Catalysis, 41 (1988) 39-52 Elsevier Science Publishers B.V., Amsterdam -
Applied
39
Printed in The Netherlands
Ethylene Oxide Oxidation over a Supported Silver Catalyst II. Kinetics of Inhibited Oxidation ALEXANDER Institute
ELIYAS*, LUCHEZAR PETROV and DIMITAR SHOPOV
of Kinetics
and Catalysis, Bulgarian Academy
of Sciences,
str. Acad. G. Bonchev
bl. 11,
Sofia 1113 (Bulgaria)
(Received 21 April 1987, accepted 7 March 1988)
ABSTRACT The inhibiting effect of dichloroethane on the complete oxidation of ethylene oxide over an Ag/ A&O, catalyst was studied by the flow-circulation method. The study was carried out under steadystate conditions, at atmospheric pressure and in the temperature range 210-300” C. The inhibitor feed concentration was varied from 1 to 28 ppm. A kinetic model of the reaction is proposed that includes the inhibitor partial pressure in its functional form. It describes adequately the dependence of the conversion on the contact time, feed composition, temperature and inhibitor concentration and also the dependence of the oxidation rate on the outlet partial pressures of oxygen and ethylene oxide. Catalytic decomposition of ethylene oxide is observed at high temperatures and with oxygen shortage.
INTRODUCTION
The complete oxidation of ethylene oxide over an Ag/A1203 catalyst: I. C,H,O + 2.5 O2 -
Ag
2 CO2 + 2 Hz0
(1)
is one of the reactions involved in the complex process of the selective catalytic oxidation of ethene: II. C2H4+0.5 0, III. C&H,+ 3 O2 -
Ag
&
CzH40 (2)
2 COz + 2 Hz0
In the industrial application of the process, trace amounts of dichloroethane (DCE), of the order of several ppm, are added to the feed to increase the selectivity for ethylene oxide. The complete oxidation of ethene III (2 ), is inhib-
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0 1988 Elsevier Science Publishers B.V.
40
ited to a greater extent by DCE than its partial oxidation II (2), hence the selectivity for ethylene oxide is promoted, which is why DCE is often called a “promoter”, considering its promoting effect on the selectivity and in spite of its inhibiting effect on the oxidation. In previous work the kinetics of reactions II and III (2) were studied both over an unpromoted silver catalyst [ 11 and also over a catalyst promoted with DCE [ 21. In Part I [ 31 we reported a separate study on the complete oxidation of ethylene oxide, I (1)) over the same silver catalyst in the absence of an inhibitor and over a wide temperature range (loo-300°C). It was shown that oxidation of ethylene oxide starts at 190°C and above this temperature oxidation of ethene over silver catalysts should be considered to proceed in accordance with the parallel-consecutive reaction scheme. A kinetic model was proposed, together with a mechanism for the catalytic oxidation of ethylene oxide [3]. An aspect of practical interest is the study of the oxidation of ethylene oxide in the presence of DCE with the aim of elucidating whether the consecutive reaction I (1) should be taken into account when modelling the industrial process, proceeding always in the presence of this inhibitor. The promotion of the selectivity of silver catalysts for ethylene oxide by the addition of Cl-containing compounds to the feed for ethene oxidation has been studied by a number of investigators [ 4-91. However, as far as we know, the catalytic oxidation of ethylene oxide has not been studied separately. The aim of this work was to construct a kinetic model of the oxidation of ethylene oxide over an Ag/A1203 catalyst in the presence of dichloroethane as an inhibitor. This model should describe adequately the quantitative effect of the inhibitor feed concentration on the reaction rate. EXPERIMENTAL
The supported silver catalyst, the apparatus and the computer processing of the experimental data have already been described [l-3]. The purities of the reagents (oxygen, ethylene oxide and argon) were specified in Part I [ 31. The purity of dichloroethane was over 99.8%. Task of the study On studying the separate catalytic oxidation of ethylene oxide, its degree of conversion Xx, under fixed conditions is sufficient for the single-valued description of the chemical transformations occurring in the reactor. The reason for this is that there is only one reaction proceeding in this instance, I (1 ), unlike the situation in previous work [ 1,2], where both reactions II and III (2) were considered. Only at 300’ C and an oxygen : ethylene oxide feed ratio of 1: 2 was an additional reaction observed, viz., catalytic decomposition of ethylene
