Thermoanalytical study of the solid state reactions in the K2CO3-MxOy systems. Evidence for a kinetic compensation effect

Article abstract of DOI:10.1023/A:1010145615439

This paper presents the results obtained in the investigation of the reactions of potassium carbonate with some transition metals oxides (TiO₂, V₂O₅, Cr₂O₃, MnO₂, Fe₂O₃). The reactions were carried out under non-isothermal conditions, and thermogravimetric analysis was used to monitor the transformation degree α. Experimental data indicated that the reaction of potassium carbonate and iron(III) oxide occurs in one stage, whereas the reactions of the oxides of titanium, vanadium, chromium and manganese are more complex, involving two-stage processes. Activation energies and pre-exponential factors were determined for all the processes taking place in the investigated systems. For the second stage of the reaction of K₂CO₃ with Cr₂O₃, and V₂O₅ the obtained values of activation energy were 59.2 and 512 kJ mol^-1 respectively. Based on the values of activation energy and pre-exponential factor, the existence of a kinetic compensation effect was postulated for the three homologous series of reactions.

Full text of DOI:10.1023/A:1010145615439

Journal of Thermal Analysis and Calorimetry, Vol. 61 (2000) 229–238
A THERMOANALYTICAL STUDY OF THE SOLID
STATE REACTIONS IN THE K2CO3–MxOy SYSTEMS
Evidence for a kinetic compensation effect
S. Miliæ1, N. Coloviæ1, M. Antonijeviæ1 and F. Gaál2*
1Technical Faculty Bor, University of Belgrade, P.O. Box 50, 19210 Bor
2Faculty of Sciences, University of Novi Sad, 21000 Novi Sad, Yugoslavia
(Received January 10, 1999; in revised form December 3, 1999)
Abstract
This paper presents the results obtained in the investigation of the reactions of potassium carbonate
with some transition metals oxides (TiO2, V2O5, Cr2O3, MnO2, Fe2O3). The reactions were carried out
under non-isothermal conditions, and thermogravimetric analysis was used to monitor the transforma-
tion degree α. Experimental data indicated that the reaction of potassium carbonate and iron(III) oxide
occurs in one stage, whereas the reactions of the oxides of titanium, vanadium, chromium and manga-
nese are more complex, involving two-stage processes. Activation energies and pre-exponential factors
were determined for all the processes taking place in the investigated systems. For the second stage of
the reaction of K2CO3 with Cr2O3, and V2O5 the obtained values of activation energy were 59.2 and 512
kJ mol–1 respectively. Based on the values of activation energy and pre-exponential factor, the exis-
tence of a kinetic compensation effect was postulated for the three homologous series of reactions.
Keywords: kinetic compensation effect, non-isothermal, potassium carbonate, solid state reac-
tions, transition metals oxides
Introduction
Reactions of the synthesis of inorganic materials based on transition metals oxides and
carbonates or oxides of other metals, occurring at higher temperatures, are very complex
[1–3], but also very interesting from both the theoretical and practical point of view [4].
The reactions of alkaline carbonates with transition metals oxides yield products
with specific characteristics [5]: titanates, vanadates, chromates, manganates, and
ferrites. These reactions can be controlled either by diffusion [6] or chemically [7].
Iron oxide, Fe2O3, is reactive at elevated temperatures. Its reactions with NiO [8],
MgO [1], Li2CO3 [2], Na2CO3 [7] etc. were investigated. In the reactions of Cr2O3 with
carbonates [9], and some other oxides (CdO, CuO, MgO, NiO, ZnO), MCr2O4 occurs as
an intermediate. The rate-determining steps are diffusion of Cr3+ through the layer of
*
Author to whom all correspondece should be addressed.
1418–2874/2000/ $ 5.00
Akadémiai Kiadó, Budapest
© 2000 Akadémiai Kiadó, Budapest
Kluwer Academic Publishers, Dordrecht

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MILIÆ et al.: POTASSIUM CARBONATE
products and oxygen transport. Titanium(IV) oxide reacts with oxides or carbonates at
higher temperatures and forms titanates. It was found that the reaction with barium car-
bonate in the presence of carbon dioxide yields BaTiO3, whereas the removal of CO2
from the system results in Ba2TiO4 [10, 11]. Manganese(IV) oxide decomposes at higher
temperatures, giving a whole range of oxides [12], the reactions being under chemical
control.
