EPA-650/2-73-020
August 1973
ENVIRONMENTAL PROTECTION TECHNOLOGY SERIES
£
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I
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EPA-650/2-73-020
CATALYTIC OXIDATION
OF SULFUR DIOXIDE
USING ISOTOPIC TRACERS
by
John Happel and Miguel A. Hnatow
New York University
School of Engineering and Science
University Heights
New York, New York 10453
Grant Number R801321
(Formerly Grant No. AP-00714-04)
Program Element No. 1A2013
EPA Project Officer: D.K. Oestreich
i
Control Systems Laboratory
National Environmental Research Center
Research Triangle Park, N.C. 27711
Prepared for
OFFICE OF RESEARCH AND DEVELOPMENT
U.S. ENVIRONMENTAL PROTECTION AGENCY
WASHINGTON, D.C. 20460
August 1973
-------
This report has been reviewed by the Environmental Protection Agency and
approved for publication. Approval does not signify that the contents
necessarily reflect the views and policies of the Agency, nor does
mention of trade names or commercial products constitute endorsement
or recommendation for use.
11
-------
ABSTRACT
Since SO- is an important atmospheric pollutant the mechanism
of the oxidation of S0_ over a commercial vanadium pentoxide catalyst
was studied using an all glass, essentially gradientless reactor at
temperatures of 470-480°C and concentrations up to several percent of
S0_. It is expected that the results will have application both in
improving the design and operation of equipment in which SO is
oxidized to SO, and in suggesting new catalyst formulations.
A theoretical development was derived for the use of isotopic
tracers to study the kinetics and mechanism of complex catalytic
reactions. Relationships developed on the basis of steady state
conditions are combined with principles of thermodynamics and transi-
tion state theory. The methodology offers a unique tool for interpre-
tation of experimental data.
35
Data were obtained using radioactive S and the stable isotope
18
0 as tracers. It was shown that the employment of two tracers
simultaneously and the employment of more than one level of marking
while still maintaining a fixed overall reaction velocity were often
advantageous.
In the case of SO^ oxidation, it was shown that oxygen chemi-
sorption is the most important mechanistic step. However, as equili-
brium is approached, desorption of SO, assumes considerable importance
also.
These findings lead to the formulation of an improved rate equation,
especially accurate near equilibrium for sulfur dioxide conversion.
35
This is important in pollution abatement processing. The use of S
in developing improved catalysts is also suggested.
iii
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CONTENTS
Page
Abstract iii
List of Figures vi
List of Tables vi
Acknowledgements vii
Sections
I Conclusions 1
II Recommendations 3
III Introduction 5
IV Theory 7
V Experimental Results H
VI Improved Rate Equation 17
VII Discussion 19
VIII References 21
IX Publications 21
Appendix A—Oxygen Tagging 23
-------
FIGURES
No. Page
1 Velocity Ratios for S02 Oxidation 14
2 Sulfur Tracer Data 15
TABLES
No. Pagti
l ft
1 Tracer Data Using J-°0 12
2 Sulfur Tracer Data 16
i ft
A-l Tracer Data Using i00 31
vi
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ACKNOWLEDGEMENTS
Drs. Dale Denny and R. M. Bethea of the E.P.A. provided timely
guidance on many phases of this study during its progress, emphasizing
the importance of keeping attention focussed on relevant national
goals. We are also grateful for critical review and comments on the
final report by Drs. D. K. Oestreich and Wade Ponder of the same
organization.
Our doctoral students A. Rodriguez, P. Rosche, and R. M. Csuha
helped with the long range approach to problems involved.
Finally, the Japanese scientists H. Odanaka and S. Oki provided
mature and stimulating guidance and advice during their association
with this project. Their help in experimental techniques was
invaluable.
vii
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SECTION I
CONCLUSIONS
Oxygen chemisorption is the most important mechanistic step in the
catalytic oxidation of sulfur dioxide over vanadium pentoxide based
catalyst.
Sulfur trioxide desorption rate is next in importance in control
of the rate of oxidation of sulfur dioxide after oxygen chemisorption.
Hear equilibrium, it assumes almost the same importance as oxygen
chemisorption.
The adsorption of sulfur dioxide and the chemical reaction between
adsorbed sulfur dioxide and adsorbed oxygen both appear to be rapid steps,
approaching equilibrium even at very low concentrations of S02 in the
ambient gas.
Convenient rate equations for the speed of the overall conversion
reaction may be developed on the basis of the previous findings. These
should be useful in the design of both sulfuric acid plants and catalytic
systems to remove S02 from stack gases.
In the case of sulfuric acid plants, the rate equation developed
will enable assessment of the value of such processes as double adsorp-
tion of sulfur trioxide to increase overall sulfur dioxide conversion.
In both sulfuric acid plants and stack gas converters a more
accurate prediction of catalyst requirement is possible for operation
very close to equilibrium.
With the mechanistic information available the use of S affords
a convenient technique for evaluation of potential catalysts to
determine their usefulness very close to equilibrium.
