
  
aurf.y conceqtautiou of adearbed A and B~molecules/ umt cat.dytlc srsa concentautim of o?LDILnt saaorption sites, equivalent molea/unit maas of catslyst ooncmtaution of vacant dnorptim sites/unit area
I
r'
2


rawtion rata, molea/unit of catslyat/unit time reaction rate, exkmd difhmion @enta average hyhulic radius of catalynt pores arslswconatant
actin
O V 0 F d Mk COUBtWlta
mean molal heat capaoity of fluid atrerun dective average diametez of catalyst particles for Thiele modulus 6/A+* dective average dinmeter of catalyst particles for Reynolds number &ient of difhrsion dectiveneaa factor d W o d correction factor (Equation 63) reactor feed rata, moles/unit time = maas velocity/unit tctsl mxa section standard fmdwqy change Plan& constant AHA heat of reaction uw mole of A AH' standard enthalpy chAE" OWall standard enthalpp change AH% atandard enthdm of s c t m t i r m k, k' k

forward abd meme reactionvelocity constante Boltamannconatant h eta. adsorption and desorption velocity constante of commnent A 4 therm& conductivitvof fluid K overall fluidphase k c t i o n equilibrium constant R' surface &ion equilibrium oonstant KA.Ke,&etol+rption equilibrium conatants of eomponeots
L L' 0)
2 PA
PA'
Pd

AandB
total molal h r p t i o n sitea/unit nuw of catalyst totalactivecenterspunitsrsaofaurface Thielemodulua a m molecular weight of reaatm feed Avopdronnmber psrtral ~RLWJE of component A in main fluid stream p m of component A at = OgmeaUOf(*  PA) and (w PAC
 p""