A kinetic compensation effect has been noticed during the study of the kinetics
of catalytic reactions [13–18], as well as in other heterogeneous reactions [19, 20],
and lately in the reactions proceeding under non-isothermal conditions [21, 22].
Many authors have attempted to explain the compensation parameter, but no satisfac-
tory explanation has been given yet [23–27]. The existence of this effect was ob-
served in the present study of the kinetics of the reaction of potassium carbonate with
a series of oxides of transition metals (TiO2, V2O5, Cr2O3, MnO2, Fe2O3) taking place
under non-isothermal conditions.
Experimental
All the reagents were of analytical reagent purity.
Initial components were K2CO3, TiO2, V2O5, Cr2O3, MnO2, and Fe2O3. Mass
change in the course of reaction was monitored on a Netzsch, Model 409 thermoscale
and the samples were analyzed by X-ray analysis.
Working procedure was the same in all experiments. First, the reacting compo-
nents (potassium carbonate+oxide) were mixed in an equimolar ratio and homoge-
nized. Afterwards, samples of the same mass (0.750 g) were taken and subjected to
heating. All reactions were investigated at various heating rates of 2, 5, 10 and
20 K min–1, in a static air atmosphere. Kinetic curves, α=f(T) or α=f(t), at different
linear heating rates were graphically differentiated, which produced kinetic curves
representing the dependence of the reaction rate on temperature or time, (dα/dT or
dα/dt). These curves were used to determine the maximal reaction rate (vmax), corre-
sponding temperature (Tm), and the duration of the treatment (tm).
Results and discussion
Kinetic curves obtained for the reactions of potassium carbonate and transition met-
als oxides (TiO2, V2O5, Cr2O3, MnO2, Fe2O3) were analyzed using the following equa-
tions [7, 28]:
dlnv
E
R
max
=−
(1)
d(1/T )
m
and
dlnt
E
m
=
(2)
d(1/T ) R
m
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MILIÆ et al.: POTASSIUM CARBONATE
231
where:
vmax – maximal rate of the chemical reaction (determined from the first deriva-
tive of the curve α=f(T) or α=f(t)),
Tm – temperature corresponding to the maximal rate of the chemical reaction,
tm – time elapsed to the moment of reaching vmax
and using the Ozawa equation [29, 30]:
dlnq
E
R
=−
(3)
d(1/T )
m
where:
q – linear heating rate.
Chemical reactions between potassium carbonate and oxides of transition metals
(TiO2, V2O5, Cr2O3, MnO2, Fe2O3) can be represented by the following equations:
K2CO3+TiO2=K2TiO3+CO2
K2CO3+V2O5=2KVO3+CO2
(4)
(5)
(6)
(7)
(8)
K2CO3+0.5Cr2O3+0.75O2=K2CrO4+CO2
K2CO3+MnO2=K2MnO3+CO2
K2CO3+Fe2O3=2KFeO2+CO2
A common characteristic of all the reactions is the evolvement of carbon dioxide
and formation of the corresponding salts: titanates, vanadates, chromates, manganates
and ferrites.
In Fig. 1 the diffractogram of the products of the reaction of K2CO3 and V2O5 is
presented, showing that the reaction product is KVO3.
Fig. 1 X-ray diffractogram of the products of reaction (5)
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Fig. 2 Kinetic curves obtained for the reaction of K2CO3 with TiO2, V2O5, Cr2O3,
MnO2, Fe2O3 (heating rate: 10 K min–1)
Fig. 3 Dependence of the transformation rate on temperature for the reaction of K2CO3
with TiO2, V2O5, Cr2O3, MnO2, Fe2O3 (heating rate: 10 K min–1)
Kinetic curves (α=f(Tm) and α=f(tm)) for all the investigated reactions are of a
similar character, which is evident from Fig. 2, showing the dependence of the con-
version degree (α) is plotted against the reaction time at a heating rate of 10 K min–1.
Graphical derivation of these curves allowed the determination of the maximal reac-
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MILIÆ et al.: POTASSIUM CARBONATE
233
tion rate (vmax) and the corresponding time (tm). The temperature corresponding to the
maximal reaction rate (Tm) is determined using the differential form of the kinetic
curve dα/dT, Fig. 3.
