Kinetics of the thermal decomposition of sodium hydrogencarbonate evaluated by controlled rate evolved gas analysis coupled with thermogravimetry

Article abstract of DOI:10.1016/j.tca.2005.01.032

Influences of the product gases on the kinetics of the thermal decomposition of sodium hydrogencarbonate, NaHCO₃, were investigated by means of controlled rate evolved gas analysis coupled with TG (CREGA-TG). From a series of CREGA-TG measurements carried out under controlled gaseous concentrations of CO₂ and H₂O by considering the self-generated CO₂ and H₂O during the course of reaction, anomalous effects of CO₂ and H₂O on the kinetic rate behavior of the thermal decomposition of NaHCO₃ were revealed, that the reaction is decelerated and accelerated by the effects of atmospheric CO₂ and H₂O, respectively. The kinetic rate behavior under controlled atmospheric condition of CO₂ = 0.1 g m^-3 and H₂O = 1.2 g m^-3 was characterized by the apparent fitting to a kinetic equation of Avrami-Erofeev type with the apparent activation energy of E_a = 111.5 ± 4.8 kJ mol^-1 and pre-exponential factor of A = (1.29 ± 0.01) × 10¹¹ s^-1. The effects of atmospheric CO₂ and H₂O on the apparent kinetic parameters were appeared as the decreases in both the values of E_a and A and the increase in the value of A, respectively.

Full text of DOI:10.1016/j.tca.2005.01.032

Thermochimica Acta 431 (2005) 38–43
Kinetics of the thermal decomposition of sodium hydrogencarbonate
evaluated by controlled rate evolved gas analysis
coupled with thermogravimetry
Shuto Yamada, Nobuyoshi Koga∗
Chemistry Laboratory, Department of Science Education, Graduate School of Education, Hiroshima University,
1-1-1 Kagamiyama, Higashi-Hiroshima 739-8524, Japan
Received 30 October 2004; received in revised form 10 January 2005; accepted 20 January 2005
Available online 17 February 2005
Abstract
Influences of the product gases on the kinetics of the thermal decomposition of sodium hydrogencarbonate, NaHCO3, were investigated by
means of controlled rate evolved gas analysis coupled with TG (CREGA-TG). From a series of CREGA-TG measurements carried out under
controlled gaseous concentrations of CO2 and H2O by considering the self-generated CO2 and H2O during the course of reaction, anomalous
effects of CO2 and H2O on the kinetic rate behavior of the thermal decomposition of NaHCO3 were revealed, that the reaction is decelerated
and accelerated by the effects of atmospheric CO2 and H2O, respectively. The kinetic rate behavior under controlled atmospheric condition of
CO2 = 0.1 g m−3 and H2O = 1.2 g m−3 was characterized by the apparent fitting to a kinetic equation of Avrami–Erofeev type with the apparent
activation energy of Ea = 111.5 4.8 kJ mol−1 and pre-exponential factor of A = (1.29 0.01) × 1011
s
−1. The effects of atmospheric CO2 and
H2O on the apparent kinetic parameters were appeared as the decreases in both the values of Ea and A and the increase in the value of A,
respectively.
© 2005 Elsevier B.V. All rights reserved.
Keywords: Thermal decomposition; Sodium hydrogencarbonate; Controlled rate evolved gas analysis; Kinetics
1. Introduction
simultaneously as the product gases is influenced sensitively
by the atmospheric concentrations of CO2 and H2O, where
the respective effects of CO2 and H2O were characterized
differently as the deceleration by CO2 and acceleration by
H2O [1,2]. In order to measure the reliable kinetic rate data
for such complicated decomposition reaction, the reaction
atmosphere should be controlled strictly even including the
self-generated reaction atmosphere. By adopting the concept
of sample controlled thermal analysis (SCTA) [4–6], we have
constructed an instrument of controlled rate evolved gas anal-
ysis coupled with TG (CREGA-TG) for the specialized pur-
pose for the kinetic analysis of the thermal decomposition
of solids which evolves more than one product gases [3].
The practical usefulness of the CREGA-TG for the kinetic
analysis of such complicated reactions has been clarified as
exemplified by the application to the thermal decomposition
of synthetic malachite [3].
It is generally accepted that kinetic rate behavior of the
thermal decomposition of solids is influenced more or less
by the gaseous concentration and/or partial pressure of the
product gases in the reaction atmosphere, because the re-
actions are in many cases reversible. For more complicated
cases which produce more than one product gases in a sin-
gle decomposition step, it is also supposed such cases that
the rate behavior is influenced differently by the respective
product gases. It has been revealed in our previous studies
[1–3] that the kinetic rate behavior of thermal decomposi-
tion of synthetic malachite which produces CO2 and H2O
∗
Corresponding author. Tel.: +81 824 247091; fax: +81 824 247091.
E-mail address: nkoga@hiroshima-u.ac.jp (N. Koga).
0040-6031/$ – see front matter © 2005 Elsevier B.V. All rights reserved.
doi:10.1016/j.tca.2005.01.032

