2159
KINETICS OF DICYCLOPENTADIENE DISSOCIATION
A Gas Chromatographic Reactor Study of the Kinetics of Dicyclopentadiene Dissociation1 by Stanley H. Langer* and James E. Patton Department of Chemical Engineering, University of Wisconsin, Madison, Wiecomin 65708 (Received November 11, 1971) Publication coats assisted by the Petroleum Research Fund
The application of the gas chromatographiccolumn as a chemical reactor and source of kinetic data was studied using the unimolecular dissociation of dicyclopentadiene as a model reaction. Rate constants and kinetic parameters were measured in a number of solvents (stationary phases) in the range of 180-200’. Solvents included hexatriacontane, a silicone, poly(pheny1 ether), a polyester, and trixylyl phosphate. Solvent effects were not great and kinetic data from the gas chromatographic reactor (gcr) were consistent with earlier studies in the gas and liquid phase, Differences could be interpreted. Mobile or gas-phase rate constants could be determined with somewhat less accuracy than liquid-phase rate constants. The gcr must be used with care but is shown to have the advantage of permitting detection of impurities and side reactions as well as being operable and giving satisfactory results in their presence. Precautions and conditions for operating the gcr effectively are indicated. The gcr is shown to be well suited for the study of reactions involving volatile products and reactants. Concurrent determination of their activity coefficients and excess thermodynamic functions for mixing in the solvent is also possible. The gcr, therefore, should be especially valuable for aiding in the conciliation of kinetic and thermodynamic factors.
Full recognition of the value of the gas chromatographic column as a chemical reactor for the study of homogeneous reactions has not been accorded to date. I n preceding publi~ations,z-~ several earlier important applications to pseudo-first-order reactions were reviewed. The use of the chromatographic reactor to study a first-order reaction involving a volatile product as well as volatile reactant has also been demon~ t r a t e d . ~ Such ” reactions often are difficult to study with conventional batch-type reactors. Herein, we report the results of a more extensive investigation of the dicyclopentadiene dissociation reaction in several potentially useful high-temperature solvents (stationary phases) in order to illustrate features and advantages as well as conditions for favorable operation of the gas chromatographic reactor. Simultaneously derived solution thermodynamic data for reactants and products calculated from chromatographic characteristics are also presented. A series of earlier investigations of the dicyclopentadiene dissociation as well as related literature data on physical properties make possible a number of useful thermodynamic observations6p6for comparison with kinetic data for different solvents. The reactor is the chromatographic column itself. Reactant introduced as a pulse is continuously converted to product, sometimes by reaction in both gas and liquid phases, as it travels through the column. Separation of product is initiated immediately and continues during the entire passage of reactant through the column. Product dilution and concerted reaction and separation processes minimize reverse reaction as well as side reactions and autocatalysis.
The gas chromatographic reactor (gcr) benefits from other features inherent in chromatography-small sample size, minimal heat effects, and simple control of operating variables. Separation from any potential inhibiting or complicating impurity also takes place. Unfortunately, the need for careful temperature control makes most standard commercial gas chromatographic equipment unsuitable for kinetic studies. We chose the dicyclopentadiene dissociation reaction for study in the gas chromatographic reactor because of its first-order homogeneous nature and the relative simplicity of the reaction, as well as the availability of earlier investigations of the reaction for comparison.
