Kinetic parameters of decomposition of some selenites: Generalized perturbation theory of chemical reactivity

Article abstract of DOI:10.1007/s10973-005-6918-y

Studying the kinetics of isothermal decomposition of thirteen selenites at isothermal heating, the values of activation energy E of the process, pre-exponential factor A in Arrhenius equation and changes of entropy Δ S^≠ for the formation of the activated complex of the reagent were calculated. Direct dependence between the thermal stability of the selenites and their cation radii on their 'hardness' or 'softness' was found. The dependence was interpreted in the terms of the generalized perturbation theory of chemical reactivity. Kinetic compensation effect was observed only for the selenites, which thermally decompose by the same mechanism.

Full text of DOI:10.1007/s10973-005-6918-y

Journal of Thermal Analysis and Calorimetry, Vol. 83 (2006) 2, 421–427
KINETIC PARAMETERS OF DECOMPOSITION OF SOME SELENITES
Generalized perturbation theory of chemical reactivity
*
L. T. Vlaev , V. G. Georgieva and S. D. Genieva
Department of Physical Chemistry, Assen Zlatarov University, 8010 Bourgas, Bulgaria
Studying the kinetics of isothermal decomposition of thirteen selenites at isothermal heating, the values of activation energy E of
¹
the process, pre-exponential factor A in Arrhenius equation and changes of entropy DS for the formation of the activated complex
of the reagent were calculated. Direct dependence between the thermal stability of the selenites and their cation radii on their
‘hardness’ or ‘softness’ was found. The dependence was interpreted in the terms of the generalized perturbation theory of chemical
reactivity. Kinetic compensation effect was observed only for the selenites, which thermally decompose by the same mechanism.
Keywords: chemical reactivity, compensation effect, generalized perturbation theory, kinetics of isothermal decomposition, selenites
Introduction
In recent years we carried out a series of studies
on the decomposition kinetics of a number of selen-
ites under isothermal and non-isothermal heating
[17–25]. The results obtained and dependencies ob-
served in the behaviour of the values of the basic ki-
netic parameters characterizing this process can be
explained using generalized perturbation theory of
chemical reactivity [26–29].
Selenites were first synthesized in XIX century [1–4].
Later, due to their very low solubility, some of them
were used in analytical chemistry for quantitative deter-
mination of some metals by the mass method [5] or by
conductivity-metric titration [6, 7]. Other selenites were
used as pigments in glass and ceramics industries [8, 9].
Many of them can be found in nature in the form of min-
erals as part of polymetallic ores [10, 11] and are used as
raw material for production of selenium. As can be seen
from the extensive review of Verma [12] and the refer-
ences cited there, selenites have been an object of inves-
tigation for quite a long time. There are publications on
the preparation and crystalline structure of different
selenites, solubility and solubility product, IR and
Raman spectra, thermal stability and transformations
under heating, etc., but data on their kinetics of thermal
decomposition was not found.
Based on our studies, the present work is an
attempt to summarize the results obtained from
experiments, find some more general dependencies
and interpret them using the generalized perturbation
theory of chemical reactivity.
Experimental
Thermal measurements
The thermogravimetric measurements were performed
on a derivatograph system Paulik–Paulik–Erdey
The development of microelectronics and high-end
technology is connected with the synthesis and charac-
terization of new compounds with practically valuable
properties. In this respect, special attention is paid to
selenites of the different elements, because many of
them have interesting optical, magnetic, and photoelec-
tric or semi-conductor properties [13, 14]. Under heat-
3 –1
MOM, Hungary) in nitrogen flow (25 cm min ) un-
(
der isothermal heating in the temperature inter-
val 723–1123 K. Depending on selenites’ thermal sta-
bility, the measurements were taken at certain
temperature intervals. For selenites with lower thermal
stability (selenites of aluminium, gallium, germanium,
antimony and bismuth), the measurements were made
in the temperature interval 723–923 K while for the
others – in the interval 923–1123 K. In all the cases
studied, the rate constants of thermal decomposition
were calculated using 4 or 5 kinetic curves in the corre-
sponding temperature interval at 50 K step. For this
purpose, 100 mg finely ground sample was placed in
open platinum crucible (7 mm diameter and 14 mm
ing of selenites in reduction media (H , CO), the corre-
2
sponding selenides can be obtained [15, 16]. They also
possess some interesting semi-conductor properties.
