Fisurc l o . Schematic rcprcrtntation of the gas chromalogrophic scparafion of compounds
A and B. CompoundB moues marc rapidly through fhc column because of a lowirparfifion cwficient for the rfnfionaryphase-gar (mobile) phast disfribution
STATIONARY PHASE
.. 10
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STANLEY H. LANGER
JAMES E. PATTON
JOANNE Y. YURCHAK
The Gas Chromatographic Column as a Chemical Reactor Small sample requirements and good control over temperature and residence time make the GC column valuable as a reactor in a wide variety of situations
hile physicochemical applications of gas chromatogW raphy have been developing a t a steady rate during the past few years (49, 80), the adaptation of the column for kinetic studies and the use of the column as a chemical reactor have been notably neglected. Even in this area, however, special exception must be made for the field of catalysis where gas chromatographic kinetic techniques have been employed on several occasions. I n this survey, we discuss the over-all potential of the gas chromatographic column as a chemical reactor, summarize and indicate the extent of most earlier work, and describe some of our own general experimental observations in this area. Before proceeding, it should be understood that our discussion basically is limited to reactions in the column p e r se. Other types of systems involving flow or batch reactors and subsequent chromatographic analysis are certainly well known but would fit more properly into a less specialized discussion. I t also should be recognized that temperature control is often the limiting consideration in contemplated kinetic applications of the gas chromatographic column, as it is with many other physicochemical applications. At present, commercial gas chromatographs seldom have the control capability to keep temperature constant and to limit gradients to 0.1 to 0.4 "C throughout the heated chamber so that meaningful kinetic experiments can be performed. An idealized schematic representation of separation of nonreactive compounds on a gas chromatographic column is depicted in Figure la. Compounds present in a mixture are independently distributed between the moving and stationary phases according to their characteristic
partition coefficients. Compounds with higher partition coefficients and greater affinity for the stationary phase tend to be retained in the column while compounds with smaller partition coefficients are swept through the column at higher velocities by the mobile phase. The unique potential of a chromatographic column as a chemical reactor stems from two major factors: (a) the presence of concerted reaction and separation processes in the column and (b) the relative ease in measuring the amount of material injected into the column and the amount eluted after a given residence time. Under the proper conditions, a rate constant and concentration dependence can then be determined. Because of the nature of the chromatographic process and the inherent presence of longitudinal diffusion and a pressure gradient, kinetic studies are usually limited to first-order or pseudofirst-order reactions with respect to the volatile component. T h e general chromatographic approach involves injection of a reactant or reaction mixture into the reactor column as a pulse. T h e distribution of injected materials between the mobile (gas or liquid) and stationary phases is then determined by individual partition coefficients. T h e mobile phase, which may itself be a reactant, sweeps reactants, products, and inerts through the column at velocities determined by their relative distribution in the mobile phase. When products differ from reactants in their affinity for the stationary phase, they travel through the column at different velocities, and separation tends to occur. O n this basis, many different types of chromatographic columns, both gas and liquid, can be utilized as chemical reactors. VOL.
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Ideal Chromatographic Reactor
T h e potential of a chromatographic reactor perhaps might best be understood by defining and characterizing a general “ideal chromatographic reactor” which differs from the three common ideal reactors-batch, plug flow, and continuous stirred tank. T h e language here is that of gas chromatography. However, the concept of the ideal chromatographic reactor is not limited to gas chromatographic reactors. I t is applicable with other types of chromatography as well. I n the ideal chromatographic reactor: (a) A nonsteady-state pulse reacts as it is swept through the column, and the resulting products are instantaneously separated from the reactant pulse, implying an infinite difference in retention volumes. T h e concept of instant separation here is in contrast to the concept of instant uniform mixing in the continuous stirred tank reactor. (b) T h e column is homogeneous i n composition; neither the mobile phase nor the stationary phase changes in composition throughout the column except during passage of small concentrations of eluents. T h e mobile phase should be incompressible so that its linear velocity is constant through the column. For a gas, the ideal chromatographic situation is approached by minimizing the ratio of inlet to outlet pressure across the column. (c) T h e height of a theoretical plate approaches zero. Peak spreading and axial diffusion on passing through the column (and the residence time distribution of reactants) are considered negligible. (d) Reaction rates are chemically controlled-i,e., mass transfer, adsorption, or absorption cannot be rate limiting to any extent. When these processes are relatively fast, partition between phases is constant and can be treated in a simple manner. (e) T h e distribution isotherms between mobile and stationary phases are linear. (f) T h e column is isothermal, and heat effects, both solution and reaction, are negligible. T h e ideal chromatographic reactor is, of course, the limiting objective for the operation of the real chromatographic reactor. Fortunately, the above characteristics are often features of the real reactor for small, narrow pulses. Given these characteristics, one can envision many of the possible practical advantages of the chromatographic reactor generally and the gas chromatographic reactor particularly. b T h e instantaneous separation of products and reactants would allow the study of reacting systems where reversibility causes kinetic complications. T h e isolation of products from reactants permits study of the forward reaction alone. Where two products are formed and they are separated from each other, reverse reaction is also eliminated. Furthermore, separation of reactants and products might make possible the study of the kinetics 12