8
as'
as!
8.
ZA @A, 0s
e, P
p PB
po
.
p~
p,

componentS standard entropy caange entropy of actnration qacevelocity moles of A aonverted/mole of reactor feed fraction of total sitea occupied by adsorbed A a n d B molecules fraction of total adsorption sites unoccupied
~osity densit offluid bulL of catalyst trued& ofcatalyticnolid d&ty o f 7 4 at standard conditions density of catdyst particle totalpreasura
Jkity
IJTERA'NIIE CITED
(1) Chilton. T. C.,and Colburn. A. P.. h. ENQ.C., !23, 913 (leal). (2) M.. 27. 266 (1935). (a) G S ~ W .B. w.. TIWAS. G.. m d HOW, 0. A,. ~mtu.~ m . m.et. E W ~ . ,39, 14 (1~3). (4) Glsastons, 8.. Laidler, K.J., and Eyring, H., "Theory of Rate Rocesaea". New York. McOnwHill Book Co., 1941. (5) Oilliland. E. R..Im. ENQ.h. 28.681 . (1984). (6) Lewis. W.K.,and Chsng, K.C.. Tram. Ani. Inst. et. Bnon.. 21. 127 (1828). (7) Natl. rcb Couna 1% Rept. of Corn. on Catalmis. John wiley & eons, 1940. (8) B h d . T. K.,"AbaomTon and Extrsotion". New York. McQmwHill Book Co.,1937. (8) Thiele, E. W.,h. EWQ. CHIOT., 31. 916 (1839).
(SOLID CATALYSTS and REACTION RATES)
Oxidation of Sulfur Dioxide
0. A. Uyehara and K . M . Watson UNIVERSITY OF WWCDNSM. MADISON, WIS.
The A m of Lmia and Riu on the oridotion of ~ I f u diocide r in a fbu, system r a plotin*ed SabeStOn Wm1r.t h o C e bssn O M h e d hO C e o d n C e with the principles outlined in the preceding papsr SI#). The &m LVO 11 represented by M equation Cmsd on the ornrmption thrt the rate arntrdling step is a mqfacs tion between .~tiartio&&ed nrlfw dbx*b ond atomic ory(yen. he sxpsriml &tcr Shot0 m  t , h t bss decktion from this g1 equation than from the empiricnl ex#n pmpowd by Let& and Rim.
ERIFICATION of the applicability of the rate eqw tions developed in the preceding paper (pagx 529) is 'di9ioult becsuse of the b c s t complete lsak of suitable published data. Msny cataly%ic rate megwrements have been carried out in static s m in which large difiusionsl conmhtion di6ereum were inevitable and controlled by aonditioue of natural convection which m not subject to ~ ~ ~ e m l i anal*. zed Of the data obtained in flow svstems. k y m &table beoauae of the large mumtratiod c b a c e o m d n g ~~KII dof convsrsion intended to
Ideally, data should be obtained under flow conditions in a di6ereuti.d reactor containing a bed of catalyst
80 shallow that relatively d chsnges of composition occur. Since h p e r a t u r e ha$ an important intluenca on reaction rate, it is desirable that the di6erential section be kept at a temperature ae uniform 88 possible. This rquirea a d l d i a m e t e r r e actor with good heat transfer at the walls. One of the most thomugbly invdgated catalytic mctions is the oxidation of sulfur dioxide over a platinum catalyst. The extensive experimental data obby Bodenatein and Ebk (9, G e t s & (a,and Taylor and Lenher (7)caunot b e d for the development of general rate equations becaw in each caee a static ayatem wae employed in which diffusional conmtmtion and temperature differenaas md&dt to predict. Each of t h inmatigatom and Benton (1) proposed empirid exp&ona repreSemting their own data, but in dl eaea di&lsionsl&e& were nepjaded and the d h t quatiom m applicable only over limited rmgea of mn6itionn. Lewisand Rim (6)carried out a aeriesof flow experimentsin reactom reasonably approximating di6ereutid operation. A plstiniren aebeetos catalyst WBS used in &I! u# tubelpsctors inuuetd in a molten metsl bath. Although dsts neeessry for the evalwtionof diffusional concentration di6erenm are not preamted, it secrms reasonable to ne&& then &e& be
INDUSTRIAL AND ENGINEERING CHEMISTRT
S4l
came of the conditions of forced flow and the Snely divided form of the catalyst. With this aeaumption the data may be used for the evaluation of a complete rate equation. €ORM OF EQUATION
In the oxidation of sulfur dioxide the following four activated rate inauencing steps are possible: activatedadsorption of d f u r dioxide, activated adsorption of oxygen, surface reaction between sulfur dioxide and oxygen, and desorption of sulfur trioxide. Since oue atom of oxygen must combme with one molecule of sulfur dioxide, it seems resaonsble to wume that oxygen is atomically adsorbed on catalysts promoting this reaction. It will a h be wumed that one of these four steps is rate controlling,and that the others are relatively so fast that they msintsin equilibrium. If the surface reaction is rate controlling and partial prek swes are sasumed to equal activities,
In this case the selection of the proper form of equation is possible by comparison of the qualitative trends of the experimental data with those called for by the various equations. Lewin and Ries found that the rata of initial oxidation was increased by inoreaeing the partial pressure of either the aulfur dioxide or the oxygen. The effect of m h dioxide concentration is large and that of oxygen relatively small, but both were definitely indicated. This behavior rules out the selection of Equation 2 as the proper form. If the adsorption of sulfur dioxide were controlling, Equation 2 would require that the initial rate of oxidation be reduced by increased oxygen cancentration. S i i a r l y , if adsorption of oxygen were controlling, the rate of initial oxidation would be d u c e d by incramd mlfur dioxide concentration. The experimental data indicate a strong retardation of the oxidation rate with i n c d sulfur trioxide concentration over the entire range of conditions invstigated. As a result of this behavior, Equation 3 is also eliminated because it Equirea that the rate of oxidation be independent of sulfur trioxide concentration under conditions where the overaU equilibrium constant K is large. Thus,EquationIrepresentsthemostlogicaIexpres4ionofthe qualitative &e& observed. A possible alternate form would result from the wumption that sulfur dioxide is not adsorbed by activation and that activationadsorbed oxygen atoms react with sulfur dioxide molecules from the gm phaae to form adsorbed sulfur trioxide molecules. The resulting equation diEers from Equation 1, in that the denominator term appear8 as a first power instead of a quare. Choice hetween thee two forma can be made only as a result of quantitative examination of the data. The &e& of nitrogen and various other inerta were invcstigated by Bodenstein and Fink (3) with the conclusion that over a considerable range the rate of oxidation was unaffected by the concentration of nitrogen. Accordingly it may be aasumed that the adsorption equilibrium constant of nitrogen is negligible, and all terms involving it are dropwd from the rate equations.
AHD'
(1
+ p s o . ~ s o +, s 
GENERAL METHOD
E~CT~
+~a&oa (psO*&
+PN~NJ' F)
mit EVALUATING
X
CONSTANTS AH"
Rearranging Equation 1 and letting E , C T e T
=
0,.
(1)
of sulfur dioxide is wumed to he the rate determining step, the following equation is obtained,corresponding to Equation 28 of the preceding paper (pfige 532):
(4)
If the overall gaaphase equilibrium constant K is calculated from thermdpamic data, this equntion contains four unknown constanta at any given temperature. These constants are readily evalunted if data are available in which the d while the concentration of one comrates are m ponent is varied, holding all others constant. For example, if only the sulfur dioxide concentration is varied, holding all other concentrationsconstant, Equation 4 may be written:
A corr8qxmding equation of 8imilar form may also be written for the o m of adsorption of oxygen aa the rata determining *P. If the degorption of sulfur trioxide is dto be the controlling step, the following equation applies, correaponding to Equation 27 of the preceding paper:
where
d

