William C. Herndon University
of
Mississippi University
I
Kinetics in Gas-Phase Stirred Flow Reactors
I n a flow reactor, a physical process (the rate of flow) is opposed to a chemical process (the rate of reaction). This opposition leads to steady-state concentrations of products and reactants in the reactor, and a determination of these concentrations combined with a knowledge of the volume of the reactor and the flow rate allows one t o determine the rate of the chemical process. Since the physical process, the flow rate, can be varied over a wide range, flow methods are applicable to a very large dynamic range of reaction rates. Reactions with half lives as small as 2 msec (1) and as large as 10,000sec (2)have been investigated in such systems. Flow techniques can be divided into two groups, tube reactor methods and stirred reactor methods. I n a tubular flow reactor, concentrations vary in a differential manner from entrance to exit with the concentration of products and reactants a t any point being invariant with time. Flow reactors for work in the gas phase have usually been of the tubular type. Benson (3) has discussed some of the disadvantages of using such flow reactors to obtain precise data in gaseous systems. Stirred flow reactors are fundamentally different from tube flow reactors because the concentrations of products and reactants are assumed to be uniform throughout the reactor volume. The time-invariant concentrations in such a system allow one to determine rates of reactions from algebraic expressions rather than differential or integrated rate equations (see below). This type of reactor has also been termed a capacity flow reactor (4),and numerous applications of liquid-phase capacity flow reactors to the study of kinetics and mechanisms may be found in the literature. The first reaction to be studied in a stirred flow reactor was a gas-phase reaction (5), but comparatively little gas-phase research is reported. Recently there has been a renewal of interest, and this article will review both past and recent work in gas-phase stirred flow reactors. I n addition some new applications and a simple experiment for the physical chemistry laboratory will be suggested.
much attention (16-19). Transient conditions (20) and design equations (21, 22) are also discussed. Various applications to complex reactions l i e polymerization (8, 25-25) and even reactions in living cells (7) have been suggested and studied. It should be pointed out that the references which have been cited are typical but not exhaustive. Early Developments in Gas-Phase Stirred Flow Reactors
Bodenstein and Wolgast (5) studied the rate of combination of hydrogen and iodine in a gas-phase flow reactor and were the first to realize that diffusion in the reactor would render the usual Emetic equations invalid. Assuming that the rates of reaction and flow are small in comparison to diffusion, they derived kinetic equations for first and second order reactions which are much different from the kinetic equations in static or tube flow systems. The derivations shown here are not exactly like those of Bodenstein and Wolgast but give rate equations of exactly the same form. The first order reaction A -+ P is assumed to take place in a stirred flow reactor of volume V . If k
Reaction A -& P
rate
Volude 'l
the flow rate is U and the first order rate constant is k,, a material balance a t the steady state gives: UIA]" = UIA] b V [ A ] (1) [ A ] "is the concentration of reactant in the entering gas stream and [ A ] is the concentration in the reactor and exit stream. Equation (1) can be rearranged to give the rate constant as shown in equation (2).