-------
SECTION II
RECOMMENDATIONS
This program was limited to laboratory study and development of
basic principles. It was not within the scope of the program to study
the economics of improved designs of sulfuric acid plants based on
optimizing procedures. Neither was it possible to evaluate various
available catalysts thought to be promising in air pollution applications,
It is recommended that both these programs be carried forward.
Designs of sulfuric acid plants very often employ rate equations
which are not based on realistic information of reaction rates close
to equilibrium. Since a very large proportion of the total catalyst
volume in a reaction system is devoted to conversions of sulfur dioxide
above the 95 percent level, it is apparent that sophisticated computa-
tional techniques must be supplemented by reliable assessment of catalyst
behavior close to equilibrium. Tracer studies, such as are reported
here, permit data of the required accuracy to be obtained. Available
computer optimization studies should be reevaluated in the light of
the information presented here.
As regards catalyst development, a number of ideas and new catalysts
are available, but very little information is known about their perform-
ance close to equilibrium. Such data are of primary importance in
minimizing atmospheric pollution. I Thus a program of catalyst evaluation
based on the tracer techniques developed here should be invaluable in
selecting and formulating catalysts especially designed for high
efficiency close to equilibrium.
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SECTION III
INTRODUCTION
The employment of isotopes has been shown to be useful in the
study of heterogeneous catalytic systems. Previous investigations
have been confined, however, to situations in which a single rate
controlling step is assumed to govern the mechanism which is followed
in a complex reaction system. This procedure has shortcomings because
it does not assess the relative importance of other significant factors
which may be involved. The purpose of the present study was to explore
the application of tracer techniques to define the important character-
istics of the sulfur dioxide oxidation reaction. The study was limited
to a commercial vanadium pentoxide based catalyst since this type is
almost universally employed in commercial systems.
The first phase of the present study involved the application of
S as a tracer^ to determine the possibility of the existence of more
than a single rate controlling step. In this study it was found that
steps involving sulfur account for some of the elementary reactions which
are important in determining the overall reaction rate but that oxygen
chemisorption appears to exert the major influence. Studies were there-
fore extended using ^°0 as a tracer-* in order to more reliably determine
the influence of oxygen on the mechanism. From these studies it was
possible to determine which of the steps in the reaction mechanism
involving sulfur was responsible for influencing the overall reaction
rate. The use of 180 is more complicated than the use of 35S because
oxygen is present in all the terminal species involved. Therefore
pertinent new theoretical development was necessary to interpret the
data obtained.
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SECTION IV
THEORY
Results of these studies are interpreted on the basis of the
following schematic representation for the mechanism of the overall
reaction written as:
2 S02 + 02 t 2 S03 (1)
for modeling the system:
Stoichiometric
Step No. Elementary reaction No. , v _
0, + 2l *. - 2 0£
2
S0 +
f\ ' ** - - ^^^^^ LJ\S ryf* fy
v-2 (2)
v-3
v-4
The Stoichiometric number (v) is defined as the number of times that
each elementary step occurs for a single occurrence of the overall
reaction as vnritten. H represents an active site associated with the
catalyst. 0&, S09i, and SO £ represent species obtained by reaction of
the gaseous reactants and products with the catalyst, v.. represents
velocities of individual mechanistic steps i = 1,2,3,4. ~
-------
This system may be exhibited in schematic form as:
(3)
One relationship between the velocities involved may be obtained
from thermodynamics and transition state theory as discussed by Csuha
and Happel. For each individual step in Equation (2) the following
relationship may be written:
Ag. = - RT
where Ag is the Gibbs free energy for a single mechanistic step, R is
the universal gas constant, and T is the absolute temperature. The total
Gibbs free energy change AG for the complete reaction is the sum of the
free energies for all elementary steps multiplied by the stoichiometric
number of each step;
AG = Ag-j^ + 2 Ag2 + 2 Ag3 + 2 Ag4 (5)
Hence, combining Equations (4) and (5), we may write:
/V+l\/V+2 V+3 V+4V
= ( \[ A
\*_l/\V-2 V-3 V-4/
Exp (- AG/RT) =
. . (g)
The squared term appears for the v.*' V+V an^ v-t-& velocities because
the stoichiometric number for these steps is 2.
For the catalytic oxidation of sulfur dioxide the Gibbs free energy
change is:
-------
AG
RT Jin
•SO.
Pso2 po2Kp
(7)
Kp is the equilibrium constant; and pgo , pgo , and pQ are the partial
pressures of the species involved. In the non-ideal case the partial
pressures would be replaced by the partial fugacities.
35 2
S data enables the velocity ratio in the sulfur path to be
determined. The sulfur path represents velocities of atomic sulfur
transfer in the forward V 2,3,4 and backward V 2»3»4 directions (see
Equation (3)). It is related to the individual step velocities by the
equation;
V
2,3,4
2,3,4
v+2 v+3 v+4
V-2 v-3 V-4
(8)
By using Equations (6) and (8) it is thus possible to determine
the velocity ratio v -/v_, for given reaction conditions.