These considerations lead to the conclusion that studies
of selenites thermal stability and particularly their kinet-
ics of decomposition under isothermal or non-isother-
mal heating is interesting from both theoretical and
practical point of view.
*
Author for correspondence: vlaev@btu.bg
1
388–6150/$20.00
Akadémiai Kiadó, Budapest, Hungary
Springer, Dordrecht, The Netherlands
©
2006 Akadémiai Kiadó, Budapest

VLAEV et al.
¹
height). a -Alumina, calcined at 1273 K was used as a
eck T
æ DS ö
E
B
æ
ö
÷
k =
expç
÷expç –
(7)
standard reference material. The sample mass was
measured continuously for 15–120 min with accuracy
of ±1 mg. The temperature was kept constant within
the interval ±2 K and the reaction progress (a ) was
from 0.05 to 0.95 [21, 25].
ç
÷
h
R
RT
è
ø
è
ø
where e=2.7183 is the Neper number, c is a transmis-
sion coefficient, which is unity for monomolecular
reactions, k is the Boltzmann constant, h is the Plank
B
¹
constant and DS is the change of entropy for the
activated complex formation from the reagent. The
comparison the equations of Arrhenius Eq. (5) and
Eyring Eq. (7) gives:
Mathematical background of kinetic calculations
The basic kinetic equation was used:
¹
da
eck T
æ DS ö
B
=
kf (a )
(1)
A =
exp
(8)
ç
÷
÷
ç
dt
h
R
è
ø
where k is the rate constant and the function f(a )
involves the decomposition progress a at moment t
calculated by the formula:
¹
The change of entropy DS for the activated
complex formation from the reagent can be calculated
by the formula:
W – W
0
Ah
a =
(2)
¹
DS = R ln
(9)
W – W
0
f
eck T
B
where W , W and W are the initial, actual and final
0 f
The existence of a linear dependence between
lnA and E in reactions of the same type described by
the equation:
sample mass. According to Šesták [30], the function
f(a ) can be written in a general form:
m
n
p
f(a ) = a (1–a ) [–ln(1–a )]
(3)
E
ln A = ln kiso
+
(10)
with respect to its correspondence to the models derived
for homogeneous reactions, nucleation-growth process,
surface process, diffusion or random nucleation, where
n, m and p are empirically obtained exponent factors,
one of them always being zero. Depending on the spe-
cific kinetic model of the process, the form of the func-
tion f(a ) would be different [23, 25, 31].
RTiso
is often discussed in the literature [32–37]. This
dependence is known as kinetic compensation effect,
isokinetic effect or q rule. Tiso is the temperature at
which the decomposition of substances proceeding
along the same mechanism is characterized by the
same rate constant k . At temperatures higher than
iso
The integral form of the function g(a )
Tiso, the decomposition of the substance with higher
activation energy continues at a rate higher than that
of the substance with lower value of E.
a
da
g(a ) =
= kt
(4)
ò
f (a )
0
at T=const. represents a linear dependence, the slope
of which is used to calculate the rate constant k at
certain temperature. The dependence of the rate
constant k on the temperature is usually described by
the Arrhenius equation:
Background of generalized perturbation theory of
chemical reactivity
Since the preparation of all selenites takes place in
2–
aqueous solutions by interaction of SeO3 anion with
the corresponding cation, the generalized perturbation
theory of chemical reactivity of Klopman and Hud-
son [26–29] can be successfully used for estimation of
the strength of the bond between them. So far as the ac-
tivation energy of thermal decomposition of selenites
depends on the strength of the bonds in the molecule,
we used the basic principles of this theory for the inter-
pretation of the changes observed in the kinetic param-
eters of the process. It is based on the supposition that
the formation of transitional state is stipulated by both
the mutual perturbation of the molecular orbitals of the
two reagents and the electrostatic interaction between
the ions. The relative reactivity of the ions in the solu-
tion is assessed by the decrease of energy of the system
æ
E ö
k = Aexpç –
÷
(5)
RT
è
ø
where A – pre-exponential factor, E – activation
energy, R – gas constant and T – temperature.
