MECHANISM OF SOME CHAIN REACTIONS
97 5
T H E MECHANISM OF SOME CHAIN REACTIONS’
F. 0.RICE
AND
K. F. HERZFELD
Departments of Chemistry and Physics, Catholic Uniuersify, Washington, D . C . Received August 10, 1960 INTRODUCTION
I t is now generally accepted that the pyrogenic decomposition of aliphatic organic compounds proceeds at least in part through a free-radical mechanism. Some years ago (19) we attempted to account for the experimental fact that the decomposition of such substances as ethane, acetone, and dimethyl ether follows the equation of an unimolecular reaction, whereas the decomposition of acetaldehyde follow an equation of an order between 1 and 2. The predominant steps in the scheme that we proposed consist first of a rupture of the substrate molecule into tu-o free radicals. The second step consists of removal of a hydrogen atom from thesubstrate by a free radical. The third step consists of a decomposition of the large free radical (i.e., the substrate minus a hydrogen atom) into an unsaturated compound and a small radical which reacts with the substrate according to the eecond step. The second and third steps, therefore, constitute a chain i\hich may be several hundred links long. The chain is terminated by a fourth reaction, which may consist of either recombination or disproportionation of the chain radicals. It was shown that if the chain terminates by reaction of the small-chain radical with the large-chain radical the overall reaction n ou’d appear to be of the first order; whereas, if tn-o small radicals react, the overall reaction would appear to be of the 1.5 order. I t nas assumed that the two large radicals would easily dissociate again even if they combined. In view of a number of anomalies that have been reported in the literature and which are discussed in the following sections we decided to examine, from the theoretical standpoint, the possibility of the existence of an intermediate transition mechanism between a purely surface reaction in the lower range of temperature and a purely homogeneous reaction in the higher rangc of temperature. It seems plausible that a range of temperature exists in which the observed kinetics of a gaseous decomposition is determined by a mechanism in which chains start at the surface, go out into the body of the gas, and are stopped at the surface. I t is n.ell knonn that this mechanism is important in oxidation reactions (12). One of the anomalies discussed in the following sections is connected with the effect of surface on a supposedly homogeneous gas reaction. The extent to which the surface of the yessel enters into the reaction mechanism of thermal decompositions is one of the most prominent and puzzling questions which cannot Presented hefore the Symposium on Anomalies in Reaction Kinetics which was held under the auspices of the Division of Physical and Inorganic Chemistry and the Minneapolis Sertion of the American Chemical Society a t the University of Minnesota. June 1%21, 1950.
976
F. 0. RICE AND K . F. HERZFELD
yet be satisfactorily answered even after thirty years of rather intensive research. Undoubtedly the effect of surface depends on the temperature range in which the decomposition is conducted. It seems to be generally agreed at present that in the very lowest range of temperature, surface reactions play a part-often a predominant part-in thermal decompositions. I n a higher range of temperature, a homogeneous decomposition sets in and presumably because of a higher activation energy becomes the predominant reaction as the temperature is raised. The foregoing is well illustrated by the thermal decomposition of acetaldehyde. At 380-40O0C.the decomposition in a silica vessel appears to be a purely surface reaction (24), yielding several products in addition to methane and carbon monoxide. If the decomposition is carried out at 500°C. or higher, only methane or carbon monoxide is formed and the rate of the reaction is almost independent of the surface:volume ratio (9). In the following sections we shall discuss various aspects of the anomalous behavior that have been reported in the study of thermal gas decompositions. We shall then propose a theory to explain thermal decompositions, in which chains start at the surface, enter the gas phase, and finally end at the surface. The discussion of the kinetics in the light of this theory will necessarily be tentative and programmatic. I n connection with any proposed program of work, it seems justifiable to state that far too much reliance has been placed on the measurement of reaction rates by pressure-time relationships. Up to a few years ago this was understandable because of the laborious and inexact methods of analysis available. hctually, a single analysis of the substances present in a gas reaction by the mass spectrometer after a measured time interval provides a far more reliable measure of the rate of a reaction than hundreds of pressure-time readings in which all too often there is considerable uncertainty as to the value of the ratio (moles of products)/ (moles of substrate decomposed) and even more uncertainty as to whether this ratio is constant throughout the reaction. Furthermore, there seems to be need for more extensive study of the effect of the presence of inert gases, especially in the early stages of a reaction. The fragmentary and contradictory data in the literature seem to be inexplicable. I t would be possible to make an experimental test of the theory proposed in this paper by studying the effect of helium and other inert gases on the early stages of reactions. NATURE OF T m SURFACE
The basic question in homogeneous gas kinetics is-do we have any reliable method for deciding whether or not a reaction occurs completely in the gas phase? One way to attempt to answer this question mould be to change the nature of the surface by using vessels of different kinds of glass, silica, etc. I t is also possible to cover the surface with a layer of such substances as paraffin wax, Drifilm,* potassium chloride, etc.
* Drifilm is a methyl silicon fluoride which is supposed t o react with glass, leaving the surface covered with methyl groups.
977
M E C H A W S M OF SOME CHhIN REACTIONS
The reaction between ethylene and bromine (14, 21, 26) takes place for the most part, if not entirely, on the wall of the containing vessel, if it is of glass or if the wall is covered with stearic acid or cetyl alcohol. On the other hand, if the vessel wall is covered with paraffin was, there is a 1-min. induction period and a much slower rate. Recently Peri and Daniels (17) studied the following exchange reaction a t 200OC. (Br* represents radioactive bromine) : CH3CH2Br
+ HBr*
-+
+ HBr
CH3CH2Br*
They found that the reaction is wall catalyzed in a Pyrex-glass vessel. In the hope of cutting down the wall effect, the vessel was given various treatments, some of which are listed in table 1, where the rate constants are compared with freshly fused glass as unity. Covering the surface with Drifilm had no noticeable effect. Actually, no method of treating the surface was found which made it less active than freshly fused glass. TABLE 1 Eflect o j surface on !he rate of ethyl bromide ezchange with bromine SCPPlCE
Freshly fused Glass cleaned Glass cleaned Glass cleaned Glass cleaned
i
glass . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . with chromic a c i d . . . . . . . . . . . . . . . . . . . . . . . . . with fuming nitric acid.. . . . . . . . . . . . . . . . with hydrofluoric acid.. . . . . . . . . . . . . . . . . . with hot 1 N sodium hydroxide . . . . . . . . . . .
