Kinetics Study on Oxidation of β-Isophorone Using Molecular Oxygen

Article abstract of DOI:10.1002/kin.20987

The oxidation kinetics of β-isophorone (β-IP) using molecular oxygen catalyzed by iron(III) acetylacetonate was investigated in a lab-scale agitator bubbling reactor. β-IP was found to give keto-isophorone (KIP) and 4-hydroxy-3,5,5-trimethyl-2-cyclohexen-1-one (HIP) along with little isomerization product α-isophorone (α-IP). The results show that the oxidation reaction took place in the pseudo-first-order fast reaction regime. The experiment was conducted under the mass transfer reaction regime as the mass transfer resistances could not be easily eliminated. The intrinsic kinetics was obtained through apparent kinetics. The activation energy of oxidation of β-IP to KIP is 70.5 ± 4.1 kJ mol^-1, and the value of ln A_KIP is 33.53 ± 1.22. Meanwhile, the activation energy of oxidation of β-IP to HIP is 86.4 ± 5.4 kJ mol^-1 and the value of ln A_HIP is 36.23 ± 1.52, which could provide theoretical basis for industrial design, amplification of reactor, and the optimization of reaction.

Full text of DOI:10.1002/kin.20987

Kinetics Study on Oxidation
of β-Isophorone Using
Molecular Oxygen
ZHIRONG CHEN, TINGTING FANG, SHENFENG YUAN, HONG YIN
College of Chemical and Biological Engineering, Zhejiang University, Hangzhou, 310027, People’s Republic of China
Received 3 September 2015; revised 19 January 2016; accepted 12 February 2016
DOI 10.1002/kin.20987
Published online 5 April 2016 in Wiley Online Library (wileyonlinelibrary.com).
ABSTRACT: The oxidation kinetics of β-isophorone (β-IP) using molecular oxygen catalyzed
by iron(III) acetylacetonate was investigated in a lab-scale agitator bubbling reactor. β-IP
was found to give keto-isophorone (KIP) and 4-hydroxy-3,5,5-trimethyl-2-cyclohexen-1-one
(HIP) along with little isomerization product α-isophorone (α-IP). The results show that the
oxidation reaction took place in the pseudo–first-order fast reaction regime. The experiment
was conducted under the mass transfer reaction regime as the mass transfer resistances could
not be easily eliminated. The intrinsic kinetics was obtained through apparent kinetics. The
activation energy of oxidation of β-IP to KIP is 70.5 4.1 kJ mol–1, and the value of ln AKIP is
33.53 1.22. Meanwhile, the activation energy of oxidation of β-IP to HIP is 86.4 5.4 kJ mol–1
and the value of ln AHIP is 36.23 1.52, which could provide theoꢀrCetical basis for industrial
design, amplification of reactor, and the optimization of reaction.
Inc. Int J Chem Kinet 48: 295–303, 2016
2016 Wiley Periodicals,
fragrance in foodstuffs and cosmetic formulations.
Nowadays, the increasing demands of KIP materials
and much more rigorous environmental requirements
make it more attractive to develop a cheap, efficient,
and environment friendly technology from β-IP to
KIP [8]. Thus many researchers devoted themselves
to pursuing new high-efficiency and high-selectivity
catalyst. Until now, catalysts such as metal–Schiff
base [8,9], metal–porphyrin [10], TiO2-supported
iron tetrasulfophthalocyanine [11], SiO2-supported
catalyst [12], zeolite-encapsulated Co(II)saloph
complexes [13], and TEMPO(2,2,6,6-tetramethyl-
1-piperidinyloxy)/NHPI(N-Hydroxyphthalimide) sys-
tem [14] were discovered and reported. However, most
of them have been found to be effective catalyst sys-
tems for the oxidation of hydrocarbons to oxygenated
derivatives of commercial importance; a few of these
catalysts are actually used in large-scale industrial pro-
duction.