Theory The most convenient approach to the gas chromatographic reactor utilizes a continuous model of a homogeneous column.2J~8 From a material balance on a (1) (a) Presented in part at 158th National Meeting of the American Chemical Society, New York, N. Y.,Sept 1969; (b) taken in part from the Ph.D. Thesis of J. E. P., Department of Chemical Engineering, University of Wisconsin, 1970. (2) S. H. Langer, J. E. Patton, and J. Y . Yurchak, Ind. Eng. Chem., 61 (4),10 (1969). (3) (a) G. L. Pratt and 8. H. Langer, J . Phys. Chem., 7 3 , 2095 (1969); (b) see also E. Gil-Av and Y . Herzberg-Minzly, J . Chromatogr., 13, 1 (1964). (4) J. Y. Yurchak, M.S. Thesis, Chemical Engineering Department, University of Wisconsin, Madison, Wis., 1966. (5) 8. H.Langer and J. H. Purnell, J . Phys. Chem., 67, 263 (1963). (6) S. H. Langer, B. M. Johnson, and J. R. Conder, ibid., 7 2 , 4020 (1968). (7) (a) E. Glueckauf, Trans. Faraday SOC.,51, 34 (1955); (b) L. Lapidus and N. Amundson, J . Phys. Chem., 56, 984 (1952). (8) J. H.Purnell, “Gas Chromatography,” Wiley, New York, N. Y., 1962,pp 94-99. The Journal of Physical Chemistry, Vol. 76, No. 16, 197.9
STANLEY H. LANGER AND JAMES E. PATTON
2 160 reactant pulse in n gas chromatographic column, a differential equation is obtained, the solution t o which relates reactant concentration to position in column, x, and time, t. Relationships may then be derived which will allow the determination of first-order rate constants. Components of a mixture injected into the column are transported by the usually inert carrier gas. Each species is partitioned between the mobile gas phase and the liquid phase (which may be coated on a porous solid support). If mass transfer is relatively rapid and the distribution isotherms are linear, the concentrations of each reactant, C, in the gas and liquid phases are related by the partition coefficient K, a function of temperature only * here. 35
K = Ci/Cg
(1)
Heats of solution and reaction are negligible because of the small sample size, so that the column temperature and partition coefficients are constant. If the column is operated under conditions such that diffusion is not a major f a c t ~ r ~(the ~ ‘ ~residence time distribution is small), a material balance on the reactant in a differential section of the chromatographic reactor undergoing a first-order or pseudo-first-order reaction in both phases yields
Physically flK/fg is equivalent to the ratio of liquidphase to gas-phase residence time or k’, the solute mass distribution ~oefficient.’~r ( x ) is the time required for the gas to travel from the column inlet to a point x. For a column of length L, T(L)is the residence time in t ~ the , the gas phase, t,, and (1 flK/f,)r(L) is t, total time in gas plus liquid phases. The total reactant entering a column of cross section A is
+
Win =
=
J
0
+
AMfgu(O)+(t)dt
AMf,u(0)Jm 0 +(t)dt
(6)
where M is the molecular weight of the reactant. The amount leaving the column is Wout
=
J
=
AMfgu(0)exp(-k,t,
0
AMjgu(L)Cg(L,t)dt
- kltl)
+(t
-
tg - ti)dt
where f~ and f g are the volume fractions of liquid and gas phase, respectively, per unit volume of column, u(x) is the linear velocity of gas in the column at distance x from the end of the column, and kl and k, are first-order rate constants in the indicated phases. Boundary and initial conditions are
CdO, t>
=
+(@;
c,P(x,0 ) = 0
(3)
Cg(x,t) is the concentration of reactant in the carrier gas (mobile phase) at distance x and time t in the column, CI(Z, t ) is the concentration of reactant in the stationary phase, and +(t) is an arbitrary input function. Gasphase velocity is dependent upon position because the finite pressure drop across the column causes the compressible gas to travel faster as it progresses through the column.’l Combining eq 1and 2
(k.
+ Y)cg = 0
(4)
This partial differential equation can be ~ o l v e d ’ with the aid of Laplace transforms for u(x)C,(x, t ) with the given boundary and initial conditions. The Journal of Physieal Chemistry, Vol. 76, No. 16, 197.8
(7)
If +(t) is bounded and equal to 0 for t < 0 (no reactant +(t) dt is present in the column before injection), hten!; must equa1.f; +(t - t l - tg)dt and eq 6 and 7 can be combined t o eliminate the integral. WoutlWin =
exp(-kgtg - klh)
(8)
Equation 8 generally does not depend upon the shape of the input function (+(t)). Furthermore, T ( X ) need be evaluated only at the outlet of the column, where it is simply t,. The recorded response of a detector at the outlet of a column in which material reacts as it passes through the column is called a reactor chromatogram. Since the (9) This is a reasonable proposition. For discussion, see W. A. Blanton, C. H. Byers, and R. P. Merrill, Ind. Eng. Chem., Fundam., 7, 611 (1968); see also M. Sueuki and J. M. Smith, Chem. Eng. Sci., 26, 221 (1971). (IO) Axial dispersion in gas-phase tubular reactors is discussed in (a) H. Kwart, S. F. Sarner, and J. H. Olson, J . Phys. Chem., 7 3 , 4056 (1969); (b) D. G. Retzloff, B. M. Coul, and J. Coul, ibid., 74, 2455 (1970). (11) A. T.James and A. J. P. Martin, Biochem. J . , 50, 679 (1952). (12) F. B. Hildebrand, “Advanced Calculus for Applications,” Prentice-Hall, Englewood Cliffs, N. J., 1962, pp 55-60. (13) G. A. Gaeiev, V. Yu Filinovskii, and M. I. Yanovskii, Kinet. Katal., 4, 688 (1963). ~ (14) ~ ~ (a) ~ A. Goldup, G. R. Luckhurst, and W. T. Swanton, Nature (London), 193, 333 (1962); (b) D. H. Desty, A. Goldup, G. R. Luckhurst, and W. T. Swanton, “Gas Chromatography, 1962,” M. Van Swaay, Ed., Butterworths, London, 1962, p 67.