Table 1 presents the values of activation energy (E) and pre-exponential factor
(A) obtained for the different heating rates, using Eqs (1) and (2), which can be pre-
sented in an expanded form as:
E
lnv =lnA−
(9)
max
RT
E
lnt =lnA+
(10)
m
RT
Table 1 Values of activation energy and pre-exponential factor for the reaction of K2CO3 with
TiO2, V2O5, Cr2O3, MnO2 and Fe2O3
Eq. (1)
Eq. (2)
Eq. (3)
Reaction
E/
A/
E/
A/
E/
kJ mol–1
59.2
min–1
kJ mol–1
74.6
min–1
kJ mol–1
1. K2CO3+Cr2O3 – stage II
2. K2CO3+Cr2O3 – stage I
3. K2CO3+Fe2O3 – direct
4. K2CO3+TiO2 – stage I
5. K2CO3+TiO2 – stage II
6. K2CO3+MnO2 – stage I
7. K2CO3+V2O5 – stage I
8. K2CO3+MnO2 – stage II
9. K2CO3+V2O5 – stage II
1.28·102
7.48·102
1.67·107
2.49·108
1.90·107
1.04·1021
1.24·1028
3.83·1013
2.04·1032
4.30·102
1.72·103
1.22·107
4.17·1010
9.40·107
1.84·1021
1.06·1033
6.31·1014
2.63·1040
70.0
70.0
69.8
77.0
186.1
196.5
209.5
371.8
381.1
400.6
512.0
182.5
227.4
230.0
379.1
448.0
442.2
637.5
182.2
216.0
232.0
374.2
443.0
380.0
615.0
As can be seen from Figs 2 and 3 the investigated reactions do not include dehy-
dration, except for the reaction involving vanadium(V) oxide.
Figure 3 shows that the reaction of K2CO3 with iron oxide proceeds in one stage,
with vmax=8.8 min–1. The temperature (Tm) that corresponds to this rate is 1143 K,
which is lower than the decomposition temperature of K2CO3 (1164 K) indicating that
a direct interaction takes place between the carbonate and oxide (reaction 8).
On the kinetic curve for the K2CO3–V2O5 system (Fig. 3) there are two peaks
with maximal temperatures of 678 and 778 K. The first peak corresponds to the first
process, which can be described by Eq. (5). In the temperature range around the first
peak (678 K) a direct reaction of K2CO3 and V2O5 takes place. At higher temperatures
(second peak) the reaction mechanism changes, so that the investigated reaction most
probably occurs as follows:
a) decomposition of potassium carbonate:
K2CO3=K2O+CO2
(11)
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MILIÆ et al.: POTASSIUM CARBONATE
b) reaction between K2O and V2O5:
K2O+V2O5=2KVO3
The decomposition temperature of potassium carbonate decreases in the pres-
(12)
ence of oxide, so it can be assumed that this reaction mechanism is correct.
The differential kinetic curves for the systems K2CO3–Cr2O3, K2CO3–TiO2 and
K2CO3–MnO2 have two peaks (Fig. 3). The first peaks in all three cases like for the
K2CO3–V2O5 system, correspond most probably to a direct interaction between
K2CO3 and the corresponding oxide (according to Eqs 4, 6 and 7 respectively), and
represent the first process. The temperatures (Tm) corresponding to the maximal rates
of the first processes for the K2CO3–Cr2O3, K2CO3–TiO2 and K2CO3–MnO2 system
(813, 1033 and 848 K, respectively) are lower than the dissociation temperature of
K2CO3.
Fig. 4 Kinetic compensation effect for reactions of K2CO3 with TiO2, V2O5, Cr2O3,
MnO2 and Fe2O3
The second processes can be explained in a similar way, as in case of the reac-
tion of potassium carbonate and vanadium oxide. In all probability, there is a decom-
position of potassium carbonate to K2O and CO2 (Eq. 11), followed by the reaction of
K2O and the corresponding oxide:
K2O+0.5Cr2O3+0.75O2=K2CrO4
K2O+TiO2=K2TiO3
(13)
(14)
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MILIÆ et al.: POTASSIUM CARBONATE
235
K2O+MnO2=K2MnO3
(15)
The experiments showed that the products K2MnO3 and K2TiO3 appear in a mol-
ten state, which means that the reactions of K2CO3 with MnO2 and TiO2 include melt-
ing, most probably, of the products, K2MnO3 and K2TiO3.