The transfer of oxygen is more complicated and requires two levels
of marking with oxygen for the determination of:
V
1,3,4
V
1,3,4
V+3 V+4
-l V-3' V-4
(9)
However, in this case it is possible to determine v+,/v_, as well.
Sufficient information is then available to solve also for vj.o^v-2
v ,,/v „ so that estimates are available for velocity ratios of all
steps of the model.
-------
It is often convenient to report the values obtained in terms of
the apparent stoichiometric number. If the tracer follows the rate
controlling step or steps, the apparent stoichiometric number will
correspond to the true stoichiometric number of the step or steps
involved. Thus if the rate controlling steps were in the sulfur path,
v,,/v_, = 1 because oxygen chemisorption would be at equilibrium. Then
from Equation (6), we would have:
2 = - AG/RT
V V V
** +3
In general, if the ratio in Equation (10) were not equal to 2, it would
still be possible to compute an apparent stoichiometric number which
would indicate the departure of the system from rate control by steps
in the sulfur path. When 35s is used as a tracer to follow the atomic
velocity of sulfur in the path through steps 2, 3, and 4 in Equation
(2), the apparent stoichiometric number can be expressed as:
- AG/RT
S = y 2,3,4
in +
v 2,3,4 (11)
The value - AG/RT can be computed from Equation (7), while the ratio
V 2>3>Vv_2,3,4 is available from the 35g tracer data. A value of
vc = 2 indicates that either step 2,3, or 4 in Equation (2) is rate
O
controlling. On the other hand, a value of vs> 2 is evidence that
oxygen chemisorption exerts an effect on the overall rate. Similar
relationships are possible using 18o as a tracer, but then two apparent
stoichiometric numbers are obtainable: oxygen can follow either steps
2,3, and 4 like sulfur, or steps 1,3, and 4.
10
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SECTION V
EXPERIMENTAL RESULTS
A recirculating reactor is used in this study to minimize
diffusional and temperature gradients exterior to the particles. A
2
full description of the eruipment is given elsewhere. Feed and prc
gases are analyzed by gas chromatographic techniques. *
35
Sulfur dioxide tagged with S and sulfur dioxide and oxygen
tagged with ^0 were obtained from New England Nuclear Corp. A Model
Unilux II (Nuclear Chicago Corp.) scintillation counter was used to
analyze for 35S. 180 content of SO- and 0. was determined by a Type
21-103C mass spectrometer (Consolidated).
18
A special technique was used to determine the degree of 0
tagging in sulfur trioxide. Sulfur trioxide and sulfur dioxide were
condensed from the effluent in an acetone dry-ice bath and the mixture
was subsequently cracked at 1000°C in a platinum catalyst reactor. The
S02 and 02 produced were analyzed for ^°0 by mass spectrometer. The
1 o
-L00 content of the SO was then calculated by performing a mass balance.
The catalyst employed was a commercial vanadium pentoxide based
catalyst (typical analysis V20_ — 9.1 wt %; K-O — 10.1 wt %) supplied
by American Cyanamid Co. Catalyst pellets were crushed and screened
2
to a size range of 0.35 - 0.71 mm. Data obtained previously indicated
that diffusional effects are not important under the present experi-
mental conditions.
Table 1 summarizes data for several different reaction conditions,
1R ^ 7
all at temperatures of 470-480°C using °0 as a tracer. ' About 80
percent N9 was employed as a diluent in these experiments. The partial
pressure of SO- was maintained at a low value of 0.003 - 0.005 atm and
11
-------
Table 1. TRACER DATA USING 18O
Run
No.
4
7
11
12
13
14
15
16
16a
23
24
23a
24a
25a
. V1 Q
(y /V ) ' '
4.453
4.453
2.138
2.138
6.785
6.785
3.52
3.52
3.742
24. 838
24.838
24. 156
13. 568
1.570
4 (V/V )2''
"T* ™*
1.431
1.431
1.356
1.356
1.545
1.545
1.303
1.303
1.520
1.469
1.469
1.392
1.327
1.276
J>4 v+iA-i
4.604
4.095
1.860
2.624
5,090
3.843
4.65
3.439
3.840
15. 575
7.431
17.353
9.116
1.896
v+ 2/v-2
1.479
1.316
1.179
1.664
1.159
0.875
1.721
1.273
1.560
0.921
0.440
1.000
0.891
1.181
v+3/v-3
0.585
0.938
0.963
0.668
1.093
0.943
0.584
0.914
0.806
1.130
2.292
1.020
1.283
0.853
(v+2/v-2)
v+4/v-4 (v+3/v-3) exp(-AG/RT)
1.653
1.160
1.194
1.221
1.220
1. 872
1.297
1.119
1.208
1.411
1.4.58.