INTRODUCTION
The oxidation of hydrocarbons using oxygen is
an important industrial reaction [1]. There are nu-
merous commercial applications of catalytic liquid
phase oxidation reactions of aliphatic [2,3], aromatic
[4], and cyclic hydrocarbons [5,6] carried out over
the years to give corresponding oxygenated deriva-
tives. Among these, the aerobic oxidation of 3,5,5-
trimethylcyclohex-3-en-1-one (β-isophorone, β-IP)
to give 3,5,5-trimethylcyclohex-2-en-1,4-dione (keto-
isophorone, KIP) also received considerable atten-
tion by both academicians and industry [7]. KIP is
not only valued as a key intermediate for produc-
ing compounds of vitamin A, E series, and various
carotenoids but also widely used as flavoring and
Correspondence to: Hong Yin; e-mail: yinh@zju.edu.cn.
ꢀC
2016 Wiley Periodicals, Inc.

296
CHEN ET AL.
Apart from the catalyst research, kinetics of oxida-
tion of β-IP was rarely reported yet, only Halligudi
et al. [1] carried out kinetic investigations under ho-
mogeneous reaction conditions and acquired the ac-
tivation energy. However, the oxidation of β-IP cat-
alyzed by iron(III) acetylacetonate using molecular
oxygen is gas–liquid reaction and it is well known that
mass transfer reaction kinetics and kinetics parameters
of gas–liquid reaction system [15] are essential theoret-
ical basis for industrial design, amplification of reactor,
and guidance of optimization of reaction. We recently
investigated the mass transfer reaction kinetics of
β-IP oxidation by air in a lab-scale agitator bubbling
reactor [16]. A correlation equation of the gas-phase
volumetric mass transfer coefficient was obtained.
However, the intrinsic reaction kinetics of the oxida-
tion of β-IP was still unknown due to its big mass
transfer resistance. As we all know, the apparent ki-
netics does limited favor to the scale up as the mass
transfer would change in different reactors [18]. Gener-
ally, the intrinsic reaction kinetics is obtained through
eliminating the mass transfer resistances by changing
stirring the rate or decreasing reaction concentration.
However, there existed some reactions whose mass
transfer resistances could not be eliminated sim-
ply by changing the stirring rate or decreasing re-
action concentration, especially some oxidation re-
actions. Thus, more and more researchers turn to
investigate the intrinsic reaction kinetics under the
mass transfer reaction kinetic regime [15,19,26].
Our preliminary experiment shows that the oxida-
tion of β-IP using molecular oxygen is also a fast
reaction.
then the intrinsic reaction rate equation is described by
Eq. (2),
− rA = km,n CAm CBn
(2)
And because the liquid-phase mass transfer coefficient
kBl was correlated with the mass transfer of gas B with-
out reaction, and the enhancement by chemical reaction
occurring in the film where the gas was consumed, the
apparent kinetics can be expressed as Eq. (3),
− RB = EkBlCBnia
(3)
The enhance factor E of Eq. (3) can be written as in
Eq. (4),
ꢂ
ꢃ
ꢄ
ꢀ
ꢁ
ꢀ
ꢁ
m/2
m/2
E
E
∞ − E
∞ − 1
E
E
∞ − E
∞ − 1
E = Ha
th Ha
(4)
where E is the instantaneous chemical reaction en-
∞
hancement factor demonstrated by Eq. (5),
DAl 1 CAl
DBl aꢁ CBi
E
= 1 +
(5)
∞
and for an irreversible reaction of m order with respect
to the reactant A in the liquid phase and n order with
respect to the solute B, the Hatta number Ha is defined
as in Eq. (6), [21]
In continuation of our work on this project, the pur-
pose of this paper is to investigate the intrinsic reac-
tion kinetics of β-IP oxidation in a lab-scale agitator
bubbling reactor using oxygen catalyzed by iron(III)
acetylacetonate. The kinetics region was determined.
