Higdon, W. T., Robinson, J. D., J . Chem. Phys. 37, 1161 (1962). Hirschfelder, J. O., Curtis, C. F., Bird, R. B., “Alolecular Theory of Gases aiid Liquids,” Wiley, S e w York, N. Y., 1967. Horth, A,, Patterson, D., Rinfret, AI., J . Polym. Sci. 39, 189 i19 .i9 -)., \ - .
Hoshino, S.,Sato, K., Chcm. Eng. J a p . 31, 961 (1967). Li, S. U., Ph.1). Iliasertation, University of Virginia, 1967. Li. S.U.. Gainer. J. L.,I.uD.ENG.CHf:Ri.. FUXDAM. 7. 433 11968). llandelkern, L , Flory, P. J. J . Chem. Phys. 19, 984 (19.51). 11rC‘abe A I Bzochem. J 104. 8 11967). 1Ieczner: A . B., in “Advances i‘n Heat Transfer,” Vol, 2, Academic Pres$;,New York, Y. Y., 19s55. lIetzner, A. B., &\-atitre 208, 267 (196,5). Kinhijima, Y.. Oster, G., J . Po(?im.Sei. 19, 337 (1956). Nishijima; Y.; Oster; G.,’J. Che&. Educ. 38, 114 (1961). Osmers, H. It., Ph.D. Dissertation, University of Delaware, 1969. Paul, I). R., IND.ENG.CHKM., FLTDAM. 6, 217 (1967). Paul, I). R., Kenip, D. R., paper presented at the 6.ith A.1.Ch.E. AIeetina. Cleveland. Ohio, 1969. Peiry, R . H . , Chilton,’C. H.’, Kirkpatrick, 9. I]., Ed., “Chemical Engineers’ Handbook,” 4 ed, AIcGraw-Hill, New York, N. Y., 1963. Quinn, J. A,, Blair, 1,. fir., Suture 214, 007 fl967). Robiricon, C., Proc. Roy. SOC.Ser. A 204, 339 (19,jO). Robinson, 11. A,, Stokes, R . H., “Electrolyte Solutions,” Butterworths Scientific I’ublicatioris, London, 1933.
Roff, W’. J., “Fibers, Rubbers and Plastics,” Academic Press, New York, N. Y., 1956. Schildknecht, C. E., “Vinyl and Related Polymers,” Wiley, ?Jew York, S. Y.,1952. Scriven, L. E., Sternling, C. I..) A.I.Ch.E. J . 5 , 514 (1959). Scriven, L. E., Sternling, C. V., Sature 187, 186 (1960). Secor, R. AI., A.I.Ch.E. J . 11, 452 (196,5). Simha. R.. Zakin. J. L.. J . Chem. Phiis. 33.‘ 1791 11960). ~, Sundelnf, L. O., A r k . kemi 2 5 , 1 (1965). Thomaes, G., Van Itterbeck, J., AIIol.Phys. 2 , 372 (1939). Wang, J. H., J . d m e r . Chem. SOC.73,,510 (19,jl). Wang, J. H., J . Amw. Chem. SOC.76, 475,j (1964). Weinberg, S., B.Ch.E. Thesis, University of Ilelaware, 1967 Wilke, C. R., Chang, P., A.I.Ch.E. J . 1, 264 (19.55). Woodqide, W., lIessmer, J. H., J . A p p l . Phys. 32, 1688 (196 Zandi, I., Turner, C. D,, Chem. Eng. Sci.25, 317 (1970).
RI.:CKIVI:D for review September 10, 1969 II1:SCIIMITTI:D A1Igust 10, 1971 ACCEPTED December 27, 1971 The funds to support this research were provided by the G . S. Department of the Interior as authorized under the Water Resources Research Act of 1964, Public Law 88-379. .4 presentation based on this paper was given at the 6.ith National 11eeting of the American Institute of Chemical Engineers, Cleveland, Ohio, May 1969.