As can be seen from Table 1, the values of activation energy and pre-exponential
factor of the investigated chemical reactions are relatively high, and the obtained ki-
netic curves (α=f(t) and α=f(T)) have a sigmoid shape, which indicates that the inves-
tigated reactions of K2CO3 with the investigated oxides are chemically controlled.
By the graphic presentation of lnA=f(E), the existence of a kinetic compensation
effect can be demonstrated for the reactions under study (Fig. 4), which can be writ-
ten in the following form:
lnA=a+bE
(16)
where a and b are the compensation constants.
The three straight lines in Fig. 4 indicate that there are three homologous series
of reactions. The points enumerated from 1 to 9 represent the corresponding reactions
and stages presented in Table 1. Compensation constants were calculated using re-
gression analysis, and their values are: for curve I, a=1 and b=0.083; for curve II,
a= –2.2 and b=0.137; and for curve III, a= –6 and b=0.2.
Fig. 5 Dependence of E/RTm on lnvmax for the reactions of K2CO3 with TiO2, V2O5,
Cr2O3, MnO2 and Fe2O3
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Experimentally established order of decrease in reactivity for the reactions of
K2CO3 with TiO2, V2O5, Cr2O3, MnO2 and Fe2O3, based on Fig. 4 is:
Curve I:
1. K2CO3+Cr2O3 – stage I
2. K2CO3+Fe2O3 – direct
3. K2CO3+TiO2 – stage II
4. K2CO3+MnO2 – stage II
Curve II:
1. K2CO3+Cr2O3 – stage I
2. K2CO3+TiO2 – stage I
3. K2CO3+MnO2 – stage I
Curve III:
1. K2CO3+Cr2O3 – stage II
2. K2CO3+Cr2O3 – stage I
3. K2CO3+V2O5 – stage I
4. K2CO3+V2O5 – stage II
It is also evident from Fig. 4 that the most reactive oxide is chromium oxide,
while the most inert is vanadium oxide. Those reactions/stages, denoted by points ly-
ing on the compensation lines of a smaller slope are more reactive, which means
lower values of the compensation parameter b. Also, more reactive are the reactions
which lie closer to the coordinate origin (in this case, these are the reactions of
K2CrO4 formation).
Fig. 6 Dependence of E/RTm on lntm for the reactions of K2CO3 with TiO2, V2O5,
Cr2O3, MnO2 and Fe2O3
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MILIÆ et al.: POTASSIUM CARBONATE
237
In their previous papers Coloviæ [28, 31] et al. have concluded that the reactivity
of particular reactions and stages can be compared and presented by plots where
x-axis is lntm or lnvmax, and y-axis is E/RTm.
The diagrams in Figs 5 and 6 contain parallel straight lines which correspond to
particular reactions and stages of the investigated reactions, allowing their compari-
son. Lines with the largest value of the term E/RTm correspond to the most inert reac-
tions. With decrease of the E/RTm value, reactivity of the investigated reaction in-
creases (from stage II of the reaction K2CO3–V2O5 to stage II of the reaction
K2CO3–Cr2O3).
Reactivity of the investigated systems in particular stages can be determined
from the position of these lines, as they contain relation between vmax and tm, on the
one hand and between kinetic parameters (E, A) and the temperature at which reac-
tion takes place, on the other. Numerical values of these parameters are basically re-
lated to the nature of the matter that transforms. Because of that, when comparing the
dependence of E/RTm on lnvmax and E/RTm on lntm for different systems, their reactivi-
ties in particular processes/stages are actually compared.
On comparing the diagrams in Figs 5 and 6 with those in Fig. 4 it can be con-
cluded that there is a good agreement of these methods for monitoring the reactivity
of the investigated oxides with potassium carbonate.
Conclusions
1. The reaction of K2CO3 and Fe2O3 is a one-stage reaction, and the value of acti-
vation energy for this reaction is 186.1 kJ mol–1.
2. The reactions of K2CO3 with the oxides of titanium (TiO2), vanadium (V2O5),
chromium (Cr2O3) and manganese (MnO2) are two-stage reactions.
3. The values of activation energy for all the reactions range from 59.2 to
512 kJ mol–1, indicating that the reactions are chemically controlled.
4. Kinetic compensation effect indicates that there are three homologous reac-
tion series for the reaction system K2CO3-MxOy.
5. Reactivities of the different reactants in particular stages can be estimated
from the series of parallel straight lines showing the dependence of E/RTm on lnvmax
and E/RTm on lntm.
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