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Figure I b . Material balance for a section of the ideal chromatographic reactor of volume V
of systems usually complicated by autocatalysis or product inhibition. b Small samples can be studied so that the ideal reactor is approached, and heat effects can be accommodated or minimized. b Systems involving volatile products and reactants become very viable. These are often most difficult to study by conventional means. b Reactants may not need to be completely purified because of the separation process in the chromatographic column. b I t is relatively simple to study temperature and residence-time effects since most chromatographs are equipped for convenient temperature change and flowrate regulation. O u r own interest was whetted by the following considerations: 1. While these reactors had been recognized as being useful in studying gas-solid reactions, little had been done on gas-liquid chromatographic systems. T h e determination of rate constants by simple variation of residence time is appealing. Even complications due to higher order reactions in the liquid phase could be diagnostic, once the simple first-order system is understood. 2. Isomerization reactions (particularly with terpenes and steroids) create complications in gas chromatographic columns. Investigations of such effects when they deliberately are made to occur in the column would enhance their recognition in columns where reactions were undesired. 3. Reversible reactions taking place in the column create special effects and complications which have been insufficiently studied. Keller and Giddings (46)recognized and discussed some of the complications in 1960. Klinkenberg treated them more extensively in 1961 (48). Theory
A material balance on a differential section of the ideal chromatographic column as shown in Figure 1b yields
with the boundary condition Cm(0, t ) = +(t) (2) and the initial condition Cm(X,0) = 0 (3) where Cm = Cm(x, t ) is the concentration of reactant in the mobile phase at distance x and time t in the column, C, = C,(x, t ) is the concentration of reactant in the stationary phase, rm is the rate of reaction in the mobile phase per unit volume mobile phase, rs is the rate of reaction in the stationary phase per unit volume stationary phase, f m is the volume of mobile phase per unit volume of column, fs is the volume of stationary phase per unit volume of column, u is the linear velocity of the mobile phase, x is the distance from the column inlet, t is the time, and + ( t ) is a n arbitrary bounded input function for which + ( t ) = 0 for t < 0. Since the isotherms are linear and constant,
Cn(x, t ) = +(t - acx)e-@ (10) T h e solution of the mass balance is most interesting when compared at two points, the inlet ( x = 0) and the outlet ( x = L) of the chromatographic column. At these points, Equation 10 becomes Cm(0, t ) = 4 ( t ) C,(L, t ) = +(t - aL)e-PL (1 1) T h e total amount of reactant entering the column is
CS - K
where F is the volumetric flow rate. Since +(t) = 0 for
(4)
Cm Combining Equations 1 and 4
Win
= =
Cm(O,t)dt
FJo”
.so”
+(t)dt
and the total amount leaving the column is W,,,
=
FSo” Cm(L,t)dt
=
Fe-PLJom +(t - 0rL)dt
t
< 0,
S,”
(13)
+(t - aL)dt, and
+(t)dt must equal Jo”
Equations 1 2 and 13 can be combined to eliminate the integral. If both the reactions are irreversible first order, rm = kmCmand rs = k,C,. T h e over-all stationary phase-rate constant, k,, is the sum of two rate constants-a rate constant associated with a homogeneous liquid-phase reaction and a second-rate constant associated with the reaction catalyzed by a solid support. T h e latter rate constant is dependent on the solid support and any liquid loading, as well as temperature. Usually, one or the other of these terms predominates. Then Equation 5 becomes
(fm
+ Kfs) (”)dt
=
-fmu(””)dX
- (fmkm
+fsksK)Cm (6)
or more simply
(7) where
+fsK fmu fmkm fsk& P = fmu Since L/u is the residence time in the mobile phase, tm, and Kf,L/u is the residence time in the stationary phase, t,, Equation 8 can be rewritten tm ts L kmtm ksts P = (9) ff=
fm
+
ff=-
+
+
Walt -
- (?-PL
Win Replacing
p
according to Equation 9 gives
For situations considered here, k , is very small and the corresponding exponential expression is nearly unity so that
wout -
-
e-ksts
Win This equation for a first-order reaction under ideal chromatographic conditions is analogous to the one which applies to the conventional steady-state flow or batch reactor. T h e reactor chromatogram is obtained from a recorder attached to a detector located at the column outlet. Since the area under a peak on the reactor chromatogram is proportional to the amount of species corresponding to that peak which leaves the column, Equation 16 can be rewritten In
(2)
=
-kst,
where SR is the area under the reactant peak from a detector located a t the column outlet and &:’ is the area under the reactant peak from a detector located a t the column inlet. Addition of a n inert to the reaction mixture produces another peak of area SI. Adding &,’ to both sides of Equation 17 and rearranging, we get:
T h e solution of Equation 7 is found readily with Laplace transforms (25) VOL.