The intrinsic kinetic constants were obtained through
the apparent kinetics constants under various oxygen
pressures and reaction temperatures. Besides, the oxi-
dation rate equation of β-IP is established. The results
will provide essential theoretical basis for industrial
design, amplification of reactor, and guidance of opti-
mization of reaction.
ꢅ
1
2
Ha =
k
m,n DBlCAml CBni−1
(6)
kBl n + 1
As for the oxidation reaction, most of which shows
first order to the reactant and oxygen, then the Hatta
number of m = 1 and n = 1 can be described as in
Eq. (7),
ꢆ
1
Ha =
k1,1DBlCAl
(7)
kBl
According to the two-film theory [22], when 3 ≤ Ha =
√
kDBlCAl
kBl
≤ E , there is E = Ha, thus the apparent
∞
BACKGROUND THEORY
kinetics can be rewritten as the following equation:
If a reaction is represented by Eq. (1), [20]
dCAl
dt
RA = −
= aꢁRB = aꢁEkBlCBia = aꢁHa kBlaCBi
aꢁA (l) + B (g) → C (l)
(1)
(8)
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KINETICS STUDY ON OXIDATION OF β-ISOPHORONE USING MOLECULAR OXYGEN
297
ꢃ
ꢀ
ꢅ
ꢄ
ꢇ
ꢁ
ꢆ
ꢈ
ꢉ
ꢁꢁ
ꢁꢂ
Figure 1 Schematic diagram of experimental apparatus: (1) gas cylinder, (2) flow meter, (3) gas inlet needle, (4) thermometer,
(5) stirring motor, (6) agitator bubbling reactor, (7) baffle, (8) condenser, (9) thermostat bath, (10) oxygen detector, and (11)
exhaust bottle.
where CBi is the interface concentration and according
to Henry’s law, Eq. (9) can be met.
NHU . O2 (purity of ࣙ99.99%) and N2 (purity of
ࣙ99.99%) were mixed to provide various oxygen
pressure gases (24.40, 46.00, 64.86, 101.35 kPa) by
Hangzhou Jingong Gas.
PB
CBi
=
(9)
H
Therefore, the apparent kinetics can be further rewrit-
ten as the following equation (10)
Experimental Setups and Procedures
As shown in Fig. 1, the experiments were conducted in
a lab-scale agitator bubbling reactor consists of a four-
neck round bottom reactor with an overhead stirrer,
four baffles fitted inside the reactor to ensure a flat
horizontal interface.
ꢆ
k1,1DBlCAl
kBl
dCAl
dt
RA = −
= aꢁ
= aꢁRB = aꢁ
kBlaCBi
(10)
ꢆ
PB
H
k
1,1DBlCAla = kobvC1/2
Al
A typical experiment process is demonstrated be-
low. 0.1 mol β-IP and 43.58 mL pyridine were fed into
the reactor heated to the desired temperature under
nitrogen atmosphere. With 0.05% mol iron(III) acety-
lacetonate catalyst added and oxygen introduced, the
reaction was considered begun. And the thermometer
was fitted to detect the temperature in the reactor during
the reaction process with an accuracy of 0.1 K. The
flux of the gas reactant is measured by the flow meter
with an accuracy of 1 mL min–1. The reaction mixture
was withdrawn from the reactor every 45 min, which
was qualitatively analyzed by gas chromatography–
mass spectroscopy (GC–MS) and quantitatively ana-
lyzed via Jing Ke GC920 gas chromatography fitted
with an OV-1701 column (30 m, 0.25 μm diameter)
and a flame ionization detector. The kinetics of β-IP ox-
idation was investigated by changing the stirring rate
(250, 350, 450, 500, 550 rpm), oxygen partial pres-
sure (24.40, 46.00, 64.86, 101.35), and temperature
(323.15, 325.15, 328.15, 331.15, 333.15, 338.15 K).
The experiments were repeated over three times, and
the values obtained were the average values.