1.365
1.160
1.271
0.866
1.245
1.135
1.111
1.267
0.826
1.004
1.164
1.258
1.041
1. 00.8
1.020
1.143
1. 0035
9.425
8.384
3.418
4.823
12.155
9.177
7.891
5.837
5.837
33. 630
16.045
33. 630
16. 045
2.357
3 OR
a Using JOS data.
-------
equilibrium was approached essentially by employment of different
partial pressures of 0? and SO .
Figure 1 presents the same information in a plot of velocity ratios.
Details of the original data and calculation procedure are given in
Appendix A. The velocity ratios for steps 2 and 3 are combined as the
product (v_j_2/v-2^ ^V+3^V-3^ ^ecause tneir individual determination is
less accurate than (v, ,/v,). For a step or combination of steps at
equilibrium the velocity ratio will be equal to unity. From examination
of Figure 1, it appears that steps 2 and 3 are close to equilibrium.
In step 4, SO- desorption is a factor in determination of the overall
rate, especially close to equilibrium for the overall reaction. Oxygen
chemisorption is always the slowest step and farthest from equilibrium.
18
Since the 0 tracer experiments indicate that steps 2 and 3 are
35
at equilibrium, the use of S permits the direct determination of the
velocity ratio v ./v.. This constitutes a considerable simplification
35
in the experimental procedure since S data are reasonably easy to
acquire.
Figure 2 is a plot of apparent stoichiometric numbers obtained
35
using S. Data are tabulated in Table 2. Further details are in
references (2) and (7). Although there is some scatter in the data,
it appears that near equilibrium for the overall reaction, at the lowest
partial pressure ratios of p /p , the apparent stoichiometric number
ol/2 W2
in the sulfur path corresponds to Vc = 3.38 + 0.21. Since the apparent
O """"
stoichiometric number is greater than 2, both S0_ desorption and 0^
chemisorption are not at equilibrium and affect the overall reaction
rate. The next section shows how this information can be employed to
develop an improved rate expression for conditions approaching equili-
brium for the overall reaction.
13
-------
1.5 2 2.5 3 4 5 6 7 8 9 10
20 25
Figure 1. Velocity ratios for S02 oxidation.
14
-------
0.3
O
Qu
Q-
cf
cc
UJ
oe
=3
oo
v>
LU
tr.
a.
0.2
0.1
NOTE: THE OVERALL REACTIONS
0.0
4 6
APPARENT STOICHIOMETRIC NUMBER, us
Figure 2. Sulfur tracer data.
15
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Table 2. SULFUR TRACER DATA
Run No.
4-1
4-2
5-1
5-2
6
9-2
10-1
10-2
12-1
12-2
13
14-1
14-2
15-1
15-2
16
17-1
19-1
19-2
20
PSO
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
2/P°2
250
246
122
126
065
336
255
270
165
174
087
071
071
077
Oil
340
335
0208
0208
0066
-A
8.
8.
5.
5.
3.
10.
7.
7.
5.
5.
3.
3.
3.
3.
3.
9.
8.
2.
2.
G/RT °
12
00
12
22
58
18
56
90
58
76
58
60
56
26
24
60
94
92
92
Vv.
3
3
2
2
3
4
3
3
3
2
2
2
2
2
2
3
3
2
2
>s'3'4
.22
.16
.78
.64
.06
.40
.56
.52
.37
.84
.03
.16
.38
.32
.24
.73
.58
.35
.18
-
»
6.
6.
5.
5.
3.
6.
5.
6.
4.
5.
5.
4.
4.
3.
4.
7.
7.
3.
3.
3.
s
94
96
00
38
12
88
94
28
58
50
04
64
10
88
02
28
02
42
74
30
16
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SECTION VI
IMPROVED RATE EQUATION
It is possible to derive a rate equation which is applicable to
near equilibrium conditions by making use of this information. Since
Equations (2) and (3) are at equilibrium, and therefore v ,2/v o = v+*
we may write:
•»
=1>
-1
1.3.4
But from Equation (6) we have:
exp ( - AG/RT) =
Now as previously noted (see Equation (11)):
v+4
[_V-4_
v+4
7-4^
- AG. v
exp
v
(12)
(13)
(14)
'S "~ -4
Substituting values from Equations (12) and (14) into (13), we obtain:
v *••*•*
+
vl,3,4
AG "
RT
* ^
1 '
\
(15)
Using the relationship V = V+1>3'4 - V_ >3' , we obtain the rate
expression:
V - V/'3'*
(16)
17
-------
Since the potential term influences behavior only near equilibrium,
it is probably a good approximation to employ the limiting form of the
exponent (v -l)/v in Equation (16). More accurate representations
O O
would be possible, if desired.