1
Thus a plot of d B 6 6
+d 9
I
p z ,
P
+ psoi Kso,
(6)
d K against p s a should E
wlt in a straight line, the slope of which is equal to K ~ O , / I & Similar plots against varying partial pressures of oxygen and sulfur trioxide at the same temperature, in each case holding 542
INDUSTRIAL AND ENGINEERING CHEMISTRY
Vol. 35, No. S
allotherpartialpressurescons~t,yieldvsluesof and K s o d d E , mpectively. These values may he substituted in Equation 4, and the result is an expression containing only Cz an unknown constant. Ct may then he found by applying this equation to each experimental observe tion at the temperature under consideration. An average d u e of C;is thus obtained, and the deviation of the individual values from the average is a measure of the accuracy of the equation. This eame general method also may be used in cases where it is not feasible to hold all concentrations except one rigorously constant in a wries of runs. This ease is generally encountered because it is experimentally difficult to vary the concentration of one component over a wide range without Borne incidental variation of the others. However, if these incidental variations are not too large, the data may he used for accurate evaluation of constants by applying the graphical method descrihed above in successive approximations. Thus, &8 a 6rst approximation incidental variations from the desired constant compositions are negleeted, and the conatants of the equation completely evaluated on this basis. This first approximation equation is then used to correct the observed individual rate data to the basis of constant compomtions. The corrected data are then used to determine a second set of corrected rate equation constants. Ordinarily, a second approximation will yield values of eatisfactory acanracy if reasonable care is used in the exparimentslwork to keep incidental variations at a minimum. APPLICATION TO LEWIS AND RIBS DATA
Lewis and Ries Csrried out three series of runs, each for the purpose of investigating the flecta of varying the concentrstion of one of the active components of the system. In the A
LbJ. 1943
series the concentration of sulfur dioxide in air was varied considerably in the low concentration range of less than one per cent by volume. Conversionswere moderate, and as a result the average sulfur trioxide concentrations were small and the oxygen concentration substantially constant. Series of runs of this type were carried out at four different temperatures. Since the concentration changes were relatively amall, it was ed in dl runs that the average partial pressurea were the logarithmic means of the inlet and outlet values for the oxygen and sulfur dioxide. The mean psrtial pressure of the sulfur trioxide was taken as the difference between the sum of the partial pressures of the entering sulfur dioxide plus sulfur trioxide and the mean partial pressure of the sulfur dioxide. Data are not included on the weights or volumes of the catalyst in the various reactors used in the experiments, and it is thus impossible to calculate absolute values of r, the rate of oxidation per nnit maea of catalyst. However, each series of runs was conducted in a single reactor with a constant weight of catalyst and at a constant rate of gas flow. ACcordingly, the readion rates, r, for each series are h d upon this constant weight of catalyst and are taken as proportional to the diSerence between the mole percentages of sulfur dioxide in the entering and leaving mixtures, since volume changes are negligible with the small concentrations employed. These concentration changea are designated aa r/w, where w is a proportionality factor depending on maea of catalyst per nnit gas flow and is unknown in all cases and different for diKerent series of runs. E k d n a t i o n of these data confirm the conclusion of Lewis and Ries that the h i t i i rate of oxidation is directly proport i o d to the lirat power of the partial prassure of sulfur di
INDUSTRIAL A N D ENGINEERING CHEMISTRY
543
._
.
..
oxide, and a plot of Equation 6 yield8 a straight line of a p proximately I B slope. ~ Accordingly it may be BsBumedthat the term pmGa in the denominator of the rate equation is negligible in compsrisOn to the 0 t h additive terms. IQ their B &ea of ~ n Lewis s and Ries varied the amount of oxygen from 20 to 1 par cent in the mixture of d w dioxide, oxygen,and nitrogenentehg the reaetor. The sulfur dioxide content d e d from 0.3 to 0.7 per cent. In the C series of runs sulfur trioxide WBS added to the mixhve en* ing the reactor, and the perc8nta@~ of both sulfur dioxide and sulfur trioxide vuried over considershle ranges. The oxygen concentration sleo varied fmm appmXimately 17.5 to 21 per cent; thia dation is not excessive; and the fluctuation of sulfur dioxide concentration does not interfem with evaluation of KO, and K m since the A series showed the adsorption eqnilibrium constent of aulfur dioxide to be negligible. These two series could be d for the evaluation of KW and K m respectivelg, by the general method outlined above except for the fact that the two series were osrried out at diffmnt tempprrstures. This situation repuires a special eimultanabua solution. For the C series with VSrJTing sulfur W e concentration, an equation 8imilar to 6 may be mitten:
+
Thin equation is of the form y1 = MI% Il, where XI = and permits epslustion of dope MI and intercept I , from a plot of the data of the wries. h m Equation 7,
j%Oi
Similarly for the B series, with varyhg oxygen concentm tion,
If y: is plotted against z, cept Is are determjned,
 6%