S. Yamada, N. Koga / Thermochimica Acta 431 (2005) 38–43
39
In the present study, the thermal decomposition of sodium
hydrogencarbonate, NaHCO3, was subjected to the kinetic
study as an alternative example of the reaction which
produces CO2 and H2O simultaneously. By applying the
CREGA-TG, the respective effects of CO2 and H2O concen-
trations in the reaction atmosphere on the kinetic rate behav-
ior of the thermal decomposition of NaHCO3 are investigated
separately. The importance of the quantitative control of the
reaction atmosphere including the self-generated atmosphere
for the reliable kinetic analysis is demonstrated through the
present study.
of decomposition reaction. A thermocouple, placed in con-
tact to the bottom of sample pan in the TG–DTA instrument,
was interfaced to another PID controller with the temperature
program of linear heating. The lower output signal from two
different PID controllers was selected suitably for heating the
sample via an infrared image furnace. The details of CREGA-
TG instrument have already been reported previously [3].
Some 20 of CREGA-TG runs were carried out under system-
atically changed reaction atmosphere by introducing mixed
gases of dry N2, wet N2, dry air and wet air at a total amount
of 200 cm3 min−1, where the heating rate of 2 K min−1 was
applied and the increase in the concentration of CO2 was
regulated to be 0.10 g m−3 during the course of reaction.
2. Experimental
3. Results and discussion
Regent grade sodium hydrogencarbonate (Sigma–
Aldrich, Japan, Special Grade) was sieved to various frac-
tions of particle size. The sample with a sieve fraction of
−170 + 200 mesh was subjected to thermoanalytical mea-
surements.
The sample of ca. 15.0 mg was weighed into a platinum
crucible (5 mm in diameter and 5 mm in height). Conven-
tional TG-DTA measurement was carried out using an in-
strument of ULVAC TGD5000 under flowing dry nitrogen
(200 cm3 min−1) at a heating rate of 10 K min−1, where the
concentrations of CO2 and H2O in the outflow gas from the
reaction chamber were monitored by an infrared CO2 meter
(IIJIMA LX-720) and a hygrometer (NTK HT20), respec-
tively.
CREGA-TG measurements were also performed using the
same instrumental configuration with the above conventional
TG–DTA–EGA. A feedback control for the constant rate
thermal analysis (CRTA) was performed using two indepen-
dent PID controllers [7]. The analogue output signal from the
CO2 meter was interfaced to a PID controller, programmed to
maintain the concentration of CO2 constant during the course
3.1. Reaction behavior
Fig. 1 shows typical conventional TG–DTA–EGA traces
for the thermal decomposition of NaHCO3 at a heating rate
of 10 K min−1 under flowing dry N2 (200 cm3 min−1). The
reaction takes place showing a smooth mass-loss curve with
an endothermic DTA peak, where the observed value of total
mass-loss, 36.8 0.6%, was in good agreement with the
value calculated by assuming the reaction:
2NaHCO3 → Na2CO3 + CO2 + H2O.
During the thermal decomposition, CO2 and H2O evolve si-
multaneously indicating peak maximums at the same temper-
ature with the endothermic DTA peak. These typical features
of the thermoanalytical curves for the thermal decomposition
of solids expose apparent drawbacks for the kinetic use of the
conventional thermoanalytical measurements carried out un-
der linearly increasing temperature [8–10]. The well shaped
endothermic DTA peak indicates that the sample temperature
Fig. 1. Typical TG–DTA–EGA (CO2, H2O) traces for the thermal decomposition of NaHCO3 (15.0 mg) at a heating rate of 10 K min−1 under flowing dry N2
(200 cm3 min−1).