Catalytic Decomposition of Nitrogen Dioxide on a Heated Platinum Wire Boo Goh O n g a n d David M. Mason* Department of Chemical Engineering, Stanford Cniversity, Stanjord, Calif. 94305
In the study of natural-convection heat transfer from a horizontally heated platinum wire to the endo0 2 ) a very large increase in the heat flux i s obthermically reacting gaseous system (2N02 S 2N0 served a t a wire temperature around 1 100°K over a range of pressure from 0.2 to 1 atm. It is postulated that this behavior i s due to the fact that below 1 100°K an oxide of platinum shrouds the wire surface which is noncatalytic with respect to NO2 decomposition. At temperatures above 1 100°K this oxide sublimes exposing pure platinum metal which catalyzes the decomposition of NO2 and correspondingly causes an increase in heat flux. Such a catalytic effect i s not observed on either gold or silica-coated heated wires. From the heat-transfer measurements it has been determined that at an 0 2 partial pressure of 1 atm platinum oxide (assumed to b e PtO2) has a sublimination point of about 1050°K. From the dependence of heat transfer rates on pressure the decomposition of NO2 appears to b e a second-order reaction with respect to NOz. Any exothermic dissociation of NO2 to the elements if occurring i s too slow under the conditions of these experiments to affect the heat transfer rates measurably.
+
T h e catalytic reactions involving osides of nitrogen are of particular interest in the fields of air pollution aiid nitrogen fixation. The catalytic decomposition of S O via
2N0
IJ
p\T2
+ 02
(9
has been measured on heated platinum wires around 1500°K b y Green and Hinshelwood (1926). Several invest~igatorsalso studied the reaction 011 supported catalysts containing platinum or osides of copper, chromium, and cobalt. A good review of the subject is given by Shelef, et a!. (1969), who conclude t h a t to date no catalyst promising for the removal of S O from autoniobile eshausts by direct decomposition is available.
Relatively little has been published on the catalytic decomposition of N O r by either the endothermic reaction 2N02 J_ 2 N 0
+ 02
or the exothermic reaction 2KO?
N?
+ 202
(3)
Brief reference to the catalytic decomposition of KO? (eq 2) on Si02is made by Emmett (1954), and Vikstrom and S o b e (1965) studied this reaction on CuO-alumina and Ce02alumina catalysts a t temperatures above 1300°K. Blyholder and Allen (1966) studied the infrared spectrum of NO? adInd. Eng. Chem. Fundom., Vol. 1 1 , No. 2, 1972
169
30
convection studies is
N204)r 2 5 0 2
; ; 20 In N
E
1"
0
C
10
I 1000
700
I
1300
I 1600
Tw (OK)
Figure 1. Natural convection heat transfer to NO2 (at T, = 500°K) from a 0.00508-cm diameter platinum wire as a function of wire temperature for various total pressures: 0 , 0 . 2 2 atm; Q0.52 atm; A, 1 .o atm
I 1000
700
I
1300 TW
I 1600
(OK)
Figure 2. Natural convection heat transfer to NO2 (at T, = 500°K) from a 0.0127-cm diameter platinum wire as a function of wire temperature for various total pressures: 0 , 0 2 2 atm; 0,0.52 atm; A, 1 .o atm
sorbed on nickel and iron. No published data on the kinetics of the catalytic decomposition of X02on platinum have been found. The role of platinum alloys in the ammonia oxidation process has received wide coverage in the literature and a review of the technology is given by Chaston (1964)and in two papers by Connor (1967), the second in the series discussing particularly the phenomenon of oxidative volatilization of platinum observed in the manufacture of nitric acid. The processes of simqltaneous heat and mass transfer occurring during catalytic oxidation of NH3 on platinum is considered by Nowak (1966) taking into account the kinetics of oxidative volatilization of platinup determined by Fryburg and Petrus (1961) Bartlett (1967) considers the dynamics of volatilization of platinum alone. d few experimental data have been published on the problem of natural convection in reacting gaseous systems particularly focusing on homogeneous reactions and not surfacecatdyzed reactions. One system that ha.s been used for natural I
170 Ind. Eng. Chem. Fundam., Vol. 1 1 , No. 2, 1972
(4)