41
oxide, as in Part I [ 31. This requires the consideration of selectivity so that the proportions of the two reactions, under certain conditions, are fixed. The task of this study was to obtain experimental data for the functional dependences: &o=f1
(T ‘, CDCE,F. : FE0 = constant)
(r)
X,,=f2(To
)
XEo=fS($-)
(7, CDCE,Fo: F,o=constant)
(3)
(T”, CDCE,r=constant) EO
Xso=fd(Cncn)
(T”, 7, FE:FEO=constant)
where 7 is the contact time (h-g cat./mol), T” is the catalyst bed temperature, c nCEis the feed concentration of dichloroethane and F. and FE0 are the inlet flow-rates of oxygen and ethylene oxide, the ratio between them fixing the feed composition. The experimental dependences (3 ) in the presence of an inhibitor could be compared with those of the uninhibited catalyst [ 31. In such a way the inhibiting effect and its variation with temperature could be described. The task of the study also included a juxtaposition of the dependences: R(1) =f5 (PO)
( T",Fo : FEO,CDCE= constant)
R ( 1)
( T" , F. : FEo, CDCE= constant)
= fG (pEO )
(4)
in the presence and absence of the inhibitor, where R ( 1) is the rate along the first route (ethylene oxide oxidation), which is equal to the rate of ethylene oxide consumption. When the second reaction is also proceeding [ethylene oxide decomposition to ethene and oxygen; rate R (2) 1, then R (1) is equal to half of the rate of carbon dioxide formation. p. and pso are the outlet partial pressures of oxygen and ethylene oxide, respectively. The final aim of this investigation was to develop a kinetic model of the process in the presence of inhibitor. The model should describe the experimental dependences (3) and (4) adequately and, if possible, the influence of dichloroethane concentration on the decomposition rate should also be considered. Experimental conditions The kinetic measurements were carried out under steady-state conditions, at atmospheric pressure and in the temperature range 210-300” C. Feeds with the following composition were studied: 16.7% oxygen, 33.3% ethylene
oxide, 50.0% argon (1: 2) +dichloroethane
(several ppm)
25.0% oxygen, 25.0% ethylene
oxide, 50.0% argon (1: 1) +dichloroethane
(several ppm)
33.3% oxygen, 16.7% ethylene
oxide, 50.0% argon (2: 1) +dichloroethane
(several ppm)
In the following the feeds will be denoted for simplicity by the oxygen : ethylene
42
oxide ratio. The contact time with respect to ethylene oxide was varied from 158 to 945 h-g cat./mol and the fixed-bed laboratory reactor contained 25 g of catalyst. The dichloroethane was added to the feed by means of a saturator [ 21, consisting of a capillary, graduated in microlitres, immersed in a thermostat. Argon was used as the carrier gas at a very low flow-rate. In this way DCE feed concentrations varying from 1 to 28 ppm were obtained. The degree of conversion under these conditions was O.l-19%. The time required by the system to reach a steady state of ethylene oxide oxidation was about 30 min. A steady-state catalytic activity in the presence of inhibitor was achieved after 15-20 h of dosing DCE, as previously [ 21. The inhibiting effect of DCE is reversible; lo-15 h after the DCE dosage is discontinued the initial high catalytic activity is restored completely. The proceeding of the reaction in the kinetic region was checked as in previous work [l-3 1, and showed no influence of diffusion. Measurement of reproducibility and stability of the catalytic activity The reproducibility of the experimental results is illustrated by the following example. At 275’ C, with a feed composition of 1: 1 and a contact time of 945 h*g cat./mol, the average outlet reagent concentrations after eight GC analyses were 18.49% oxygen, 5.36% carbon dioxide, 5.36% water, 22.06% ethylene oxide and 48.73% argon (the decrease in argon concentration in the converted mixture (48.73 < 50.00% ) is due to a volume increase of the converted mixture, compared with the feed, as a result of the reaction). The standard deviations of the outlet concentrations of the reagents are 0.21 for oxygen, 0.37 for carbon dioxide and water and 0.27 for ethylene oxide. Some of the experiments were repeated later to check the stability of the catalytic activity. The average deviation was about 9%. RESULTS AND DISCUSSION
