The kinetics of complex formation in the trithiadiazoletri[3,4-di(4-tert- butylphenyl)-pyrrole] macrocycle-copper(ii) acetate-dmfa-h2o system

Article abstract of DOI:10.1134/S0036024409100112

The paper presents the results of a study of the kinetics of coordination of a macroheterocyclic compound with an increased coordination cavity of the (3 + 3) McH₃ composition consisting of sequentially alternating 1,3,4-thiadiazole and 3,4-bis

Full text of DOI:10.1134/S0036024409100112

ISSN 0036ꢀ0244, Russian Journal of Physical Chemistry A, 2009, Vol. 83, No. 10, pp. 1694–1700. © Pleiades Publishing, Ltd., 2009.
Original Russian Text © T.N. Lomova, E.G. Mozhzhukhina, E.A. Danilova, M.K. Islyaikin, 2009, published in Zhurnal Fizicheskoi Khimii, 2009, Vol. 83, No. 10, pp. 1877–1883.
CHEMICAL KINETICS
AND CATALYSIS
The Kinetics of Complex Formation
in the Trithiadiazoletri[3,4ꢀdi(4ꢀtertꢀbutylphenyl)ꢀpyrrole]
Macrocycle–Copper(II) Acetate–DMFA–H2O System
T. N. Lomovaa, E. G. Mozhzhukhinaa, E. A. Danilovab, and M. K. Islyaikinb
a Institute of the Solution Chemistry, Russian Academy of Sciences, Ivanovo, Russia
b Ivanovo State University of Chemical Technology, Ivanovo, Russia
eꢀmail: tnl@iscꢀras.ru
Received April 6, 2007
Abstract—The paper presents the results of a study of the kinetics of coordination of a macroheterocyclic
compound with an increased coordination cavity of the (3 + 3) McH3 composition consisting of sequentially
alternating 1,3,4ꢀthiadiazole and 3,4ꢀbis(4ꢀtertꢀbutylphenyl)pyrrole fragments to dehydrated Cu(OAc)2 in
dimethylformamide with and without H2O admixtures. The reaction could be controlled spectrophotometꢀ
rically over the salt and ligand concentration ranges (0.175–0.55)
×
10–4 and (0.16–0.64)
×
10–5 mol/l,
respectively, at temperatures of 288–303 K. A kinetic equation of an unusual form with a negative order with
respect to the salt was for the first time obtained experimentally for a macrocyclic ligand by the method of
excess concentrations. The kinetics of the complex formation reaction was given a theoretical interpretation.
Quantitative characteristics were obtained, and the role played by water in the kinetics of complex formation
was studied. These data were of importance for practical applications, for the development of optimum conꢀ
ditions increasing the yield of complexes when they were synthesized in complex formation reactions.
DOI: 10.1134/S0036024409100112
INTRODUCTION
for the example of the reaction with Ni(OAc)2 [11, 12].
Quantitative data on the reactivity of thiadiazoloporꢀ
phyrinoid consisting of six sequentially alternating thiꢀ
adiazole and 3,4ꢀbis(4ꢀtertꢀbutylphenyl)pyrrole fragꢀ
ments linked by six aza bridges (McH3) were obtained.
It was shown that the reaction proceeded as a step
introduction of the metal cation into the coordinating
After the discovery and determination of the strucꢀ
ture of new macroheterocyclic compounds (3 + 3)
based on 2,5ꢀdiaminoꢀ1,3,4ꢀthiadiazole and substiꢀ
tuted 1,3ꢀdiiminoisoindoline or 2,5ꢀdiiminopyrroline
by experimental and calculation methods [1–5], interꢀ
esting for practical applications properties of these
27 heteroannulenes were found. Lyotropic mesomorꢀ
phism of compounds with phenol and 4ꢀhydroxyaꢀ
zobenzene spacer groups [6], radioprotection properꢀ
ties [7], and electrocatalytic activity in the reduction
of oxygen [8] were observed and studied. Note that the
compounds exhibit these properties in the form of
complexes with metals and with effectiveness that
depends on the nature of the metal cation fairly
strongly. This is also true of complexes of thiadiazoleꢀ,
triazoleꢀ and isoindoleꢀcontaining macroheterocyclic
compounds with a different stoichiometry with respect
to condensed rings and heterorings, such as (3 + 1) or
(2 + 2) complexes [9, 10]. In spite of this circumstance,
the physicochemical properties of (3 + 3) complexes
with metals, not to mention the complex formation
reaction itself, remain almost unstudied. It is only
space of МсН3
.