Because of extremely high homogeneous reaction rates t'his system is effectively a t equilibrium under the physical conditions of natural-convection studied. Homogeneous reaction rates in the system of eq 2 are low enough t'hat the system behaves in a nonequilibrium fashion. Thus the influence of homogeneous kinetics on natural convection can be studied with this system as was done by Ong and Mason (1971) employing noncatalytic gold-heated wires. For endot'hermic reactions such as the dissociation of KOz (eq 2) and X204 (eq 4) if either homogeneous and/or heterogeneous reaction rates are large compared to mass-transport rates the thermal conductivity, and thus convective heat transfer, is markedly increased by reaction (Beer, 1965;Beer and Deubel, 1966;and Ong and Mason, 1970). Brokaw (1961) discusses t'he general problem of the influence of kinetics on thermal conductivity and Svehla and Brokaw (1966)present thermodynamics and kinetics for the S204-S02-NO-02system. Beer (1965) and Beer and Deubel (1966) measured natural-convection heat transfer rates from a 10-mm diameter tube to the equilibrium system of eq 4 a t 297°K and from 0.05 to 1 a t m . Ong and Mason (1970) studied the same system employing a 2.3-mm diameter heated cylinder over a wider range of variables: Grashof numbers from 10 to lo5,pressures from 0.1bo 20 atm, and bulk temperatures from 275 to 380°K. The effect of t'he catalyticity of platinum on natural-convection heat transfer to dissociating NOz (eq 2) is displayed by peculiar S-shaped heat flux density us. surface temperature curves presented first by Bopp and 11ason (1965) and reproduced in this study (Figures 1 to 3). The role of platinum in catalyzing the dissociation of KO2 and leading to the unusual heat-transfer behavior was positively confirmed only recently by Ong and Mason (1971).They demoristrated that a gold or silica-covered platinum wire behaves noncatalytically with respect to the S O z system and t'he corresponding heat flux density us. temperature curves a t 1 atm for these surfaces are not S-shaped. Under these conditions the ratio of homogeneous reaction rate to the diffusion rate (the so-called Damkohler number) is less than corresponding to a frozen or effectively nonreacting system (Ong and JIason, 1971). The oxidative volatilization of platinum by the reaction Pt(s)
+ On(g) If PtOz(s) If Pt02($)
(5)
plays an important role in the behavior of natural-convection heat transfer to the catalytically reacting KO,system. Thermodynamic properties for the Pt-0 system are given by Brewer (1953) and Chaston (1964), but unfortunately, precise thermodynamic properties such as the sublimation point, molar enthalpy, and free energy function for the species PtO,(s) are not available making a n unambiguous interpretation of the complex kinetics and siinultaneous transport processes involving KO2 and PtO, difficult. In spite of these difficulties it will be shown that natural-convection heattransfer measurements present a direct and simple experimental method of analyzing in a semiquantitative fashion physical situations involving a coniplex coupling of rates of transport' and reaction kinetics. The experimental apparatus and techniques are identical with those described by Ong and 1Iason (1971).The curves of heat flux density, q, us. wire temperature, T,v,are shown in Figures 1-3 for a bulk temperature of 50OoK with platinum wires of diameter ranging from 0.00508to 0.0254em and total pressure from 0.2 to 1 a t m . Tables I and I1 listing the complete
NO2 data together with N2 calibration data are available from the American Chemical Society microfilm depository service and from Ong (1970). It should be noted t,hat the sharp points of inflection and rapid rise in the curves occur in every case in the region of T , = 1050 to 110OoK. It is also noteworthy that some of the S-shaped curves display a drop in T , with a n increase in p indicating a n increase in the amount of surface react'ion with a decrease in T,. It is obvious that such behavior cannot be attributed to a n Arrhenius effect, for a large negative activation enthalpy would be implied. Even in the cases where the wire temperature rises with increasing heat flux density, the act'ivation enthalpy necessary to explain the observed steep slopes in the reaction rate-temperature curves exceeds 100 kcal, which is improbably large since the enthalpy of reaction of t'he uncatalyzed homogeneous reaction (eq 2 ) is only 27 kcal.