o
r
a
The Btandard enthalpy change of aotivated admrption of either component may be evaluated from Equation 45 if a iugb d u e of the adsorption equilibrium constent is known at any temperature and if AS' is taken aa the rough approximation value of 28 recommended in the preoeding paper. Bowever, since no valw of the equilibrium constenta are known initially, Equation8 12, 13, and 14 muat be solved eimultaneoualy by s u d v e approximations. Approximate values of AH& and AH&, are fuet reamed, and the c o r n nponding valuea of a and 8 cslculsted. FGst approximation then cal&ted from %l+%t!m v a l w of Kmo, and Kpr 12, 11, and 10. Using these fuet vslues of the eqllllrbnum constenta, second approximations of A",., and AH& are calculated from Equation 45 of the preceding papea, and the entire dculation is repeated to obtain second approximations of the equilibrium constante. The above procedure wm carried out, fuet neglectins VsMtiOns in oxygsn concentration in the C w r k rum and variationn in sulfur trioxide concentration in the B series. From the equation thua evduuted, the two series were corrected to constent oxygen and nulfur trioxide mc8ntrstiom, respeativelJr, and the aonstents of the eqllatiolle reevaluated. Tha oollsoted data for the 5.d detarminationrS of MJII and MJZ: from Equatiom 7 and 9 ara plotted in Figurm 1 and 2. AB pointed out hy Lewis and Flien, the data of the C d e s of runa dearly indicate an o d gmplmee d o n quil i b b constent of approximately 120, with psrtial pressures e x p d in atmosphere, at 425O C. Thin value is approximately half that calculated from the recent t h e r m d d c data of Bichowslry and Rosrdni (8) and of KeUey (4). This dismpancy migbt be due to (a) di5mnces hetween the true reactor temperaturea and the bath temperatures measnred by Lewis and Rim, (b) slight errom in the determination of EXMU quantities of sulfur dioxide in the preaence of large quantities of anlfw trioxide, or (c) poesible m m in the thermdynSmic data. It is felt thst explanation b is the most plausible; accodngly the low values of K correspondingto the observed Le& and Rka data were used in plotting Figurea 1 and 2. However, it is recommended that the thermdynamic values he employed in application of the resultant rate quation.
and the slope Mt and inter
MI, rr
(14)
I
G
I
I
1
1 +~eoiKsoa
$ti
+ ~ O , K ~ J
(10)
Smce the two eariea are at ditIerent temperahma, the &Ption equi!ibrium constent8 will differ. Let
Combining Equationa 8,10, and 11,
If a and 0are known, Equation 12 may be solved direotly for KJ~o,. By mhstituting this value in Equations 10 and 11, Kan, and Kpr are also determined. Expressions for a and 0 may he derived fmm Equation 45 of the preceding paper (page 634) :
T ' G 8
AH; a
!i44
e
(18)
Once the equilibrium constants of Equation 1 are completaly evaluated aa function8 of tempmature, it is poeaible to evaluate A""' from the data of the &OUS A &ea nma at t e m p e r a h by plotting values of In ( E A C ~ ~ ) The slope of this Line is equal to AH"/R. Average vduen of the group of runa at the four Wemnt temperaturea of the A Series am plotted in Figure 3. di5t
againat 1/T.
INDUSTRIAL A N D ENGINBERING CHEMISTRY
Vol 35, No. 5
Th6 points of Figure 3 do not cloeely appmximate a linear relation and might be interpreted as indicating an optimum temperatwe of maximum rata above which oxidation rate would be redud by i n d temperature. From theoretical coneiderations this appetve to be an improbable aituation, and it is believed that the deviations of the points fmm the indicated Btrsight line of Figure 3 are not much greater tbsn the probable eorperimentelerror of the measnrements.
1
2
6 7 6
FINAL EQUATION
8
9 10 11 ia
As a rasult of the above d y u k , the following values are recommended for the terms of the equation:
ia
14 Av.
I.
aa.980
19.96
= e7  7
AP'
+m
EvaIuation of the group of constants WEACwill q u i r e speci6c rate data on any particular catalyst nnder conaideration.
h.l@ Figure 5. w e c t of Tempemtun,
...
7.68 19.811 16.46 16.81 18.80 16.62 m.61 24.08 16.811 19.80 10.08 9.87
+64.00 8.71 +W.6
m.es
+24.7 +?&1
0,169 0.218 0.111
18.14
18.5
0.178
2s.m
8 4
ie.za
14.78
1a.70 4.89
++28.7 7.68
p&
o:m1
0.180 0,170 0.117 0.1H) 0.187 0.119 0.161 0.2%
.... + 41.7 .0
+iah 81.4 19.1
Sa?: 12.7  8.1 +29.6
$E::
17.6
The 04 standard enthalpy term AH" is small as comp d to the usual swalled energies of activation calculated for reuctions of this typ. This d t a from the ooneiderable &e& of tempautm on the SaaDrption equilibrium constants in the denominator of the equation, and also from the fact that AH" includes the sum of the standard enthalpies of adsorption of the reactants as well as the enthalpy of activation. The calculated value of AHo'slso would be i n d by any corntiom applied for the ditrusional eflecta which were neglected entirely in this andyeis. CONCLUSIONS
The pmposed form of equation repreants the experimentr$ data at le& as ~~ourstely 8 6 the empirical equation dereloped by Lewis and Ities. It would be expeoted that the apparent ademption equilibrium constants and the overall temperature d c i e n t term AH" evaluated from tbeae data &odd be roughly applicable to other platinum catalysts for tbis reaction. However, the AH'' values are mmewhat uncertain because of the limited range of temperaturea inveatigated e x ~ ~ theyneglect , of ditiuaionsl &e&, and the values 888umBd for the standard entropy ahangea of aativated adsorption. ACKNOWLILDGME"
The acauracy of thisequation is indicated by the deviations of the individual points fromthe C~WBBof & !? !?a 1 , a and