Taking the logarithm of Eq. (5) gives:
E
ln k = ln A –
(6)
RT
The value of E – calculated from the slope of the
straight line and A – from the cut-off from the
ordinate. Using the equation of Eyring [23, 25] from
the theory of the activated complex (transition state):
422
J. Therm. Anal. Cal., 83, 2006

KINETIC PARAMETERS OF DECOMPOSITION
DEtotal. The highest reactivity and, respectively, the
established two possible pathways and energetic con-
trols for any couple of ions.
highest bond strength showed the ions the interaction
of which leads to the highest values of DEtotal. The ba-
sic equation used to determine DEtotal for the interaction
between the ions is as follows [28, 29]:
According to this approach, the interactions
between cations and anions in aqueous solutions may
take place as charge controlled reactions or orbital
controlled reactions. The charge-controlled reactions
are facilitated when highly hydrated cations with
qc qa
DEtotal
=
+
R e
ca
23
2+
2+
3+
small radii (Be , Mg , Al , etc.) take part. Vice
1
electrostatic term
versa, the orbital controlled reactions are facilitated
+ 3+
when little hydrated cations with big radii (Ag , In ,
+
Au , etc.) take part [29]. Since the same anion takes
(
11)
2
Db
m
(C )
2
n
(C )
2
ca
+2
å
144444424444443
c
å
a
*
*
(Em – E )
occ
unocc
n average
2–
part in selenites formation (SeO ), the reaction by
3
covalent term
which the interaction with the cation would proceed
to obtain the corresponding selenite should depend on
its radius or, respectively, on its atomic orbital. It has
been shown in the framework of the perturbation
model that the most energy efficient reactions occur
between ions, which facilitate either electrostatic or
orbital interaction only. In the first case, the reacting
ions are denoted as ‘hard’ (hard donor-anions or hard
acceptor-cations). These are cations with small radii,
which form ionic type of bond. In orbital interactions,
the reacting ions are ‘soft’ – these are ions with big
radii, which form covalent type of bond. The
differences in the thermal stabilities of the selenites
studied and the dependencies observed in the change
of the kinetic parameters characterizing their thermal
decomposition can be explained using generalized
perturbation theory of chemical reactivity [26–29]
and empirical classification of ions as ‘hard’ or ‘soft’
donors/acceptors of electrons reported in [29, 38].
where DEtotal is the total change in perturbation energy
due to the partial formation of a bond between an
anion and cation, respectively, q and q are the total
a
c
initial charges for anion and cation, R is the distance
ca
between two ions, e is related to the local dielectric
constant of the solvent, (C ) and (C ) are the
m
2
n
2
c
a
2
frontier electron density, Dbca is the change in the
resonance integral between the interacting orbitals of
*
anion and cation, (Em – E ) is the difference in
*
n
energy between the highest occupied orbital of the
anion and the lowest empty orbital of the cation.
*
When the difference between Em and En for the
*
*
*
frontier orbitals is large, Em – E >> 0, then very
little charge transfer occurs (Scheme 1).
n
Results and discussion
On Fig. 1 are shown the curves of thermal decomposi-
tion of Ge(SeO ) , Sn(SeO ) , PbSeO , Sb (SeO )
Scheme 1 Charge-controlled effect
3
2
3 2
3
2
3 3
and Bi (SeO ) at several temperatures. It can be seen
2 3 3
that selenites with higher cation radii have higher
thermal stability at T=const, i.e. their degree of
decomposition (a ) decreases from top to bottom of
the group in the Periodic table.
In such a case, obviously, the perturbation
energy is determined mainly by the total charge of the
two ions. Since the electron transfer is quite small, the
reaction will be called a charge-controlled reaction.
On the other hand, when the two frontier orbitals are
The study of the kinetic of isothermal decomposi-
tion of 13 selenites [17–25] showed that the best linear
dependence between g(a ) and t (Eq. (4)) was obtained
when the f(a )-function (Eq. (3)) was used where m and
p are zero, while 0.50<n<1.0. Then, after separation of
variables and integration of Eq. (4) gives:
*
*
degenerate, i.e. Em – E » 0, then, there interaction
becomes predominant (Scheme 2),
n
In this case the electron transfer between them is
extensive. Therefore, such reactions will be called or-
bital-controlled reactions. In this connection, we have
1–n
1
– (1– a )
– n
=
kt
(12)
1
This linear equation is known as mechanism
non-invoking equation and, according to a number of
authors [31, 39, 40], describes quite well the kinetics of
thermal decomposition of various compounds if proper
Scheme 2 Orbital-controlled effect
J. Therm. Anal. Cal., 83, 2006
423

VLAEV et al.
values of the parameter n are selected. On this basis,
tivation energy of decomposition E, pre-exponential
factor in Arrhenius equation A and the change of en-
the rate constants of thermal decomposition of the
selenites studied were calculated at certain tempera-
tures. Then, using Eqs (6) and (9), the values of the ac-
¹
tropy DS for the activated complex formation from the
reagent were calculated. We found a relationship be-
tween the values of these parameters, cation radius of
selenites and their thermal stability (Table 1).