8
- 6
I I
N
E
1" 0 4 P
2
Discussion
1100
f )O
Role
of P t O z in Inhibiting Catalytic Decomposition of 011 of the
NO?.In order t o give a satisfactory explanat
shape of the heat transfer curves shown in Figures 1-3, it is necessary to consider the chemistry of platinum oxides, thermodyiiamic properties for which are presented by Brewer (1953) and summarized by Bartlett (1967). Platinum metal in anoxygen atmosphere a t room temperatureisnormally covered by a very thin layer of PtOz (Chaston, 1964), but in the environment of the equilibrium r\T02-KO-Oz mixture peculiar to these nat'ural convection measurements when platinum is heated for several hours near 1000°K and then cooled t'o room temperature, the layer is thick enough to be visible to the naked eye. Since the brst' step of the reaction in eq 5 is exothermic ( A H z g 6= -32 kcal) and the second step thevaporizalion of Pt02(s) is of course endot'hermic (AHZ98= 73 kcal), a t a given partial pressure of O 2 and a sufficiently high temperature, PtOn(s) becomes thermodynamically unstable and only PtOs(g) is present'. There is a dearth of information on the vapor pressure of Pt02(s), the only data reported being the sublimation point of 750°K for a n 0 2 partial pressure of 1 a t m (Brewer, 1953), As ill be discussed subsequently, it appears from the natural convection experiments that the actual sublimation point is considerably higher, around 1050-1100°K. The enthalpy of vaporization of PTOz(s) given by Brewer (1953) has a large uncertainty of i10 kcal. The probable explanation of the abrupt' rise in q (in Figures 1-3) is the onset of appreciable endothermic decomposition of ??On (eq 2 ) when by volatilization of surface platinum oxide at temperatures above 1050 to 1100°K clean platinum metal surface becomes exposed to the reactant S O z . The platinum oxide is apparently noncat'alytic with respect to XOZ decomposition, for below 10OO"II (Figures 1-3) the heat flux is near-frozen as would be the case if only the homogeneous reaction predominated (Ong and Mason, 1971). Pt02 has been found also to be inert to oxygen atom recombination below 500°C (Fryburg and Petrus, 1960). The enthalpy of vaporization of the oxide can be eliminated as contributing significantly to the abrupt rise in the heat flux density curves since a 0.0127-cni diameter platinum wire would have been completely volatilized in less than 1 hr under the conditions of the experinients and no such marked attrition of the wires mas observed. Thus it' can be concluded that the evaporation of the noncatalytic P t 0 2 surface exposing catalytic metallic platinum causes NO2 to dissociate and the p curves to rise around 1050 to 1100°K under the conditions of the experiments.