1/2
Hence, it can be found that the slope of 2CAl versus
t should be the apparent kinetics constant kobv and the
intrinsic reaction rate constant can be obtained through
apparent kinetics rates according to the formula k1,1
=
ko2bv
H
(
)2. The relationship between k1,1 and kobv
2
aꢁ DBl aPB
was derived from Eq. (10).
EXPERIMENTAL
Chemicals
Pyridine (purity of ࣙ99.5%), purchased from
Sinopharm Chemical Reagent (Shanghai, China) was
used as a solvent. Methyl benzoate (purity of ࣙ99.5%)
was purchased from Sinopharm (Shanghai, China) and
was used as the internal standard for GC. Iron(III)
acetylacetonate (purity of ࣙ99%), purchased from
Sinopharm (Shanghai, China) was used as a cata-
lyst. β-IP (purity of 99.5%) was provided by Zhejiang
International Journal of Chemical Kinetics DOI 10.1002/kin.20987

298
CHEN ET AL.
RESULTS AND DISCUSSION
Reaction Network
Physical Parameters
The density among various temperatures was measured
through density gauge, and the viscosity was deter-
mined through an Ubbelohde viscometer. And the sur-
face tension was measured by an OCA20 contact angle
measuring device. The diffusion coefficients [23,24]
were estimated using the Wilke–Chang semiempirical
equation (Eq. (11)). The solubility of oxygen was cal-
culated by the Katayama method [25] (Eqs. (12) (13)).
All the results are listed in Table III.
GC–MS was used to qualitatively analyze the reaction
mixture, and β-IP was found to give mainly KIP along
with small amounts of 4-hydroxy-3,5,5-trimethyl-2-
cyclohexen-1-one (HIP) and little α-isophorone (α-IP).
The reaction scheme is shown in Fig. 2.
The detailed concentration during the whole pro-
cess is shown in Fig. 3. Figure 3 shows that almost
80% of β-IP was consumed during the first 7 h, which
may be explained by the fast oxidation rate. It is cal-
culated from Fig. 3 that the selectivity of main product
KIP is over 94% and the selectivity of by-product HIP
is over 5%, whereas the selectivity of the isomeriza-
tion product is nearly 1%. With solvent more pyridine
used, the isomerization would have restrained and it is
reasonable to neglect the isomerization reaction when
doing kinetics calculation. To better discuss the reac-
tion of KIP and HIP, Fig. 4 is presented. KIP and HIP
concentrations were in good linear relationship, and
the reaction of KIP and HIP can be treated as a parallel
reaction with the same reaction order.
(∅MB)1/2
T
DAB = 7.4 × 10−15
(11)
μVA0.6
−−→
−−−→
ꢀFA
ꢀFben
− logSA = −logSben
+
−
(12)
(13)
2.303RT
2.303RT
−−→ −−−→
ꢀFA − ꢀFben = (δ − δben) (aδ + β)
Mass Transfer Parameters
The liquid mass transfer coefficient kL can be described
by a relationship of dimensionless numbers just as the
following equation shows [26,27]
Sh = 0.0253 Re0.84 Sc0.5
(14)
(15)
ρLωd2
μL
μL
kLd
DA
Re =
Sc =
Sh =
Figure 2 The reaction scheme of oxidation of β-IP.
ρLDA
And the interfacial area can be determined by the fol-
lowing equations:
1.8
1.6
1.4
1.2
6∅
a =
(16)
db
1.0
0.8
0.6
0.4
0.2
0.0
β−IP
IP
ꢀ
ꢁ
α
KIP
∅
Vs2/3
(gl)1/3
ρL
= 0.5
HIP
1 − ∅
ρL − ρG
ꢀ
ꢁ
0.1
δ0.6
μL
μG
db = 0.7
(17)
ꢇ
ꢈ
0.4
ρL0.2
P
V
0
2
4
6
8
10
12
t(h)
where db refers to the average bubble size and ∅ means
the gas holdup. The gas holdup can be estimated by
using the Kudrewizki equation [28,29], and db can be
calculated by the equation proposed by Parthasarthy
et al. [30] (Eq. (17). The results of various temperatures
are also listed in Table III.