As can be seen from Table 1, the values of the
activation energy of thermal decomposition increase
with the radius of selenite cation from top to bottom
of the groups. The thermal stability increased by the
same order. It has been reported [40] that the stronger
the bond or bonds which are to be broken, the higher
is the value of the activation energy.
It is well-known that the pre-exponential factors
for solid-phase reaction are expected to have a wide
range of values (six or seven orders of magnitude).
Empirical first order pre-experimental factors may
5
16
–1
vary from 10 to 10 min [40–43]. The low factors
will often indicate a surface reaction, but if the reac-
tions are not dependent on surface area, the low factor
may indicate a ‘tight’ complex. The high factors will
usually indicate a ‘loose’ complex. In case of bulk de-
composition, any molecule is as likely to react as any
other, irrespective of its location – corners, edges, sur-
face, defects or sites of previous decomposition. There
are four special cases, which will indicate the range in
values for the pre-exponential factors for the rate con-
14
–1
stants. In case I (A»10 min ) there is no change in
degree of the rotational excitation between the reac-
tions and the complex. There are two subcases – com-
pletely free rotation and completely restricted rotation.
The first one probably can only refer to unimolecular
15
–1
reactions. In case II (A»10 min ) the complex has a
‘freer’ condition than the reagents [42]. This may be
most likely to occur on a surface where the complex
might extend itself from the surface and perhaps rotate
parallel to the surface. The reactant is assumed to be
Fig. 1 Kinetics curves of isothermal decomposition of:
A – Ge(SeO
873; PbSeO
a – 623; b – 773; Bi
3
)
2
: a – 723; b – 873; Sn(SeO
: e – 1023; f – 1173 and B – Sb
(SeO : c – 773; d – 923 K
3
)
2
: c – 773; d
–
3
2
(SeO
3
)
3
:
11
–1
completely restricted. In case III (A»10 min ) the
2
3 3
)
Table 1 Cation radii and kinetic characteristics of isothermal decomposition of some selenites
–
1
rion/
E/kJ mol
0.50
Al
164
Me
m
(SeO
3
)
n
2 3 3
(SeO )
–
1
¹
–1 –1
K
9
A/min
DS /J mol
1.23×10
–121
209
0.72
232
0.83
241
0.62
0.53
Ge(SeO
189
CuSeO
3
ZnSeO
3
Ga
2
(SeO
3
)
3
3
)
2
1
1
13
11
10
8
6
.31×10
.13
–68
314
1.74×10
–62
257
1.58×10
–80
238
1.47×10
–101
1
1.03
0.92
0.71
212
0.90
Sb
137
Ag
2
SeO
3
CdSeO
3
In
2
(SeO
3
)
3
Sn(SeO
3
)
2
2
(SeO
3
)
3
1
2
12
12
10
8
.91×10
–51
6.11×10
–51
1.48×10
–63
5.66×10
–90
5.72×10
–126
203
1.05
136
1.21
272
1.16
Tl
4
(SeO
3
)
4
PbSeO
3
2 3 3
Bi (SeO )
8
13
11
1.82×10
–137
2.18×10
–42
1.41×10
–82
424
J. Therm. Anal. Cal., 83, 2006

KINETIC PARAMETERS OF DECOMPOSITION
complex is highly restricted in rotation. For the
unimolecular reaction the complex would be expanded
in size and hence interact more strongly with its neigh-
larly, the thermal stabilities of Au SeO and HgSeO
2 3 3
would be close to that of Ag SeO since their cations
2 3
behave as ‘soft’ ions and all the three selenites decom-
pose along the same scheme with formation of the
corresponding metal.
5
–1
bors. In case IV (A»10 min ) the reagents are in equi-
librium with a surface adsorbed layer. The adsorbed
species on the surface then react via the activated com-
plex to give products. In conclusion of the activated
complex has freer rotation than the reactant; the first
order pre-exponential factor is high [42].