I 1400
I
0
TW(*K)
Figure 3. Natural convection heat transfer to NO2 (at T, = 500°K) from a 0.0254-cm diameter platinum wire as a function of wire temperature for various total pressures: 0 , 0 . 2 2 atm; 3 , 0 . 5 2 atm;A, 1 .o atm
1
J
WIRE TEMPERATURE, TW
Figure 4. Sketch of behavior of natural convection heat transfer to NOz from a platinum wire as a function of wire temperature for various degrees of platinum oxide covera g e and catalycity: t example of behavior experi, behavior expected mentally observed in this study. under certain conditions; curve a, noncatalytic surface in which slow homogeneous reaction alone affects heat transfer; curve b, strongly catalytic surface leading to equilibrium heat transfer behavior; curve c, surface of intermediate catalycity; curve d, region in which inhibiting platinum oxide coat is subliming (numerals discussed in text)
-
------
A sketch qualitatively describing the physicochemical processes is presented in Figure 4. It is assumed that for all t'he curves that at the pressure of the studies the rate of the homogeneous react,iorl (eq 2) is low compared to the rate of diffusion and thus the homogeneous reaction contribution to the heat flux is negligible. Curve a represents a surface chemically inert with respect to the KO2 catalytic decomposition: e.g., a gold surface, or a surface covered with noncatalytic material such as silica or platinum oxide. Curve b represents a completely catalytic surface with chemical equilibrium in accordance with eq 2 being achieved and a maximum heat flux being displayed. Curve c represents a clean surface of finite catalyticity and curve d corresponds to the type of Ind. Eng. Chem. Fundam., Vol. 1 1 ,
No. 2, 1972
171
i-
'O'O
would be a continuous rise in the surface temperature for a given heat flux density until a new dynamic equilibrium were reached on a curve of finite catalyticity which for an exothermic reaction would lie below curve a. Rate of Catalytic Decomposition of NOL from HeatTransfer Measurements. T h e heterogeneous rate of decomposition of NO2 can be determined from a knowledge of q., the heat flux density due to reaction, and if a simple irreversible nth-order reaction is assumed, there results (Brokaw, 1961) from the conversation of mass and energy a t steady state the following expression for a perfect gas
I
F
GI1' = kpwn = qr/AHr
(6) Implicit in the form of eq 6 is that the system is far enough removed from equilibrium that only the forward step in eq 2 is significant. qr can be calculated from the measured total heat flux density, q, knowing the frozen heat flux density, qr, and the radiant heat flux density, grad
t I
I
l
I
l
I
I
l
l
q r = q - gf
1.0
0 .I ,P ( a t m l
Figure 5. Reacting heat flux density as a function of the partial pressure of NOz in the bulk gas for T,v = 1400°K and To, = 500'K and various diameter wires: 0, 0.00508 cm; 0~0.0127cm; b,0.0254 cm 2
I
I
I
I
I
I
I
I
- qrad
(7) @ad, the radiant heat flux density from the wires, is taken into account using a value for the emissivity e of between 0.25 and 0.30 obtained by calibrating with nitrogen. A somewhat lower value of 0.192 is given by hlcridams (1954) for the emissivity of a heated platinum wire. It is assumed that negligible radiation is absorbed by the KO2 gas. gr and g, are calculated from the Nusselt number
I
\
values for which can be obtained from experimental values of the Grashof number
I
0
I
I
I
I
I
N Nis~obtained from the available Nusselt-Grashof number
I
0.5 P, ( a m )
IO
Figure 6. Logarithmic slopes of the curves of Figure 5 vs. partial pressure of NOz in the bulk gas for various diameter cm; b,0.0254 cm wires: 010.00508 cm; 0~0.0127
curves experimentally observed. Below a wire temperature corresponding to point 0 of about 1050'K, it is assumed the wire is covered with a platinum oxide coating and the experimental curve coincides with curve a , the inert, nonreacting curve. Once volatilization of the platinum oxide coating becomes significant and the NO2 molecules interact with some clean platinum surface, the heat flux density rises above the inert curve a toward curve e. Point 1 corresponds to a surface partially covered with platinum oxide. If the surface had been perfectly clean, the wire temperature corresponding to this value of the heat flux density would be that of point 2, whereas if the surface had been completely inert, the wire temperature would have been that of point 3. At the observed point (1) a balance exists between the rate of platinum oxide formation and evaporation. Point 2 cannot be realized, for the noncatalytic platinum oxide is stable a t the temperature corresponding to this point and the heat flux density would lie on curve a as observed. If the reaction occurring on the platinum surface were exothermic, such as N O n decomposition to the elements (eq 3), S H a oxidation, or 0 atom recombination, then the region near point 1 would be unstable. Once the platinum oxide volatilization temperature were reached, there 172 Ind.