+
+
Similarly for a second-order reaction, A B -+ P. UIA]" = UIAI klVlA1 IBI
+
(3)
Background
The theory of continuous stirred systems is discussed in detail by Denbigh and various other workers (4, 6-8). Hammett and several co-workers (9-1 3) have published papers in which various techniques and applications of liquid-phase stirred flow reactors are described. A summarizing article by Denbigh and Page (14) also gives some applications. The designs of stirred flow reactors have been considered (15), and the mixing process in such reactors has received
Bodenstein and Wolgast studied the hydrogen and iodine reaction with hydrogen in large excess using an equation similar to equation (4), and they obtained results which agree quite well with those of previous (26) and later workers (27). They also state that the experiments of Jellinak (28) on the thermal decomposition of nitric oxide are better correlated with the stirred flow reactor equations. Jellinak had used a Volume 47, Number 8, August 7964
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425
tube of large d~anieterand had not considered the factor of diffusion. Later, Bodenstein and Durant ($9) used their diusion-stirred reactor t o investigate the gas-phase reaction of carbon monoxide with chlorine to give phosgene. Diffusion and Volume Change
Of course, the preceding work assumed that there was no volume change in the reacting gas. Langmuir (30)pointed this assumption out and also derived some eq~ationsfor a gas-phase flow reactor in which only partial mixing by diffusion occurs. Forster and Geib (51) considered flow reactors from much the same point of view as Langmuir. In addition, experimental work has been done in partially mixed gasphase flow reactors. For example, RlcLane (52) has studied the thermal deconlposition of hydrogcn peroxide under conditions where diffusion was important but not sufficient to completely mix the contents of his reactor. In part, he used the equations of Hulbert (53) to correlate his data. KcLane (32) also designed a stirred flow reactor in which diffusion and the velocity of the entering gas were utilized in the mixing process. His rate constants a t different flow rates agreed well with each other, indicating that uniform con~position was obtained without mechanical stirring even with quite rapid rates of reaction (k, sec-I = 0.46). Harris (34) has considered four cases of gas-phase reactions in flow systems where a volume change takes place in the reacting gas. Equations are derived for nC and A B nC under condithe reactions A tions of negligible diffusion and complete diffusion. Under conditions of complete mixiig for the first order reaction A -+ nC,the first order rate constant can be found from equation (5). I n this equation U" is the
-
+
-
velocity of flow of the entering gas, NA0is the number of moles of reactant entering the reactor per unit time, and No is the number of product C leaving the reactor per unit time. If no volume change is involved in the reaction (either n is 1 or a large excess of inert carrier gas is used), equation (5) can be simplified to (6).
Lewis and Herndon ($), Mulcahy and Williams (35), and de Graaf and Kwart (36) derive the same type of equation for a first-order reaction as equation ( 5 ) , and each points out the same simplification. From an experimental point of view, one should note that complications of the kinetic equations in stirred flow reactors are always avoided if one measures the flow rate of the effluent gas rather than that of the entering gas (2). Simple Reactions
A few simple first-order gas-phase reactious have been studied in stirred flow reactors and the results compared with those obtained from other experimental techniques. Mulcahy and Williams (55) studied the low-pressure decomposition of di-t-butyl peroxide over the tem426
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lournol of Chemical Education
perature range 154-274°C. The precision of the calculated rate constants was about lo%, and the d u e s obtained for the rate constants are in excellent agree ment with those obtained by others (87). De Graaf and Kwart (56) give an excellent summary of the advantages of gas-phase stirred flow reactors (capacity flow reactors) in comparison to tube flow systems. The most significant advantages are probably the facile elimination of temperature gradients in the stirred reactor and the simplified mathematical analysis of complex reactions. As a test of their stirred flow reactor, de Graaf and Kwart chose to investigate the pyrolysis of ethyl acetate to yield ethylene and acetic acid. Close correspondence to the results of Blades and Giderson (38) is found. However the rate constants of de Graaf and Kwart, taken over the large temperature range 376-531°C, show a departure from a linear Arrhenius plot. Because of the inherent accuracy of their experimental technique, de Graaf and Kwart conclude that the deviation from linearity is real and controlled by a change in mechanism for the pyrolysis. The reactor of de Graaf and Kwart was stirred mechanically. Mechanical stirring of a gas-phase flow reactor is also reported by Bricker (59) during a study of a gas-phase Claisen rearrangement. Herndou, Henly, and Sullivan (40) estimated the random and systematic errors for a diffusion-stirred gas-phase flow reactor. They conclude that the error in a calculated rate constant for a first-order reaction is &2..5Y0with most of this error being due to the use of a soap solution and buret in measuring the effluent flow rate. The thermal decomposition of cyclohexyl chloride which had previously been investigated by Swinbournc (41) was reinvestigated over a much larger temperature range and substantial agreemeut was obtained. Complex Reactions
As mentioned before, a major advantage of stirred flow reactors is the simple mathematical expressions which are obtained for complex reactions. For example, first-order concurrent reactions are treated as shown below. If a number of experiments at different effluent flow rates are done, a plot of U/V
- U[B] Vk*[A] - U[C] Vk,[A]
=
0 (material balance)
(7)
=
0 (material balance)
(8)
versus [A]/[B] should have a slope of kl and an intercept of zero. If the mechanism is not as postulated, important terms in flow rate and concentrations are introduced and the plot is not linear. First-order consecutive reactions are as easily handled. With experiments a t different flow rates a plot of U/V versus [A]/[B] should have slope k, and intercept -k? if the gross mechanism is correct.