40
S. Yamada, N. Koga / Thermochimica Acta 431 (2005) 38–43
Fig. 2. Typical CREGA-TG traces for the thermal decomposition of NaHCO3 (15.0 mg), recorded by regulating the increase of CO2 concentration during the
course of reaction at 0.1 g m−3, under flowing dry N2 (200 cm3 min−1).
deviates more or less from the programmed linear heating
and a possible temperature distribution within the assemblage
of sample particles is caused, called sometimes as the self-
cooling effect [11]. The rate of reaction is directly influenced
by the temperature deviation and distribution result from the
self-cooling effect. Similarly, the changes in the reaction at-
mosphere during the course of reaction due to self-generated
gaseous products are also the possible factors affecting the
experimentally resolved shape of TG and DTG curves [10].
It has been expected from the time of development [4–6]
that CRTA as one of the modes of sample controlled thermal
analysis can be a possible solution of the problems inherent
in the kinetic use of the conventional thermal analysis. Fig. 2
shows typical CREGA-TG traces recorded by regulating the
increase of CO2 concentration during the course of reaction
at a constant value of 0.1 g m−3. Although the concentration
of H2O should be increased by 0.1 g m−3 during the course
of reaction as is with CO2, the expected change in the H2O
concentration could not be detected due to lower sensitivity
of the present hygrometer. Because the reaction advances
at a very slow constant rate, the undesirable influence
of self-cooling effect on the precise control of sample
temperature and on the rate behavior can be restrained
largely in the CREGA-TG measurement. Evolution rates of
the product gases are also kept constant during the course of
reaction so that the influence of the self-generated reaction
atmosphere on the rate behavior is also under control. The
feedback temperature control by referring EGA signal
employed in the present study as CREGA-TG enable us to
control quantitatively the concentration of a specific gaseous
product in the reaction atmosphere even for the complicated
decomposition reaction where more than one gases are
produced at different rate behaviors. Thus the influence of
a specific product gas in the reaction atmosphere on the
apparent kinetics of the thermal decomposition of solids can
be examined by considering the increase in the concentration
of a specific product gas during the course of reaction,
in addition to the applied reaction atmosphere for the
measurement.
In order to evaluate the respective influences of at-
mospheric CO2 and H2O on the kinetics of the thermal
decomposition of NaHCO3, CREGA-TG measurements
were carried out under various concentrations of CO2 and
H2O in the inflow gas by regulating the increase in the
concentration of CO2 in the outflow gas at 0.1 g m−3. Irre-
spective of the applied concentrations of CO2 and H2O in the
inflow gas, the mass-loss proceeded at a constant mass-loss
rate of (−5.48 0.08) × 10−2 mg min−1. Fig. 3 shows the
temperature profiles of the CREGA-TG measurements car-
ried out under various concentrations of CO2 and a restricted
H2O concentration of 1.2 g m−3. The reaction temperature
Fig. 3. Comparison of the temperature profiles of the CREGA-TG measure-
ments carried out under various concentrations of CO2 and a restricted H2O
concentration of 1.2 g m−3
.

S. Yamada, N. Koga / Thermochimica Acta 431 (2005) 38–43
41
nucleation process by the existence of atmospheric H2O.
The similar behavior of the abnormal effect of atmospheric
H2O has been also observed for the thermal decomposition
of synthetic malachite, Cu2(OH)2CO3 [1–3].
3.2. Kinetic analyses
Because the reaction rate behavior of the thermal de-
composition of NaHCO3 is influenced sensitively by the
atmospheric CO2 and H2O including the self-generated
these gases, any changes of reaction atmosphere during the
course of reaction and among a series of rate data for kinetic
calculation are desired to be diminished for measuring
the reliable kinetic rate data. As a possible method to
record a series of kinetic rate data at different reaction
rates without any practical changes of reaction atmosphere
during the course of reaction and among the series of kinetic
measurements, a simple method of measuring a pair of
temperature profiles of CREGA-TG was employed in the
present study [3]. One measurement was carried out as
usually by setting single sample cell weighed 15.0 mg of
sample to the sample holder (single sample). For alternating
the constant reaction rate, another measurement was carried
out using twin sample cells weighed every 15.0 mg of sample
in the respective sample cells by setting one to the sample
holder for the TG–DTA measurements and another to the
holder for the reference material of DTA measurement (twin
samples). Fig. 5 shows the CREGA-TG traces recorded for
the measurements of single sample and twin samples under
flowing dry N2 (200 cm3 min−1) by controlling the increase
of CO2 concentration in the outflow gas at 0.1 g m−3. In
the case of the measurement of twin samples, the constant
mass-loss rate decreases by half compared with that for the
measurement of single sample, because both the samples
contribute equally to the increase in the concentration of
CO2 during the course of reaction.
Fig. 4. Comparison of the temperature profiles of the CREGA-TG measure-
ments carried out under various concentrations of H2O and a restricted CO2
concentration of 0.1 g m−3
.
shifts to higher temperature with increasing the concentration
of CO2 from 0.1 to 0.3 g m−3. This is apparently the normal
effect of atmospheric CO2 from the view point of chemical
equilibrium. Fig. 4 compares the temperature profiles of
the CREGA-TG measurements carried out under various
concentrations of H2O and a restricted CO2 concentration of
0.1 g m−3. Unexpectedly, the reaction temperature decreases
with increasing the atmospheric concentration of H2O.
It is indicated by the opposite effect of the atmospheric
H2O on the reaction temperature that the atmospheric
H2O promotes the reactivity. Comparing the shapes of
the reaction temperature profiles, a trend of temperature
increase observed at the initial part of the reaction (α < 0.1)
is restrained with increasing the atmospheric concentration
of H2O, which indicates possibly the acceleration of surface
Fig. 5. Comparison of CREGA-TG traces recorded using single sample and twin samples.