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If a standard reaction mixture is always used, the initial weight ratio, and thus the initial area ratio, of inert to reactant will remain essentially constant regardless of the v-olume of the sample injected into the column. Consequently, In (S,/S;) is a constant. Since In and t , can be obtained experimentally, k , can be evaluated. The detector sensitivity for each individual component is assumed to be independent of flow rate and sample size. Consequently, the sensitivity terms do not appear in Equation 18 (107). A hypothetical reactor chromatogram for a volatile reactant going to a volatile product with a smaller characteristic retention volume is shown in Figure 2. T h e open area shows the product band and indicates how it interferes with the reactant peak for a real case where separation is incomplete. A reasonable estimate can be made of the relative amount of product occurring in an eluted reactant peak so that Equation 18 can be applied. In early chromatographic investigations, and even in much recent work, reactions occurring in tha chroniatographic column have been considered a complicating feature. Hesse (42) compiled a review of reactions occurring during chromatographic separations. Although analytical use has been made of these reactions and reviews of the field are available (5, Y), the scope of this paper is limited to kinetic and catalytic studies of reactions occurring in the gas chromatographic reactor.
(s,/s,)
irreversible Reactions
Bassett and Habgood ( 4 ) assumed a linear adsorption isotherm in their landmark publication in deriving an equation relating the first-order heterogeneous rate constant for the irreversible catalytic isomerization of cyclopropane to the fractional conversion, the chromatographic retention volume of the reactant on the solid catalyst, and the carrier gas-flow rate. Their equation is similar to Equation 18. They then calculated the Arrhenius form of the rate constant and the heat of adsorption for the reactant. Although they used a catalytic microreactor attached to an analytical column for the major portion of their work, they obtained a reactor chromatogram in a separate experiment which demonstrated that a longer reactor could partially separate the products and reactants. Again, the method works only for first-order reactions since the partial pressure of the reactant varies along the reactor, and it is only for a first-order reaction that the fractional conversion is independent of the pressure. Gil-Av and Herzberg-Minzly (35) first studied a bimolecular reaction by using one reactant in large excess as the stationary phase to obtain a pseudo-first-order reaction. For the Diels-Alder addition between chloromaleic anhydride and aliphatic dienes, the reactive nonvolatile liquid anhydride was used as the stationary phase. Since practically no anhydride was consumed by 14
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Figure 2. Hjpothetical reactor chromatogum j o r an irreuersible ,firstorder reaction with thelormation of a volatile product
the small diene pulse during each run, the anhydride composition remained essentially constant. T h e dienes were injected together with an inert internal standard, and the course of the reaction was followed by noting variation of eluted diene relative to the standard (Equation 18). T h e nonvolatile reaction product remaining in the column did not interfere with the eluted reactant peak and separation was complete. This tends toward the ideal reactor prototype in that the difference in retention times is infinite and separation is fast. Pseudo-firstorder rate constants and activation energies calculated agreed with literature values obtained by conventional methods. Berezkin et al. (6) extended Gil-Av's work by using maleic anhydride dissolved in tricresyl phosphate as a liquid phase on firebrick. They calculated true rate constants by determining the concentration of maleic anhydride in the liquid phase. By varying the maleic anhydride concentration, they found the order with respect to the anhydride to differ from unity. T h e reactor chromatogram expected from a reactor as shown in Figure 2 illustrates the complications inherent in a real situation when reaction products are volatile. Some incompletely separated product often appears in and distorts the reactant peak shown as a shaded area. While a correction can be readily estimated as is apparent from the figure, it may be difficult to do with ultimate accuracy. IllustratiL-e reactor chromatograms from our study of the variation of conversion of trioxane to formaldehyde arc shown in Figure 3. T h a t the reaction is firstorder in trioxane is apparent from Figure 4 where the logarithm of the ratio of the initial amount injected to the amount eluted is plotted against the residence time in the stationary phase as suggested by Equation 18. I n the figure, the ordinate was adjusted by subtraction of In S,/S! from the logarithm of the ratio of inert to reactant eluted. For reaction at 124 "C for 157, poly-
Figure 3. Reactor chromatograms.for the trioxane ( I ) depolymerization to formaldehyde ( 2 ) at 124 "C; the internal standard is o-xylene ( 3 ) . ( a ) E = 33.0 cc/min, 47y0 conversion; ( b ) E = 23.2 cc/min, 58% conversion; (6) F = 12.8 cc/min, ?iyOconversion; ( d ) F = 9.7 cc/min, 85% conversion
phenyl ether on firebrick (Gas Chrom RZ), we measured a first-order rate constant of 2.65 X sec-l. T h e consequence of a complex reaction with a variety of volatile products of varying characteristic columnretention volumes is illustrated in Figure 5 . This is for the isomerization and decomposition of &pinene. Reactant peak 3 is difficult to treat and analyze because of the varying and ambiguous nature of the products and their interference with eluted reactant. Nevertheless, it is apparent that a reaction constant more accurate than an order of magnitude can be estimated (107). Several theoretical treatments of irreversible reactions occurring in a chromatographic reactor have been reported. O n e of the most important of these was that of KaIlen and Heilbronner (45)who developed a theoretical model which added a first-order irreversible reaction to the plate theory of Martin and Synge (65). From their distribution functions, they simulated chromatograms using different combinations of rate constants and retention times. Their equations do not neglect the peak broadening processes of the pulse as it travels along the column as does Equation 18. Nakagaki and Nishino (74) extended the plate theory by integrating the distribution functions and obtained an equation for the first-order rate constant in terms of the number of theoretical plates, the carrier gas-flow rate, and the conversion. T h e rate constant, k,, may be k , = N(l - Wout/Win)l'(N+l)(l/t8) (19) where N is the number of plates in the column for the
Figure 4. First-order plots for the trioxane depolymerization in a 64-in. at column O'J polyphenyl ether (15yG) and silanized jirebrick (85yG) 124 "C ( k = 2.65 x 10-3 sec-1) and at 150°C ( k = 11.2 x 10-3 sec-1)
Figure 5. Reactor chromatogramsf o r the &pinene (3) decomposition to several products ( 4 ) at 100 "C; the internal standards are benzene ( 1 ) and toluene ( 2 ) . ( a ) F = 58.8cc/min, 70yGconversion; ( b ) E = 29.9 cc/min, 91% conversion
redrawn reactant peak and t , is the residence time of the reactant. A plot of N ( l - W o u t / ~ n ) l ' ( N f us. l ) residence time gives a straight line with a zero intercept as predicted. We found that the rate constant determined with this expression for the depolymerization of paraldehyde to acetaldehyde is in agreement within 3y0 with that obtained by using Equation 18 (107, 108). Roginskii and Rozental (85) derived the kinetic equaVOL.