Conversion of ethylene oxide, in the presence of DCE, starts at higher temperatures (200-210°C) than in the absence of the inhibitor (190°C). A full set of experiments with the three feeds and contact times from 158 to 945 h-g cat./mol were carried out at 210, 250, 275 and 300°C. On adding DCE to the feed it was not always possible to obtain a definite, required, inhibitor concentration. This experimental difficulty was a result of the low flow-rates of the reagents. Different inhibitor feed concentrations may easily be obtained by repeating the experiment, preserving the same catalyst bed temperature, contact time and oxygen : ethylene oxide feed ratio and varying only the temperature of the DCE saturator or the carrier gas flow-rate. It was much more difficult to obtain a constant DCE concentration throughout
43
a whole experimental series, but nevertheless we achieved this in some instances. Fig. 1 shows the dependence of degree of conversion of ethylene oxide on the contact time, X,, =fi (z). A decrease in conversion in the presence of DCE is caused by 5.5 ppm of DCE in a 1: 1 feed at 250°C. The inhibiting effect of DCE decreases with increase in temperature when the feed composition, contact time and inhibitor concentration are kept constant. If we denote the conversion decrease by AX,,, AX
=(x~o-x~o).loo
EO
(5)
(Igo)
-Go
where XU,, is the conversion of ethylene oxide over the uninhibited catalyst and XL0 over the inhibited catalyst. Table 1 illustrates the temperature dependence of the conversion, X,, =fi ( T” ), f or a 1:2 feed, a contact time of 236 h-g cat./mol and 5.5 ppm of DCE. The data for the inhibited and uninhibited catalyst are juxtaposed. The decrease in dX EOwith increase in temperature is also shown. The degree of conversion of ethylene oxide increases with increase in the oxygen content in the feed at constant temperature, contact time and inhibitor concentration (Fig. 2). The series X,, =f3 (F. : FE0 ) at 275’ C, 8 ppm of DCE and 236 h-g cat./mol is shown for both the inhibited and uninhibited catalyst. The comparison shows a decrease in conversion of 24-25% for such an inhibitor concentration at this temperature. Fig. 3 shows the degree of conversion of ethylene oxide as a function of the
CONTACT
T/ME
T (h.g
cohdl)
Fig. 1. Dependence of experimental and model degrees of conversion of ethylene oxide on the contact time at 250°C and feed composition 25% oxygen, 25% ethylene oxide, 50% argon, 5.5 ppm dichloroethane [Xf (0 ) = experimental conversion over the inhibited catalyst; XF ( n ) =model conversion over the inhibited catalyst; Xz ( 0 ) = experimental conversion over the uninhibited catalyst ] .
44
TABLE 1 Comparison of the temperature dependence of the degree of conversion of ethylene oxide over inhibited and uninhibited catalysts for 1: 2 feed with a contact time of 236 h-g cat./mol Temperature (“C)
Ethylene oxide conversion (% )
Go
250 275 300
)’
1.7 4.7 7.1
0.5
FEED
Model WE0 )”
Experimental (Xii0
RATIO
I.5
Inhibitor concentration
34.0 17.5 5.0
5.5 5.5 5.5
(ppm) c DCE
1’
2.6 5.7 7.5
1.0
Decrease of ethylene oxide conversion (%) AX,,
1.1
3.9 5.8
2.0
02’C2H40
Fig. 2. Influence of the feed composition on the model and experimental degrees of conversion of ethylene oxide at 275”C, contact time 236 h-g cat./mol and inhibitor concentration 8 ppm [XT (0 ) = experimental conversion over the inhibited catalyst; Xf” ( n ) = model conversion over the inhibited catalyst; X: (0 ) cexperimental conversion over the uninhibited catalyst].
inhibitor concentration, X,o =f4 ( CDCE) , at constant temperature, contact time and oxygen : ethylene oxide feed ratio. The dependence is linear in the studied range of inhibitor concentrations, 1-28 ppm. Fig. 3 shows the experimental series at 3OO”C, with a feed composition of 1: 1 and a contact time of 945 h-g cat./mol. At CDCE=0 the value of the conversion over the uninhibited catalyst under the same experimental conditions is given. The results indicated a need to measure the degree of inhibition of the catalyst by DCE. It is more convenient to use the decrease in carbon dioxide concentration, dCco2, in the converted mixture over the inhibited catalyst compared with that over the uninhibited catalyst under the same conditions
45
: 2
DCE
6
10
:
i
.:
14
: 18
CONCENTRATION
. 26
22
(ppm)
Fig. 3. Comparison of experimental and model degrees of conversion of ethylene oxide as a function of the feed inhibitor concentration at 3OO”C, contact time 945 h-g cat./mol and feed composition 25% oxygen, 25% ethylene oxide and 50% argon [XT (a) =experimental conversion over the inhibited catalyst; Xr = model conversion over the inhibited catalyst; X: ( 0 ) = experimental conversion over the uninhibited catalyst].
