Determination of the chemical reaction kinetics using isothermal reaction calorimetry supported by measurements of the gas production rate: A case study on the decomposition of formic acid in the heterogeneous Fenton reaction

Article abstract of DOI:10.1016/j.tca.2017.04.006

One of the most important steps in studying chemical reaction kinetics is to determine a rate law for the reaction. In this paper, a method for the identification of the reaction kinetic model using isothermal calorimetric data and additional measurement of the rate of pressure change in a constant volume of a calorimetric vessel is described. This method can be applied to fairly fast chemical reactions (i.e. those that can be completed within about 2?h) that produce gaseous products. The decomposition of formic acid in the heterogeneous Fenton process is employed as a case study to demonstrate the use of the developed method for the kinetic analysis of a complex reaction system. It was found that the rate of decomposition of hydrogen peroxide can be described by the Langmuir–Hinshelwood type of equation in the form r?=?kC_P/(1?+?K_PC_P) (where C_P is a molar concentration of H₂O₂) both in the case of the decomposition of the aqueous hydrogen peroxide solution as well as during the oxidation of formic acid. A simple, purely empirical rate equation for the decomposition of formic acid was also proposed.

Full text of DOI:10.1016/j.tca.2017.04.006

Accepted Manuscript
Title: Determination of the chemical reaction kinetics using
isothermal reaction calorimetry supported by measurements of
the gas production rate. A case study on the decomposition of
formic acid in the heterogeneous Fenton reaction
Authors: Lech Nowicki, Dorota Siuta, Mariusz Godala
PII:
S0040-6031(17)30099-0
DOI:
Reference:
http://dx.doi.org/doi:10.1016/j.tca.2017.04.006
TCA 77725
To appear in:
Thermochimica Acta
Received date:
Revised date:
Accepted date:
3-1-2017
28-3-2017
9-4-2017
Please cite this article as: Lech Nowicki, Dorota Siuta, Mariusz Godala,
Determination of the chemical reaction kinetics using isothermal reaction calorimetry
supported by measurements of the gas production rate.A case study on the
decomposition of formic acid in the heterogeneous Fenton reaction, Thermochimica
Actahttp://dx.doi.org/10.1016/j.tca.2017.04.006
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Determination of the chemical reaction kinetics using isothermal reaction calorimetry
supported by measurements of the gas production rate. A case study on the
decomposition of formic acid in the heterogeneous Fenton reaction.
a*
a
b
Lech Nowicki , Dorota Siuta , Mariusz Godala
aLodz University of Technology, Faculty of Process and Environmental Engineering,
Wolczanska 213, 90-924 Lodz, Poland
bBureau for Chemical Substances, Dowborczyków 30/34, 90-019 Lodz, Poland
*Corresponding author Tel.: +48 426313781, E-mail address: lech.nowicki@p.lodz.pl
Highlights



A new method for the identification of the reaction kinetic model is proposed.
The method can be applied to chemical reactions that produce gaseous products.
Decomposition of H
study.
2
2
O and oxidation of HCOOH catalysed by goethite is showed as a case

Usefulnessof aL-H type of rate law for H
2
2
O decomposition is confirmed.
Abstract
One of the most important steps in studying chemical reaction kinetics is to determine a rate
law for the reaction. In this paper, a method for the identification of the reaction kinetic model
using isothermal calorimetric data and additional measurement of the rate of pressure
change in a constant volume of a calorimetric vessel is described. This method can be
applied to fairly fast chemical reactions (i.e. those that can be completed within about 2
hours) that produce gaseous products. The decomposition of formic acid in the
heterogeneous Fenton process is employed as a case study to demonstrate the use of the
developed method for the kinetic analysis of a complex reaction system. It was found that the
rate of decomposition of hydrogen peroxide can be described by the Langmuir-Hinshelwood
type of equation in the form r = kC
P
/(1+K
P
C
P
) (where C
P
is a molar concentration of H
2
2
O )
both in the case of the decomposition of the aqueous hydrogen peroxide solution as well as
during the oxidation of formic acid. A simple, purely empirical rate equation for the
decomposition of formic acid was also proposed.
Keywords: Hydrogen peroxide; Formic acid; Fenton reaction; Heterogeneous catalysis;
Reaction kinetics
1