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tion for chromatographic reactions from the statistical theory of adsorption and catalysis for heterogeneous surfaces. They related the kinetic constants to experimental data for low degrees of surface coverage. After a preliminary investigation of the hydrogenation of propylene in hydrogen carrier gas, Chang et al. (13) solved an equation for a first-order irreversible reaction proceeding under conditions of both equilibrium and nonequilibrium gas chromatography. By relating the rate constant to the other variables in the column and to the mass center of the reaction (the position on the chromatogram where one half the product has been eluted), they derived an implicit equation to calculate the rate constant directly from the chromatogram. T h e mass center method appears more sensitive to the neglected diffusion term than do the other methods, so that the rate constants obtained may be less accurate. We had difficulty in applying this method (107). Gaziev et al. (25) extended a n earlier qualitative treatment of Roginskii et al. (87) and solved the material balance for an nth-order reaction making essentially the assumptions described earlier. I n addition, they considered the effect of zero-, first-, and second-order reactions on the shape of the exit peak for rectangular and triangular peaks, and compared the formulas for the resulting k values with those used in dynamic reactors. They did not attempt to justify the assumption of constant partial pressure of reactant for the zero- and second-order reactions. Roginskii and Rozental (83) treated essmtially the same problem but also analyzed the case in which the rates of adsorption and desorption were commensurate with the rate of surface reaction. I n a later work, Roginskii et al. (89) enumerated those conditions essential for a reaction to proceed in the “chromatographic regime.” T h e methods and equations developed were then utilized for the investigation of the catalytic dehydrogenation of cyclohexane (26, 82, 88, 89) and of the oxidative dehydrogenation of butenes (82, 86, 90, 92, 93, 109). Filinovskii et al. (23) used the same experimental apparatus but calculated the rate constants from the yield curve of one of the products instead of the reactant. Experiinents have been performed to test the accuracy of results obtained from the chromatographic method. Schwab and Watson (91) compared the pulse method of Gaziev (25) with the more common steady-state flow reactor for the dehydrogenation of methanol. Activation energies and reaction orders calculated by the two procedures agreed within experimental error. However, when Gaziev compared the chromatographically determined activation energy for the dehydrogenation of cyclohexane with that determined in a static reactor, he found the former 2-3 kcal/mol lower. Roginskii (82) hypothesized that a chemical reaction had a lower activation energy and fewer side reactions in a chromatographic column. Among interesting variations in the use of the column as a reactor is the work of Berezkin et al. (7, 8) and Phillips et al. (79). Berezkin et al. (7, 8 ) applied the concept of linear variables with the chromatographic method to analyze 16
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the oxidation of benzaldehyde to benzoic acid. When air was used as a carrier gas, the oxidation of the benzaldehyde dissolved in the stationary phase was pseudofirst-order in benzaldehyde.
