J . Phys. Chem. 1988, 92, 6852-6853
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vacuum system and tilted to allow exposure of the benzenes-18C6 mixture to the potassium mirror. After dissolution of a mole of potassium metal for each mole of 18C6, the bulb containing the excess potassium (bulb b) was sealed from the apparatus at point 2, and the apparatus was reconnected to the vacuum system. All of the unreduced benzenes were then distilled under vacuum into a container on the vacuum line and saved as phase 1 for mass spectral and N M R analysis. The remaining potassium-crownbenzene complex was then left exposed to high vacuum (10” Torr) to ensure complete removal of the unreduced benzenes. About 5 mL of diethyl ether containing a molar excess of iodine was then distilled and sublimed directly onto the potassium-crown ether-benzene complex. The resulting reaction reoxidizes and liberates the benzenes, reaction 4. These reoxidized benzenes (phase 2) were then distilled and submitted to mass spectral and N M R analysis. In all experiments phase 2 proved to be highly enriched in the light isotopic isomer as compared to phase 1. Naphthalene Experiments. Mixtures of naphthalene and perdeuteriated naphthalene (1:4) were prepared by dissolving carefully weighed portions of each in diethyl ether. The ether solution was then divided into two portions, and the ether was allowed to evaporate under a nitrogen atmosphere. Both portions were reduced in T H F on a potassium metal mirror in the apparatus shown in Figure 3. However, for one portion, bulb b was charged
with only half of the stoichiometric amount of metal needed for complete reduction, and the other portion was completely reduced with an excess of metal. Water was then added to both reactions through the stopcock. The resulting organic materials were extracted with ether. The ether was dried with sodium sulfate and removed via evaporation. The naphthalene-dihydronaphthalenemixtures were then sublimed and dissolved in deuteriated chloroform for N M R analysis. Integration of the proton decoupled N M R spectra shows that each component of the C-D vinyl carbon triplet is more intense than the C-H vinyl carbon singlet by a factor of 1.2 for the completely reduced sample. However, this ratio is only 0.80 for the partially reduced sample. This corresponds to a separation factor of 1.5. All I3C N M R spectra were recorded in IO-mm tubes on a Joel FX 90Q N M R spectrometer. Mass spectral analysis was carried out on a Hewlett-Packard 5790 GC mass spectrometer with 30-m, 0.25 mm i.d. capillary columns of methylphenyl silicone. The isotopic ratios were determined from eight independent measurements of the 84/78 peak intensities.
Acknowledgment. We thank the National Science Foundation (Grant CHE-8411827) for support of this work. Registry NO. 18C6, 17455-13-9; C6H6, 71-43-2; C$6, 7440-09-7; CIOHg, 91-20-3; CIoDs, 1146-65-2.
1076-43-3;
K,
COMMENTS Photocatalytic Reactor Design: An Example of Mass-Transfer Llmltatlons wlth an Immobillzed Catalyst Sir: In a recent article,] a novel coiled glass-tube reactor was used to examine heterogeneous photocatalytic degradation kinetics. Earlier studies of kinetics of heterogeneously photocatalyzed systems2-s have characteristically used slurries of fine catalyst particles of, e.g., 0.1 wt % catalyst. For 0.2- and 0.03-pm particles, as typify earlier Fisher Chemical and Degussa T i 0 2 sources, in 0.001 weight fraction of solids (density 3.9 g/mL), the maximum reactant diffusion distance to the catalytic solid is half the mean particle spacing, or 3 and 0.5 pm, respectively. For the coiled tube reactor of 2-mm radius, the corresponding maximum transport distance is the centerline-to-catalyst coated wall distance of 2000 r m (2 mm). Thus, this reactor configuration, as well as a catalyst-coated packed bead column,6 clearly increases the average distance which a dissolved reactant must diffuse in order to reach the photocatalytically active surface. One must consider that the dependence of reactant removal rate on solution-to-catalyst diffusion/convection mass transfer, found to be negligible for 0.1 wt 7% catalyst slurry ~ y s t e m s may , ~ be significant for thin films of fixed catalyst. If so, the mass-transfer influence must be recognized and included in a proper kinetic analysis, as is traditionally d ~ n e . ~ . ~ ( 1 j Matthews, R. W. J . Phys. Chem. 1987, 91, 3328. (2) Ollis, D. F. Enuiron. Sci. Technol. 1985, 19, 480. (3) Matthews, R. W. Aust. J . Chem. 1987, 40, 667. (4) Okamoto, K.; Yarnamoto, Y.; Tanaka, H.; Tanaka, M.; Itaya, A. Bull.Chem. SOC.Jpn. 1985, 58, 2015. ( 5 ) Serpone, N. Presented at the AIChE Meeting, New York, Nov. 1987. (6) Serpone, N.; Borgarello, E.; Harris, R.; Cahill, P.; Borgarello, M.; Pelezzetti, E. Solar Energy Mater. 1986, 14, 121. (7) Schwartz, D. T. M.S. Thesis, University of California, Davis, 1985. (8) Hill, C. G.An Introduction to Chemical Engineering Kinetics and Reactor Design; Wiley: New York, 1977.