V~,[AI v ~ > [ B ]- UIB] = k,[A]/[B]
o
(material balance for B )
- k~ = U/V
(9)
(10)
Lewis and Herndon (2) have studied the gas-phase thermal decompositiou of 2-butyl chloroformate, a reaction which involves four concurrent first-order reactions, in a manner analogous to that above. /1 2-chlorobutme CHa-CH-CHz--CHs
1
-+ cis-2-butene
+ tTans.2.bUtene
I I-butene
\c/ II
0
Good precision is obtained, and the coucurrence of the data to the rate equations is taken as evidence for concurrence to the postulated reaction scheme. The treatment of competing reactions of different substrates is also a very simple matter in a gas-phase stirred flow reactor. Herndon, Sullivan and Henly (43) have reported the competitive dehydrochlorination of a series of chlorocycloalkanes. Relative rate constants were obtained a t several temperatures which gave very accurate and precise differences in activation parameters (standard deviations in activation energy were about 200 cal).
Seay (43) has used a diffusion-stirred gas-phase system to study relative rates during photochemical chlorine exchange with aromatic bromides. The ratio of the rate constants is as shown in equation (12) a t any extent of completion. klk' = ( [ArCI'] /[Arc11 )( [ArBrl/[ArBr'])
(12)
The thermal decomposition of hicyclo[2.2.1]hepta2,s-diene (BCH) is a complex reaction involving three concurrent first-order reactions and one consecutive reaction (44-48) as shown below. It is possible to
obtain exact integrated rate equations for the variation with time of each moiety for use in a static gas system, but the utilization of a stirred flow system makes the kinetic analysis much simpler. Herndon and Lowry (48) have determined the rate constants for all four of these reactions in the manner illustrated below. First the material balance equations are wrikten for the system, and then the equations are rearranged to give equations (14a), (14b), and (14~). k,V[BCH! - U[CPD] = 0 k2V[BCH] - U[CHT] knVIBCHl - WIT]
(13%)
- krV[CHT] = 0
+ knV[CHT]
=
0
UIV = k,(BCH)/[CPD] U/V = kdRCH)/ICHT] - k, U/V.(T)/[CHT] = ksLBCHI/[CHT]
(13b) (13~) (14a) (14b)
+ k,
(1k)
With analyses of the conteuts of the reactor a t various flow rates, the rate constants can be determined from the slopes and intercepts of straight lmes. If toluene were formed solely from cycloheptatriene, equation (14e) would give a straight line with a zero slope. If toluene were formed only from bicycloheptadiene, equatiou (14e) would yield a straight line with a zero intercept. The results obtaiued were quite precise and consisteut with the scheme proposed. Some other applications of stirred flow react,ors which may be noted are a study of chlorination by de Graaf (49) and an investigation of thermal cracking of ethane in a stirred fluidized catalyst bed (50). Numerous studies on conlbustion processes in stirred flow reactors have also been published (51-54). Finally, gas-phase stirred reactor kinetic experiments have been combined with mass spectrometric analyses by IGstiakowsky and Volpi (55) during a study of the reactions of nitrogen atoms. A Simple Oar-Phase Kinetic Experiment Bicyclo[2.2.l]heptene decomposes in the gas phase to yield cyclopentadiene and ethylene a t a convenient rate in the temperature range 300 to 50O0C (56).