42
S. Yamada, N. Koga / Thermochimica Acta 431 (2005) 38–43
Fig. 6. Influence of atmospheric CO2 on the α-dependence of Ea under
atmospheric H2O at 1.2 g m−3
Fig. 7. Influence of atmospheric H2O on the α-dependence of Ea under
controlled atmospheric CO2 at 0.1 g m−3
.
.
The fundamental kinetic rate equation of the Arrhenius
type was applied for analyzing the kinetic analysis of the
present thermal decomposition:
dicated the constant Ea values in the whole course of reac-
tion, i.e. for the reactions under controlled concentrations of
(CO2, H2O) = (0.1, 1.2), (0.3, 1.2) and (0.1, 3.2) g m−3. Us-
ing the averaged values of Ea for the respective processes, the
measured rate data were extrapolated to infinite temperature
according to the following equation [12,13].
ꢀ
ꢁ
dα
dt
Ea
= A exp
−
f(α)
(1)
RT
where A, Ea, and f(α) are the pre-exponential factor, appar-
ent activation energy, and kinetic model function in differen-
tial forms, respectively. The other symbols have their usual
meanings. The values of Ea at selected α were determined
from a pair of kinetic rate data using a simple isoconversional
method which has been utilized as the rate jump method [7].
ꢀ
ꢁ
dα
dθ
dα
dt
Ea
=
exp
(3)
RT
where θ is the generalized time and/or reduced time proposed
by Ozawa [12,13] and indicates the simulated reaction time
at infinite temperature. Fig. 8 compares the shapes of the
simulated kinetic rate data at infinite temperature as the plots
of (dα/dθ) normalized by dividing the value at α = 0.5, i.e.,
(dα/dθ)/(dα/dθ)0.5, against α [14]. The simulated rate data un-
der three different atmospheric conditions indicated the sim-
ilar rate behavior of decelerate process with slightly convex.
As referenced by the reaction under the lowest CO2 and H2O
concentrations examined, the values of (dα/dθ)/(dα/dθ)0.5 for
the higher CO2 concentration deviate to the higher values
at α > 0.5. Oppositely, deviation of (dα/dθ)/(dα/dθ)0.5 to the
lower values was observed at α > 0.5 for the reaction under
the higher H2O concentration.
RT1T2
(dα/dt)1
Ea = −
ln
(2)
T2 − T1 (dα/dt)2
where the data point (Ti, (dα/dt)i) are on the respective ki-
netic rate curves at a restricted α. Fig. 6 shows the val-
ues of Ea evaluated at various α for the reactions under
different CO2 concentrations, 0.1 and 0.3 g m−3, and a re-
stricted H2O concentration of 1.2 g m−3. Although the val-
ues of Ea at various α indicated acceptable constant values in
the wide range of 0.1 ≤ α ≤ 0.9 irrespective of CO2 concen-
trations applied, the averaged value of Ea decreased about
30 kJ mol−1 by increasing the CO2 concentration from 0.1
to 0.3 g m−3, i.e., 111.5 4.8 and 78.5 3.0 kJ mol−1 in the
range of 0.1 ≤ α ≤ 0.9. Fig. 7 compares the α-dependence
of Ea calculated for the reactions at a controlled CO2 con-
centration of 0.1 g m−3 and various H2O concentrations. Ir-
respective of the H2O concentrations controlled, the values
of Ea for the first half of the reaction remain unchanged.
For the second half (α > 0.5), the values of Ea tend to de-
viate gradually to the lower values from the constant value
with increasing the atmospheric concentration of H2O. This
trend is clearly observed for the reaction under controlled
concentrations of CO2 = 0.1 g m−3 and H2O = 6.3 g m−3. For
the reactions under the lower H2O concentrations, 1.2 and
3.2 g m−3, the values of Ea averaged over 0.1 ≤ α ≤ 0.9 were
determined as 111.5 4.8 and 109.6 5.2 kJ mol−1, respec-
tively.Further kinetic characterization was made for the pro-
cesses under three selected atmospheric conditions which in-
Fig. 8. Comparison of the simulated kinetic rate data at infinite temperature
for the reactions under three selected atmospheric conditions.