In this work, we present the results of a kinetic
study of the complexꢀforming ability of МсН3
,
N
N
N
H
S
N
N
S
N
N
N
N
H
H
N
N
N
N
known that, with Ni as distinct from the other 3d metꢀ
als, the formation of the complex occurs more effecꢀ
tively under the condition of template assembly of the
macroheterocycle from heterocyclic fragments.
The first quantitative study of complex formation
from a readyꢀmade (3 + 3) compound was performed
N
N
S
(McH3, 1)
1694

THE KINETICS OF COMPLEX FORMATION
Table 1. Rate constants (
1695
k
eff and
k
) for complex formation
in its reaction with Cu(OAc)2 or Cu(OAc)2 Н2О in
⋅
between 1 and Cu(OAc)2 in DMFA with water admixtures
dimethylformamide (DMFA). The (3 + 3) composiꢀ
tion of this compound was substantiated in [13–15] by
the UV, visible, IR, and 1H and 13C NMR spectral data
and liquid secondary ion mass spectrometry (LSIMS)
and also by quantumꢀchemical calculations.
cCu(OAc)
×
104,
keff
×
105,
s–1
k
1014,
×
2
T, K
mol–2 l2 s–1
mol/l
0.016% H2O
0.35
0.4
298
298
303
303
298
4.7 0.23
3.4 0.19
29.0 1.2
22.0 0.8
2.3 0.14
7.06
1.41
EXPERIMENTAL
МсН3 was synthesized as described in [1]. The
electronic absorption spectrum (chloroform), λmax
nm log ): 265 (4.45), 328 (4.28), 428 (4.69),
452 (4.69), 515 (shoulder), and 552 (3.73).
The kinetics of coordination of by copper cations
,
0.45
0.5
(
ε
1
0.048% H2O*
in DMFA was studied spectrophotometrically under
polythermal conditions. The temperature of reaction
mixtures was maintained constant to within 0.1 K in a
special cell of an SFꢀ26 spectrophotometer. Changes in
0.175
0.225
288.5
288.5
1.37 0.08
1.2 0.055
* Secondꢀorder equilibrium constants with respect to McH , k
×
3
eff
5
–1 –1
10 , mol l s
.
the concentration of
1 were monitored by measuring
the optical density of the reaction mixture at the workꢀ
ing (optimized) wavelength 420 nm on SFꢀ26. Changes
in the composition of the reaction mixture were deterꢀ
mined by recording the electronic absorption spectra
over the frequency range 200–900 nm on an Agilent
8453 spectrophotometer. Analyses for Cu were perꢀ
formed on an AASI atomic absorption spectrometer.
Table 1 and Figs. 1–3 contain data on the complex
formation reaction in DMFA–0.016% H2O. To eluciꢀ
date the influence of water in amounts much larger
than the concentrations of the reagents, we also studꢀ
ied the kinetics of the coordination reaction in
DMFA–0.048% (2.53
×
10–2 mol/l) H2O (Table 1)
We used reagents of kh. ch. (chemically pure)
grade. Anhydrous copper acetate was prepared by the
and the kinetics of the reaction with copper salt crystal
hydrate; that is, when water was present in the coordiꢀ
nation sphere of initial salt molecules (Table 2, Fig. 4).
As follows from these data, the experimental kinetic
equation has the form
recrystallization of Cu(OAc)2 Н2О from aqueous aceꢀ
⋅
tic acid; the product was dried at 373 K until its weight
ceased to change [16]. DMFA was dehydrated followꢀ
ing the standard procedure [17]. The content of water
in DMFA determined according to Fischer was
–dc1/dτ = kc01c0
(3)
0.016% (0.84
10–2 mol/l).
