetic acid in the given
medium. Its concentration in solution can be expressed
by
½Dꢃ ¼ c=2
ð2Þ
The concentration of monomer, M, in the solution is
given by Eqn (3)
pffiffiffiffiffiffiffiffiffiffiffiffi pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
½Mꢃ ¼ KD½Dꢃ ¼ KDðc=2Þ
ð3Þ
where KD is the dissociation constant of the dimer giving
the monomer. After introducing the concentrations of
monomer and dimer from Eqns (2) and (3) into Eqn (1),
we obtain
According to literature data,33,35 trichloroacetic acid
predominantly exists as a dimer in non-polar solvents.
The dissociation constant KD of the dimer to monomer is
low in non-polar solvents (e.g. KD ¼ 0.0018 in toluene;
unknown for hexane). The dissociation of monomeric
trichloroacetic acid to its conjugated base and proton is
obviously negligible, and thus only the monomer, dimer
pffiffiffiffiffiffiffiffiffiffiffi
pffiffiffiffiffiffi
K1½kHA KD ðc=2Þ þ kHA2ðc=2Þꢃegc
1 þ K1ðc=2Þegc
kobs
¼
ð4Þ
The quality of fitting experimental points by the curves
calculated from Eqn (4) is shown in Figs 1 and 2. The
Copyright # 2004 John Wiley & Sons, Ltd.
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ACID-CATALYSED DECOMPOSITION OF 3-ALKYL-1,3-DIPHENYLTRIAZENES
347
pffiffiffiffiffiffi
Table 1. Number of measurements n of observed rate constants, values of rate constants kHA KD and kHA2, values of
dissociation constant K1 and values of parameter g in Eqn (4), their standard deviations and residual standard deviation s (the
constants not given are statistically insignificant)
pffiffiffiffiffiffi
kHA KD
kHA2
K1
(dm3 molꢀ1
g
Substituent
n
(dm3 molꢀ1 sꢀ1
)
(dm3 molꢀ1 sꢀ1
)
)
(dm3 molꢀ1
)
s (sꢀ1
)
CH3
CH3CH2
CH3CH2CH2
CH3(CH2)2CH2
CH3(CH2)3CH2
(CH3)2CH
61
69
63
66
64
77
79
92
57.4 ꢂ 0.3
75.8 ꢂ 0.5
87.3 ꢂ 0.3
87.7 ꢂ 0.5
85.6 ꢂ 0.4
5.92 ꢂ 0.5
2.39 ꢂ 0.4
4.22 ꢂ 0.43
4.67 ꢂ 0.53
4.97 ꢂ 0.32
5.44 ꢂ 0.43
6.37 ꢂ 0.43
22.3 ꢂ 2.9
72.8 ꢂ 5.4
219 ꢂ 44
49.0 ꢂ 2.1
51.8 ꢂ 2.7
49.0 ꢂ 1.5
55.8 ꢂ 2.1
55.3 ꢂ 1.8
140 ꢂ 8
1.39
2.70
1.68
2.23
1.89
1.21
7.52 ꢂ 0.12
2.86 ꢂ 0.10
5.32 ꢂ 0.04
CH3CH2(CH3)CH
cycloC6H11
89.3 ꢂ 8.5
66.3 ꢂ 13.3
0.983
1.14
values of statistically significant parameters in Eqn (4)
and their standard deviations are presented in Table 1.
The course of observed rate constant, kobs, on concen-
rate constant between neutral bipolar molecules of tria-
zene and trichloroacetic acid on the properties of solvent
can be expressed28 by
tration of trichloroacetic acid, c, depends on the ratio of
pffiffiffiffiffiffi
!