1. Introduction
Information about the kinetics of a chemical reaction can be usefully applied in many different
fields, such as the interpretation of reaction mechanisms and catalytic phenomena, process
design and optimization and process safety. The main difficulty that arises during the kinetic
study of a chemical reaction is the development of suitable experimental technique to collect
reliable reaction rate data. Typically, in order to experimentally determine reaction rates, the
concentrations of reactants or products are measured in samples of the reaction mass taken
over the course of the reaction. In some cases, changes in the physical properties
of a reacting system can be used to measure the reaction progress. The main advantages
of these methods are that they do not disturb the system and are less laborious and thus
faster. Examples of these measurements include changes in the mass, volume and pressure
in a constant volume of a gas phase reaction and changes in the temperature and absorption
of a solution, etc.
Apart from many other applications, isothermal reaction calorimetry has found widespread
application in the kinetic analysis of chemical reactions. In this technique, the flow rate of the
heat released in a chemical reaction is measured by the instrument as a function of time, as
the heat flow rate during the chemical reaction is proportional to the reaction rate. The kinetic
analysis of the experimental data can be straightforward using differential methods of
analysis. For a first-order homogeneous reaction, the profile of the heat flow rate can be
directly used to determine the reaction rate constant as well as the reaction enthalpy by
plotting the logarithm of the heat flow rate against time, which should result in a straight line
with a slope that is equal to the negative value of the reaction rate constant [1]. However, for
multiple reaction systems and reactions involving any type of physical processes in which
heat is absorbed or released, reaction calorimetry alone is not sufficient to give information
about the rates of individual steps. In such cases, it is necessary to incorporate additional on-
line measured values or concentration data to identify the reaction enthalpies and kinetic
models [2].
For reactions with gaseous reagents, measurement of the gas production or uptake rate can
be a source of additional information about the process kinetics. To date, very few studies
have been published in which this technique was combined with the typical isothermal
reaction calorimeter measurement. Sempere et al. [3] measured the oxygen effluent as a
function of time to calculate the heat effect caused by hydrogen peroxide decomposition
during calorimetric experiments involving the N-oxidation of 2-methylpyridine. Le Blond et al.
[
4] measured the hydrogen uptake to calculate the overall rate and enthalpies of the reaction
2

steps during the hydrogenation of a nitro group. In both cases, the calorimetric experiments
were performed under isothermal and isobaric conditions in semi-batch operations. The rate
of oxygen production was measured directly by means of a mass flowmeter, whereas the
hydrogen uptake rate was obtained indirectly by measuring the profile of the pressure drop in
the gas reservoir. To perform these measurements, it was necessary to equip the calorimeter
with additional components. In a simpler way, the extent of the reaction in which a gaseous
product is formed can be monitored by measuring the gas pressure in the reactor under
isochoric conditions. In such a case, the pressure change profile must be differentiated to
calculate the reaction rate. It is worth noting that modern reaction calorimeters are usually
equipped with fast response pressure transducers so that reasonably accurate rate data can
be obtained. The numerical differentiation of pressure data is highly susceptive to data noise
and can result in errors, so it must be performed using effective smoothing tools. Godala and
Nowicki [5] have shown that the heat and amount of oxygen released during the reaction can
be used for the determination of the kinetics of the hydrogen peroxide decomposition
reaction, leading to very consistent results.
The main aim of this study is present a combined approach involving simultaneous reaction
calorimetry and gas effluent measurements to obtain the kinetic and thermodynamic
parameters for complex chemical reaction. An example concerning the oxidation of formic
acid in the heterogeneous Fenton reaction is used to illustrate the proposed method and the
possibilities it creates. A simple kinetic model for destruction of formic acid in heterogeneous
Fenton process will be proposed.
2. Fenton processes using goethite as an iron source
The Fenton process has been considered as an alternative technology for the low-
temperature treatment of wastewater containing biologically non-degradable organic
pollutants [6]. The traditional Fenton process is based on the reaction of hydrogen peroxide
2
+

with the ferrous ion (Fe ) in acidic solution to produce OH radicals - a powerful, non-
selective oxidant. The oxidation of an organic compound through Fenton's process is
exothermic and results in the formation of carbon dioxide and water as final products. Except
for soluble iron salts, solid iron oxides or iron immobilized on a solid support can be used as
the catalyst in the so-called heterogeneous Fenton reaction, which can also provide efficient
organic pollutant oxidation [7-10]. In this study, goethite, an iron oxyhydroxide, was used as
the catalyst. This natively found iron oxide has been widely employed in the heterogeneous
3