S. Yamada, N. Koga / Thermochimica Acta 431 (2005) 38–43
43
Table 1
Summary of the apparent kinetic parameters evaluated for the reactions under various controlled reaction atmosphere
Controlled reaction atmosphere
From Eq. (2) Ea (kJ mol−1
)
From (dα/dθ) vs. m(1 − α)[−ln(1 − α)]1−1/m plot
CO2 (g m−3
)
H2O (g m−3
)
m
A (s−1
)
γa
0.1
0.3
0.1
a
1.2
1.2
3.2
111.5 4.8
78.5 3.0
109.6 5.2
1.25
1.15
1.30
(1.29 0.01) × 1011
(9.19 0.08) × 106
(1.65 0.02) × 1011
0.9981
0.9977
0.9971
Correlation coefficient of the linear regression analysis.
Combining Eqs. (1) and (3), the following equation is de-
rived [12,13–15].
gases in the reaction atmosphere influence differently on the
rate behavior of the thermal decomposition. As is expected
from the chemical equilibrium of the reaction, the reaction
rate of the forward reaction is decelerated apparently by the
atmospheric CO2. On the other hand, opposite effect was ob-
served for the atmospheric H2O which enhances the reaction
rate within the range of H2O concentration examined in the
present study.
CREGA-TG was successfully applied for measuring the
kinetic rate data under a quantitatively controlled condition of
reaction atmosphere including the self-generated conditions.
The rate behavior of the thermal decomposition was charac-
terized apparently by a kinetic equation of Avrami–Erofeev
type, where the appropriate kinetic exponent decreased and
increased by the effects of atmospheric CO2 and H2O, re-
spectively. The enhancement of the reactivity by the effect
of atmospheric H2O was expressed by the increase in the
value of A without any practical change in the value of Ea.
The normal effect of chemical equilibrium observed for the
effect of atmospheric CO2, i.e., the decrease in the reac-
tion rate, appeared as the decreases in both the values of
Ea and A.
dα
= Af (α)
(4)
dθ
By plotting dα/dθ against f(α), a straight line with slope
A is obtained when an appropriate function of f(␣) was
applied for the plot. Through plotting dα/dθ against vari-
ous f(α) for the reactions under three different controlled
atmospheric conditions, Avrami–Erofeev model [16], i.e.
f(α) = m(1 − α)[−ln(1 − α)]1 − 1/m with the values of m close
to unity, was selected as the most appropriate kinetic model
function. Although the apparent fit to the Avrami–Erofeev
model derived originally for the nucleation and growth type
reaction should be further investigated from the physico-
geometrical view points [10], the empirical fitting to a partic-
ular kinetic model enable us to determine the apparent value
of A and to compare the values among the series of reactions
under investigation.
Table 1 summarizes the apparent kinetic parameters eval-
uated for the reactions under three different controlled atmo-
sphere. The change in the rate behavior at the second half
of the reaction depending on the atmospheric condition is
reflected apparently by the change in the kinetic exponent
m in the Avrami–Erofeev equation. The changes in the re-
action temperature at a restricted reaction rate depending on
the atmospheric condition observed as the changes in the
temperature profiles of the CREGA-TG measurements, see
Figs. 3 and 4, can be expressed by the changes in the value
of A. Unexpected decrease in the reaction temperature with
increasing the atmospheric H2O concentration from 1.2 to
3.2 g m−3 appears as the increase in the value of A without
any practical change in Ea. As for the increase in the reaction
temperature with increasing the CO2 concentration from 0.1
to 0.3 g m−3, the value of A decreases drastically, but the ef-
fect of the large decrease in A on the reaction temperature is
compensated partially by the decrease in Ea.
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4. Conclusion
The reaction rate behavior of the thermal decomposition
of NaHCO3, which evolves CO2 and H2O simultaneously, is
influenced sensitively by the atmospheric CO2 and H2O in-
cludingtheself-generatedthesegases. Therespectiveproduct