Figure 3 The concentration of the compounds existed in
the reaction system versus time. Reaction condition: 0.1 mol
β-IP, 43.58 mL pyridine, 0.05% mol iron(III) acetylacet-
onate; oxygen 30 mL min–1, the stirring speed 450 rpm,
temperature 323.15 K.
International Journal of Chemical Kinetics DOI 10.1002/kin.20987

KINETICS STUDY ON OXIDATION OF β-ISOPHORONE USING MOLECULAR OXYGEN
299
0.07
0.06
0.05
0.04
0.03
0.02
0.01
0.00
1.8
1.6
1.4
1.2
the range for calculating the slope
1.0
0.8
0.6
0.4
0.2
0.0
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
0
2
4
6
8
10
12
CKIP(mol/L)
t(h)
Figure 4 Plot of the KIP concentration versus HIP concen-
tration.
Figure 6 Range for slope calculated. Reaction condition:
0.1 mol β-IP, 43.58 mL pyridine, 0.05% mol iron(III) acety-
lacetonate; oxygen 30 mL min–1, the stirring speed 450 rpm,
temperature 323.15 K.
The Effect of Stirring Rate
ture and oxygen pressure experiment was carried out at
450 rpm.
The stirring rate experiment was conducted, and results
are shown in Fig. 5. To choose the suitable stirring rate
to carry out kinetics experiment is necessary as too low
stirring rate causes too high mass transfer resistances
and too high stirring rate leads to strong turbulence.
It can be concluded from Fig. 5 that the reaction rate
of β-IP and KIP at the stirring rate of 450 rpm was
slightly faster than that at 550 rpm; vortex would oc-
cur when the stirring rate was too high, and the vortex
would lead to the oxygen spillover. The reaction rate
of β-IP and KIP at 450 rpm was faster than that at
350 rpm since the increase of the stirring rate could
decrease the high mass transfer resistances. Therefore,
a proper stirring rate was determined and the tempera-
Reaction Order with Respect to β-IP
To verify the reaction order, the intrinsic kinetics was
assumed to be first order of both β-IP and oxygen.
As background theory shows, the apparent kinetics
would appe√ar to show half order of β-IP in case of
kDBlCAl
3 ≤ Ha =
≤ E . Figure 6 shows the range
∞
for calculationk.BTl he integral method was used to de-
termine the slope as shown in Fig. 7. Figure 7 shows
a good linear relationship between 2CA1/2 and t, which
was consistent with the assumption and indicated a
first-order dependence on β-IP.
1.8
1.6
1.4
1.6
1.4
1.2
1.2
250r/min
250r/min
350r/min
450r/min
500r/min
550r/min
1.0
0.8
0.6
0.4
0.2
0.0
1.0
0.8
0.6
0.4
0.2
0.0
350r/min
450r/min
500r/min
550r/min
0
2
4
6
8
10
12
14
0
2
4
6
8
10
12
14
t(h)
t(h)
Figure 5 The concentration of β-IP versus time (left) and the concentration of KIP versus time (right) at different stirring
rates.
International Journal of Chemical Kinetics DOI 10.1002/kin.20987

300
CHEN ET AL.
2.6
Table I Apparent Reaction Constants Determined
from Fig. 8
2.4
2.2
2.0
1.8
1.6
1.4
1.2
1.0
Oxygen
Pressure (kPa)
kobv
(kmol1/2 m−3/2 h−1
)
R2
24.40
46.00
64.86
101.35
0.0606 0.0048
0.1453 0.0038
0.1801 0.0035
0.2590 0.0098
0.9846
0.9991
0.9994
0.9965
R=0.9906
0.30
0.25
0.20
0.15
0.10
0.05
2
4
6
8
10
12
t(h)
1/2
Figure 7 The plot of 2CA versus t.