Fenton and photo-Fenton processes [11-18] due to its attractive properties for large-scale
applications [16,17,19].
The oxidation efficiency in the Fenton process is directly related to the concentration of OH
produced by the catalytic (or photocatalytic) decomposition of hydrogen peroxide. This
reaction (Eq. 1) is a disproportionation reaction in which water and oxygen are formed:
2
H
2
O
2
 2H
The decomposition of hydrogen peroxide in aqueous solution catalysed by goethite has been
studied by Lin and Gurol [9]. These authors have found that the decomposition of H is a
2
O + O2(g)
(1)
2
O
2
heterogeneous process. The contribution of a homogeneous reaction was negligibly small
due to the very low concentration of iron ions, which passed into the solution as a result of
-3
leaching from the mineral (at a slurry concentration of 3 g∙dm , the dissolved iron
-3
concentration was less than 0.1 mg∙dm ). They proposed a reaction mechanism in which the
reaction pathway is initiated by the adsorption of a hydrogen peroxide molecule on the active
III
site of the catalyst (≡Fe –OH group) and then proceeds through several steps involving the
formation of hydroxyl and hydroperoxyl radicals. These authors assumed that the iron is
always attached to the solid and the active sites are constantly regenerated for new H
2
O
2
molecules at neutral pH. Based on this mechanism, the following Langmuir-Hinshelwood type
of rate equation for the catalytic decomposition of hydrogen peroxide was developed:
kC w
P
cat
r1 
(2)
1
 K CP
P
The validity of Eq. 2 has been confirmed by examining the data obtained in a reaction
-3
calorimeter at a range of concentrations of H
2
O from 0.05 to 0.082 mol∙dm and at catalyst
2
-3
concentrations of 2.5 to 7.5 g∙dm [20].
Formic acid is often present in effluent from the textile industry as a result of textile
dyeing and finishing technologies and is also an intermediate or final product that forms as a
result of the different advanced oxidation processes (AOPs) of high-molecular-weight
compounds [21-25]. In the decomposition of formic acid by Fenton’s reagent, two parallel
reactions occur: the decomposition of hydrogen peroxide (Eq. 1) and the oxidation of formic
acid (Eq. 3)
HCOOH + H
2
O
2
 CO
2
(g) + 2H
2
O
(3)
These exothermic reactions are accompanied by endothermic physical process associated
with the desorption of oxygen and carbon dioxide from the reaction mixture. Decomposition
of formic acid in a water solution using the Fenton and photo-Fenton processes has been
extensively studied including kinetic modelling [26, 27].
4

In contrast to the oxidation of formic acid and other organic substances in
homogeneous Fenton’s reactions, there is not much information regarding the mechanisms
and especially mechanistically based kinetic models of the heterogeneous Fenton reactions.
The results obtained from the decomposition of 2-chlorophenol employing small particles of
goethite as a catalyst at acidic pH showed that, in fact, this reaction occurs in the liquid phase
with the participation of iron ions, which were dissolved from the surface of the catalyst [12].
Studies of the oxidation of 2-chlorophenol using goethite as the catalyst under similar
operating conditions have also been conducted by [16-17]. These authors have developed a
rigorous model of the reaction mechanism based on a combined scheme of heterogeneous
processes for the release of iron ions from the goethite surface of the catalyst and the typical
homogeneous Fenton reaction. According to this mechanism, the decomposition of the
peroxide is independent of the oxidation of the organic substance and is an undesired
competitive reaction, which reduces the efficiency of the entire process.
3. Experiments
3.1. Chemicals and catalyst
Hydrogen peroxide (30 wt.-%) and formic acid (85 wt.-%) were supplied by POCh (Poland).
Goethite (the catalyst), -FeOOH containing approximately 35 wt.-% iron, was provided by
Fluka. The catalyst particle size was less than 100 m. Lin and Gurol [9] observed that the
reaction rate is independent of the goethite particle size for particle sizes less than 600 m.
3.2. Reactor
Experiments were carried out in a RC1 HP60 stainless steel reactor (Mettler-Toledo) with a
3
nominal volume of 2 dm . The reactor was equipped with a thermostatic cover to minimaze
heat loses to the environment. The reaction mixture was stirred continuously at a constant rate.
of 150 rpm. Calibration of the measuring system of the calorimeter was performed before each
experiment allowing the evaluation of the overall heat transfer coefficient. The RC1 calorimeter
was also equipped with a standard pressure sensor and Mettler Toledo In Pro 6000 Series
sensor to measure an oxygen content in the gas evolved during the reaction. The evaluation of
heat evolution due to the reaction as a function of time was calculated using the software of the
apparatus.
3.3. Operation procedure
The reactor was filled with distilled water and the desired amount of formic acid and hydrogen
peroxide. After reaching steady-state temperature of 293 K the prescribed goethite was added
5