2
DCE
6
10
14
18
CONCENTRATION
22
26
ippmi
Fig. 4. Dependence of the degree of catalyst inhibition on the inhibitor concentration at different reaction temperatures: (1) 21O”C, (2) 25O”C, (3) 275°C (4) 300°C. Feed: (0) 1:2, (A) l:l, (0) 2:l.
rather than the decrease in conversion calculation:
A&on =
Go,-cco2).100 Go:!
(7)
0
(eqn. (5) ), because of the simpler
(6)
46
I
:,:,
: 0.303
0.300 C,$-$O
PARTIAL
:
0.306
: 0.309
PRESSURE
: 0.312
(atml
Fig. 5. Juxtaposition of model and experimental ethylene oxide oxidation rates as a function of the outlet ethylene oxide partial pressure at 250°C and feed composition 16.7% oxygen, 33.3% ethylene oxide, 50.0% argon, 6 ppm dichloroethane [R (1 )f ( l ) = experimental rate over the inhibited catalyst; R (1 )f ( q) =model rate over the inhibited catalyst; R (1): (0 ) = experimental rate over the uninhibited catalyst]. TABLE 2 Juxtaposition of experimental and model ethylene oxide oxidation rates as a function of the outlet oxygen partial pressure and inhibitor concentrations under different conditions Exp. no.
R(1)’ (mol/h.gcat.)
R(l)” (mol/h.gcat.)
C (;E)
F,:F,, r
‘;itm)
4.46.10V5 5.43.10-5 6.33.1O-5 7.04.10-5 7.74.10-5 5.44.10-5 7.79.10-5 1.02.10-4 9.31.10-5
4.70.10-5 4.92.10-5 5.26.1O-5 5.51.10-5 6.05.10-5 7.18.10-5 7.78.10-5 1.05.10-4 7.94.1o-S
0.186 0.199 0.204 0.205 0.208 0.221 0.248 0.260 0.276
9.0 10.0 10.5 10.0 9.0 19.5 23.0 11.0 27.5
1:l 1:l 1:l 1:l 1:l 2:l 2:l 2:l 2: 1
T"
(h-g cat./mol)
(“C)
473 315 236 189 158 945 473 315 236
275 275 275 275 275 300 300 300 300
The superscripts u and i denote “uninhibited” and “inhibited”, respectively. The decrease in carbon dioxide concentration is also a linear function of the inhibitor concentration, CDCE: AGO:! = ~CIXE
(7)
The physical meaning of the proportionality coefficient c~ is the decrease in carbon dioxide concentration that would be caused by the addition of 1 ppm of dichloroethane to the feed. The coefficient cy is a function of temperature. We determined the following values of LYat experimental temperatures from 210 to 300°C:
47
a(210)
=8.9
(x(250) =6.2 a(275)
~3.1
a(300)
=0.9
(8)
The value of A! decreases with increase in temperature and therefore it would serve as a measure of the effectiveness of the inhibitor at a given temperature, as the effectiveness also decreases with increase in temperature (see above). The dependence of the degree of catalyst inhibition, dCcon, on the feed DCE concentration, Cncn, at different temperatures is shown in Fig. 4. It can be seen that at a fixed temperature all the experimental points lie on a straight line, although the feed composition is different. As a result of experimental difficulties with precise dosing of DCE to the feed, the dependences R (1) =f5 (po) and R (1) =f6 (pEO) have different graphical forms in the different experimental series. In the series with an approximately constant inhibitor concentration, the oxidation rate R (1) increases monotonously with increase in the outlet partial pressures p. and pno [Fig. 5 and Table 2 (experiments l-5 ) 1. In other experimental series, where CDCE varies considerably, a maximum of the function (at the minimum C&s) is possible (Table 2, experiments 6-9). Catalytic decomposition of ethylene oxide at high temperature and with oxygen shortage The decomposition of ethylene oxide to ethene and oxygen was observed over the inhibited catalyst at 300°C with a 1: 2 feed, in addition to the oxidation, just as in Part I [3] using an uninhibited catalyst. Evidence for the occurrence of the decomposition reaction is the presence of ethene in the converted mixture. In this special case we had to calculate, in addition to the rate along the first route (oxidation ), R ( 1)) also the rate along the second route (decomposition), R (2 ). Because of the presence of a second reaction, consideration of the selectivity for carbon dioxide was essential [ 31. Selected experimental data are listed in Table 3. The values of the integral selectivity, Si, were calculated using the outlet concentrations of carbon dioxide ( Cco2 ) and ethene ( CCzHl) : 0.5 Cc02 si= (0.5 cco~+CCZHq)~lOO (%) In addition to the value of the selectivity of the inhibited catalyst, Si, that of the uninhibited catalyst, Sp, is also given for comparison. The selectivity of the inhibited catalyst for carbon dioxide increases with decrease in the inhibitor concentration and the contact time. The last correlation was also observed
