Kinetics of catalytic carbon black oxidation

Article abstract of DOI:10.1016/j.tca.2004.11.011

Kinetics of the catalyzed oxidation of carbon black (CB) in the presence of Ce-Al oxides is studied. The activation energies for CB combustion are determined from the DTA-TG data. The catalysts performances are compared on the basis of thermal analysis and calculated kinetic parameters. In this investigation, a convenient method for the rapid calculation of the kinetic parameters from single DTA-TG curves is proposed.

Full text of DOI:10.1016/j.tca.2004.11.011

Thermochimica Acta 428 (2005) 165–171
Kinetics of catalytic carbon black oxidation
a
a
b
b
a
M.N. Bokovaa,b,∗, C. Decarne , E. Abi-Aad , A.N. Pryakhin , V.V. Lunin , A. Aboukaıs
¨
a
Laboratoire de Catalyse et Environnement E.A., 2598, MREI, Universite´ du Littoral, Coˆte d’Opale, Dunkerque, France
b
Catalysis and Gas Electrochemistry Laboratory, Chemistry Department, M.V. Lomonosov Moscow State University, Moscow, Russia
Received 19 July 2004; accepted 3 November 2004
Available online 13 December 2004
Abstract
Kinetics of the catalyzed oxidation of carbon black (CB) in the presence of Ce–Al oxides is studied. The activation energies for CB
combustion are determined from the DTA–TG data. The catalysts performances are compared on the basis of thermal analysis and calculated
kinetic parameters. In this investigation, a convenient method for the rapid calculation of the kinetic parameters from single DTA–TG curves
is proposed.
© 2004 Elsevier B.V. All rights reserved.
Keywords: Catalytic soot oxidation; Ce–Al oxides; Oxidation kinetics; Activation energy; Pre-exponential factor; Thermal analysis
1. Introduction
Some research has been performed on the kinetics of non-
catalytic and catalytic soot oxidation [2,9–13]. Data from
kinetics and mechanism studies of the catalyzed oxidation of
soot might help in developing more active or selective soot
oxidation catalysts. Differential thermal analysis and ther-
mogravimetry (DTA–TG) has been widely studied by many
investigators in order to evaluate kinetic parameters [11–17].
Most of the methods are very complicated and have to be
solved by a trial and error approach to obtain the values of
activation energy and pre-exponential factor of Arrhenius
equation [14–17]. Some of them require a supplementary
experiments and variations of different parameters, such as
heating rate. In this work, we propose a convenient method
for the rapid calculation of the kinetic parameters from single
DTA–TG curves. The objective of this study is to compare the
Ce–Al–O catalysts for CB oxidation according to its activity
and kinetic parameters.
The emission of carbon particles in the atmosphere has
led to serious environmental problems. Catalytic oxidation
of the soot is one of the solutions proposed for the reduc-
tion of particulate emissions. Catalyst can be added either
through the fuel, in which case it is incorporated into the soot
spherules as they form, or physically mixed in after collec-
tion of soot. The latter would correspond to the case of a soot
filter whose surface is impregnated with catalyst via a wash
coat [1,2]. Ceria oxide (CeO2) is an important constituent
of the redox catalysts [3]. Three main properties make ceria
an essential component in such catalysts: its oxygen storage
capacity (OSC) [3], its redox properties (Ce4+/Ce3+) and its
thermal stabilizing influence on alumina [4,5]. Moreover, lit-
erature data show that ceria oxide is very active for catalytic
soot combustion [1,2,6–9]. The presence of cerium additives
favors the reactivity of the doped soot and shifts the combus-
tion reaction towards low temperatures [8,9]. Cerium-coated
traps ate also found to be effective for catalytic soot oxidation
[1].
2. Experimental
2.1. Catalysts preparation
∗
Corresponding author. Tel.: +33 032 8658262; fax: +33 032 8658239.