Assuming that the retention time of 2-butene pulsed periodically through the column was a linear function of the benzoic acid concentration in the stationary phase, they found
where T~ was the relative retention time of 2-butene in the benezaldehyde stationary phase, r o) was the relative retention time of 2-butene in a benzoic acid stationary phase, and r was the relative retention time of 2-butene in a binary mixture with benzaldehyde at concentration C,(t). T h e measured rate constant agreed with one obtained in a static reactor. Phillips et al. (79) eliminated the second column by utilizing a stopped-flow technique. After introduction of the reactant into the gas-solid chromatographic column, the carrier gas was interrnittently switched on and off. These periods of stopped flow produced sharp peaks superimposed on the continuous chromatograms. T h e first-order rate constants could be calculated from the positions, widths, and areas of two stopped flow peaks. T h e method was illustrated with the cyclopentyl chloride, cyclopentyl bromide, and cyclohexyl chloride dehydrohalogenation reactions. Microreactors
T h e pioneering effort of Kokes et al. (20, 52) gave significant impetus to the use of gas chromatographic methods for kinetic and catalytic studies. Kokes et al. pulsed a small amount of reactant into a small reactor attached directly to the inlet of a gas chromatographic column. I t should be stressed that the processes occurring in such a microreactor are identical with those occurring in the gas chromatographic reactor as defined by this paper. T h e sample pulse is diluted with carrier gas in both situations. T h e major difference between the two is that since the microreactor is possibly two orders of magnitude smaller than the gas chromatographic reactor, the sample pulse can be longer than the microreactor, and a significant separation of reactants and products cannot be effected. I n this case, a nonreactive auxiliary column is used for analytical purposes only. T h e mathematical analyses of the two are the same. Hall and Emmett (19,37, 38) refined the microreactor technique before the final design, theoretical treatment, and experimental applications were described by Hall et al. (39). Other studies have included the application of the microreactor to zero-order reactions (10)and to higher order reactions (11). Early attention to design features of the microcatalytic reactor certainly contributed to its widespread use in catalytic studies. Publications include instructions for the conversion of a commercial chromatograph into a micro-
catalytic reactor ( 2 4 , a detailed construction design for an automatic precision microreactor (40), and a design for a high pressure reactor (95, 98, 99). T h e convenience and rapidity of the microreactor make it especially attractive for comparing different catalysts for the same reaction (53, 72, 75, 110). Various catalysts were investigated for efficacy in the oxidation of automobile exhaust (I, 22, 43, 96, 97); catalysis by semiconductors (28-31) was investigated by similar procedure. Silica-alumina catalysts were tested for cracking isobutane and cumene (70), for the depolymerization of ethylene ( 7 4 , for the isomerization of cyclopropane (60), isobutane ( 7 4 , and isopentane (64), and for the conversion of acetaldehyde (44). Hydrogenation (11, 12, 18,41, 69,93),dehydrogenation (104,and thermal degradation ( 3 ) have also been studied. T h e reactivities of naphthenes over a platinum reforming catalyst (47), the hydrodesulfurization of thiophenes (16, 76-78), and the isomerization of cycloalkenes on aluminum oxide (54, 55) were similarly investigated. General reviews of microreactors and gas chromatography as used in catalysis research are available (24, 51, 73, 88, 102).
whereas a t 100 "C, for the same residence time, asingle peak is observed. T h a t the latter single peak is due to rapid interconversion of syn- and anti- forms is seen in Figure 7c where the two forms there are separated again at the same temperature by a faster flow rate. Thus, for ki
the reversible reaction A e B , if klt and k2t are small relaka
tive to unity, separation is possible. Conversely, if k l t and k2t are relatively large, a single peak with characteristic retention volume somewhere between that of A and B is obtained. T h e application of the theory for perturbation of local equilibrium has been extended to chemically reacting compounds traveling through a coIumn for both gas-solid (14) and gas-liquid chromatography ( 2 ) . Reacting systems were allowed to achieve chemical and physical equilibrium before introduction of a pulse-like perturbation. With radioactive isotopes one may work close to
Reversible Reactions
Reversible reactions are also amenable to studies in a gas chromatographic reactor. Klinkenberg (48) derived the material balance for a first-order/first-order reversible system. H e then made a transformation of variables to obtain a n equation previously solved by Walter (103). T h e rate constants would be determined from the peak broadening for the near-equilibrium situation and the position of the equilibrium peak with respect to the calculated position of the two pure isomers. Although Klinkenberg presented no data, he suggested that his equations could be applied to Moore and Ward's results (67, 68) for the interconversion of ortho- and parahydrogen. Keller and Giddings (46) calculated the probability distribution for the relative times spent in the product and the reactant forms for a reversible first-order/firstorder system. They then computed typical curves by assuming values for the initial concentrations, the rate constants, the average diffusivity, and time. A hypothetical chromatogram for a mixture of A and B where there is a reversible isomerization A e B is simulated in Figure 6. One peak is produced by molecules which have spent their entire residence time as the A isomer and the other peak by molecules which have existed only as the B isomer. Between the peaks is a n interfering regime produced by molecules which have traveled through part of the column as A and the rest as B. An additional complication due to differences in residence time is created by the fact that B is in the column longer than A. Figure 7, taken from our own experimental work (107), illustrates a real example of the situation theoretically considered by Klinkenberg and by Keller and Giddings. T h e reaction involved is the reversible interconversion of syn- and anti-acetaldoxime in polyethylene glycol. T h e two forms are seen to be separable in Figure 7a at 70 "C;
Figure 6. Hypothetical reactor chromatogramfor the reversible isomerization A e B
1200
800
400
0
1200
800
400
0
100
200
0
Figure 7. Reactor chromatograms illustrating the resolution obtained during the reversible isomerization between anti-(3) and syn-(4) acetaldoxime; the internal standards are toluene (1) and benzene ( 2 ) . ( a ) T = 70 "C, F = 108 cc/min; ( b ) T = 100 "C, F = 30 cc/min; ( c ) T = 100 "C, F = 166 cclmin VOL.