3 and by the values in Table I for EACTC ,calculated for the conshbtemperam runs of the C aeries in which mtuimum variations of sulfur dioxide and Bulfur trioxide concentrations were invwtigated. For these csldations the o v e r d equilibrium constant of 120 indicated by Lewis and Rka data was used. For comparison the comapowling constants of the Lewis and Ries empirical equation are also tabulated. Lewis and Riss did not apply their equation to nma 1 and 2 (Table I) which were close to equilibrium conditions. However, the p m t equation includes theee pinta with fair agreament, in view of the uncerbintq of tbe experiments1 valuea. The average deviation of the equation for dl fourteen runs is lS.5 per cent, that for runs314, inclusive, is 15.0 per cent as compared to Lewis and Rim deviation of 17.5 per oemt for the e8me nma. The data are not sufficiently acumute to demonstrate conclusively whether Equation 1 or the alternate form implying no Saeorption of sulfur dioxide is c o d . However, it a p y w n that slightly tetter correlation is obtained with Equab n 1 in which the denominator gmup is aquared than when this group e n h as the firat power. h Y ,
1943
The work reported here was made pwible through hcisl mpport of the Wisoonain Alumni Research Foundation. NOMXNCLATUPB
The 8Jrmbola are those used in the preceding paper (page
540) with the following additions:
Il. I ,
MI,Id, etc. W
Qd

intemepts of plob to determine h r p t i o n eqnilibriummnstants slopes of ts to determine h r p t i o n equilibrium
e
constan
partial pmsure of S0,; atmospheres proroportmdity feotor relating mnmntration change
to M i o n rater ration of 0, and 801 h r p t i o n equilibrium mnatants at tampraturea Ts and T,, mpctivdy LlTERAmEcITm
(1) Benton. A. F.. IUD. ENQ.CREM.,19.494 (1827).
Bib
.nd Romini, "Tbermwhsmiatru of Chemioal aukNew Y e t , Reinbold Publiahina Cow.. 1836. (3) Bods~tainsnd Fink, 2. Chsm, Bo. 1 (1907). (4) Kellsy. K K., U.8. Bur.Mine+ B d . 434 (1941). (6) Knietsoh, Em.. 34,4083(1901). (6) Iari.,W.K.,and %ea. E. D..IND. Ewe. CBY.. IS,880 (ma?). (7) Twlm. 0. B.. .nd Lenher, 8.. 2. ph@. C h . . Bode~ e s t t m d , x  a (mi). (2)
at.noas".
&&.
INDUSTRIAL A N D ENQINEBRING CHEMISTRY
5(5