The forward velocity V
1,3,4
could be established by experimenta-
tion far from equilibrium, which is usually the case for studies reported
in the literature. A suitable form of forward reaction velocity based
Q
on a careful experimental study is given by Simecek et al. If this
is incorporated into Equation (12), together with the results we have
obtained to assign the value (v -l)/v = 0.704, the resulting rate
D O
equation is:
k K p
SO,
V =
2
1 [ PS°3 ^
VL ?« K i
^so2 ro2 p
0.704'
(17)
Since the data of Simecek et al. were obtained with a different vanadium
pentoxide catalyst than that employed in this study, values should not be
assigned to the constants k and K. Use of the exponent 0.704, however,
does substantially improve the agreement of the correlation of Simecek's
data near equilibrium using Equation (17). We 4id not have the oppor-
tunity to develop the appropriate constants for the Cyanamid catalyst
because the present investigation was terminated due to more pressing
goals.
The basic procedure is straightforward and it seems clear that
the employment of Equation (12) should effect substantial improvement
in the correlation of sulfur dioxide oxidation data.
18
-------
SECTION VII
DISCUSSION
Rate Equation (13) represents a new approach to the development
35
of kinetic relationships i^ear equilibrium. By using S data it is
possible to independently assess the importance of the sulfur trioxide
desorption step close to equilibrium. Previous relationships have all
been based on the assumption that one step is rate controlling, either
a step in the sulfur path or more frequently oxygen chemisorptioh.
Aside from the development of an improved rate expression, the
35
use of S should constitute a sensitive method for catalyst evalua-
tion near equilibrium. It is possible that an improved catalyst formu-
lation will be possible by this more discriminating experimental
procedure which enables the relative importance of oxygen chemisorption
and SO. desorption to be estimated.
19
-------
SECTION VIII
REFERENCES
1. Happel, J., Catalysis Reviews,6, 221 (1972).
2. Happel, J., H. Odanaka, and P. Rosche, Chem. Eng. Progr..
Symp. Ser. No. 115, 67, 60 (1971).
3. Happel, J., M. A. Hnatow, A. Rodriguez, and S. Oki, AIChE
Synp. Ser. No. 126, 68, 155 (1972).
4. Csuha, R. S., and J. Happel, AIChE Jl. 17. 927 (1971).
t
5. Bond, R. L., W. J. Mullin, and F. J. Pinchin, Chem. Ind.
(London), Nov 30, 1963, p. 1902.
6. Obermiller, E. L., and G. 0. Charlier, J. Gas Chromatog. 6,
446 (1968).
7. Rodriguez, A., D.Ch.E. Thesis, New York University (1973).
8. Simecek, A., B. Kadlec, and J. Michalek, J. Catalysis, 14,
287 (1969).
SECTION IX
PUBLICATIONS
References 2, 3, and 4 were published directly as a result of
the project.
21
-------
APPENDIX A
OXYGEN TAGGING
Table A-l summarizes the calculated data plotted in Figure 1. In
this table the tracer data are as reported in terms of a notation given
^
by Csuha and Happel:
net rate at which tagged atoms of e
leave a reactant or enter a product
species (gm atoms per hour per gm
»of catalyst) ,
Clumber of atoms "I
jf e in a molecule!
jf species d J
coefficient of the species
d in the chemical equation
of the overall reaction
z = fraction of tagged atoms e in species d
i
The following discussion gives details of the method of calculation
to obtain the results presented in Table 1 of the main body of the report
for oxygen tracing.
0 SO
(t_ 2, t- 2, and tn
that:
There are three tagged atomic velocities for oxygen
SO
3 ), which are restricted by stoichiometry such
«
SO,
(A-l)
Here the subscript 0 denotes atomic oxygen. The tagged atomic
velocities t may be derived by material balances as:
(A-2)
SO
SO
(Z
SO, A
V-2)/2
(A-4)
23
-------
t S°2 = (z v - z v )/2
C0 U0 Z +3 0 J v-3''
SO, , SOJ.
3 = (ZQ 3
SO
. . ..
3 v_4)/2
(A-5)
(A-6)
Since it is not possible to measure the concentrations of isotopic
surface fractions on the catalyst, they must be eliminated. Substitu-
OJl SO &
tion of values for ZQ and zn 3 from Equations (A-2) and (A-6)
yields the relationship:
-o
z S°3 = z °
Z0 3 Z0
-l V-3 V-4
trr'o2
v_4/
2 V, , v+3
T
V -V V ,V V .
-3 -4 -1 -3 -4
(A-7)
Similarly, elimination of the isotopic surface fractions from Equations
(A-3), (A-5), and (A-6) yields the expression:
, SO. SO.