Alumina is synthesized by sol–gel method [18]. Sec-
E-mail addresses: bokova@kge.msu.ru (M.N. Bokova), abiaad@univ-
littoral.fr (E. Abi-Aad).
ondary aluminum butylate (Al(OC4H9)3, Fluka, ∼11.0 wt.%
0040-6031/$ – see front matter © 2004 Elsevier B.V. All rights reserved.
doi:10.1016/j.tca.2004.11.011

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M.N. Bokova et al. / Thermochimica Acta 428 (2005) 165–171
Table 1
CB/catalyst mixtures for the kinetics studies of carbon black
Composition of the solidsa
combustion [21]. In real conditions, the soot-to-catalyst ratio
varies widely from 1/2.1 to 1/35, which is attributed to irre-
producibility in the collection of soot on the catalyst powder
and probably to the inhomogeneity of the layer of the catalyst
on the filter [19]. In our study, we use carbon black-to-catalyst
ratio of 1/5. This ratio is close to that for cerium-coated
traps and the practical application for our results is rather
justified.
Sample
CeO2 (wt.%)
Specific area (m2/g)
Al2O3
1Ce10Al
3Ce10Al
10Ce10Al
CeO2
–
360
241
144
99
25.23
50.31
77.14
100
53
a
The number before chemical symbol represents the atomic content in
the solid.
The catalytic tests towards the combustion of CB are
studied by simultaneous gravimetric and differential thermal
analysis (TG–DTA) with a NETZSCH STA 409 apparatus.
10–50 mg of the CB/catalyst mixture is loaded in an alu-
mina crucible and heated from room temperature to 700 ◦C
(5 ◦C/min) in airflow (75 mL/min). In the experiments per-
formed under isothermal conditions, the mixture of 20 mg
was heated (5 ◦C/min) up to the reaction temperature (370,
380 and 390 ◦C) under airflow (75 mL/min) and then the ox-
idation was carried out at constant temperature till the total
CB combustion.
Al) is dissolved in butan-2-ol (Fluka, purity ≥99.5%) at
85 ◦C. Then, complexing agent (butan-1,3-diol, Fluka, pu-
rity ≥98%) preliminary heated at 60 ◦C is added before hy-
drolysis. Hydrolysis is performed by addition of water to the
solution at 85 ◦C. The gel is dried and calcined at 500 ◦C
for 6 h with a temperature rate of 0.5 ◦C/min before used as
support for preparing the Al2O3-supported CeO2 catalysts.
With this method, alumina is characterized with specific area
of 360 m2/g and pore volume of 2.3 mL/g. The diameter of
alumina grains varies between 0.6 and 4.7 ␮m. There are also
a lot of little grains of 0.1 ␮m.
3. Results and discussion
Ceria is prepared by precipitation of Ce(NO3)3·6H2O
(Prolabo, total amount of rare earth oxides is 99.5%) in an
ammonia aqueous solution (0.7 mol/L). The solid is filtered,
washed, dried at 100 ◦C and calcined at 600 ◦C for 4 h with
a temperature rate of 0.5 ◦C/min.
Different Ce–Al oxides are prepared by incipient wet-
ness of cerium nitrate solution onto alumina pre-calcined at
500 ◦C. Then the sample is dried at 100 ◦C and calcined for
4 h in a flow of dry air at 600 ◦C. Cerium-containing solids are
denoted 1Ce10Al, 3Ce10Al and 10Ce10Al where the num-
ber before chemical symbol represents the atomic content in
the solid. Table 1 summarizes the composition of Ce–Al–O
catalysts.
3.1. Carbon black catalytic combustion
Fig. 1 shows an example of TG–DTA curves. A weight
loss of ∼20 wt.% is observed on TG curve, corresponding
to the combustion of the total mass of carbon black. The
TG curve gives the temperature values Ti (beginning of the
carbon black combustion) and Tf (complete conversion of
carbon black). The maximum of DTA curve (Tm) corresponds
to the temperature of the highest combustion velocity. The
value ꢀT = Tf − Ti determines the reaction velocity. Catalytic
properties of the solids are evaluated by comparing the values
of Tm and ꢀT with those of CB combustion without catalyst
in the same conditions.