Reaction Order with Respect to O2
To find out the reaction order with respect to the O2
interface concentration, Eq. (3) was changed into the
following equation:
R2=0.9829
0.00
0
ꢆ
20
40
60
80
100
120
k1,1DBlCAl
kBl
dCAl
dt
− RA = −
= aꢁ
= aꢁRB = aꢁ
kBlaCBi
P(kPa)
Figure 9 The apparent kinetic constant versus various oxy-
1
ꢆ
gen pressures.
PB
k1,1DBlCAla = kobvCA2 l
(18)
H
The oxygen pressure experiments were carried out,
and the apparent reaction rates were obtained. The re-
sults are shown in Fig. 8 and Table I. A good linear
relationship between kobv and oxygen pressure was ob-
tained. The results are shown in Fig. 9. The reaction
can be treated as a first-order dependence on oxygen.
ꢆ
PB
kobv = aꢁ
k1,1DBla = f (PB)
(19)
H
2.6
2.4
2.2
2.0
1.8
1.6
1.4
1.2
1.0
0.8
0.6
0.4
P=24.44kPa R2=0.9846
P=46.00kPa R2=0.9991
P=64.86kPa R2=0.9994
P=101.35kPa R2=0.9965
Temperature Experiment and Kinetics
Parameters
The temperature experiments were conducted to deter-
mine the activation energy. The apparent reaction rates
kobv from temperature 323.15 to 338.15 K were ob-
tained by the integral method. The results are shown in
Fig. 10. Table II shows the slope regressed by the inte-
gral method ranged from temperature 323.15 to 338.15
K. Since the reaction orders with respect to β-IP and
oxygen were determined above and both the physical
and mass transfer parameters are obtained, Ha can be
calculated. The results are presented in Table III.
0
2
4
6
8
10
t(h)
1/2
Table III shows that 3 ≤ Ha ≤ E , thus the as-
∞
Figure 8 The plot of 2CA
versus t using the inte-
sumption made before is demonstrated and the total
intrinsic kinetic constant k can be obtained by the equa-
tion deduced above. As mentioned before, the isomer-
ization can be neglected, thus the total intrinsic kinetic
gral method at different oxygen pressures. Reaction con-
dition: 0.1 mol β-IP, 43.58 mL pyridine, 0.05% mol iron(III)
acetylacetonate; the stirring speed 450 rpm, temperature
333.15 K; oxygen pressure 24.40, 46.00, 64.86, 101.35 kPa.
International Journal of Chemical Kinetics DOI 10.1002/kin.20987

KINETICS STUDY ON OXIDATION OF β-ISOPHORONE USING MOLECULAR OXYGEN
Table II Apparent Reaction Constants in Different
301
2.6
2.4
2.2
2.0
1.8
1.6
1.4
1.2
1.0
0.8
0.6
T=323.15K R2=0.9906
Temperatures from Fig. 10
T=325.15K R2=0.9920
T=328.15K R2=0.9882
kobv
T=331.15K R2=0.9902
Temperature (K)
(kmol1/2 m−3/2 h−1
)
R2
T=333.15K R2=0.9883
T=338.15K R2=0.9866
323.15
325.15
328.15
331.15
333.15
338.15
0.1365 0.0074
0.1588 0.0101
0.1860 0.0127
0.2269 0.0101
0.2443 0.0120
0.3064 0.0157
0.9906
0.9920
0.9882
0.9902
0.9883
0.9866
The ln k as the dependent variable and 1/T as the
independent variable, the results are presented in
Fig. 11.
0
2
4
6
t(h)
8
10
12
Figure 10 Plot of 2CA1/2 versus t using the integral method
at different temperatures. Reaction condition: 0.1 mol β-IP,
43.58 mL pyridine, 0.05% mol iron(III) acetylacetonate; the
stirring speed 450 rpm, oxygen 30 mL min–1;temperature
323.15, 325.15, 328.15, 331.15, 333.15, 338.15 K.