48 TABLE 3 Experimental values of oxidation and decomposition rates and of the integral selectivity for a 1: 2 feed at 300 ’ C Exp. no. R(l): (mol/h*g cat.)
R(2); (mol/h*gcat.)
sj (%)
sp (%)
c DCE
1
3.95.1oP
2 3 4 5 6
7.54.10-s 9.73*1o-5 1.02.10-4 2.20.10-4 3.16*10-4
1.65.1O-5 2.64*10-5 3.45.10-5 2.58*10V5 2.44*10-5 2.38*1O-5
83.6 82.0 88.9 90.3 90.9 92.7
86.8 92.0 95.0 93.7 94.2 96.6
9.0 28.0 19.0 9.5 9.5 10.0
(h-g cat./mol)
(ppm) 945 473 315 236 189 158
with the uninhibited catalyst. Probably the second factor (contact time) is more important for the selectivity than is the presence of the inhibitor, judging from a comparison of the results of our previous work [ 31. In the absence of inhibitor the selectivity always remains higher, so obviously DCE lowers the selectivity for carbon dioxide. On comparing the values of the rates along the routes over the inhibited catalyst (Table 3) with those over the uninhibited catalyst [ 31, it is found that the decomposition rate undergoes an insignificant decrease in the presence of DCE unlike the oxidation rate. Therefore, it can be concluded that the decomposition rate of ethylene oxide is not influenced by DCE at the concentrations considered. The ethylene oxide oxidation rate, however, is influenced to a considerable extent by DCE. Its inhibition is the reason for the decrease in the selectivity for carbon dioxide. Nevertheless, the number of experiments in which both oxidation and decompostion have been observed is too small so it is not possible to draw categorical conclusions about the effect of DCE with respect to the decomposition rate of ethylene oxide. Kinetic model The previous model [3] was used again for the description of the experimental data. The presence of the inhibitor this time required a modification of the model, viz., the introduction in the numerator of an additional term, reflecting the decrease in ethylene oxide oxidation rate caused by the DCE: R(l)=
k, PO PEO -
k, po PEO P &x
( 1 + k,Po + k&i5 + &Pm + k7P,soPo”.5 >’
(10)
where pncn is the dichloroethane partial pressure. This rate equation is valid for the temperature range 250-300°C and inhibitor concentrations up to 30 ppm. If the DCE concentration is lower than 1 ppm then the previous model [ 3 ] should be used, which is valid for the same temperature range. The model corresponds to a mechanism in which oxygen and ethylene oxide
49
adsorption are fast steps at equilibrium. The oxidation proceeds in two stages, adsorbed formaldehyde being the intermediate, with the participation of both atomic and molecular adsorbed oxygen. These two steps are irreversible, slow and, therefore, rate-limiting [3]. Attempts to deduce a new kinetic model on the basis of the previous mechanism [3] by the addition of a new step, DCE adsorption, met insurmountable mathematical difficulties, because DCE adsorption does not lead to the formation of products (carbon dioxide and water ) , so the stoichiometric number of this step is zero. At the same time, DCE adsorption changes the balance equation of the concentrations of the surface intermediates, introducing a new unknown, viz., the adsorbed DCE concentration, [ ZC!,H,Cl,] . However, it is not possible to add a new equation to the already obtained system of equations, based on Temkin’s method [ 10 1, as the step’s stoichiometric number is zero. Hence the system of equations becomes indeterminate and it is impossible to derive expressions for the concentrations of the surface intermediates and to obtain a kinetic equation. The values of the kinetic constants of the model (10) were determined by a computer program, based on the algorithm of Nelder and Mead [ 111 (Table 4). The constants obey the Arrhenius law. The calculation procedure of Marquardt [ 121 was used to compute the 95% confidence intervals of the constants (Table 5 ) . The quantities in eqn. (10) are measured in the following units: [R(l)]
=mol/h*gcat.