2.2. Activity tests
According to the literature data, the sample mass can sig-
nificantly influence the results of TG–DTA [22–25]. For this
study, the mixture of 10 wt.% CB with 90 wt.% CeO2 is pre-
pared and five sample masses are used: 10, 20, 30, 40 and
Commercial available carbon black (CB) (N330 Degussa:
97.23 wt.% C, 0.73 wt.% H, 1.16 wt.% O, 0.19 wt.% N,
0.45 wt.% S) is used as a model soot. The average diame-
ter of the CB spherical particle is 0.08–0.25 ␮m. Before the
catalytic test, CB (10–20 wt.%) and catalyst (90–80 wt.%)
are mixed in alumina ball miller for 40 min. It was shown
that under practical conditions the contact between soot and
catalyst is poor [19,20]. In our paper, we used the prepara-
tion method of the mixture of carbon black with the catalyst
which gives more tight contact than in real conditions. It was
chosen to use a mechanical mill to establish close contact
between soot and catalyst in order to define an intrinsic cat-
alytic activity under optimal conditions. The objective of this
study is to rank the CB oxidation catalysts according to its
activity and kinetic parameters, thus it is necessary to ob-
tain the reproducible and comparable results. For this reason,
some authors use the most reproducible method to prepare the
Fig. 1. Example of DTA–TG curves.

M.N. Bokova et al. / Thermochimica Acta 428 (2005) 165–171
167
of CB occurs between Ti = 540 ◦C and Tf = 630 ◦C and in-
significant difference is observed when the reaction is per-
formed in the presence of Al2O3. For the other samples,
combustion temperature decreases, showing the reactivity of
ceria-based catalysts. Ceria oxide is the most reactive sam-
ple with a combustion temperature Tm of 389 ◦C. For the
Ce–Al oxides, reactivity increases with increasing ceria con-
tent. Thus, the temperature Tm decreases from 584 ◦C for
the 1Ce10Al sample to 473 ◦C for the 3Ce10Al sample and
to 411 ◦C for 10Ce10Al sample. Comparing the ꢀT values,
the slight increase of the reaction rate can be observed with
the increase of ceria content in the catalyst. Thus ꢀT falls
from 170 ◦C for 3Ce10Al to 130 ◦C for CeO2. However,
non-catalyzed CB combustion occurs within more narrow
temperature range with ꢀT of 90 ◦C. Nevertheless, all the
characteristic temperatures of non-catalyzed CB combustion
are higher than those for CB combustion in the presence of
catalyst.
3.2. The kinetic parameters calculation
3.2.1. Non-isothermal conditions
The temperature Tm depends on heating rate and sample
mass, thus it is more reasonable to characterize the catalyst
activity using the rate constant. At different temperatures, the
rate constant is determined by Arrhenius equation:
k = k0 e−(E /RT)
(1)
a
Fig. 2. Evolution of the DTA–TG curves as a function of sample mass for
the mixture of 10% CB + 90% CeO2.
where k is the rate constant, k0 the pre-exponential factor, Ea
the activation energy, R (8.314 J/mol K) the gas constant and
T the temperature of the reaction.
In this paper, the convenient method is proposed to cal-
culate the activation energy and pre-exponential factor using
one TG and one DTA curve. This method allows to obtain the
exact solution according to the model proposed without any
complementary approaches. The method can be described
here as follows.
50 mg. Fig. 2 presents the results of TG–DTA obtained dur-
ing the combustion of the samples. As shown in this figure,
the form of the signals varies with the sample masses. For
the sample masses below than 30 mg, one exothermic peak is
observed on DTA curve which is accompanied by the weight
loss in one stage. For higher sample masses, two peaks are
observed and the weight loss passes into two stages. The first
peak is steep and sharp, whereas the second peak is broad
and smooth. The temperatures at the maxima of these sec-
ond peaks coincide reasonably well with the temperatures at
the maxima of the peaks obtained for the smaller samples
without the runaway peak. Thus, part of the carbon black
is burned fastly in a steep runaway peak, while the second
part combustion is slower and takes part at higher tempera-
tures. This phenomenon can be explained by mass and heat
transfer limitations [7,22–25]. Indeed, the oxygen diffusion
influences significantly the kinetics of carbon black combus-
tion. The more larger the sample mass, more higher is the
level of the sample placed in the crucible. Thus, oxygen of
air has more difficulties to diffuse in the bulk of the mixture.
In addition, during the combustion of the sample center, the
heat flow limits the oxygen transfer.
The expression for the solid-state oxidation reaction under
the constant oxygen concentration can be written as
dm
= −k0 e−(E /RT)mn
(2)
a
dt
where m is the mass of the substance, t the time and n the
reaction order. The unit for the pre-exponential factor k0 in
the system SI is kg1−n/s. But in our paper the unit for k0 was
selected as mg1−n/s in order to be consistent with the sample
mass units.