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We will calculate mass-transfer rates based entirely on geometry and fluid properties to show that the results reported by Matthews were completely or largely dependent on reactant convective diffusion to the tube wall rather than inherent surface reaction kinetics. Carbonell made similar use of mass-transfer relations to show a mass-transfer influence on enzyme kinetics in a coiled tube.I0 The T i 0 2 deposited film thickness was approximately 0.2 pm, roughly an order of magnitude less than that required for opacity,” and therefore a nearly constant illumination intensity was expected on the tube wall. We proceed by calculating mass-transfer coefficients (or equivalently mass-transfer Nusselt numbers, Nu) for both the straight tube and coiled tube cases. Rates of removal based on the mass flux from the moving fluid to the interior tube surface will be compared to Matthews’ experimental results. Matthews examined the degradation of several aromatic compounds and reported an increase in rate of reactant disappearance with increasing flow rate, a strong clue of diffusionally influenced kinetics. For salicylic acid, he reported a series of reaction rates for flowrates from 30 to 420 mL/min. These flows represented Reynolds numbers from 180 to 2500; thus the reactor was in the laminar flow regime everywhere. (The upper values appear to be within the transition region from laminar to turbulent flow, usually taken to begin at Re = 2100 for smooth straight tubes. However, fluid flow through coiled tubes is stabilized so that the laminar flow region is extended to higher Re.I2) Most of the correlations for transfer in coiled tubes were developed for heat transfer.I3 However, the established similarity of the heat- and mass-transfer mechanisms make the relations (9) Carberry, J. J. Chemical and Catalytic Reaction Engineering; McCraw-Hill: New York. 1976. (10) Carbonell, R. G . k t e c h n o l . Bioeng. 1975, 17, 1383. ( I 1) Formenti, M.; Juillet, F.; Meriaudeau, P.; Teichner, S.J. CHEMTECH 1971, I , 680. (12) Kalb, C. E.; Seader, J. D. J . Heat Mass Transfer 1972, 15, 801. (13) Berger, S.A.; Talbot, L.; Yao, L.-S. Annu. Reu. Fluid Mech. 1983, 15, 461.
0 1988 American Chemical Society
J . Phys. Chem. 1988, 92, 6853-6854
0
100
200 300 400 F l o w r a t e (mL/min)
500
Figure 1. Variation of initial rate of salicylic acid disappearance with flow rate. Data from ref 1. Curves 1 and 2 represent maximum removal rates due to mass transfer toward tube wall with an infinite wall reaction rate for a straight and coiled tube, respectively. Curve 3 employs a log mean concentration term to account for concentration decrease with axial distance in the coiled reactor. Curve 4 includes both mass-transfer and kinetic limitations (see eq 3, text).