I= [PEO I = [k,] =mol/h.g
~DCE
[Iz,] =mol/h*g
cat:atm3
[PO
I= atm
cat:atm’
[IQ] = [I+] = [k6] =atm-’ k3, k7 = dimensionless quantities TABLE 4 Values of pre-exponential factors, activation energies and kinetic constants at different reaction temperatures Pre-exponential factor (k,)
h k, k, k, k, k, k,
1.029*10-3 2.001*10-1 order with respect to 4.253*1O-5 4.585.10-4 3.001~10-1 2.000~10-’
E, kJ/mol 91.96 117.04 DCE 150.48 108.68 41.80 50.16
Kinetic constants 250°C
275°C
300°C
7.264.10-4 0.1284 0.60 7.518*10-5 6.919*10-4 0.3515 0.2419
1.907.10-3 0.4388 0.60 1.549.10-5 2.211*10-4 0.2267 0.1429
4.603.10-” 1.3466 0.60 3.665*10-’ 7.805.10-5 0.1519 0.08835
50 TABLE 5 95% Confidence intervals for pre-exponential factors, activation energies and reaction order with respect to dichloroethane Pre-exponential factor (k,)
Activation energy (kJ/mol)
Lower limit
Upper limit
Lower limit
9.760*10V4 0.1863 0.58
1.082*10-” 90.71 0.2139 114.95 0.62 (Reaction order with respect to DCE)
93.21 119.13
4.134.1o-5 4.420*10-4 0.2863 0.1874
4.372*1O-5 4.750*10-4 0.3139 0.2126
153.41 113.28 42.22 51.83
147.55 104.08 41.38 48.49
Upper limit
The construction of a kinetic model for the decomposition rate was not possible because of the small number of experiments in which it was detected. Also, all these experiments were carried out at the same temperature (300 ‘C ) . The average model deviation was 15.5%. Its adequacy is clearly illustrated in Figs. 1,2, 3 and 5 and Tables 1 and 2 - the quantities with a superscript m are the model values. The model describes reasonably well the dependence of the degree of conversion of ethylene oxide on temperature (Table 11,contact time (Fig. 1) , oxygen : ethylene oxide feed ratio (Fig. 2 ) and inhibitor concentration (Fig. 3). The model predicts oxidation rates fairly close to the experimentally measured values (Table 2, Fig. 5). It should be noted that for the series in which a rate maximum was observed experimentally, the model also predicts a maximum and at the same outlet oxygen partial pressure (Table 2 ) . The numerical analysis of the terms in the numerator of eqn. (10) indicates that the constant K, has a higher value than K,. In spite of this, the second term in the numerator of eqn. (lo), kg op EOp zcE, always has a lower value than the first term, &pOpEO. The reason for this is the much lower value of the dichloroethane partial pressure, pDCE = 10-5-10-6, than the values of p. andpno (ca. 10-l atm). All the kinetic constants of the model (10) have different values (different pre-exponential factors and activation energies) compared with the values of the respective constants in the kinetic model [ 31. Similar changes in the values of the constants in the presence of the inhibitor were ascertained in our previous work [ 21, juxtaposed with the constants determined earlier over the uninhibited catalyst [ 11. The explanation of this fact lies in the complex nature of the constants [ 31. Most of the kinetic constants are, in fact, expressions including rate and equilibrium constants of the different elementary steps [ 31. A change in the correlation between the rates of the different elementary steps,
52
ene oxide to ethene and oxygen proceeds in addition to the oxidation. Dichloroethane concentrations up to 30 ppm do not influence the ethylene oxide decomposition rate.
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