KINETICS OF DICYCLOPENTADIENE DISSOCIATION area under a peak is proportional to the total weight of the corresponding compound which passes the detector, eq 8 can be rewritten In (SRO/SR)=
kttl
+ k,t,
(9)
where SRis the reactant peak area from a reactor chromatogram and SROwould be the reactant area from a hypothetical detector located a t the inlet. Inclusion of an inert compound with the reactant produces a constant peak of area SI. Adding In (SI)to both sides of eq 9 and rearranging In (SI/SR)=
kapptl
+ In (SI/SRO)
where the apparent rate constant, IC,, k,,,
=
kl
+ (t,/tl)k,
(10)
would be (11)
The initial area ratio SI/SROis the same if all samples are taken from the same reaction mixture. SR,SI,and 11 are measured readily. For reactions which take place only in the liquid phase, k,t, may be eliminated. I n a packed column where t, is very small relative to t l , the effect of the gas rate constant could be ignored. As we will show, a reasonable estimate of k, is accessible from a gas chromatographic study when the extent of gas-phase reaction is significant. Fortunately, the reaction under consideration has recently been carefully investigated in the gas phase by two different groupsloa,16so that we have available unusually accurate data. Most of our work is based on the value of k, = 101a.olexp(-33,970/RT) sec-' by Herndon, et a1.,16which was initially accessible to us.
Experimental Section Our apparatus, based on an earlier mode1,6'8was designed to give constant temperature control over a wide range of operating conditions. The 9 X 36-in. cylindrical air bath was located inside a 14 X 14 X 36-in. aluminum box containing vermiculite-insulated walls. A 7-in. diameter copper cylinder inside the oven carried 12 33-in. NIarinite strips on which nichrome heating wire was noninductively wound. A 6.7-in. centrifugal Torrington fan powered by a l/3-horsepower, 3450-rpm motor pulled air down the inner cylinder and pushed it up the annular section between the inner cylinder and the oven wall. The temperature was controlled by means of an external resistor switched in and out of the nichrome heating wire circuit which operated at constant voltage. A nickel resistance thermometer sensed the oven temperature for the controller so that the temperature was controlled to .tO.Ol" during the course of an experiment. The oven temperature, measured with a precision deep-immersion thermometer calibrated against an NBS thermometer, was corrected for the small ( 20), the ratio t,/tl is small so that the liquid-phase rate constant is not very sensitive to changes in k,. Customarily chromatographic injector ports are operated at a higher temperature than the columnz1to ensure rapid vaporization and introduction of sample. This may be a poor procedure for systems involving potential gas-phase reactions. Figure 5 illustrates the effect of this practice for a reaction taking place in a 25% hexatriacontane column at about 180". Addi(18) S. H.Langer, J. Y . Yarchak, and C. M. Shaughnessy, Anal. Chem., 40, 1749 (1969). (19) B.S.Khambata and A. Wasserman, J . Chem. Soc., 375 (1939). (20) B. Raistrick, R. H. Shapiro, and D. M. Newitt, ibid., 1761 (1939); see also P. J. Wilson and J. H. Wells, Chem. Rev., 34, 1 (1944). (21) F. H. Pollard and C. J. Hardy, Chem. Ind. (London),1145 (1955).
The Journal of Physical Chemistry, Vol. 76, No. 16,1079
STANLEY H. LANGER AND JAMES E. PATTON
2164
IF( IPL 1NJ.T 8 180'C 600
1200
1800
I N J . T = 190'C
TIME (SEC) ~~~
0
600
I200
1800
TIME (SEC)
Figure 5. Effect of injector temperature on "preconversion" of dicyclopentadiene in the injector. Product spike from "preconversion" is eliminated when injector is operated a t column temperature of 180". F = 50.2 cma/min and PI/Po = 1.68 for 12-ft, 25% n-hexatriacontane column.
tional product formed by the faster reaction in the injection port 50" above column temperature is obvious from the spike appearing in the reactor chromatogram; some distortion of the chromatogram is even apparent for a temperature of 190°, only 10" above the reactor temperature. Consequently, care must be taken in adjusting injector temperature to minimize the effect of reaction in the port. Some further advantages of the chromatographic kinetic technique are apparent from the reactor chromatogram of Figure 6. Commercial dicyclopentadiene is a mixture of two geometric isomers.
-
99% endo
N
1% ex0
The ex0 form is considerably less reactive than the endo isomer (ICexo/ICendo