into the solution to initiate the reaction. After adding the catalyst, the reactor was closed to
allow accumulation of the gaseous products. The total heat evolution rate of the system, q, and
the increase in the reactor pressure, P, were measured and recorded continuously as a
function of time during the reactions. For quantitative analysis of the heat flow data, a baseline
value of heat flow was recorded prior to initiation of the reaction and, in some experiments,
after its completion.
4. Results and discussion
4.1. Decomposition of hydrogen peroxide
Four experiments were performed on the goethite-catalysed decomposition of H
2
2
O to verify
the reproducibility of the experimental data and to calibrate the measurement system,
especially the oxygen sensor placed in the gas space of the reactor. The first reaction was
initiated by adding the catalyst to the aqueous solution of hydrogen peroxide (run P1). In the
next three experiments (runs P2 - P4), the reaction was continued by adding another portion
of fresh peroxide solution to a slurry of the catalyst remaining in the reactor after completion
of the previous run. The experimental conditions are presented in the Table 1. Fig. 1 shows
the total heat flow rate of the process, q, and the changes in the reactor pressure P as a
function of time in four experiments performed under isothermal conditions (293 K).
As seen in Fig. 1, both the heat flow and the pressure change profiles have similar shapes
and small differences in the total heat released and the final pressure, perhaps due to errors
in the run start-up. The reproducibility of the results also shows that the catalyst does not lose
its catalytic properties when reused, although careful examination of its stability would require
a larger number of repetitions. The volume of the gas space in the reactor must be known to
evaluate the pressure data. This parameter was calculated based on the amount of oxygen
formed in the reaction. In fact, some of the oxygen formed is accumulated in the liquid phase
owing to the increased partial pressure of oxygen in the reactor. However, due to the small
pressure change and poor solubility of oxygen in water, its accumulation in the reaction
mixture was ignored. Taking the Henry's law constant for the oxygen-water system of 729
3
-1
dm ·bar·mol [28], it was estimated that less than 4% of the oxygen formed in the reaction
was not evolved into the gas space.
The heat flow rate determined during a reaction experiment, q(t), can be integrated to yield
the total amount of heat released from the system, Q , which involves the heat of chemical
f
6

reaction (exothermic) and the heat of the desorption of oxygen from the reaction mixture
endothermic). For an isothermal and constant-volume process, the integrated form of the
(
heat balance equation can be written as Eq. 4:
tf
G
Q  q(t)dt 

 ΔHr ,1

X V ΔP
(4)
f

1,f
f
0
where t is the integration limit of time (time needed for completion of the reaction). As all the
f
hydrogen peroxide charged to the reactor was decomposed, the final reaction extent X1,f is
equal to n0,P/2, and Eq. 4 can be used to calculate the enthalpy values for hydrogen peroxide
decomposition (the pressure-volume work was ignored because of its small value). These
values are given in Table 1.
The average enthalpy obtained from four calorimetric experiments carried out at 293 K
was -188.3 ± 2.8 kJ∙mol (-94.2 kJ∙molH2O2-1). The resulting reaction enthalpy is comparable
with the experimental values obtained by other authors (from -89.9 to -100.4 kJ∙molH2O2-1) for
homogeneous catalysts [5, 29-30].
-1
When the reaction enthalpy is known, the thermally defined reaction extent, X
1
(t), can be
calculated from the fractional heat evolution of the process (Eq. 5).
t
q(t)dt

0
X1
t


(5)

ΔHr,1
The extent of the hydrogen peroxide decomposition reaction can also be obtained from the
pressure change data using the ideal gas law. Comparison of the kinetic curves expressed
as changes in the extent of the reaction calculated in two different ways is shown in Fig. 2a.
The profiles for all four experiments were similar when superposed, so only one case is
shown. As seen in Fig. 2a, the two profiles almost overlapped with each other, although more
precise analysis shows that the extent of the reaction was slightly higher at lower conversions
when calculated from the pressure. This difference is probably due to the higher inertia of the
measurement system of the reaction calorimeter. However, this difference appears to be
within the scope of the experimental error, which can be estimated based on the reaction
extent profiles obtained for four runs from the thermal data, which are presented in Fig. 2b.
Analogously to Eq. 5 for the fractional heat released by the process, the relationship between
the heat flow rate and the reaction rate can be expressed. Thus, the time-varying reaction
rate can be calculated from the following equation (Eq. 6):
7

q
 
t
r
1
t


(6)
L
V

 ΔH

r,1
The reaction rate data were then used to test the applicability of the Langmuir-Hinshelwood
type of rate equation (Eq. 2), which can be converted to the following form (Eq. 7):
1
KP 1 1