×
Cu(OAc)22
for the reaction of
1
with anhydrous copper(II) acetate
RESULTS AND DISCUSSION
The effective (experimental) rate constants (k
eff, s–1,
in DMFA–0.016% H2O and copper(II) acetate
hydrate, when the concentration of H2O in DMFA
was 0.048%. For the reaction with anhydrous copꢀ
per(II) acetate in DMFA–0.048% H2O, Table 1 conꢀ
tains constants second order in the concentration of
because a linear “reagent concentration (optical denꢀ
Table 1) for coordination in the presence of excess
copper salt (Cu(OAc)2 or Cu(OAc)2 H2O) with
⋅
respect to
1
(the concentrations of
1
were (0.16–0.64)
×
10–5 mol/l) were found using the method of least
1,
squares through the optimization of the dependence
A0 – A
A – A
τ
∞
lnꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀ = keffτ,
∞
(1)
log((A0
−
A
)/(
A
−
A ))
∞
∞
τ
where A0, A , and A are the optical densities of soluꢀ
τ
∞
tions at the working wavelength at time 0, , and after
τ
1
0.2
reaction completion, respectively. The linearity of the
dependences in the coordinates of Eq. (1) means that
the coordination reaction is firstꢀorder in the concenꢀ
2
3
tration of 1 (Figs. 1, 2).
0
50
100
150
τ
, min
The negative reaction order with respect to the
copper salt concentration, which was approximately
–2 (–1.98 at 298 K), was found through processing
the linear dependences
Fig. 1. Dependences of log
the reaction of macrocyclic compound
(
(A
–
A
)/(
1
A
–
A
)
) on
τ
for
0
∞
τ
∞
with Cu(OAc) in
2
5
DMFA–0.016% Н О at 298 K; cCu(OAc)
×
10 , mol/l:
2
2
logkeff
=
logk + nlog[Cu(OAc)2]
(2)
(
1
) 3.5, (
2
) 4.0, and (
3
) 5.0 (ρ = 0.997, 0.995, and 0.988,
by the method of least squares (Fig. 3).
respectively).
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1696
LOMOVA et al.
log((A0
−
A
)/(A
τ
−
A
))
−
log
c
∞
∞
4.5
4.4
4.3
1
1.2
0.8
0.4
0
2
3.4
3.8
4.2
1
3
4.6
2
−
logkeff
4
Fig. 3. Dependences of log
k
on logcCu(OAc) for the
eff
2
reaction of macrocyclic compound
DMFA–0.016% H O at , K: ( ) 298 and (
0.992 and 1.0, respectively).
1 with Cu(OAc) in
2
ρ
T
1
2
) 303 ( =
2
rence of the following three reactions during complex
formation:
50
100
150
τ
, min
K
1
Fig. 2. Dependences of log
the reaction of macrocyclic compound
Н О in DMFA at 288.5 K; cCu(OAc)
(
(
A
–
A
)/(
1
A
–
A
)
) on
τ
for
0
∞
τ
∞
МсН3 + 2Сu(OAc)2
McH3
⋅
2Cu(OAc)2, (5)
with Cu(OAc)
⋅
2
K
2
5
⋅
Н О
×
10 , mol/l:
Cu(OAc)2
[Cu(OAc)]+ + OAc–,
(6)
2
2
2
(
1
) 1.75, (
2
) 2.5, (
3
) 2.75, and (
4
) 3.0 (ρ = 0.998, 0.995,
k
3
[Cu(OAc)]+ + McH3
McH2Cu(OAc) + H+. (7)
0.987, and 0.988, respectively).
According to this scheme, the slow complex forꢀ
mation stage is preceded by equilibria with noncovaꢀ
sity in the spectrophotometric method)–time” correꢀ
lation is then observed in the 1/ coordinates rather
than in the coordinates of Eq. (1).
For complex formation with nickel(II), a positive
reaction order 2 with respect to the salt was found [12],
lent complex formation between salt molecules and
1
A–τ
and salt ionization with the detachment of the acetate
ion. This scheme is followed by the majority of enzyꢀ
matic processes because of low enzyme concentraꢀ
tions compared with substances undergoing transforꢀ
mations [18]. Reaction (6) does indeed occur in
DMFA. According to [19], equilibrium is strongly
shifted to the right, although the K2 value remains
unknown. The rate equation for limiting stage (7)
written taking into account preceding equilibria has
the form
–dc1/dτ = kc1c
.
(4)
Ni(OAc)22
The conclusion can be drawn that the reaction order
with respect to the salt in Eq. (3) is evidence of a more
complex mechanism of complex formation with copꢀ
per(II).
The negative reaction order with respect to the salt
can be interpreted on the assumption of the occurꢀ
–dc1/dτ = k3c1c
+
[Cu(OAc)]
(8)
Table 2. Rate constants for reaction between
Cu(OAc)2
1
H2O in DMFA with 0.048% H2O at 288.5 K
and
=
k3K–11K12/2
c
c1 ⋅ 2Cu(OAc) .