ꢁ2
ꢁ2TAA;eff
the magnitudes of the constants kHA KD (the reaction of
triazene with the participation of one molecule of tri-
chloroacetic acid), kHA2 (the reaction of triazene with the
participation of two molecules of trichloroacetic acid)
and K1 (the dissociation of non-reactive associate A1-2. If
1 NA "r ꢀ 1 ꢁ2T
¼
ln k ¼ ln k0 ꢀ
þ
ꢀ
rT3 rT3AA;eff r3
4ꢂ"0 RT 2"r þ 1
¼
ð5Þ
K1 is small, and kHA2 is significantly greater than the
pffiffiffiffiffiffi
where k is the rate constant kHA or kHA2 in the given
medium, k0 is the rate constant of the same reaction in
the standard state, "r is the relative permittivity of
the medium, ꢁT is the dipole moment of triazene,
ꢁTAA;eff is the effective dipole moment of all forms of
product kHA KD, then only the reaction with the parti-
cipation of two molecules of trichloroacetic acid makes
itself felt kinetically. The dependence for low concentra-
tions of trichloroacetic acid increases approximately
exponentially and forms a plateau at high concentrations
(typically 1-methyl-1,3-diphenyltriazene, Fig. 1). This
course was observed with all the 3-alkyl-1,3-diphenyl-
trichloroacetic acid in the given medium, ꢁ is the dipole
¼
moment of the activated complex of reaction and
rT; rTAA;eff and r are the radii of the corresponding
¼
triazenes having linear alkyl groups (the constant
kHA KD is statistically insignificant). For opposite ratios
pffiffiffiffiffiffi
particles. Formally identical is the description of the
dependence of the equilibrium constant on the properties
of solvent by
pffiffiffiffiffiffi
of the magnitudes of kHA KD and kHA2, the kinetically
dominant reaction is that involving one molecule of
trichloroacetic acid. The dependence at low acid concen-
trations also increases almost exponentially, but at high
!
ꢁ2TAA;eff
rT3 rT3AA;eff
1 NA "r ꢀ 1 ꢁ2T
ꢁA2
rA3
ln K ¼ ln K0 ꢀ
þ
ꢀ
4ꢂ"0 RT 2"r þ 1
concentrations there is a drop corresponding to the
pffiffiffiffiffiffiffi
reciprocal of c=2 (typically 3-sec-butyl-1,3-diphenyl-
triazene, Fig. 2). This course was observed with isopropyl
ð6Þ
and sec-butyl substituents. If K1 is sufficiently high, and
pffiffiffiffiffiffi
where K is the equilibrium constant (K1, K31 orK32 in
Scheme 1) in the given medium, K0 is the equilibrium
constant in the standard state, ꢁA is the dipole moment of
the associate of triazene and trichloroacetic acid, rA is its
radius, and the other symbols are as in Eqn (5). The
dependence of the Kirkwood function on the concentra-
tion of the polar co-solvent in the non-polar aprotic
solvent is approximately linear;36 for associating car-
boxylic acids it is sometimes necessary to add a quadratic
term.37,38 In the narrow range of concentrations of
trichloroacetic acid used, this dependence can be con-
sidered linear, i.e.
kHA2 is negligible compared with the product kHA KD,
then the exponential increase is suppressed at low con-
centrations of trichloroacetic acid, and only the decrease
pffiffiffiffiffiffiffi
corresponding to the reciprocal c=2 is observed (as is
the case with 3-cyclohexyl-1,3-diphenyltriazene; the con-
stant kHA2 is statistically insignificant.
Evaluation of effect of trichloroacetic acid
as co-solvent
The necessity for involvement of the exponential term
with parameter g in Eqn (4) indicates the effect of change
in reaction medium on the reaction under study. A semi-
empirical description of the dependence of the reaction
"r ꢀ 1
ꢄ ꢃc
ð7Þ
2"r þ 1
Copyright # 2004 John Wiley & Sons, Ltd.
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O. PYTELA, R. BEDNAR AND J. KAVALEK
´
348
where ꢃ is a constant of proportionality. The comparison
of Eqns (4) and (5) or Eqns (4) and (6) taking into account
Eqn (7) shows that parameter g in the exponential term of
Eqn (4) is a measure of the difference between polarities
of the transition state and the educts, or that between the
polarities of the associate and its components.
presumption that the associate is A1-2 in Scheme 1. The
constant characterizing sensitivity to steric effects is
positive, and the branching of alkyl (described by the
indicator variable Ind) increases the value of the disso-
ciation constant K1 even more. From what has been said,
it follows that a dominating part in the formation of
associate A1-2 is played by steric effects, which lower the
stability as expected.
The dependence of the logarithm of rate constant kHA2
from Table 1 is quantitatively described by Eqn (9) for all
the substituents except cyclohexyl (where kHA2 is statis-
tically insignificant):
As already stated, the found values of parameter g are
positive for a given substitution derivative (Table 1) and
identical in both the numerator and denominator of kinetic
model (4), hence they are obviously due to the same
process. From the form of the kinetic model (4), it follows
that the exponential term is connected with the dissocia-
tion constant K1, whereas the rate constants kHA and kHA2
are independent of the parameter g. The dependence of the
dissociation constant K1 on changes in the properties of
the solvent is, according to Eqn (6), given by the differ-
ence between the polarities of the components in this
equilibrium. As the dipole moment of trichloroacetic acid
dimer (predominating form in the reaction mixture) is
approximately zero38 and that of triazene39 is low
(ꢁ ¼ 0.79), obviously in the respective associate the pro-
ton is transferred to a considerable extent. On the other
hand, the absence of the effect of the change of the
medium on the rate constants kHA and kHA2 according to
Eqn (5) indicates a small difference in polarities of the
educts and the activated complex. Therefore, it can be
deduced that the reacting species is probably the polar
monomer of trichloroacetic acid (ꢁ ¼ 3.0)29 or the open
dimer, the proton being transferred to the substrate to only
a small extent in the transition state.