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equilibrium where partition coefficients and isotherms are locally linear with respect to the isotope, even though the system may be nonlinear with respect to major components whose behavior is represented by the isotope. Reaction times of peaks generated by the perturbation were related to the stoichiometry of the reaction, partition coefficients, and the chemical equilibrium constants. This approach has also been suggested as a potential source of near-equilibrium reaction rate data (49). Some Industrial Implications
T h e possibility of obtaining products in yields greater than those predicted from equilibrium data has a special appeal to industry. Roginskii et al. (87) and later Matsen et al. (66) recognized and described the potential of gas chromatography for running reactions toward completion when reversibility and thermodynamic complications occur. Thus, in the catalytic dehydrogenation of cyclohexane to form benzene and hydrogen, the use of the chromatographic reactor is advantageous in that the reverse reaction is minimized by separation of product hydrogen from benzene which is eluted after reactant cyclohexane. Per cent conversion in the pulse reactor (gas chromatograph) was compared with that under equilibrium conditions and found to be higher in every case. This approach is most advantageous where equilibrium constants and reaction rates are small. Magee (63) treated a model for a special form of reversible reaction in the gas chromatographic reactor: C. H e solved the case of that of the type A e B instantaneous equilibrium among products and reactants with an analog computer. Although he presented equations for noninstantaneous equilibrium, he did not attempt to solve them explicitly. From the analog computer solution, he concluded that a reversible reaction limited by equilibrium could be forced to completion in a chromatographic reactor if the equilibrium constant were greater than 2 X IO-' atm. T h e potential for achieving yields beyond equilibrium was recognized in patents awarded to Dinwiddie (17),Magee (62), and Gaziev (27). Matsen et al. (66) claimed yields of 30y0 beyond that predicted for equilibrium for the dehydrogenation of cyclohexane under optimum conditions; they found that conversion was practically independent of residence time for instantaneous equilibrium but depended upon the ratio of pulse size to column length. Roginskii et al. obtained yields for the conversion of butene to butadiene that were 20 to 30y0 higher in the chromatographic reactor than in other dynamic reactors (90) and yields for the dehydrogenation of cyclohexane that were higher than those obtained in dynamic reactors and also than that of the equilibrium conversion (89). Gore (36), using a model quite similar to that of Matsen et al. (66),compared the performance of a chromatographic reactor subjected to repetitive feed pulses with a steady-flow reactor by simulation on a digital computer. H e found that the chromatographic reactor gave a better conversion but required more catalyst per unit of feed flow. As expected, desirable factors were fast reaction rates and an impulse-like feed with a frequency
that gave effective separation without excessive interaction. Similarly, Roginskii and Rozental (84) concluded that conversions greater than equilibrium could be achieved with optimized reactor length. They also presented a method for obtaining the kinetic characteristics of the catalysts. Isotope Exchange
T h e gas chromatographic reactor already has been shown to be useful for specialized preparative isotope labeling. Senn et al. (81, 94) obtained nearly quantitative exchange of the enolizable hydrogen of a number of ketones during a single pass through a 10-ft column pretreated with D 2 0 and acid (81) or base (94). A similar procedure attempted for acid-catalyzed 0 1 8 labeling resulted in 40 to 60% exchange (81). Tadmor (100, 101) pretreated solid support with HC136. GeC14, SnC14, AsC13, and FeC13 were all successfully labeled with C136 in a Sil-0-Cel column. Solid support activity and efficiency were also studied in the course of the labeling. Disadvantages and limitations of the Chromatographic Reactor
Fewer assumptions might make the model of the chromatographic reactor more rigorous and realistic. If only the assumption of a homogeneous isothermal column is retained, the resulting over-all material balance on the reactant is
+
18
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and the material balance on the reactant in the stationary phase is
where the linear velocity of the mobile phase is now a function of position because of the pressure drop in the column, D ( x ) is the diffusivity dependent upon pressure and, consequently, upon position, and k' is the mass transfer coefficient between the mobile and the stationary phases. A combination of interrelationships, the boundary conditions of Equations 2 and 3, and the proper forms of rm and rs describe the chromatographic reactor. T h e rigorous material balance equations are complex and difficult to solve. All solutions to date have involved the assumption that the pressure and the velocity of the
AUTHORS Stan19 H . Langer is Professor of Chemical Engineering at the University of Wisconsin, Madison, W i s . 53706. Joanne Y.Yurchak obtained her M.S. degree in chemical engineering at Wisconsin in 1966. Sames E. Patton is at present a Graduate Research Student at Wisconsin. T h e authors gratefully acknowledge sufiport o j this work by the Petroleum Research Fund, administered by the A C S , the n D E A (fellowship to J E P ) , the Wisconsin Alumni Research Foundation, and the E . I . du Pont Co.