(7)
r
1
k1 k1 cP
where k1  k wcat (1/s). The validity of this model can be verified by plotting 1/r versus 1/c
and determining whether a straight line is obtained. The slope of this line should be equal to
/k1 , and an intercept can be used to determine the second parameter, K . Appropriate plots
P
1
P
are shown in Fig. 3. The plots presented in Fig. 3 include only data collected for the reaction
excess, varying from 5 to 95% of its maximum value to avoid the influence of experimental
errors. The measured signal (heat-flow rate) is usually distorted by different phenomena
occurring in the reaction mixture and in the instrument, especially at the beginning and near
the end of the process [2]. It is also known that the heterogeneous Fenton process has an
induction period with a slow reaction rate [16,17].
The kinetic parameters k
1
and K derived from the parameters of the regression line are
P
given in Table 1. The kinetic model predictions of the hydrogen peroxide concentration
-3
-1
versus time calculated for the average values of the parameters (k
1
= 1.4610 s and K
p
=
3
-1
9
.8 dm ∙mol ) are compared with the experimental data points in Fig. 4. As can be seen, the
model correctly predicted the concentration over the whole range of reaction times.
As stated by the manufacturer, goethite used in this study contains about 35 wt.-% of iron. So
the reaction rate constant k (independent of catalyst concentrarion) expressed in
1
3
-1 -1
dm ∙moleFe ∙s ) is equal to 0.023 and this value is within the range determined by Lin and
Gurol [9] for the decomposition of hydrogen peroxide catalysed by goethite carried out at
different pH (from 0.019 for pH=5 to 0.067 for pH=10). However, it is different in the case of
3
-1
the K
p
. We obtained the average value of 9.8 dm ∙mol , where Lin and Gurol give the value
3
-1
of 0.24 dm ∙mol , but their experiments were performed at very low initial concentrations of
-3
H
2
O
2
(0.0010.01 mol·dm ). At these confitions K
denominator in the rate equation (2) is negligible. Therefore, the experimental data collected
for law concentration of hydrogen peroxide can not lead to reliable estimation of K . It also
seems that low sensitivity of the reaction rate to variations of K and random and systematic
P
C
P
<<1 and significance of the
P
p
8

errors of calorimetric measurements may explain the different values of this parameter
obtained for various runs in our study (see Table 1).
4.2. Decomposition of formic acid in the heterogeneous Fenton reaction
4.2.1. Evaluation method
During the degradation of formic acid in the Fenton process, two parallel reactions occur: the
decomposition of hydrogen peroxide (Eq. 8) and the oxidation of the organic compound
(Eq. 9)
2
H
2
O
2
 2H
2
O + O2(aq), Hr,1
aq) + 2H
(8)
HCOOH + H
2
O
2
 CO
2
(
2
O,
Hr,2
(9)
These exothermic chemical reactions are accompanied by an endothermic physical process
associated with the desorption of oxygen (Eq. 10) and carbon dioxide (Eq. 11) from reaction
mixture.
O
2(aq)  O2(g), Hd,O
(10)
(11)
CO2(aq)  CO2(g), Hd,C
The following assumptions were used in the development of a mathematical model of the
process:
1. The rate of desorption of oxygen from the liquid is equal to the rate of its formation in the
chemical reaction, so there is no accumulation of oxygen in the reaction mixture (as
discussed earlier).
2. The desorption of the carbon dioxide product from the reaction mixture is fast compared to
the chemical reaction. Dissolved CO
space of the reaction vessel.
2
is always in equilibrium with the CO inside the gas
2
The changes taking place in the reactor can be described using the extent of reaction X
the reaction (Eq. 8) and X for the oxidation of formic acid (Eq. 9) by the following set of
stoichiometric balance equations:
1
for
2

n
A
P
= n
A
P
– n0,A = -X
2
(12)
n
= n
– n0,P = 2-X
1
- X
2
(13)
9

The relationship between the parameters X
1
and X and the directly measured values (the
2
heat flow rate of the system, q, and the reactor pressure changes, P) can be found starting
from the heat and mass balance equations, given by
t
G
C
Q

t

 q(t)dt  2

 ΔHr,1

X1

t



 ΔHr,2

X2

t

 ΔH Δn

t

(14)
(15)

d,C
0
G


X1

t

 nC

t RT




P

t


G
V
G
where nC

t

is the amount of carbon dioxide released to gas phase. As the accumulation of
G
oxygen in the liquid phase is negligible, nO

t


 X1 t

. Furthermore, if there is equilibrium
between the gas and liquid phases, then
L
RT V
G
L
G
G

nC

t


 nC

t

 nC

t

 nC

t

 nC

t

 X2

t

(16)
G
V HeC
and
X2

t

G
nC

t

(17)
(18)
a
where
L
RT V
a  1
G
He V
C
Finally,
t
Q

t

 q(t)dt  bX

t

 cX2

t

(19)
(20)

1
0


X2
 
t
 RT

P

t

  X1
t





G
a
V



where
b  2

 Hr,1

(21)
(22)