Eng. Chem. Fundam., Vol. 1 1 ,
No. 2, 1972
correlation which is applicable to both reacting and nonreacting systems (Ong and hlason, 1970). Physical properties appearing in eq 8 and 9 are available from Svehla and Brokaw (1966). T o solve fork in eq 6 it is necessary to know p , (or z,), the value of the concentration of NOz a t the wire surface. I n general, the Stefan-Maxwell diffusion equation combined with the conduction equation in cylindrical coordinates assuming a stagnant fluid-film model allows the composition a t the surface to be calculated by numerical methods. For the specific stoichiometry of eq 2, employing the fact that the binary diffusion coefficients are nearly equal in this system, a simple analytical expression can be derived for the film model as described by Ong (1970)
It is shown by Ong and Mason (1971) that the film model works very well in treating natural-convection heat-transfer data in the nonequilibrium KOz system reacting homogeneously in the presence of a heated gold cylinder. Thus it is reasonable to assume that this model should work well for catalytic systems. The following procedure is then used for obtaining catalytic rate data from the heat-transfer data. (a) For an initial guess assume that x,, = zw, and compute a value of A'G~based on the corresponding values of p,, and uav. (b) Compute ATN, from the Nusselt-Grashof correlation (Ong and Mason, 1970) and qf and 4.. from eq 8 employing values
x
for from Svehla and Brokaw (1966). (c) Compute qr from eq 7 using qf calculated from (b) with qrad and q being determined experimentally. (d) Estimate a new value of the wall composition, z, by substituting the value of q. from (c) and qs from (b) into eq 10 or by using the Stefan-Maxwell equations for a more general case. (e) With the value of 2 , determined in (d) , recalculate Norand repeat steps (b) through (e) until the value of q. converges to the desired accuracy. Values of q. were obtained in this fashion for platinum wires of 0.00508-0.0254-cm diameter at total pressures from 0.12 to 1.0 a t m and all the data are listed in Tables I and 11. Values of q. were selected from these data a t wire temperatures above l l O O O K where the abrupt rise in the heat flux is observed (Figures 1-3), it being assumed that under these conditions essentially a n oxide-free platinum surface is present. It was found that z, and hence cw calculated from eq 6 were not accurate enough to permit quantitative values of k to be obtained. The main source of error is uncertainty in the value of qrad used in eq 7 to calculate 9. with small errors in qT leading to large errors in z, calculated from eq 10. The most unambiguous way of determining IC would be to plot q. (obtained in the fashion described above) vs. p,, the partial pressure of NO2 in the bulk gas which is accurately known, and extrapolate the curves to low pressures where p , + p , . Representative data a t T, = 1400°K and T, = 500°K are shown in Figure 5 , where q. us. p , is presented on a log-log plot. It is evident that data would have to be taken a t lower pressures than in the present study for the curves to coincide and p , p,. Values of d log qr/d log p , were obtained by taking slopes of the curves such as in Figure 5 and these slopes are plotted 216. p , in Figure 6. As p , +. 0 and p , +. p , , d log q,/d log p , should approach n as indicated by eq 6. From Figure 6 i t is seen that as p , +.0, ?z + 2, and similar results were obtained for wire temperatures of 1200 and 1300°K. Hence it may be concluded that the rate of heterogeneous decomposition of NO2 on a platinum surface under the conditions of these experiments can be best fitted with a n expression second order with respect to NOz. Certain errors may occur in the treatment of the data. First it is assumed that the wire surface is completely clean once its temperature is higher than the vaporization point as indicated b y the abrupt rise in the heat flus density curves (Figures 1-3). Secondly, the geometric area of the wire is assumed though examination of samples after runs with XOZ shows that there is some pitting on the surface, which would increase the actual surface area used in the calculations by an amount which was not determined. The error in area due to roughness would tend to cause the values of y as reported here to be too large. I n cases of small diameter wires i t is seen in Tables I and I1 that the physically impossible situation of q. > qre in a few cases ,md this behavior could be accounted for by employing too small a n area in converting the heat fluxes to heat flus densities as well as too small values of &,d being employed. I n no cases in the near equilibrium portion of the y curve were there observed values of q. unexpectedly smaller than qre, Thus the exothermic decomposition (eq 3) which would lower yre is assumed not to occur a t a n appreciable enough rate to influence the heat-transfer measurements. Estimation of the Vapor Pressure of PtO?. It is proposed that the behavior of the natural-convection heat-transfer curves (Figures 1-3) interpreted in the foregoing light of inhibition of XOa decomposition by PtOz(s) can yield information on the sublimation point of PtOz(s).