ZQ 3 = zQ 2
V+2 V+3
v-2 V-3 V-4
2 v+4 | 2
1 4
'
(A-8)
From previous studies, ' the following relationships are
available for the combined path velocities in terms of individual
steps:
V 1'3'4 v v V
1,3,4
(A-9)
V ''
v-2 v-3 V-4
(A-10)
24
-------
134 = v"+vv +vvv (A~11)
2 2 v+4 2
2,3,4
Using these relationships, Equations (A-7) and (A-8) may be expressed
as:
1,3,4
(to 2 . to
SO SO, |V.2'3'4\ t.S02 2
2 _i - ^__ (t so2 so3)
The velocity in a path is related to the overall velocity by:
V = V 2'3'4 - V_2'3'4 = V lj3'4 - V_1>3'4 (A-15)
Use of this relationship gives:
V 1'3'4
+
1 1 /.
n n IT ^0
t_ 2 - V z_ 2 ) = t_ 2 - V zn 3 + 2V
0 \j \) U ^^
tr \.^*
n 2 - t
SO
•ft
v -
(t0 2 - V Zo 2) - t02 - V
25
-------
The overall velocity of a complex chemical reaction can also be
represented in terms of the forward and backward velocities of the
steps in the mechanism as:
V = (v+± - v_±)/vi (A-18)
Thus for step 4:
V - (v^. - v ,)/v. = (V., - v ,)/2 (A-19)
v +4 -4 4+4-4
This equation can be rewritten as:
2V = V+4 -i
V-4 V-4 (A-20)
By use of Equations (A-20) and (A-l), Equations (A-16) and (A-17) can
be further simplified to obtain:
• ' - + °
0 - *0 - (t 2 -
v+2,3,4
, . , (to 2"v zo 2) = fco 2"v zo 3 -£i-Jti A /t o? . so
v 2'3'4 \3 7T J( o 2 co 2)
v_ \ v-4 /
(A-22)
If Equation (A-22) is multiplied by 2 and subtracted from (A-21), the
following relationship is obtained:
26
-------
J^_ (t0 °2 -V z0°2) + 2
v 1»3,4 v 2,3,4
(t0 °2 -V z0°2) + 2 V (t S02 - V Z()S02) - 2 t()S02 + tQ02 -3 V
(A-23)
Now, since Equation (A-23) has two unknown quantities — (V ,/V )^>3>^
and (V /V )2»3,4 — experiments with two levels of marking at a given
overall V using 18 Q as a tracer will establish the values of these
velocity ratios. Once they are obtained, substitution into Equation
(A-21) or (A-22) will provide a value for v A/V_, .
The following equation appears as Equation (6) in the main body of
the report:
Exp - AG
RT
,v v v , 2
+1\ / +2 +3 +4\
— J ( 1 (A-24)
_J \v_2 v_3 v_4;
From Equations (A-10) and (A-24), the relationship to calculate
v,,/v 1is obtained:
T+l » RT
2,3,4 A2 (A-25)
V
T Q /
From previously computed values of (v+./v_^) and (V+/V_)*• >J' *, and
Equation (A-9), the value of (v+3/v_3) may be computed as:
27
-------
v 1,3,4
(A-26)
V-3 ,v,_, v,
Finally, from the previourly calculated values and Equation (A-10) ,
v 7/v _ is obtained:
V+2'3'4
y_2.3.4
=
(A-27)
As an example of the application of this procedure, consider the
data from runs 23 and 24 in Table A-l. In order to solve Equation
(A-23), we will first compute the following coefficients from run 23:
tQ °2 - V ZQ °2 - (1.3828 - 12.292 (0.10687)) x 10~4
= 0.06914 x 10~4
en en _A
tQ 2 - V ZQ 2 =(- 0.15167 - 12.292 (0.012459)) x 10
= -0.30481 x 10"4
tin n qo _A
2 tfl 2 + tQ 2 - 3V ZQ 3 = (2(-0.15167) + 1.3828 - 3(12.292) (0.006998))xlO
= 0.82142 x 10"4
Upon substitution of these values into Equation (A-23), we obtain:
~ (V+/V_)1>3'4 + 8.8177 (V+/V_)2'3*4 =-11.8812 (A-28)
28
-------
A similar computation of the data in Table A-l for run 24, under
overall velocity conditions similar to run 23, gives the following,
upon substitution into Equation (A-23) :
- CV./V )1'3'4 + 78.9419 (V./V )2'3'4 = 91.1601 (A-29)
T ~ T —
Simultaneous solution of Equations (A-28) and (A-29) gives the
following values of the overall velocity ratios :
(V./V )2»3'4 = 1.4694-
-J. — .
(V+/VJ1*3*4 = 24.8380
The overall velocity ratios are used to calculate v ,/v using
Equation (A-25). Thus for run 23:
33.63
(1. 4694)2
For run 23, v+,/v , may be calculated by Equation (A-22), using
the following values of coefficients:
tQ S°2 - V ZQ S°2 = (-0.15167 - 12.2918 (0.012459)) x 10~4
= - 0.30481 x 10~4
tQ S02 - V Z()S03 = (- 0.15167 - 12.2918 (0.006998)) x 10~4
= - 0.23779 x 10"4
o «>n -4
tQ 2 - tfl 2 = (1.3828 + 0.15167) x 10
• 1.5345 x 10"4
and v+,/v_, = 1.4110
29
-------
The velocity ratio for step 3 will be:
. -- 24.838
V+3/V-3 " -- - -"1.1302
(V44/V 4) (15.575) (1.4110)
Finally the velocity ratio for step 2 is:
(V+/V_)2'3'4 1.4694
v+2/v-2 = = • 0.9214
(v+3/v_3) (v^/v_4) (1.1302) (1.4110)
Note that additional values for runs 23 and 24 appear in Table A-l
based on values for (V /V )2»3'^ using 35S tracing simultaneously with
1 o
A00 tracing. In this case it is only necessary to substitute the value
of (V+/V^)2>3»4 into Equation (A-23) and solve directly for (V+/V )1»3'
Two simultaneous equations are not required as in the case of
tracing alone.