Mass transfer and oxygen depletion can influence the
results and lower the apparent activation energy [22–26].
However, thepurposeofourcalculationsistocomparetheap-
parent kinetic parameters for different catalysts for CB com-
bustion. These parameters are useful for the mathematical
modeling of combustion process as far as for the analysis of
catalysts activity at different temperatures. The catalytic tests
for every catalyst were carried out at the same conditions,
thus we can provide the catalysts comparison even without
Fig. 3 shows the reactivity of Ce–Al–O catalysts in CB
combustion. For the non-catalyzed reaction, the combustion

168
M.N. Bokova et al. / Thermochimica Acta 428 (2005) 165–171
Fig. 3. The characteristic temperatures of carbon black combustion in the presence of Ce–Al oxides: (ꢀ) Ti (beginning of the carbon black combustion); (᭹)
Tm (temperature of the maximum of the DTA curve); (ꢁ) Tf (complete conversion of carbon black).
information about the detail mechanism of the process, as
oxygen transfer limitations and oxygen depletion. Apparent
parameters can be the functions of elementary stages rate
constants and contain, for example, the diffusion coefficient
and oxygen mass transfer coefficients. If oxygen concentra-
tion also influences the rate of oxidation, equation for k0 can
be written as
Substitution of Eq. (6) into Eq. (7) yields
ꢂ
ꢃ
ꢄ
k0
β
dm
n−1
)
n
)
inf
e−(E /RT + minf e−(E /RT
a
a
inf
nm
inf
dT
inf
ꢀ
ꢁꢅ
ꢃ
ꢄ
Ea
R
1
Ti2nf
× −
−
= 0
(8)
where minf is the mass of the substance in the point of inflec-
tion on TG curve.
k0 = k0ꢀ f(CO
)
(3)
2
The transformation of Eq. (8) gives
In this case, the unit for k0 rests the same (mg1−n/s), but the
unit for k0ꢀ is mg1−n/(s f(mol/L)). Even if the oxygen diffu-
sion limitations and oxygen depletion take place, they will
influence all of the apparent kinetic parameters at the same
time and our results are comparable.
ꢃ
ꢄ
RTi2nf
Ea
n
dm
= −
(9)
minf dt
inf
The dependence of DTA curve from the temperature is de-
scribed by the following equation:
Under constant heating rate, the temperature is a linear
function of the time during the experiment:
dm
E = α
(10)
dT
T = T0 + βt
(4)
where α is the proportionality constant and E the DTA signal.
The maximum of DTA curve will occur when
where T0 is the initial temperature and β the heating rate.
ꢃ
ꢄ
In this case
dE
dT
= 0
(11)
m
dT = β dt
(5)
(6)
Taking into consideration Eqs. (7) and (11), it is possible to
demonstrate that
and Eq. (2) takes the following form:
Tinf(TG) = Tm(DTA)
and Eq. (9) is changed for
(12)
dm
dT
k0
β
a
= −
e
−(E /RT)mn
ꢃ
ꢄ
The point of inflection on TG curve occurs when
Ea
n
RTm2 dm
= −
(13)
ꢀ
ꢁ
minf dT
inf
d2m
dT2
= 0
(7)
Thus, when the peak temperature and the sample mass in
the point of inflection are known, the relation Ea/n can be
inf

M.N. Bokova et al. / Thermochimica Acta 428 (2005) 165–171
169
calculated. It is necessary to find Tm on the DTA curve (the
temperature of maximum), which according to Eq. (12) co-
incides with Tinf on TG curve (the temperature of inflection).
After this the value of minf (the mass of inflection) on TG
curve can be found. Then linear approximation of the TG
curve near the point of inflection gives (dm/dT)inf and ac-
cordingly Ea/n by Eq. (13).
activation energy for non-catalytic CB combustion is found to
cover a range, namely between 102 and 210 kJ/mol [2,9,10].
Values between 140 and 170 kJ/mol appear frequently. The
activation energy obtained for CB + Al2O3 mixture in this
work is similar close to the reported experimental values of
168 kJ/mol [10] and 164 kJ/mol [13] for non-catalytic soot
oxidation. Probably, in the case of uncatalyzed CB combus-
tion, the contribution of internal burning is less important and
the shrinking-core behavior applies with a value of n close to
2/3 [10].