mobile phase were uniform throughout the column. Since the conversion is independent of pressure for a first-order reaction, a mean pressure can be substituted into the material balance with little error for that case. However, the constant-pressure assumption does present some obstacle when applying the solution to reactions which are not either first-order or pseudo-first order. Most treatments assume linear isotherms with the rates of adsorption and desorption much greater than rates of reaction. Although this assumption is quite valid in many cases, it too imposes some limitation on the applications of the chromatographic approach. On the other hand, those treatments which include commensurate rates of adsorption (14,50,83) give complications which make them difficult to utilize. T h e inclusion of the diffusion term results in a second-order partial differential equation the solution of which is complex, even if an average diffusivity is used (50) or if the reaction rate is zero (59, 106). A discussion of internal diffusion effects in the pulsed chromatographic regime is available (15). Mathematical analyses of nonequilibrium chromatography with diffusion and constant flow were performed by Lapidus and Amundson (59), Yamazaki (106), and Giddings (32-34). Although none of the latter authors included chemical reactions in his analysis, these works could be developed in that direction. Kocirik (50) has extended Lapidus and Amundson's treatment of chromatographic conditions including constant diffusivity, nonequilibrium mass transfer, and constant pressure to include first-order reactions in both the mobile and the stationary phases. H e used the first normal statistical moment and the first four central moments to characterize the chromatographic curves resulting from an arbitrary input. Five independent physical constants, including the rate constants, were obtainable from the five moments. T h e extraction of any one constant, however, was exceedingly difficult because of the complexity of the moment equations. A practical limitation in the range of reactions studied is the potential effect or the participation of the solid support surface in the reaction. Unless the surface is the specific subject of interest, reactions should not be catalyzed by the support surface nor should the reactants injected into the reactor affect the surface treatments. Actually, we have used the catalytic characteristics of the support, for certain reactions, as a means of studying support treatment or deterioration of that treatment (58). T h e range of reactions amenable to study by the gas chromatographic method is further limited by the need for a relatively involatile solvent (liquid phase) and a vaporizable reactant. There are limitations to the methods of analysis mentioned previously. T h e inert substance method, well suited to a single irreversible reaction, may suffer some loss of accuracy when applied to simultaneous or consecutive reactions. This is apparent from inspection of Figure 5 . Analysis is more accurate if reactant and product retention volumes are quite different. I t is most accurate when the products are not eluted from the column. Obviously, it is not possible by the methods
covered here when the product and reactant retention volumes are identical. If a second analytical column is added (4,the analysis is more versatile, but with this comes a more difficult experimental procedure and possible errors due to the transfer from the reactor to the analytical column. T h e range of flow rates which can be considered in a gas chromatographic kinetic study is limited by experimental complications due to longitudinal diffusion, ineffective mass transfer, or column pressure drop. I n addition, the range of practical conversion is limited since overlapping of peaks makes the measurement of peak areas inaccurate at the extremes. When we consider a range of conversion between 10 and 9570, the measurable range of rate constants is approximately 5 In 100/9O 200 In 100/5 < k(sec-') < (24.4 60 Vp'W 60 VTW 0.008 10 - < k(sec-l) < V,' w where V,' is the specific retention volume a t column temperature of the reactant and W is the weight of the stationary phase. This is assuming a flow range of 5 to 200 cc/min. Less stringent limits, of course, allow measurement of a wider range of rate constants. Limits are also wider if peaks are completely separated in the real chromatographic reactor as they are in the ideal chromatographic reactor. Incorporation of a second (analytical) column or study of formation of a nonvolatile product extends the useful range of the chromatographic method to practical conversions as low as 1 to O.lyo. If the reaction is too slow to be studied at a given temperature, an increase in temperature will only enable the reaction to be studied if the increase in rate of the reaction has more effect than the decrease in residence time due to a decrease in the specific retention volume and vice versa. For a given reaction, there is a range of temperatures over which the reaction can best be studied by the reactor chromatogram method if conversions are to be kept within the indicated limits. Reaction tempert u r e sensitivity c a n b e estimated f r o m t h e typical Arrhenius equation
w
v,'
k
= A,-EA/RT
(25)
Sensitivity of Vg to temperature is given by
- B~AHs/RT vbT=-
(26) where B is a constant for a given solute (reactant) and column, and AHs is the differential molar heat of vaporization of the reactant from solution of the surface. Then substituting Equations 25 and 26 into Relationship 24a, the temperature range over which reaction can be studied is AH, - EA AH8 - EA < 7-< R I ~ R I ~0.008 (27) ABW ABW If we consider a range of conversion and residence time of 90% in 10 sec to 10% in 5 hr, the range of firstorder rate constants to be obtained by the reactor chromatogram method is approximately 10-1 to 10-5 sec-l. This range could be expanded somewhat by
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attaching an analytical column to the outlet of the reactor column. If restrictions on conversion and time limits are relaxed, a wider range of values can be studied, with some possible loss in accuracy. I t should be remembered that the need for a linear isotherm and other requirements does limit the chromatographic reactor to small samples where kinetic and mechanistic studies, rather than conversion, are the important considerations. While impurities in reactants can sometimes be neglected when they are separated on the column, this is not always true since it is possible for impurities in the sample to cause a change in the liquid phase or indeed to react with the solid support which in turn could cause a change in the stationary phase and thus the rate of reaction. Therefore, as in most other kinetic techniques, reactive impurities in the sample cannot always be neglected although their effect is often minimized by the small sample size and the separation characteristics of the column. Conclusion