The activation energy of oxidation of β-IP to KIP is
70.5 4.1 kJ mol–1, and the value of ln AKIP is 33.53
1.22. The activation energy of oxidation of β-IP to KIP
is really close to the value 16.12 kcal mol–1 acquired
by Halligudi et al. [1] under homogeneous reaction
condition. The activation energy of oxidation of β-IP
to HIP is 86.4 5.4 kJ mol–1, and the value of ln AHIP is
36.23 1.52. Therefore, the intrinsic kinetics of β-IP
to KIP and HIP can be expressed as, respectively,
constant k should be the sum of the reaction constant
kKIP and kHIP. With the reasonable assumption men-
tioned before that the reaction of KIP and HIP can be
treated as the parallel reaction with the same reaction
order, the ratio of kKIP and kHIP should be the slope of
KIP and HIP concentration as shown in Fig. 4. Hence,
kKIP and kHIP can be obtained. The results are presented
in Table IV.
rKIP = kKIP
C
β−IPC
O2
ꢀ
ꢁ
ꢁ
8479.7
= 3.65 × 1014 exp −
Cβ−IP CO
2
T
As it is well known that the activation energy and
preexponential factor can be determined by the follow-
ing Arrhenius equation:
rHIP = kHIP
C
β−IPC
O2
ꢀ
10392.1
E
R
1
= 5.41 × 1015exp −
C
β−IP CO
lnkA = lnA −
×
(20)
2
T
T
Table III Values of Intrinsic Kinetic Constant, Ha Number, and Infinite Enhancement Factor
CAl
(mol L−1
CBi
DAl, ×10−9 DBl, × 10−9 kL, × 10−4
ktotal
(m3 kmol−1 s−l
T (K)
)
(10−4 mol L−1
)
(m2 s−1
)
(m2 s−1
)
(m s−1
)
)
Ha
Eꢀ
323.15
323.15
325.15
325.15
328.15
328.15
331.15
331.15
333.15
333.15
338.15
338.15
1.70
0.10
1.70
0.10
1.70
0.10
1.70
0.10
1.70
0.10
1.70
0.10
3.39
3.39
3.43
3.43
3.49
3.49
3.55
3.55
3.58
3.58
3.68
3.68
1.31
1.31
1.35
1.35
1.42
1.42
1.51
1.51
1.57
1.57
1.69
1.69
3.98
3.98
4.11
4.11
4.30
4.30
4.58
4.58
4.75
4.75
5.13
5.13
1.17
1.17
1.20
1.20
1.24
1.24
1.30
1.30
1.34
1.34
1.42
1.42
1407
1407
1801
1801
2412
2412
3082
3082
3387
3387
4670
4670
26.4
6.4
29.6
7.2
33.9
8.2
37.6
9.1
39.1
9.5
45.0
10.9
826
50
815
49
805
48
790
47
786
47
762
46
aSymbols (CA, DBl, DAl, CBi, kL, ktotal, Ha, and Eꢀ) refer to the concentration of β-IP, the diffusion coefficient of oxygen in the liquid film,
the diffusion coefficient of β-IP in the liquid film, the equilibrium concentration of oxygen, the mass transfer coefficient of oxygen in the liquid
film, the total intrinsic kinetic constant of the oxidization of β-IP, Hatta number, and infinite enhancement factor, respectively.
International Journal of Chemical Kinetics DOI 10.1002/kin.20987

302
CHEN ET AL.