Hd,C
c   Hr,2



a
4.2.2. Experimental data
A series consisting of 5 oxidation reactions of formic acid using the heterogeneous Fenton
reagent was conducted under the conditions listed in Table 2. In these experiments, the pH
1
0

was not adjusted and increased from the initial value of approximately 3. Moreover, in
addition to the heat flow rate of the system, q, and the reactor pressure changes, P, the
change in oxygen partial pressure, p , was also measured by a sensor located in the gas
O
space of the reactor. Fig. 5 shows the heat flow rate and the measured process variables as
a function of time, obtained under isothermal (293 K) conditions. As is apparent from Fig. 5a,
-3
at a catalyst concentration in the slurry of 5 gdm (runs A1-A2), the process occurred very
slowly, and a long reaction time was required to achieve higher conversion. This makes it
difficult to determine the correct position of the baseline and may affect the accuracy of the
measurement. To avoid this problem in the following experiments, the catalyst concentration
was increased (runs A3-A5).
Eqs. 19 and 20 could be used to calculate the reaction progress using the measured values
of q(t) and P(t) if the enthalpies of both reactions and other parameters were known in
advance. The enthalpy of H
2
2
O decomposition, Hr,1, was determined in the previous section,
but the enthalpy of the formic acid oxidation step needed to be identified. This identification
would have been easy if all reactions had been completed, but this was not the case under
the process conditions used. Thus, to assess the final value of the reaction extent for the
hydrogen peroxide decomposition, the amount of oxygen released was estimated based on
the measured change in the partial pressure of O
2
. This, in turn, allowed calculation of the
final progress of the second reaction, X , from Eq. 20, and the reaction enthalpy, Hr,2, was
2 f
,
then evaluated from the total amount of heat released in the process (Eq. 19). The heat of
desorption and Henry’s law constant were taken from the literature for the carbon dioxide-
-1
3
-1
water system: Hd,C = 19.9 kJ∙mol [31] and He
C
= 27.0 dm ·bar·mol [32]. The evaluated
values of the enthalpy of formic acid oxidation are given in Table 2. The average value of
-1

H
r,2 calculated based on 5 experiments, was –3499 kJ∙mol .
In Figs. 6a and 6b, the extent of the two reactions as a function of time based on Eqs. 19 and
0 is shown. The extent of the H decomposition reaction was independently calculated
2
2
O
2
from data on the partial pressure of oxygen (symbols in Fig. 6). As seen from Fig. 6, both
methods yielded similar results, which confirms the correctness of the proposed evaluation
method for calorimetric data.
4.2.3. Kinetic analysis
The experimental kinetic curves presented in Fig. 6 can be used to identify the rate laws and
to estimate the kinetic parameters using the integral method of kinetic analysis. However, in
1
1

this study, another method is proposed to obtain the kinetic model of the process. Rates of
-3
-1
the two reactions, r
1
and r , occurring in the process, expressed in mol∙dm ∙s can be
2
calculated from the following equations:
L
q

t



br1

t

 cr2

t


V
(23)
(24)
L
P

t



r2

t
 RTV


r

t




1
G
dt
a
V



which are the differential forms of Eqs. 19 and 20. To solve these equations for r
1
and r , the
2
derivative of P needs to be determined, and this operation must be performed carefully to
avoid additional errors because the numerical differentiation of experimental data is highly
sensitive to data noise. In our case, the P curve was fit with a polynomial regression line
from which the derivative was calculated.
With the time-varying concentrations of reagents and the corresponding rates of the
reactions, it is possible to quickly and easily verify different kinetic models, independently for
each reaction occurring in the system.
To verify the applicability of rate Eq. 2 to describe the decomposition of H
2
O
2
, r
1
(t) and c (t)
P
data were converted according to Eq. 7, which is shown in Fig. 7a for the experiments
performed with the higher concentrations of the catalyst. Analysis of data presented in Fig. 7
leads to the conclusion that the adsorption surface reaction model can be applied to
hydrogen peroxide decomposition in the acidic environment of formic acid for H
2
O
2
-3
-3
concentrations above 0.01 mol·dm or 0.015 mol·dm in the case of experimental run A4.
Below this concentration, the experimental data deviate from a straight line, which may
indicate a change in the reaction mechanism but may also be due to larger experimental
errors. The kinetic parameters appearing in Eq. 7 calculated from the slope and intercept of
-4
-1
the linear part of the experimental data presented in Fig. 7a are k
1
= 1.3410 s and K =
p
3
-1
1
1.2 dm mol .
It was also found that the reaction of formic acid with hydrogen peroxide can be well-
described by a power law equation of the form
m
r
2
= k
2
(C
P
C
A
) ,
(24)
s and the exponent
-3
3 -0.36 -1
as shown in Fig. 7b, with the rate constant k
2
= 7.4510 (moldm )
m = 0.68.
In Figs. 8a,b,c, kinetic model predictions are compared with experimental data for the
hydrogen peroxide and formic acid concentrations, and good agreement is obtained. Fig. 8d
presents the data obtained for the experiment performed with a smaller amount of catalyst. In
1
2