completely analogous with the use of the appropriate dimensionless group^.'^.'^ The case of mass transfer to the wall of a straight tube is described by the semiempirical L W q u e equation.ls In coiled tubes, the centrifugal force involved establishes a secondary circulation pattern which enhances mass-transfer rates.13 Several relations for Nu have been suggested for this configuration; the one most applicable to the conditions of Matthews’ system was formulated by Dravid et al.:I6 Nu = (0.65De1I2 0 . 7 6 ) S ~ O . ’ ~ ~ (1)
+
Once having determined Nu for the straight and curved tube cases, the defining equation of Nu was used to estimate the mass-transfer coefficient, kL, and the corresponding reactant flux toward the tube wall: N = ~ L A ( -C Cwall)5 Nua),A(C - CwalJ/d (2) In our calculations, the diffusivity of benzoic acidI7 was used to approximate that of salicylic acid. If the surface reaction rate constant is infinite, Cwall= 0. Thus, the concentration driving force (C - Cwan)in eq 2 was taken to equal the feed (maximum possible) concentration. The calculated results for removal of reactant with an infinite reaction rate at the wall and the maximum possible driving force throughout the reactor length are shown as curves 1 and 2 in Figure 1. As expected, reactor coiling (curve 2) results in higher predicted mass-transfer rates compared to a straight tube (curve 1). Note that the observed rate lies between these two curves. The removal rates depicted are referred to initial conditions. To correct for the decrease in reactant concentration with axial distance, a log mean concentration differencels was substituted for the driving force in eq 2. The results of replacement of (C - Cwa,,)by ACiogmean are shown as curve 3 in Figure 1. Wall concentration, Cdl, was kept at zero in these calculations. Despite correction (curve 3), at higher flow rates the prethe AClogmean dicted removal rates exceed those observed experimentally. Agreement was closer at lower flow rates where mass-transfer effects were expected to be most significant. If the surface reaction rate was rapid but finite, Cwallwould no longer equal zero. For example, if the surface reaction rate then the observed rate can be written is given by r = kcAcCwall, as 1 observed rate = (1 /mass transfer) + (1 / k ~ c C w a l J(3) (14) Bird, R. B.; Stewart, W. E.; Lightfoot, E. N. Transport Phenomena; Wiley: New York, 1960; p 645. (1 5) Reference 14, p 405. (16) Dravid, A. N.; Smith, K. A,; Merrill, E. W.; Brian, P. L. AIChE J . 1971, 14, 1114. (17) Reid, R. C.; Prausnitz, J. M.; Sherwood, T. K. The Properties o/ Gases and Liquids, 3rd ed.; McGraw-Hill: New York, 1977; p 577. (18) Bird, R. 8.;Stewart, W. E.; Lightfoot, E. N. Transport Phenomena; Wiley: New York, 1960; p 391.
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Using the AClogmean modified form of eq 2 for the mass-transfer dependence along with the observed removal rates, the kinetic term in eq 3 can be estimated. Since the surface reaction is here assumed to be proportional to the wall concentration, assumed to be constant and nonzero, the derived kinetic term is also a constant. This assumption oversimplifies the kinetic dependence, yet is sufficiently accurate in light of the greater importance of the mass-transfer influence. From eq 3, the kinetic term was estimated as about 25% of the denominator for the highest flow rate (420 mL/min). With this single point estimate, a curve corrected for both mass transfer and reaction kinetics was calculated; the resulting fit is curve 4 in Figure l . Matthews’ operating conditions are shown in the present analysis to have been in a regime which was largely, if not entirely, mass-transfer dependent. Future studies with this coiled tube or other immobilized photocatalyst configurations must take both mass-transfer and chemical kinetic influences into proper account if fundamental meaning is to be assigned to the observed parameters.
Glossary
sc
reactor interior surface area catalyst surface area flow-averaged concentration, pmol/L interior tube diameter; reactant diffusivity,cm2/min Dean number, Re(rw/Rc)’12 catalytic rate constant mass-transfer coefficient, cm/min axial tube length molar flux toward wall, mol/min mass-transfer Nusselt number ( k L d / B s ) flow rate, mL/min rate of reactant removal, mol/min interior tube radius radius of curvature of tube coil Reynolds number (4Qp/rd&) Schmidt number ( p / p D , )
P P
fluid viscosity fluid density
A AC C
d B S
De kC kL L N Nu
Q r
rw
Rc
Re
Department of Chemical Engineering North Carolina State University Raleigh, North Carolina 27695- 7905
Craig S. Turchi* David F. Ollis
Received: April 25, 1988
Response to the Comment “Photocatalytic Reactor Design: An Example of Mass-Transfer Limitations with an Immobilized Catalyst” Sir: The analysis by Turchi and Ollis’ shows that the flow rate dependence observed in the coiled glass-tube reactor2 can be quantitatively explained in terms of a combination of reaction characteristics and mass-transfer limitations. N o mass-transfer limitation is expected for photocatalysis using slurries of very fine catalyst particles of, e.g., 0.1 wt % Fisher Chemical or Degussa P25 Ti02 catalysts since the maximum diffusion distance is very small. Differences in reaction rates observed under identical conditions in these systems have been attributed solely to the inherent surface reaction characteristics of different reactants on the photocatalyst. Turchi and Ollis state that because of masstransfer limitations in the coiled reactor the results reported* may have little relevance to inherent surface reaction characteristics but may be completely or largely dependent on the reactive convective-diffusion to the tube wall. If this is true then there should be a correlation between reaction rates and diffusion (1) Turchi, C. S.; Ollis, D. F. J . Phys. Chem., preceding paper in this issue. (2) Matthews, R. W. J . Phys. Chem. 1987, 91, 3328.
0 1988 American Chemical Society