Cu(OAc)2
2
–3 ⁄ 2
⋅
The experimentally found negative reaction order
with respect to the salt is in conformity with Eq. (8),
but this equation does not coincide in detail with the
experimental rate equation (Eq. (3)) containing the
initial reagent concentrations. The equilibrium conꢀ
keff
104, s–1
×
cCu(OAc)
×
105, mol/l
2 ⋅ H2O
1.75
2.0
3.1 0.08 (5.35)
2.4 0.16
2.25
2.5
2.0 0.07
centration c1 ⋅ 2Cu(OAc) can approximately be set equal
2
1.7 0.13
to c01 , but cCu(OAc) equals cC0 u(OAc)
– c[Cu(OAc)]+ because
2
2
2.75
1.4 0.08
equilibrium (6) is shifted to the right in DMFA [19].
The reason for discrepancies can be experimental conꢀ
ditions, namely, a not too large excess of the salt with
3.0
1.1 0.07
13
–2 2 –1
Note: The k × 10 , mol l s value is given in parentheses.
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THE KINETICS OF COMPLEX FORMATION
1697
A
−
log
c
(а)
4.8
4.7
4.6
4.5
3.4
1
0.4
3.6
3.8
2
0.2
0
A
0.4
4.0
logkeff
400
500
600
(b)
λ
, nm
−
1
Fig. 4. Dependence of log
k on logcCu(OAc) for the
eff
2
reaction of macrocyclic compound
1
with Cu(OAc) Н О
⋅
2 2
in DMFA–0.048% H O at 288.5 K (
ρ
= 0.99).
2
2
0.2
respect to the ligand in the reaction. The excess was on
average one order of magnitude only; this is the smallꢀ
est possible excess in the method of excess concentraꢀ
tions for obtaining rate constants with errors smaller
than 10%.
0
400
500
600
λ
, nm
To check the validity of scheme (5)–(7), complex
formation was studied spectrophotometrically with
varying the ratio between salt and ligand concentraꢀ
tions over a wide range. The rate of the reaction was
estimated from the time of complete conversion. The
theoretically obligatory reversal of the dependence of
the rate on the concentration of the salt or regions in
which the rate was independent of salt concentration
were not observed.
Fig. 5. Electronic absorption spectra of (
) the products of its complex formation with (a) nickel
[12] and (b) copper salts in DMFA.
1) МсН and
3
(
2
do not change under the conditions of reaction kinetꢀ
ics studies.
The absence of complete step complex formation
in the coordination of
1
with Cu2+ is proved by the
spectral data (Fig. 5). The electronic absorption specꢀ
trum of the reaction product is sharply different from
the spectra of 1 : 3 complexes with Ni2+ (Fig. 5,
Special experimental studies were performed to
substantiate the nature of the complex formation reacꢀ
tion products and possible reaction occurrence to the
equilibrium state. The reversibility of the reaction was
observed spectrophotometrically by adding AcOH to
reaction products. A shift of equilibrium to the left
caused the restoration of the initial twoꢀband elecꢀ
tronic absorption spectrum of macroheterocyclic
curves 2). In addition, the separation (by thinꢀlayer
chromatography) and analysis of nonequilibrium
reaction mixture components after the solvent was disꢀ
tilled off in a vacuum gave the following results. The
product of Cu2+ coordination was a mixture of three
compounds, the electronic absorption spectrum of
compound 1. The spectrum was displaced toward
shorter waves by 12 nm.
one of which coincided with the spectrum of
mobilities of these compounds in thinꢀlayer chroꢀ
matographing (Silufol, CHCl3) were different, Rf
0.80, 0.82, and 0.83. After equilibrium was estabꢀ
lished, the product, in addition to , contained only
1. The
According to our data [14], such a hypsochromic
shift of electronic absorption spectra in the presence of
acids is indicative of the dissociation of the copper
=
1
complex with
1. It is related to the single protonation
one colored compound, which was, according to analꢀ
yses for copper, McH(Cu(OAc))2. It was shown
experimentally that equilibrium was established in
4 h on average, which allowed us to measure the rate
of the forward reaction fairly accurately (Tables 1, 2).