The reaction is exceptionally cleau with no other products detectable by high-sensitivity chromatographic methods. Nitrogen, helium, carbon dioxide, and even steam have heeu used as carrier gases with no effect upon the rate constant. The conditions of the walls of the vessel have no effect upon the rate, and in our laboratory rate constants determined a t the same temperature in either a stirred reactor or a tube flow reactor were identical. Bicyclo[2.2.l]heptene is readily available comn~ercially and requires no purification. It can be vaporized by simply directing a stream of carrier gas over the solid. A conveuient molten lead constant temperature bath can be constructed from a stainless steel beaker and heating mantle. Temperature is easily controlled to 0.5' with a powerstat and can be measured with a Chromel-Alumel thermocouple inserted in the reacting gas. The flow rate of the carrier gas is usually controlled by a needle valve, and the efluent gas flow rate is measured with a soap-bubble flow meter. The most convenient analysis is by gas chromatography, for cyclopentadiene and bicycloheptene are easily separable. The data are usually processed by the method of least squares using an IBM 1620 computer. A list of rate constants at different temperatures for this reaction is available from this laboratory. Acknowledgment
The support of the National Science Fonndat,ion for much of the work a t the University of Mississippi in gas-phase stirred flow reactors is gratefully acknowledged. I also wish to tha.nk Prof. Edward S. Lewis, Rice University, who first suggested to me the use of the stirred reactor for gas-phase kinetics, and Prof. Michel Boudart, University of California, who suggested this article. Volume 41, Number 8, August 1964
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Literature Cited
(29) BODENBTEIN, M., AND DURANT,G., 2. physik. Chem., 61, 437 -- . 119IlRI - - - ,. (30) LANCMUIR, I., J . Am. Chem. Soc., 30,1742 (1908). (31) FORSTER,T.,AND GEIB,K. H., Ann. Physik, 20,250 (1934). (32) MCLANE,C. K., J . Chem. Phys., 17,379 (1949). (33) HULBERT,H. M., Ind. Eng. Chem., 36, 1012 (1944); 37, 1063 (1945). (34) HARRIS,G. M., J . Phys. Chem., 51, 505 (1947). (35) MULCAHY, M. F. R., AND WILLIAMS,D. J., Ausbalian J. Chem., 14,535 (1961). (36) DE GRAAF,J., AND KWART,H., J . Phgs. Chem., 67, 1458 (1963). (37) See references in (36),p. 543. A. T.. AND GILDERSON, P. W., Can. J . Chem.,. 38,. (38) . . BLADES, 1407 (1960): (39) BRICKER, J. H., "A Theoretical and Experimental Analysis of the Claisen Rearrangement in the Ges Phase," PhD. Thesia, Univ. of Pittsburgh, 1961, p. 22. (40) HERNDON, W. C., HENLY,M. B., AND SULLIVAN, J . M., J. Phys. Chem., 67,2842 (1963). (41) SWINBOURNE, E. S., Australian J. Chem., 11,314 (1958). (42) HERNDON, W. C., SULLIVAN, J. M., AND HENLY,M. B., "Abstracts of Papers," 145th Meeting of the American Chemical Society, 1963,p. 280. (43) SEAY,H. W. G., JR., '5Solvent Effects in Aromatic Hdogen Exchange," IMS Thesis, Univ. of Mississippi, 1963, pp. 224. (44) WOODS,W. G., J . Org. Chem., 23,110(1958). G., SWIFT,E. W., AND POLLARD, (45) HALFER,W. M., GAETNER, G. E., Ind. Eng. Chem., 50, 1131 (1958). (46) BIRELY,J. H., AND CHESICK,J. P., J. Phys. Chem., 66, 568 (1962). J. P., J . Am. Chem. Soc.,85, (47) KLUMP,K. N., AND CHESICK, 130 (1963). (48) HERNDON, W. C., AND LOWRY,L. L., "Mechanism of Pyrolysis of Bicyelo[2.2.l]heptadiene, Kinetics of the Bicyclo[2.2.llheptildiene to Toluene Isomerization," J. Am. Chem. Soc.,in press. (49) DE GRAAF,J., "A