Taking into account Eq. (10), the kinetic equation (2) for
the curve DTA is transformed as
E = αk0 e−(E /RT)mn
(14)
a
It is evident that the presence of ceria has significant influ-
ence on the CB oxidation kinetics. Catalyst reaction mecha-
nisms are evidently different from the uncatalyzed condition.
The catalyst generally lowers activation energy, typically by
30–80 kJ/mol, that is from 170 to 120 and 151 to 100 kJ/mol
[2]. The rate of the reaction can be influenced by the activa-
tion energy and by the pre-exponential factor. The decrease of
activation energy and/or the increase of pre-exponential value
leads to the increase of the combustion rate, clearly shown
in our case by the decrease of Tm and ꢀT. From Table 2,
we can see that the sample 1Ce10Al has low activity in CB
combustion. We assume that the reaction order is also 2/3 for
CB + 1Ce10Al combustion. Activation energy (169 kJ/mol)
and ln k0 (18.1) are also close to those of non-catalytic com-
bustion. The calculation of Ea for the samples 3Ce10Al,
10Ce10Al and CeO2 with a value for n of 1 in Eq. (15) gives
the results more close to literature data, than with a value for n
of 2/3. It is possible that the internal burning takes place dur-
ing catalytic oxidation of CB. These catalysts are active in the
reaction of CB combustion and they change the kinetics of the
process. In the case of 3Ce10Al catalyst, the activation energy
(119 kJ/mol) is lower than for non-catalytic CB combustion
and the value of ln k0 is also low (12.7). The most active cat-
alysts are 10Ce10Al (Ea = 90 kJ/mol, ln k0 = 9.4) and CeO2
(Ea = 90 kJ/mol, ln k0 = 10). The activation energy for these
systems is rather low and the value of k0 is significantly high.
The choice of n (n = 2/3 or 1) in Eq. (13) leads to values for
Ea which agree with those derived from Eq. (15) (Table 2). It
means that our method is useful for DTA–TG data obtained.
Using the activation energy and k0 we can evaluate the
dependence of catalyst activity from the temperature due
to Arrhenius equation in logarithmic form. The linear
dependence of ln k0 versus 1/T for the Ce–Al–O systems is
presented in Fig. 4. From this figure, it is possible to
create the following row of activity increase Al2O3 ≈
Eq. (14) is divided by mn and taking the logarithm gives
ꢃ
ꢄ
E
mn
Ea
ln
= ln(ak0) −
(15)
RT
The approximation of the dependence of ln(E/mn) versus 1/T
by linear function gives the value of activation energy Ea
according to Eq. (15).
From Eqs. (6) and (12), the expression for k0 is following:
ꢆ
ꢇ
dm
dT
e(E /RT)
β
a
inf
k0 =
(16)
mninf
Theshrinkingcoremodel, usedforCBcombustionprocesses,
requires that reaction order n be 2/3. In this model, the rate of
combustion is proportional to the surface of the CB spherules
[10]. However, some authors conclude that internal burning
takesplaceduringtheoxidationofCBatthelowtemperatures
[2]. In the case of complete internal burning, the oxidation
rate is proportional to the remaining mass, i.e. n = 1. Partial
internal burning will result in n being between this value and
that for the surface burning case, which gives shrinking core
behavior (1 > n > 2/3). Thus we calculated our data with the
both values for n of 1 and 2/3 in order to compare the values
for Ea obtained with those in the literature. For more precise
calculations, the fractal character of CB surface should be
taken into account [27] that will be done in our future work.
The kinetic parameters derived from the TG–DTA data
for CB combustion in the presence of Ce–Al oxides are pre-
sented in Table 2. Using the reaction order value of 2/3 in Eq.
(15), the oxidation of CB in the presence of Al2O3 has ac-
tivation energy value of 163 kJ/mol. Since alumina does not
present catalytic activity in the reaction of CB combustion,
the oxidation of CB in the presence of Al2O3 may be com-
parable with non-catalyzed CB oxidation. Low-temperature
Table 2
Kinetic parameters of carbon black catalytic combustion in the presence of Ce–Al oxidesa
Catalyst + CB
Tm (◦C)
Ea/n (kJ/mol) (Eq. (13))
Ea (kJ/mol) (Eq. (15))
ln k0 (Eq. (16))
n = 2/3
n = 2/3
n = 1
n = 1
Al2O3 + CB
1Ce10Al + CB
3Ce10Al + CB
10Ce10Al + CB
CeO2 + CB
a
595
584
473
411
389
252
233
117
83
163
169
75
63
65
251
250
119
90
19.2
18.1
5.9
5.0
5.7
31.4
29.5
12.7
9.4
78
90
10.0
Standard deviation is 20%.