According to Klopman’s generalized perturbation
theory of chemical reactivity and Pearson’s empirical
classification of ions, a strong ionic bond is formed by
the interaction of ‘hard’ cations and anions while the in-
teraction between ‘soft’ cations and anions results in a
strong covalent bond. Therefore, the more similar are
the interacting ions, the stronger is the bond between
As can be seen from Table 1, the values of the
12
8
–1
pre-exponential factor A varied from 10 to 10 cm ,
increasing from top to bottom of each group of the
Periodic table.
2–
them. Since the SeO3 behaves as ‘soft’, it would form
stronger bonds with ‘soft’ cations. As cation ‘softness’
increases from top to bottom of the groups in the Peri-
odic table and from left to right, the bond strength in
selenites should increase by the same directions as well
as their thermal stability. The hypothesis suggested was
confirmed by the tendency of increase of activation en-
ergy E values observed by the thermal decomposition of
the selenites studied. Similar relationships for the ther-
mal stability of some sulfates and carbonates depending
on their cation radius have been reported in [40, 44].
The explanation of the effect, however, was based on
the different polarization ability of the cations. Studying
the kinetics of decomposition of hydroxides from the
IIA and IIB groups of the Periodic table, L’vov and
Ugolkov [45] also found that the thermal stability, acti-
vation energy and the change of enthalpies of the pro-
This dependence was interpreted using Klopman’s
generalized perturbation theory of chemical reactivity
and Pearson’s empirical classification of ions as a ‘hard’
or ‘soft’ donors/acceptor of electrons. Table 2 shows
some orbital electronic characteristics according to the
empirical classification of Pearson [29, 38].
Table 2 clearly shows that the differences in or-
bital energy DE (DE=E –E ) of cations depend on their
radii and degree of oxidation. Highly hydrated ions
1 2
2+
3+
small radii, Be , Al , etc.) behave as ‘hard’ while
(
+
+
lowly hydrated ones (big radii, Ag , Au , etc.) – as
2–
‘soft’ [29, 38]. Since SeO3 anion behaves, as ‘soft’
electron donor, then its bond with the cation would be
as stronger as the ‘softer’ is the corresponding cation
and the thermal stability of the selenite would be
higher. Therefore, the selenites of heavy metals would
be characterized by higher thermal stability and, re-
spectively, higher values of the thermal decomposition
activation energy. Vice versa, the selenites of light
metals would be characterized with low thermal stabil-
cesses increased from Be(OH) to Ba(OH) and from
2 2
Zn(OH) to Cd(OH) . Besides, these values are higher
2 2
for the hydroxides of IIA group compared to these of
IIB group of the Periodic table which conforms abso-
lutely with Pearson’s empiric orders of electrophility
and nucleophility and Klopman’s generalized perturba-
tion theory of chemical reactivity. This was considered
enough to conclude that the hypothesis suggested has
other experimental confirmations, too.
ity and lower values of E . This tendency is quite clear
A
within a single group of the Periodic table. Taking into
account the values of DE shown in Table 2, it could be
predicted that the thermal stabilities of BeSeO and
3
MgSeO would be close to that of Al (SeO ) . Simi-
3 2 3 3
Table 2 Hydrated radii and calculated orbital electro negativity of ions in water [29]
Ionization
Electron
Orbital
energy, E /eV
Desolvation
Differences of Characteristic
Ion
rion+0.82/
potential/eV
affinity/eV
1
energy, E
2
/eV energy, DE/eV
of ions
3
+
Al
28.44
18.21
15.03
30.70
17.57
17.96
16.90
7.57
18.82
9.32
26.04
15.98
13.18
28.15
15.44
15.82
14.93
6.23
1.33
1.17
1.48
1.44
1.54
1.56
1.79
2.08
1.77
2.19
1.92
32.05
19.73
15.60
29.60
14.99
14.80
12.89
3.41
6.01
3.75
2
+
Be
2
+
Mg
7.64
2.42
­
3
+
Ga
20.51
9.05
1.45
hardness
softness
¯
2
+
Cu
–0.55
–1.02
–2.04
–2.82
–3.37
–4.35
–4.64
2
+
Zn
Cd
Ag
9.39
2
+
8.99
+
+
+
2.20
3
Tl
29.30
9.22
20.42
2.70
27.45
7.59
24.08
3.24
Au
2
+
Hg
18.75
10.43
16.67
12.03
J. Therm. Anal. Cal., 83, 2006
425

VLAEV et al.
These considerations, as well as the correctness
Tl Se O ® 2Tl SeO +SeO +O
4
3
12
2
4
2
2
of the values E calculated, are confirmed by the
existence of kinetic compensation effect revealed by
the linear dependence between lnA and E [35–38].