this case, parameters k
satisfactory agreement between the simulation results and the experimental data, the rate
constant k was reduced six times, whereas the parameter k was reduced only four times.
This confirms the fact, as known from the literature, that an increase in catalyst concentration
increases the rate of H decomposition much more than the rate of the degradation of
organic compounds in the Fenton process [33].
1
and k
2
needed to be adjusted to new values. Interestingly, to obtain
1
2
2
O
2
5. Conclusions
The advantage of using a reaction calorimeter for the kinetic analysis of chemical reactions is
the on-line measurement of the reaction rate. However, this method is highly efficient only for
single reactions. The combination of heat flow measurements by a calorimeter with additional
measurements of the gas production rate based on pressure changes in the gas space of the
reaction vessel may lead to significant improvement of the kinetic analysis of more complex
reaction systems that produce gaseous products. In this study, the proposed evaluation
algorithm for isothermal calorimetric reaction data along with pressure change data allows
the use of an integral or a differential method of kinetic analysis to calculate the unknown
parameters of the reaction model. In the latter case, numerical differentiation of the pressure
change data is required.
It was found that to avoid significant experimental errors the kinetic experiment should not
last more than about two hours. If the reaction was too slow, it was difficult to determine the
baseline and the calorimetric and pressure signals were very unstable.
An example process in which the proposed method of analysis can be used is the oxidation
of formic acid by the Fenton reagent. In this process, two competing reactions with gaseous
products occur. Although the oxidation of formic acid was only an illustrative example of the
application of the proposed method, some conclusions regarding the process itself can be
drawn:
1. Formic acid can be well decomposed in the Fenton process using goethite as a
heterogeneous catalyst if hydrogen peroxide and the catalyst are added in sufficient
amounts.
2
. Increasing the amount of the catalyst increases the rate of both reactions, but the H
decomposition reaction is affected much more than the formic acid oxidation reaction.
. At pH 7, the rate of decomposition of hydrogen peroxide can be described by the
2
O
2
3
Langmuir-Hinshelwood type of equation (Eq. 2), which may suggest that the active iron is
always attached to the solid.
1
3

4
. It was found that the same equation (Eq. 2) can be applied in an acidic environment with
varying pH.
. The hydrogen peroxide decomposition occurred much faster at neutral pH than in the
5
presence of formic acid.
Symbols
a, b, c – parameters defined by Eqs. (18), (21) and (22), respectively
C
A
P
- molar concentration of formic acid
,
mol·dm-3
C
- molar concentration of hydrogen peroxide
,
mol·dm-3
3
-1
He
C
- Henry’s law constant, dm ·bar·mol
decomposition, dm ∙gcat-1∙s-1
3
k - reaction rate constant for H
2
O
2
k
k
1
2
- rection rate constant for H
2
O
2
decomposition, s-1
- reaction rate constant for formic acid destruction, (moldm3)1-2m s-1
3
K
P
- adsorption equilibrium constant of hydrogen peroxide (dm /mol)
m - partial reaction order in Eq. (24)
n
n
n
n
0,A - initial number of moles of formic acid, mol
0,P - initial number of moles of hydrogen peroxide, mol
A
P
- number of moles of formic acid, mol
- number of moles of hydrogen peroxide, mol
q- heat flow rate measured using a calorimeter, W
- total heat released in the process, J
Q
f
-1
-1
R - universal gas constant, J∙mol ∙K
-
3
-1
r
r
1
2
- rate of H
2
O
2
decomposition, mol∙dm ∙s
-
3
-1
- rate of formic acid destruction, mol∙dm ∙s
T - temperature, K
t - time, s
G
3
V - volume of the gas space in the reactor, dm
L
3
V - volume of the reaction mixture, dm
cat - concentration of the catalyst in the slurry, g·dm-3
w
1
4

X
X
X
X
1
- extent of H
1,f - final reaction extent, mol
- extent of HCOOH decomposition reaction, mol
2,f - final reaction extent, mol
2
O
2
decomposition reaction, mol
2




H
d,C - heat of desorption for the carbon dioxide-water system, Jmol-1
d,O - heat of desorption for the oxygen-water system, Jmol-1
r,1 - enthalpy of the hydrogen peroxide decomposition reaction, Jmol-1
r,2 - enthalpy of the formic acid oxidation, Jmol-1
H
H
H

P - changes in the reactor pressure, bar



P
f
- overall increase in reactor pressure, bar
- changes in oxygen partial pressure, bar
p
O
A,f - final conversion of formic acid decomposition
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1
7