30
-------
Table A-l. TRACER DATA USING 180
u>
Run No.
Wt of catalyst, grams
Reaction press., atm
Reaction temp, °C
PN2, atm
°2, atm
^5 »• T f\ £
*S02 x -LU , atm
S(>3 / atm
Pso2/po2
V x 103, g mol/ g cat. hr
t°2 x 104
S02 4
t x 10
SOq 4
t 3 X KT
0
Oo 9
zo x 10
SO? 2
ZQ X 102
zs°3 x io2
0
K x IO"3, atm""1
-AG/RT
exp{-AG/RT)
2
0.3956
1.0496
472
0.8258
0.1773
2.6220
0.0203
0.148
10.49
1.6165
14.1262
9.9561
3.649
3.178
3.849
8.20
7.795
2424
0
1
0
0
2
0
0
14
7
-0
2
4
0
1
9
3
.3956
.0870
470
.8152
.2300
.3180
.0186
.101
.598
.2388
.2043
.3007
.495
.270
.508
.00
8.078
3219
0
1
0
0
0
0
0
1
-0
1
0
0
1
4
.7941
.0632
472
.8177
.2001
.3195
.0422
.016
.476
.1951
.4980
.9636
.235
.738
0.613
8.23
2.245
9.425
7
0 . 7941
1.0490
476
0.8233
0.1806
0.3418
0.0417
O.~019
2.580
0.0514
1.2854
0.8782
0.448
1.880
0.797
6.90
2.103
8.384
0
1
0
0
0
0
0
2
0
1
8
. 7941.
.0534
474
.9097
.0977
.5682
.0403
.058
.381
.0678
.5512
1.0567
0,
4,
.644
.524
1.709
7.55
2.687
14.684
9
0.7941
1.0647
476
0.9160
0.0444
8.3003
0.0213
1.871
6.641
-1.9694
3.8679
1.9220
0.572
3.084
1.437
6.90
8.450
4.641 i;
10
0.7941
1.0647
478
0.9240
0.0388
7.0434
0.0315
1.818
8.864
11.450
3.782
6.344
12.960
2.819
3.050
6.30
7.130
>4ft t;
11
0.7941
1.0440
476
0.9451
0.0585
0.3474
0.0369
0.059
1.152
1.0423
-0.0318
0.3262
4.321
0.481
0.148
6.90
1.228
•a A-\ Q
-------
Table A-l (continued). TRACER DATA USING 180
w
to
Run No.
Wt of catalyst, grams
Reaction press., atm
Reaction temp, °C
?N2, atm
°2, atm
D v^ n r\ £1 t
*S02 X ' atm
PS03, atm
?S02/P02
V x 103, g mol/ g cat. hr
t°2 x 104
tS°2 x 104
0
tS°3 x 104
Z X 10
so 9 , •>
Z Z x 10^
0
zs°3 x io2
0
K x 10~3, atm"1
-AG/RT
exp(-AG/RT)
12
0.7941
1.0440
480
0.9408
0.0620
0.4295
0.0373
0.069
1.152
1.0584
0.7024
0.8164
4.850
2.039
0.369
5.75
1.572
4.823
0
1
1
0
0
0
0
1
4
-0
1
26
1
1
7
13
.7941
.0750
475
.0377
.0183
.4410
.0145
.241
.434
.4787
.3479
.3081
.088
.578
.298
.20
2.495
12.155
0
1
1
0
0
0
0
1
-0
1
0
0
1
1
7
14
.7941
.0750
475
.0354
.0192
.4535
.0158
.236
.828
.0927
.5953
.9069
.492
.929
.010
.20
2.205
9.177
15
0.7494
1.0603
477
1.0170
0.0215
0.4139
0.0175
0.193
1.984
-0.1100
1.8090
1.1694
0.421
2.123
0.963
6.60
2.064
7.891
0
1
1
0
0
0
0
1
4
-0
2
17
1
1
5
16
. 7494/
.0603
480
.0152
.0222
.4026
.0189
.182
.639
.0981
.2951
.4315
.837
.854
.893
.78
1.765
5.837
17
0.7494
1.0645
478
0.9657
0.0595
0.2340
0.0369
0.039
1.651
2.7536
0.1522
1.0193
13.013
1.427
0.673
6.30
0.410
1.507
18
0.7494
1.0633
478
0.9521
0.0684
0.3328
'0.0395
0.049
1.503
-0.00921
0.7842
0.5205
0.263
3.540
0.348
6.30
1.120
3.061
19
0.7494
1.0633
479
0.9552
0.0657
0.3474
0.0389
0.053
1.339
-a 0721
0.3792
0.2288
0.284
2.732
0.405
6.05
1.154
3.171
-------
Tatole A-X Ccontinued). TRACER DATA USING
18,
0
U)
Run No.