-
-5
:
n 0
-10
-
0,
ON
-15
t
I -
'83kcol
I
I
I
I
I
I
I
I
X o experimental data are available in the literature for the sublimation point pressure and temperature although a n estimate of the decomposition temperature of Pt02(s) in equilibrium with 1 a t m of 0 2 (eq 5) is given as i5O"K and the enthalpy of sublimation is given as i 3 f 10 kcal by Brewer (1953). The available data for the equilibrium partial pressure of Pt02(g) in equilibrium with P t and O2 (cf. first equilibrium step eq 5) given b y Alcock and Hooper (1960), Schafer and Tebben (1960), and Xorman, et al. (1967), are all at' temperatures above 1300°K at low enough values of P O ? t'hat Pt02(s) is unstable. Values of the equilibrium partial pressure of PtOz(g) were calculated from these references with ( P O , ) , being taken as the bulk equilibrium value in accordance with the reaction of eq 2. I n Figure 7 are plotted three equilibrium lines of pPtO?LIS. l / T for values of p ~ of ?0.008, ~ 0.015, and 0.023 a t m corresponding to experimental bulk total pressures of 0.22, 0.52, and 1.0 atm, respectively, and a bulk tempersture of 500°K. Since it is assumed that the abrupt rise in the heat flux curves occurs due to volatilization of the solid PtOz from the surface, bhe temperature a t which the rise initially occurs in the curves is assumed to represent the sublimation point. From the experimental sublimation temperature thus determined, together with the known pptoi is calculated for the equilibrum of eq 5 and the resulting pointsare presentedin Figure7 for the three different wire diametersindicated.Though the sublimation t>emperaturesare reasonably well established there is great uncertainty in the slopes of the experimental points as seen from Figure 7 and hence in the enthalpy of vaporization. A solid straight line is drawn through the cluster of points with a slope corresponding to an ent'halpy of vaporization of 7 3 . The dashed lines represent the limits of error of & l o kcal in the enthalpy of vaporization given by Brewer (1953). If the solid vapor pressure line is extrapolated to PO, = 1 a t m a sublimation temperature of 137OOK results which is considerably above the i50°K estimated by Brewer (1953). This discrepancy in sublimation temperature needs to be resolved and a precise value of the enthalpy of sublimation should be determined. Conclusions
It is concluded from the heat-transfer measurements that the catalytic decomposition of NO2 on platinum can be fitted with an empirical expression second order with respect to Ind. Eng. Chem. Fundam., Vol. 1 1 ,
No. 2, 1972
173
KO2. More precise measurements need to be made to determine the rate coefficient and enthalpy of activation. Because of the considerable interest in the N02-NO-02 and Pt-0 systems in engineering problems, further investigations leading to a better understanding of the detailed mechanism of the reaction steps should be made both with further refinements of the heat-transfer techniques as well as direct studies in an isothermal reactor, e.g., a platinum tubular flow reactor. For the purpose of studying more accurately the heterogeneous decomposition of oxidizing gases on heated platinum wires, the wire temperature is sufficiently high (>lOOO°C) that any error in the radiation corrections are relatively large and thus very fine wires and perhaps forced convection should be used in order to reduce the amount of radiation relative to convective heat transfer. The explanation herein that the abrupt rise in the heat flux is due to the exposure of clean platinum surface caused by the volatilization of the surface oxides needs verification by independent physical chemical techniques. In situ inspection of the surface under different catalytic conditions should be performed and analysis of the chemical composition of the oxide coating to confirm that indeed PtOz is the species present needs to be established. Nomenclature