1
1
1
4
2
0
8
6
4
2
0
1.4
1.2
1.0
0.8
0.6
0.4
0.2
0.0
P1
P2
P3
P4
0
1000
2000
3000
t, s
Fig. 1.Total heat flow rate and changes in the reactor pressure during the catalytic
decomposition of hydrogen peroxide at 293 K for four experiments (P1-P4).
0.05
0.04
0.03
0.02
0.01
0.00
0.05
0.04
0.03
0.02
0.01
0.00
(
a)
(b)
from heat flow
from pressure
P1
P2
P3
P4
0
1000
2000
3000
0
500
1000
1500
2000
2500
3000
t, s
t, s
Fig. 2. Kinetic curves for the hydrogen peroxide decomposition reaction: (a) comparison of
the reaction extent obtained from the heat flow (lines) and pressure change (symbols)
data; (b) reproducibility of the reaction progress curves for four experiments.
0.3
0.2
0.1
0.0
P1
P2
P3
P4
0
100
200
300
3
-1
1
/c , dm mol
P
1
8

Fig. 3. Plots of the linearized form of the Langmuir-Hinshelwood reaction rate model for the
decomposition of hydrogen peroxide catalysed by goethite (symbols - experimental data P1-
P4; lines – model prediction).
0.10
0.08
0.06
0.04
0.02
0.00
0.10
0.08
0.06
0.04
0.02
0.00
P1
P2
P3
P4
0
1000
2000
3000
0
1000
2000
3000
t, s
t, s
Fig. 4. Concentration of the reagent as a function of the reaction time for the isothermal
decomposition of hydrogen peroxide over the goethite catalyst. Symbols represent the
experimental data points from the heat flow measurements, and lines show the
concentration profiles predicted from the kinetic model.
3.0
2.5
2.0
1.5
1.0
0.5
0.0
1.0
0.8
5
4
3
2
1
0
0.8
A1
A2
A3
A5
0.6
0.6
Total
0.4
Oxygen
0.4
0.2
0.2
0.0
600
0.0
0
120
240
360
480
0
60
120
180
t, min
t, min
Fig. 5. Heat flow rate and change in the reactor pressure during the catalytic decomposition
of formic acid using 5 g for A1, A2 experiments (a) and 30 g (b) of goethite for A3, A5
experiments.
1
9

Fig. 6. Kinetic curves for the two reactions occurring during formic acid oxidation using the
heterogeneous Fenton reagent (symbols are used for the extent of reaction calculated
based on the oxygen partial pressure change).
1
2
0
8
6
4
2
0
-11
-12
-13
-14
-15
-16
-17
(
a)
(
b)
1
A3
A4
A5
Intercept = 80820
Slope = 7445
Slope = 0.68
Intercept = -7.53
0
30
60
90
120
150
180
-13 -12 -11 -10
-9
-8
-7
-6
1/CP
Ln(C C )
P A
Fig. 7. Rate of reactions occurring during formic acid oxidation in the heterogeneous Fenton
process: (a) H
2
2
O decomposition and (b) oxidation of formic acid for A3, A4, A5
experiments.
0.05
0.04
0.03
0.02
0.01
0.00
0
0
0
0
.08
.06
.04
.02
A4
A3
CP
CA
CP
CA
0.00
0
30
60
90
120
150
180
0
30
60
90
120
150
180
t, min
t, min
0.06
0.05
0.04
0.03
0.02
0.01
0.00
A1
A5
0.08
CP
0.06
0.04
0.02
CP
CA
CA
0.00
0
30
60
90
120
150
180
0
200
400
600
t, min
t, min
Fig. 8. Comparison of the kinetic model predictions (lines) with the experimental data A1, A3,
A4, A5 (symbols) for the hydrogen peroxide and formic acid concentration profiles.
2
0

Table 1. Experimental conditions, experimental results, calculated results for the hydrogen
peroxide decomposition process.
Experimental
conditions
Experimental
results
Calculated results
Run
number
K
P
n
0,P
P
f
Hr,1
3
-
[
-]
m
cat [g]
Q
f
[J]
k
1
[1/s]
[dm ∙mol
[
mol]
[bar]
[kJ/mol]
-188.3
-185.8
-190.6
-188.7
1]
1
.2010-
P1
P2
P3
P4
10
10
10
10
0.088
0.090
0.090
0.090
1.170
1.206
1.220
1.234
8302
8608
8380
8768
4.8
16.7
9.3
8.5
3
1
.7710-
.5710-
.3010-
3
1
3
1
3
Table 2. Conditions and selected results of experimental runs of formic acid oxidation
process.
Experimental
Experimental conditions
Calculated results
Run
results
number [-]
n
0,P
n
[mol]
0.028
0,A
P
f
po,f
[bar]
0.413
Hr,2
m
cat [g]
 [-]
Q [J]
f
A,f
-
1
[
mol]
[bar]
[kJ∙mol ]
A1
A2
A3
A4
A5
5
0.088
0.110
0.076
0.057
0.057
0.707
0.88
0.98
0.72
0.49
0.66
12260
13710
7478
-366
5
0.028
0.018
0.030
0.030
0.816
0.508
0.867
0.667
0.489
0.345
0.701
0.427
-358
-345
-329
-346
30
30
30
10467
10323
2
1