Using the values of the activation energy
presented in Table 1 and the pre-exponential factor in
Arrhenius equation, the dependence of lnA on E was
plotted (Fig. 3).
According to [32–37] at temperatures higher than Tiso
,
the compounds characterized by higher activation
energy begin to decompose with a rate higher than
that of compounds having low values of E. Arrhenius
plots for thermal decomposition of studying selenites
are presented in Fig. 2.
Fig. 3 Kinetics compensation effect of thermal decomposition
of some selenites
The linear dependence found between lnA and E
confirms the existence of kinetic compensation effect
by the thermal decomposition of the selenites studied.
The exceptions are silver and thallium selenites due to
their specific schemes of decomposition.
Fig. 2 Arrhenius plots for thermal decomposition of some
selenites
It can be seen also from the data presented in
Table 1 that the values of the change of entropy for
the formation of the activated complex from the
As can be seen from Fig. 2, the Arrhenius plot dis-
plays a single point of concurrence. Such a plot gener-
ally indicates the occurrence of true compensation ef-
fect. The straight lines representing the kinetics of ther-
mal decomposition of selenites in Arrhenius co-ordi-
nates cross at the so-called isokinetic point. At this point
the rate constants of the decomposition of the different
selenites are equal and the temperature at which this can
be observed is about 1455 K. Above this temperature,
the selenites characterized by higher values of E begin
to decompose at a rate higher than that of selenites with
¹
reagent DS was negative in all the cases studied. It
means that the activated complex has more ordered
structure than the reactant, and that the reaction is
slower than normal [48]. Besides, the more complex
is the configuration of the activated complex and the
more limited are its degrees of freedom, the more
¹
negative would be the value of DS . Furthermore, it
¹
can be seen that the values of DS become less
negative with the increase of cation radius within
each group of the Periodic table. In addition, a
correlation between the values of the activation
energy and the change of entropy for the formation of
the activated complex from the reagent was found.
The linear dependences found between lnA and E, as
lower values of E. The only exceptions are Ag
SeO and
2 3
Tl Se O due to their different scheme of decomposi-
4 3 12
tion. The decomposition of all the other selenites can be
schematically summarized by:
¹
M (SeO ) ® M O +nSeO
well as between E and DS , are directly connected
with selenite cation radius and its ‘softness’ or
m
3 n
m
n
2
while silver selenite decomposes to metal silver,
selenium dioxide and oxygen by the scheme [46]:
‘
hardness’ as an acceptor of electrons. Obviously,
harder is the cation, the higher is the thermal stability
Ag SeO ® 2Ag+SeO +0.5O
of the selenite and the higher are the values of E, A
¹
2
3
2
2
and DS by its thermal decomposition. The suggested
and the decomposition of Tl Se O
4 3
involves
12
3
+
+
intramolecular reduction of Tl to Tl and oxidation
hypothesis can be sustained by redundant data
reported by other authors [40, 44, 45, 49–51] who
also observed similar tendencies in their studies on
4
of Se to Se according to [47]:
+
6+
426
J. Therm. Anal. Cal., 83, 2006

KINETIC PARAMETERS OF DECOMPOSITION
the kinetics of decomposition of various types of
compounds. These authors, however, did not use the
generalized perturbation theory of chemical reactivity
to interpret the relationships they observed.
22 L. Vlaev, G. Gospodinov and S. Genieva, Thermochim. Acta,
17 (2004) 13.
3 L. Vlaev, M. Nikolova and G. Gospodinov,
4
2
2
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J. Solid State Chem., 177 (2004) 2663.
4 L. Vlaev, G. Gospodinov and V. Georgieva,
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5 L. Vlaev, V. Georgieva and G. Gospodinov,
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6 G. Klopman and R. F. Hudson, Theor. Chim. Acta,
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Conclusions
In conclusion, we believe that the generalized pertur-
bation theory of chemical reactivity can be very useful
not only to understand the tendencies in the change of
kinetic parameters of the reactions of chemical decom-
position but also for the interpretation of the regulari-
ties in the change of solubility and solubility product of
slightly soluble compounds and the shift of character-
istic absorption bands in IR spectra of compounds of
similar type.
27 R. F. Hudson and G. Klopman, Tetrahedron Lett.,
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Received: January 26, 2005
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DOI: 10.1007/s10973-005-6918-y
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427