d g
=
diameter of wire, cm
= gravitational acceleration, cm/sec2
A H , = enthalpy of reaction, kcal/mol A H , = enthalpy of vaporization, kcal/mol
k
n
= =
surface rate coefficient (eq 6), moles/cm2 see atm“) empirical order of reaction p = partial pressure (of SO2 unless otherwise stated), atm q = heat flux density, cal/cm2 see a’’ = surface reaction rate, moles/cm2 sec T = absolute temperature, OK AT = temperature difference between wire and bulk fluid, z
= mole fraction of
“K
KO2
DIMESSIONLESS NUhlBERS
Grashof number = g d a ( p , / p , - l)/vav2 Nzu = Susselt number = qrd/Xr,,AT = qled/X,,AT
NGr
=
GREEKLETTERS
X
= temperature integrated thermal conductivity, cal/cm
sec
OK
174 Ind. Eng. Chem. Fundam., Vol. 1 1 , No. 2, 1972
Y,,
p
= =
linear average of wall and bulk viscosity, cm2/sec density, g/cm3
SUBSCRIPTS e = equilibrium f = frozen equilibrium r = reacting contribution rad = radiation contribution w = wall conditions m = properties of bulk fluid including equilibrium composition of NO2-NO-O2 system literature Cited
Alcock, C. B., Hooper, G. IT,, Proc. Roy. SOC.Sei-. A 254, 551 (1960). Bartlett, R. W., J . Electrochem. Soc., 114, ,547 (1967). Beer, H., Chem. Zng. Tech. 2.37, 1047 (1963). . (1966). Beer, H., Deubel, W., 2. F l u g w ~ s 14,281 Blvholder. G.. Allen. M ,C.. J . Phus. Chem. 70,352 11966). Bopp, G. ‘R.,’Mason, D. A I . , IXD:ENG.CHEM.,FLXDAM.4, 222 i1F)66\
Brewer;’L., Chem. Rev. 52, l(1953). Brokaw, R. S., J . Chem. Phys. 35, 1569 (1961). Chaston. J. C.. Platznum Metals Rev. 8, 50 (1964). Connor, H., Platicum Metals Rev. 11, 2, 60 (1967). Emmett, P. H., Catalysis. Volume I. Fundamental Principles (Part I),’’p 162, Reinhold, Sew York, S . Y., 1954. J . Chem. Phys. 32,622 (1960). Fryburg, G. C., Petrus, H. M., Fryburg, G. C., Petrus, H. M.,J . Electrochem. Soc. 108, 496 (1961). Green. T. E.. Hinshelwood. C. N.. J . Chem. SOC.(London) 128, 1709 (1926). McAdams, R. H., 3rd ed., McGraw-Hill, Xew York, K. Y., 14.54
Norman, J. H., Staley, H. G., Bell, W. E., J . Phys. Chem. 71, 3683 (1967). Kowak, E. J., Chem. En9. Scz. 21, 19 (1966). Ong, B. G., Ph.D. Thesis, Department of Chemical Engineering, Stanford University, Stanford, Calif., Aug 1970. Ong, B. C., Mason, D. M., J . Chem. En9. Data 15, 556 (1970). Ong, B. G., Mason, D. >I., Chem. Eng. Scz. 26, 1689 (1971). Schafer, H., Tebben, A. , Z . Anorg. Allg. Chem. 304, 249 (1960). Shelef, 31 , Otto, K., Gandhi, H., Atmos. Envzron. 3 , 107 (1969). Svehla, R. A., Brokaw, R. S., NASA TX D-3327, March 1966. Rikstrom, L L., Nobe, K., Ind. Eng.Chem., Process Des. Develop. 4, 191 (1965). RECEIVED for review September 1970 ACCEPTEDFebruary 7, 1972 Tables I and I1 containing heat transfer and calibration data will appear following these pages in the microfilm edition of this volume of the journal. Single copies may be obtained from the Business Operations Office, Books and Journals Division, American Chemical Society, 1155 Sixteenth St., N.W., Washington, D. C. 20036, by referring to code number FUND-72-169. Remit check or money order for $4.00 for photocopy or $2.00 for microfiche.