Stirred-GBS-Flow Reactor, Kinetica of the Chlorin&m of Chlorobenzene." PhD Thais. Univ. of Leiden, 1963. (50) A. M..KALINENKO. R. A.. AND LAVROSKY. K. P.. . , BRODSKY. J . ~ h e kSoe.,'1960,4443. ' (51) NIXON,I. S., as in reference (14),p. 150. (52) LONGWELL, J. P., AND WEISS, M. A,, Ind. Eng. Chem., 47, 1634 (1955). (53) SCHNEIDER,G. R., "Kinetics of Propane Combustion in a Well Stirred Reactor," PhD Thesis, M.I.T., 1960, and references cited therein. (54) NERHEIM,N. M.,"The Combustion of Carbon Monoxide in a Well Stirred Reactor." PhD Thesis. M.I.T.. 1960. (55) KISTIAKOWSKI, G. n., AND'VOLPI, G. G.; J. ~ h e k Phys., . 27, 1141 (1957); 28, 665 (1958). (56) HERNDON, W. C., COOPER,W. A,, AND CHAMBERS, M., J. Phys. Chem., in press \
(1) For a review of measurement of rates of rapid reactions in flow systems see the chapter entitled "Rapid Reitctions" by ROUGHTON, F. J. W., AND CHANCE, B., "Technique of Organic Chemistry," Vol. VIII, part 2, 2nd ed., John Wiley and Sons, New York, 1963, pp. 703-93. (2) LEWIS, E. S., AND HERNDON, W. C., J. Am. Chem. Soc., 83.195513961 --,-... ~ -). ~ ~ - , ~ BENSON, S. W., "The Foundations of Chemical Kinetics," McGraw-Hill Book Co., New York, 1960, p. 62. STEAD, B., PAGE,F. M., AND DENRICH, K. G., Disc. Faraday Soe., 2,263 (1947). BODENSTEIN, M., AND WOLGAST, K., 2.physik. Chem., 61, 422 (1908). DENBICH,K. G., Trans. Faraday Soe.,40, 352 (1944). . . DENBICH.K. G.. HICKS. M.. AND PAGE.F. M.. Trans. ~ o r n d o ;Soe . 44. li9411i. , 479 ~ ---,~ (8) G., Trans. Faraday Soc.,43, 648 (1947). (9) YOUNG, H. H. JR., AND HAMMETT,L. P., J . Am. Ch'hem.Soc., 72,280(1950). (10) SALDICK, J., AND HAMMETT, L. P., J . Am. Chem. SOC.,72, 283 (1950). L. P.. J . Am. Chem. Soc.. (11) RAND.M. J.. AND HAMMETT.
DENRICH;KI ~
~
~~~~~~
.
~
~
.
(12) HUMPHREYS, H: M., AND HAMMET, L. P., J. Am. Chem. Soc., 78,521(1956). (13) BURNETT, R. L., AND HAMMETT, L. P., J. Am. Chem. Soc., 80,2415(1958). (14) DENBIGH, K. G., AND PAGE,F. M., Tram. Faraday Sac., 50,145 (1954). ~ M., Trans. Famday Soc.,49,1033 (1953). (15) P A CF. (16) DANKWERTS, P. V., Chem. Eng. Sci.,2, l(1953). (17) R. E.. JOHNSON. R. L..' AND NOW. H. D.. . , GREENHALGH. Chem. Eng.'~rog.,55, 44 (1959). (18) CHOLETTE, A., AND CLOUTIER, L., Can. J. Chem. Eng., 37, l(15 ,*""",. (lO5QI --"
(19) CHOLETTE,A., BLANCHET, J., AND CLOUTIER, L., Can. J. Chem. Ens., 38, 7 (1960), and other references cited therein. (20) MASON,D. R., AND PIRET, E . L., Ind. Eng. Chem., 42, 81711950). . . (21) JOHNSON, J. D., AND EDWARDS, L. J., T ~ a n sFaraday . SOC., 45,286 (1949). (22) ARIS, R., AND AMUNDSON, N. R., Chem. Eng. Sci.,9, 250 (1959). C. J., AND FLORIN, R. E., J. Polymw (23) WALL,F.T., DELBECQ, Sci.,9,177(1952). J. J., J. Polymer Sci., 11, (24) HORIKX,M. M., AND HERMANS, 325 (1954). (25) LEE. C. L.. SMID.J.. AND SZWARC. M.. J . Am. Chem. Soc.. ,~
~ - - ~ - , ~
- -
(26) BODENSTEIN, M.,2.physik. Chem., 29, 295 (1898). (27) SULLIVAN, J. H., J . Chem. Phys., 30, 1292,1577 (1959). (28) JELLINEK, K.,2.anorg. Chem., 49, 229 (1906).
MCA Honors Three College Chemistry Teachers T h e 1964 College Chemistry Teacher Awards of t h e Manufacturing Chemists' Association were presented on June 11,1964 a t t h e annual meeting, White Sulphur Sprinss, W. Va. Those honored were: Dr. Sara Jane Rhoads, University of Wyoming, Laramie, Wyoming Dr. John H. Wolfenden, Dartmouth College, Hanover, New Hampshire Dr. Hubert N. Alyea, Princeton University, Princeton. New Jersey
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Journal o f Chemicol Education