The data considered above allow the summary equaꢀ
of studied quantitatively by spectral methods and
1
theoretical calculations. These data and the spectra
shown in Fig. 5 lead us to conclude that the reaction
between
1 and Cu(OAc)2 is not a simple acidꢀbase
transformation or macroring structure modification
catalyzed by the salt. The acidꢀbase reaction with the
base (acetate ion) should also be excluded. Indeed, the
tion for complex formation between
written as
1
and Cu2+ to be
electronic absorption spectra of
1 in DMFA in the
presence of Na(OAc) with acetate ion concentrations
coinciding with those from the copper salt in reaction
mixtures (Table 1) are similar to curves 1 in Fig. 5 and
McH3 + 2Cu(OAc)2
(9)
McH(Cu(OAc))2 + 2AcOH.
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1698
LOMOVA et al.
K
To substantiate this equilibrium, we performed the
spectrophotometric titration of compound with
2
[Cu(OAc)]+ + McH
McH2Cu(OAc) + H+, (10)
3
1
anhydrous copper acetate in the DMFA–0.016% H2O
solvent. The process required holding reaction mixꢀ
tures of all compositions for 4–6 h. It was found from
the titration curve that equilibrium could be comꢀ
pletely shifted from left to right as the salt concentraꢀ
+
McH2Cu(OAc) + [Cu(OAc)]
(11)
k
McH(Cu(OAc))2 + H+.
3
tion changed from 3.5
equilibrium constants were
303 = (3.0 1.0) 104 mol/l. Since Сu(OAc)2 experiꢀ
enced dissociation in the solution under consideration equilibrium (9) is the dissociation of the binuclear
with the detachment of one acetate ion and existed at complex of copper with
formed in reaction (11)
equilibrium with [Cu(OAc)(DMFA)5
+, the concenꢀ under the action of protons released in the reaction.
×
10–5 to 5.5
298 = (1.6 1.0)
×
10–5 mol/l. The
For the Back Reaction of Equilibrium (9)
The limiting transformation in the back reaction of
K
×
105 and
K
×
1
]
tration of the latter particle being higher, titration was Like the forward reaction, the back reaction proceeds
performed over the range of salt concentrations close in two stages,
to those used in kinetic experiments. At higher salt
McH(Cu(OAc))2 + H+
concentrations, there could be additional equilibria
with the dissociation of the second acetate ion or
dimerization.
k
McH2Cu(OAc) + [Cu(OAc)]+,
(12)
(13)
4
It follows that the experimental
K constant is in
essence the product of two equilibrium constants,
those of salt ionization and complex formation
between McH3 and Cu(OAc)2. The presence of
three colored compounds in the nonequilibrium
reaction mixture and only two colored compounds
after reaction completion is explained by another
scheme of elementary reactions during complex
formation.
In order to theoretically describe the elementary
stages and kinetics of overall reaction (9), we considꢀ
ered the following scheme of the reversible complex
formation reaction; the scheme was in agreement with
experiment.
slowly
McH2Cu(OAc) + H+
K
+
4
McH3 + [Cu(OAc)] , fast.
The rates of the forward and back reactions of equiꢀ
librium (9) are limited by slow stages (11) and (12),
where Kа is the equilibrium constant of acetate ion
protonation (acid dissociation of AcOH),
–dcMcH Cu(OAc)/dτ = –dc1/dτ
2
=
k3cMcH Cu(OAc)
c
= k3K2c2
+c c–H1+
+
(14)
(15)
1
For the Forward Reaction of Equilibrium (9)
2
[Cu(OAc)]
[Cu(OAc)]
K21K2k3c1c2Cu(OAc) cH–1+c(–O2Ac)
,
First,
Cu(OAc)2(DMFA)4] with the detachment of one
acido ligand and the formation of the
equilibrium
of
ionization
of
=
–
2
[
+
[Cu(OAc)(DMFA)5
] solvato complex is established
–dcMcH(Cu(OAc)) /dτ = k4cMcH(Cu(OAc))
c
2
H+
2
at a high rate. (In what follows, solvent molecules are
omitted from the formula of the solvato complex.)
After this, the limiting reaction of the coordination of
=
k4KacMcH(Cu(OAc)) cAcOHc–1
.
(OAc)
–
4
the cationic copper complex to ligand
complex formation reaction proceeds in two stages;
the first stage is also reversible,
1 occurs. The
If the forward and back reactions have the same
transition state, the equilibrium constant is as follows:
K' = (k4KaCMcH(Cu(OAc)) CAcOHC–1 )/(K2K k c c2 cH–1+c–(O2Ac)
2 3 1 Cu(OAc)2
)
–
–
1
2
(OAc)
(16)
(17)
=
const(cMcH(Cu(OAc)) c2AсOH)/(c1cC2 u(OAc) );
2 2
K = (cMcH(Cu(OAc)) cA2 cOH)/(c1cC2 u(OAc) ).