Table IV The Intrinsic Reaction Rate Constants of KIP and HIP
T (K)
kHIP/kKIP
k (m3 kmol−1 s−l
)
kKIP(m3 kmol−1 s−l
)
kHIP(m3 kmol−1 s−l
)
323.15
325.15
328.15
331.15
333.15
338.15
0.0396
0.0410
0.0440
0.0470
0.0480
0.0500
1406.69
1801.45
2412.12
3082.53
3387.12
4670.58
76.26
1353.11
1730.51
2310.47
2944.16
3231.98
4448.17
73.36
53.58
70.95
101.66
138.38
155.14
222.41
2.90
4.51
6.94
6.16
7.62
11.39
114.58
164.70
137.21
166.37
239.29
110.06
157.76
131.05
158.75
227.89
9
8
7
6
5
4
3
NOMENCLATURE
HIP R2=0.9802
KIP R2=0.9840
a
Gas-liquid surface area, m−1
cBi
The equilibrium concentration of gas B,
mol, L−1
Ea
activation energy, kJ mol−1
km,n The intrinsic kinetic constant
PB
VA
aꢁ
The pressure of gas B, kPa
Molar volume of solute, cm3 mol−1
Stoichiometric coefficient for reactant A
The concentration of A in the bulk liquid,
mol L−1
cAl
dB
d
Bubble diameter, m
Agitator blade diameter, m
0.00294 0.00296 0.00298 0.00300 0.00302 0.00304 0.00306 0.00308 0.00310
1/T(1/K)
DAl Diffusivity of reactant A in the liquid film,
m2 s−1
Figure 11 Plot of ln k versus 1/T.
DBl Diffusivity of reactant B in the liquid film,
m2 s−1
E
The reaction enhancement
CONCLUSION
Eꢀ The infinite reaction enhancement
g
Gravity acceleration, m s−2
Hatta number
The oxidation of β-IP catalyzed by iron(III) acety-
lacetonate using molecular oxygen was investigated
using a lab-scale agitator bubbling reactor. The reac-
tion scheme can be simplified to two parallel reactions.
The reaction was found to be a pseudo–first-order fast
reaction regime system, which accounted for the dif-
ficulty to get the intrinsic kinetics by eliminating the
mass transfer resistances. Thus the intrinsic kinetics
was obtained under the mass transfer reaction kinetic
regime. A method was proposed for gaining the intrin-
sic kinetics from the apparent kinetics. The activation
energy of oxidation of β-IP to KIP is 70.5 4.1 kJ
mol–1, and the value of ln AKIP is 33.53 1.22. Mean-
while, the activation energy of oxidation of β-IP to HIP
is 86.4 5.4 kJ mol–1 and the value of ln AHIP is 36.23
1.52. The intrinsic kinetics equations of β-IP to KIP
and HIP are obtained, which was supposed to do favor
for the kinetics study of fast reactions and provide ba-
sis for industrial design, amplification of reactor, and
optimization of reaction.
Ha
H
kBl
Henry’ primes constant, kmol m3 kmol−1
Mass transfer coefficient in liquid phase,
m s−1
ktotal The total intrinsic kinetic constant of oxidation
of β-IP
kobv The apparent kinetic constant of oxidation of
β-IP
kKIP The intrinsic kinetic constant of β-IP to be oxi-
dized to KIP
kHIP The intrinsic kinetic constant of β-IP to be oxi-
dized to HIP
m, n The reaction order
R
Gas constant, 8.314 m3 Pa K−1 mol−1
Reynolds number
Schmidt number
Sherwood number
Temperature, K
Re
Sc
Sh
T
th
ω
Hyperbolic tangent function
The stirred speed of the agitator, s−1
International Journal of Chemical Kinetics DOI 10.1002/kin.20987

KINETICS STUDY ON OXIDATION OF β-ISOPHORONE USING MOLECULAR OXYGEN
303
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GREEK LETTERS
σ
Surface tension, m Nm−1
ρl Liquid density, k g−3
ρG Gas density, k g−3
μL Liquid viscosity, Pa · s
μg Gas viscosity, Pa · s
Ø
Gas holdup, dimensionless
This work was supported by the program for Zhejiang Lead-
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