Application of the chromatographic column as a chemical reactor has been seen to be frequently advantageous. T h e operating procedure is simple, and experiments for the determination of a rate constant or chemical conversion can be performed in a short time. T h e small sample size is a great advantage when only limited amounts of sample are available and when reactants or products are corrosive or toxic. I n addition, problems in temperature control which arise when a reaction is highly exothermic and when large amounts of reactants are used may be eliminated. After initial design of apparatus for good temperature control ( 0.1 "C) with time and position in the column, reactions can be conveniently studied over a wide range of temperatures, from well below zero to greater than 500 "C. T h e range of reactions which can be studied through variations in procedure is wide. T h e liquid phase, or a substance dissolved therein, can be a reactant. One reactant may sometimes be added in a stream or it may be added as a pulse. Both reversible and irrebersible reactions have been studied; products formed may be volatile with some reactions, while with others, they may never be eluted from the column. T h e direct use of the reactor chromatogram in determining conversions is especially advantageous in that it eliminates extra sample collection equipment at the outlet of the column, a second chromatographic column, and possible errors which could be caused by this collection procedure. I t also gives an indication of the residence time distribution of the system which may be useful for studying reactions of higher order. Because of ease of operation, versatility, and speed, gas-liquid chromatography should eventually become invaluable as a kinetic tool, especially to organic chemists since many reactions are first order or pseudo-first order. I n addition to the determination of kinetic parameters, a second use which can be suggested from this work is the determination of trace impurities in substances used as 20
INDUSTRIAL
AND
ENGINEERING
CHEMISTRY
liquid phases. Wet methods for determination of small concentrations of impurities are often inaccurate and at times impossible. For example, the trioxane and paraldehyde depolymerizations are known to be extremely sensitive to trace amounts of acids and metal ions (107) in given liquid phases; it is conceivable that after proper calibration, the rates of these reactions at given temperatures could be used as indicators of acid in some liquid phases. T h e gas chromatographic method of studying chemical reactions in the liquid phase has disadvantages and limitations. However, many of these are not significant upon comparison with other kinetic methods of studying reactions, many of which require specific chemical properties of reactants and products, and others of which require a given stoichiometry--e.g., measurement of pressure increase. T h e study of reactions of a volatile reactant in a given solvent to form a volatile product by conventional procedures often has proved difficult because of evaporation before the amount of conversion can be determined. I n the reactor chromatogram procedure, a written record of the conversion at a given residence time is provided for the experimenter with little effort on his part, and with little chance of human error, or product or reactant loss. T h e assets of the technique far outweigh the liabilities in many cases. I t is apparent that gas chromatography will prove a valuable tool for the investigation of a number of liquid phase reactions and for performing conversions of limited quantities of material.
Nomenclature A B
= Arrhenius frequency factor, sec-' =
Cm(x,t) = = C,(t) Cs(x, t ) = = = = =
= = = = = = =
= =
= = = = =
= = = =
pre-exponential in retention volume equation, c c / g mol of stationary phase concentration of reactant in the mobile phase, g-mol/l. concentration of reactive stationary phase, g-mol/l. concentration of reactant in the stationary phase, gmol/l. diffusivity of reactant in the mobile phase, cm2/sec Arrhenius activation energy, cal/g-mol carrier gas flow rate, cc/sec volume of mobile phase per unit volume of column volume of stationary phase per unit volume of column partial molar heat of vaporization of reactant (solute) from solution, cal/g-mol partition coefficient of reactant between stationary and mobile phases mass transfer coefficient, sec-l first-order rate constant for the forward reaction of a reversible isomerization, sec-l first-order rate constant for the reverse reaction of a reversible isomerization, sec-l first-order rate constant for a n irreversible reaction in the mobile phase, sec-l first-order rate constant for a n irreversible reaction in the stationary phase, sec-l length of column, cm number of theoretical plates in a column gas constant, caljg-mol "K reaction rate in mobile phase, g-mol/l. sec reaction rate in stationary phase, g-mol/. sec area under inert peak on reactor chromatogram area under reactant peak on reactor chromatogram area under reactant peak on chromatogram a t zero conversion temperature, "K time: sec
tm
= residence time in the mobile phase, sec
ts U
= =
VT
=
W Win WOut
= =
X
=
=
residence time in the stationary phase, sec linear velocity of carrier gas, cm/sec corrected retention volume of reactant at column temperature, cc/gram stationary phase weight of stationary phase, g total amount of reactant entering column, g total amount of reactant leaving column, g distance from column inlet, cm
Greek Letters L Y
= combination of variables equivalent to ( t ,
P
=
7
=
7
=
TcO
=
#(t)
=
+ t8)/L, +
sec/cm combination of variables equivalent to (k,t, ksts)/L, cm-‘ residence time of 2-butene in a benzaldehyde and benzoic acid stationary phase, sec residence time of 2-butene in a benzoic acid stationary phase, sec residence time of 2-butene in a benzaldehyde stationary phase, sec an arbitrary input pulse of reactant into the ideal chromatographic reactor, g-mol/l.
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