2
2
Equation (17) corresponds to the equation for the equiꢀ reaction (9), which allows us to write the general scheme
librium constant of experimentally substantiated overall of complex formation between and copper acetate:
1
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THE KINETICS OF COMPLEX FORMATION
1699
Forward reaction
Equation
Back reaction
K
1
Fast preequilibrium
Limiting reaction
Fast postequilibrium
Cu(OAc)2
McH3 + 2[Cu(OAc)]+
AcOH
H+ + (OAc)–
[Cu(OAc)]+ + (OAc)–
McH(Cu(OHAc))2 + 2H+
Fast postequilibrium
Limiting reaction
Fast preequilibrium
It is easy to get an idea of the transition state for
reaction (9) from Eqs. (11) and (12),
In complex formation with nickel(II) [12], the
reaction proceeds to completion with the formation of
the 1 : 3 trinuclear complex involving all the three
coordination centers of the macrocyclic ligand with an
extended (compared with porphin) coordination cenꢀ
ter. With copper(II), the stability of even the binuclear
N
DMF
S
complex with ligand
1 is fairly low, and the complex
N
dissociates under the action of trifling amounts of the
acid released during the reaction. The conclusion can
be drawn that the reason for differences between the
coordination reactions is the too large size of the Cu2+
cation compared with Ni2+ (their covalent radii
according to Batsanov are 1.17 and 1.11 Å, respecꢀ
tively), whose size fits the coordination space of the
macrocycle. This conclusion offers promise for
obtaining the complete series of complexes with the
1 : 1, 1 : 2, and 1 : 3 compositions with a large variety
of complex forming cations and for the synthesis of
heteronuclear complexes.
Cu
CH3 COO
N N
N
DMF
H
N
N
S
N
We see that the kinetics of complex formation
between ligand and Cu(OAc)2 is described by the
1
An increase in the concentration of H2O in DMFA
theoretical scheme of the reversible coordination of increases the rate of complex formation. External proꢀ
McH3 to two [Cu(OAc)]+ cations, in which the forꢀ cess parameters should then be changed to correctly
ward and back reactions are fast preequilibrium of solꢀ measure the rate of the reaction spectrophotometriꢀ
vato complex dissociation with the detachment of one cally (Table 1). Most importantly, the transition to a
acetato ion and fast postequilibrium of the acid ionizaꢀ higher water content changes the order of the reaction
tion of AcOH (vice versa for the back reaction) with with respect to ligand 1 from the first to second, as was
respect to the slow irreversible reaction with the tranꢀ already mentioned above (Fig. 6). An increase in the
sition state shown above. Equilibrium of formation– order with respect to the macrocyclic ligand is likely
dissociation of AcOH is of no significance for the related to its dimerization when H2O is added to
kinetics of the forward reaction.
DMFA.
1/A
1/A
(а)
(b)
6.4
6.2
6.0
8.2
7.8
7.4
7.0
0
40
80
120
50
100
150
, min
τ
Fig. 6. Dependences of (1/
A) on
τ
for the reaction of macrocyclic compound
1
with Cu(OAc) in DMFA–0.048% H O at
2 2
5
288.5 K; cCu(OAc)
×
10 , mol/l: (a) 1.75 and (b) 2.25 (
ρ
= 0.996 and 0.994, respectively).
2
RUSSIAN JOURNAL OF PHYSICAL CHEMISTRY A
Vol. 83
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2009

1700
LOMOVA et al.
Dimerization equilibrium with a K1 constant of
105 mol–1 was studied in [12]. According to that
work, at a (0.16–0.64)
10–5 mol/l concentration of
(this is the concentration used in this work), equilibꢀ
rium is fully shifted toward the monomer in DMFA
with 0.016% H2O. The introduction of one aqua
ligand into the coordination sphere of the initial salt
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⋅
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Press, New York, 1981; Mir, Moscow, 1978), Vol. 2.
This work was financially supported by the Russian
Foundation for Basic Research, project nos. 05ꢀ03ꢀ
33003ꢀa and 09ꢀ03ꢀ975ꢀpꢀcentre, and RAS Presidium
Program for Fundamental Research no. 18.
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Vol. 83
No. 10
2009