Wt of catalyst, grams
Reaction press., atm
Reaction temp, °C
PN2, atm
p
°2, atm
o v«* i r\ ** »
fgQ2 X O.U , atm.
PSO3, atm
P /p
S02/F02
V x 103 , g mol/ g cat. hr
t°2 x IO4
S02 4
SOo 4
t(J 3 x IO4
Z°2 x IO2
zs°2 x io2
0.
1.
1.
0.
0.
0.
0.
1.
2.
-0.
0.
23.
2.
20
7494
0453
481
0125
0110
5416
0164
492
240
5030
7423
3395
838
977
0.
1.
1.
0.
0.
0.
0.
1.
0.
4.
3.
0.
4.
21
7494
0466
479
0051
0203
5628
0156
278
708
0330
5087
0168
356
776
0.
1.
1.
0.
0.
0.
0.
1.
1.
-0.
0.
22.
2.
22
7494
0453
481
0127
0108
5229
0166
487
127
8903
6244
1936
928
787
0
1
1
0
0
0
0
1
1
-0
0
10
1
23
.7505
.0549
477
.0147
.0223
.579
.0121
.260
.229
.3828
.1517
.3598
.687
.246
0.
1.
1.
0.
0.
0.
0.
1.
0.
1.
1.
0.
3,
24
7505
0558
477
0160
0216
456
0136
211
458
0135
8373
2294
313
912
25
0.7502
1.0612
478
1.0239
0.0239
0.1505
0.0120
0.063
0.218
0.9696
-0.1889
0.1973
10.406
2.370
zs°3 x io2
0
0.523
2.712
0.395
0.700
1.742
0.606
K x 10~3, atm"1
-&G/RT
exp(-AG/RT)
5.55
1.896
6.673
6.05
2.774
16.010
5.55
1.782
5.940
6.60
3.513
33.63
6.60
2.775
16.045
6.30
0.857
2.357
-------
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-------
BIBLIOGRAPHIC DATA
SHEET
1. Report No?
EPA-650/2-73-020
3. Recipient's Accession No.
5. Report Date
August 1973 '
4. Title and Subtitle
Catalytic Oxidation of Sulfur Dioxide Using Isotopic Tracers
6.
7. Author(s)
John Happel and Miguel A. Hnatow
8. Performing Organization Rept.
No.
9. Performing Organization Name and Address
New York University
School of Engineering and Science
University Heights
New York, New York 10453
10. Project/Task/Work Unit No.
11. Contract/Gram No.
R801321
(formerly AP-00714-04)
12. Sponsoring Organization Name and Address
EPA, Office of Research and Development
NERC-RTP, Control Systems Laboratory
Research Triangle Park, North Carolina 27711
13. Type of Report & Period
Coveted
Final
14.
IS. Supplementary Notes
16. Abstracts The report gives results of a study of the oxidation of S02 over a commercial
vanadium pentoxide catalyst, using an all-glass, essentially gradientless reactor at
470-480°C and at concentrations up to several percent of S02. A theoretical develop-
ment was derived for the use of isotopic tracers to study the kinetics and mechanism of
complex catalytic reactions. Relationships developed on the basis of steady state con-
ditions are combined with principles of thermodynamics and transition state theory.
Data were obtained using radioactive sulfur 35 and the stable isotope oxygen 18 as tra-
cers. The employment of two tracers simultaneously and the employment of more than one
level of marking while still maintaining a fixed overall reaction velocity were often
advantageous. Oxygen chemisorption was found to be the most important mechanistic step
in S02 oxidation. However, as equilibrium is approached, desorption of SOS also assume
considerable importance. These findings led to the formulation of an improved rate
equation, especially accurate near equilibrium for S02 conversion. The use of sulfur 35
17. Key words and Document Analysis.
Air Pollution
Sulfur Dioxide
Oxidation
Vanadium Oxides
Catalysts
Kinetics
Chemisorption
Sulfur Isotopes
Oxygen Isotopes
17b. Identifiers/Open-Ended Terms
Air Pollution Control
Stationary Sources
Isotopic Tracers
Sulfur 35
Oxygen 18
Rate Equations
17c- COSATI Field/Gtoup
Pescriptors
07D, 13B
18. Availability Statement
Unlimited
19.. Security Class (This
Report)
UNCLASSIFIED
20. Security Class (This
Page
UNCLASSIFIED
21. No. of Pages
41
22. Price
FORM NTIS-3S (REV. 3-72)
34
USCOMM-DC 149B2-P72
------- |