170
M.N. Bokova et al. / Thermochimica Acta 428 (2005) 165–171
Table 3
Kinetic parameters of carbon black combustion in the presence of cerium oxidea
Kinetic parameter
Equation
Sample
80% CeO2 + 20% CB (20 mg)
80% CeO2 + 20% CB (40 mg)
90% CeO2 + 10% CB (20 mg)
Tm (◦C)
–
385
78
89
389
78
90
374
93
105
11.7
Ea/n (kJ/mol)
Ea (n = 1) (kJ/mol)
ln k0 (n = 1)
a
(13)
(15)
(16)
8.6
10.0
Standard deviation is 20%.
ferent percentage of CB (10 and 20%) the value for Ea/n
differs at 20% that could be regarded as comparable results
(78 and 93 kJ/mol). The values of Ea calculated from Eq. (15)
correlates with those calculated from Eq. (13) taking n = 1. In
addition, the values of activation energy for different systems
CeO2 + CB are close to each other (taking into consideration
20% error). It indicates that the method proposed is useful
for CB combustion.
3.2.2. Isothermal conditions
To verify the activation energies determined from non-
isothermal conditions, the reaction of CB combustion in the
presence of CeO2 was carried out at constant temperatures
(370, 380 and 390 ◦C). The isothermal curves are shown in
Fig. 5. For the three isothermal experiments, the loss of CB
before reaching the isothermal temperature is negligible, thus
the isothermal data are comparable.
Fig. 4. Arrhenius plots of carbon black combustion in the presence of Ce–Al
oxides.
1Ce10Al < 3Ce10Al < 10Ce10Al ≈ CeO2. These data are in
accordance with those obtained for catalytic tests. Thus, the
activity of the catalyst revealed from TG–DTA data (Fig. 3)
and from the kinetic parameters (Table 2) correlate with each
other.
To verify our method, for the most active catalyst CeO2
we calculated the kinetic parameters for the TG–DTA data
of the mixtures of 40 and 20 mg (80% CeO2 + 20% CB) and
20 mg (90% CeO2 + 10% CB). The values for activation en-
ergy and ln k0 calculated from Eqs. (13), (15) and (16) for
these systems are presented in Table 3. It should be noted
that for the sample of 40 mg the calculations were carried out
for the second exothermic peak. From Table 3, we can con-
clude that for the mixtures of CB with the same catalyst CeO2
but with different sample mass (20 and 40 mg) the value for
Ea/n is the same (78 kJ/mol). For the systems with the dif-
The kinetics of soot combustion under isothermal condi-
tions is described by the following differential equation:
dm
= −kmn
(17)
(18)
dt
where m(t = 0) = m0.
If the reaction order is 1, Eq. (17) gives
dm
= −km
dt
The transformation of Eq. (18) gives
dm
= −k dt
(19)
(20)
m
or
ln m − ln m0 = −kt
Fig. 5. Isothermal curves for the mixture of 20 mg (20% CB + 80% CeO2) at 370, 380 and 390 ◦C.

M.N. Bokova et al. / Thermochimica Acta 428 (2005) 165–171
171
Thus, the rate constant can be determined with the help of
Eq. (20) by the approximation of the dependence ln(m(CB))
versus the time by the linear function for every isotherm.
The region of the linear approximation was chosen as the
first 60 min of the curve. Then using the Arrhenius equation,
the activation energy was calculated. The values for Ea of
96 kJ/mol and for ln k0 of 11.3 were obtained. The values for
activation energies, obtained for the same sample treated at
different conditions (during the TG–DTA analysis and under
isothermal conditions) gives the comparable results (89 and
96 kJ/mol). Thus two independent methods give the same
values for activation energies. It permits us to conclude that
they both adequately describe our experimental data.
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The catalytic combustion of carbon black has been inves-
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temperature of the maximum of the carbon black combus-
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lower activation energy to 90 kJ/mol and change the reaction
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