log kHA2 ¼ ð1:74 ꢂ 0:24Þ ꢀ ð25:6 ꢂ 7:3Þꢅi
ð9Þ
ꢀ ð1:90 ꢂ 0:51Þꢄ ꢀ ð1:14 ꢂ 0:11Þ Ind
n ¼ 7; R ¼ 0:998; s ¼ 1:68 ꢅ 10ꢀ2; Fð2; 4Þ ¼ 586:3
where ꢅi are substituent constants41 describing the in-
ductive effect and the other symbols are as in Eqn (8).
The reaction constant describing the inductive effect is
negative and very large. Its sign is in accordance with the
mechanism involving the splitting off of electrofuge
(diazonium cation) in the rate-limiting step of the reac-
tion. The magnitude of the reaction constant indicates a
high sensitivity to changes in electron density at the
reaction centre. The reaction constant describing steric
effects is again negative, as expected, and its magnitude is
comparable to that in Eqn (8). However, as the attack by
reagent takes place at the atom carrying the substituent,
the steric effects should make themselves felt more
markedly. Therefore, it can be deduced that the reaction
does not go via associates A3-1 and A3-2 (Scheme 1) but
proceeds in a single reaction step. The arrangement of the
activated complex is less organized in comparison with
associate A1-2, and the proton transfer to substrate is less
advanced. This conclusion is in accordance with the
above-mentioned conclusion following from the inter-
pretation of the change of medium on the rate constants
Evaluation of substitution effects
The dependence of the logarithm of the dissociation
constant K1 on substitution is quantitatively described by
log K1 ¼ ꢀð0:435 ꢂ 0:160Þ þ ð1:83 ꢂ 0:25Þꢄ
ð8Þ
þ ð0:444 ꢂ 0:117ÞInd
kHA and kHA2
The values of rate constant kHA KD of the reaction
.
pffiffiffiffiffiffi
n ¼ 8; R ¼ 0:993; s ¼ 9:28 ꢅ 10ꢀ2; Fð2; 5Þ ¼ 169:6
with the monomer are statistically significant only for
pffiffiffiffiffiffi
branched-chain alkyls. The values of kHA KD decrease
with increasing substituent constant ꢅi, in the same way
as with the constant kHA2 [Eqn (9)]. Therefore, it can be
deduced that the reaction course is similar, but this
hypothesis is impossible to verify quantitatively owing
to the small number of substituents studied.
where ꢄ are the Charton constants for the description of
the steric effects of substituents,40 Ind is the indicator
variable taking into account the differences between
straight- and branched-chain alkyls (Ind being 0 and 1
for the former and latter, respectively), n is number of
points, s is residual standard deviation and F is the
criterion of statistical significance of the explaining
variables in the regression. From Eqn (8), it is obvious
that the dissociation constant K1 depends exclusively on
steric effects, whereas the inductive effect described by
the constant ꢅi41 is statistically insignificant. Therefore, it
follows that trichloroacetic acid molecules are associated
at such a site of triazene that is separated by several bonds
from the substitution site. This confirms the original
The dependence of the values of the parameter g
(describing the effect of change of medium on the
dissociation constant K1) on the Charton constants40
ꢄ
is represented in Fig. 3. The picture clearly shows the
difference between linear and branched alkyls as sub-
stituents. The values of g for branched-chain alkyls are
higher and (in contrast to those of linear-chain alkyls)
depend markedly on the bulkiness of the substituent. This
can be caused by the above-mentioned (see Introduction)
Copyright # 2004 John Wiley & Sons, Ltd.
J. Phys. Org. Chem. 2004; 17: 343–349

ACID-CATALYSED DECOMPOSITION OF 3-ALKYL-1,3-DIPHENYLTRIAZENES
349
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The course of the dependence of observed rate constant
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Acknowledgement
The authors are indebted to the Ministry of Education,
Youth and Sports of the Czech Republic for financial
support (Research Project CIMSM 253 100001).
Copyright # 2004 John Wiley & Sons, Ltd.
J. Phys. Org. Chem. 2004; 17: 343–349