1
1. 1.2 2.4 2.9 6.0
In oxidation reactions the nature of the wall surface has a very marked effect, which is perhaps most strikingly shown by covering the surface with potassium or sodium chloride (16). I t is very disconcerting to find that so many pyrogenic decompositions give abnormal results in a clean glass or quartz vessel. Frequently it is only when the surface has been “conditioned” by being covered with carbonaceous material that one obtains reproducible results. This effect occurs in many thermal decompositions in greater or less degree, although it is especially evident when studying the thermal decomposition of alkyl halides. A detailed description is given by Brearly, Kistiakowsky, and Stauffer (2), who studied the thermal decomposition of tert-butyl and tert-amyl chlorides. After pumping out the reaction vessel and rinsing it with the substrate vapor they concluded that “with no further tresnment of the flask consistent results could not he obtained and the reaction procecded quite rapidly; evidently this was caused by :I heterogeneous reaction occurring on the walls of the flask. I t was,therefore, found necessary t o treat the flask and the best method evolved was to allow some of the chloride t o decompose in the flmk at about 500”and thus deposit a fine roherent coating of carbonized material over the sut.face of the glass. One or two such treatments for an unpacked flask were found to he sufficient t o give consistent results which were not lowered upon further treatment. I t was foutl,! that a long or a very thorough evacuation of the flask destroyed the usefulness of this carbon deposit, and that also if any oxygen were pernlitted to enter the flask after it had I)een
978
F. 0. RICE AND K. F. HERZFELD
so treated, the heterogeneous reaction set in again and could not be removed except by
burning off the carbon coating and re-treating the flask. In order to prevent the destructive effects of allowing the flask t o stand evacuated for any length of time, and 8180 t o decrease the likelihood of air leaking into the flask, each run was left in the flask until the next run was to be begun and then i t was evacuated with the oil pump only.”
The more recent work of Barton and Onyon (1) describes similar effects in the pyrolysis of 1,1,1-trichloroethane. “In general when a saturated chlorinated hydrocarbon is pyrolyzed in a clean-walled reactor the rate of decomposition is fast and heterogeneous. As the walls of the reactor become covered with a carbonaceous film the heterogeneous mechanism is suppressed, the rate of decomposition falls, and eventually reproducible results are attained. These effects were also noted with 1,l,l-trichloroethane and all the results recorded below refer to experiments made after this initial period of irreproducibility.”
A great many similar instances are recorded in the literature, although the effect is not so marked as with the alkyl halides. A typical example is the decomposition of dimethyltriazine (18), in which the first run gives a 12 per cent higher value than succeeding runs. The authors state: “Earlier preliminary runs had likewise shown that opening the cell to the air or washing
it out gave a slightly higher rate for the next two or three runs, so that apparently some conditioning of the surface or removal of impurities was necessary to eliminate catalysis completely. We conclude that the reaction rates reported were not influenced by the extent of wall surface and that the reaction is therefore homogeneous.”
It does seem that in the pyrogenic decomposition of organic compounds we are dealing, in most cases if not in all, with a surface of carbonaceous material and it is only after the original surface is covered that reproducible results are obtained. EXTENT O F SURFACE
Changing the surface: volume ratio by a considerable factor is commonly regarded as the most dependable method of detecting surface effects. Unfortunately much work has been done in which the reaction vessel was partially filled with a coarse powder of glass or quartz. It would be much better to have the increased surface distributed more evenly throughout the reaction vessel by filling it, for example, with thin-walled tubing. One of the most striking examples of the effect of changing the surface:volume ratio occurs in the thermal decomposition of phosphine. This reaction, which was first studied carefully by Trautz and Bhanderkar (23), owes its importance to the fact that it formed the basis of extensive discussions of the fundamental mechanism of homogeneous gas decompositions. Trautz and Bhanderkar were aware of the possibility of the surface of the vessel playing a part but unfortunately did not take the precaution of changing the surface: volume ratio. When this was done later by Hinshelwood and Topley (11) it was found that the reaction occurred wholly on the surface of the vessel. I n much of the work in the 1920’s thermal decompositions were tested for
hlECHAKISM O F SOME C H A W REACTIOKS
979
heterogeneity by the addition of a large quantity of powdered silica. The increase in area was 10- to 16-fold but the increase in rate usually was in the range of 10-30 per cent. On the basis of these results it was concluded that the heterogeneous part of such decompositions occurring in an empty bulb could not be more than 1 per cent of the total. Winkler and Hinshelwood (27) reexamined the effect of surface on the thermal decomposition of acetone and acetaldehyde by making a more uniform distribution of the increased surface. The authors concluded that there is no appreciable surface reaction in either case. There are a number of reactions that show no change in rate when the surface is considerably increased by adding thin-walled tubing. For example, in the dimethyltriazine decomposition (18) the surface:volume ratio was increased 11.5-fold by the addition of Pyrex tubing but in two runs made a t 200°C. and 230°C. the rates were the same as in the unpacked bulb. The rate of decomposition of sulfuryl chloride (20) showed a 3- to 4-fold increase a t 280°C. with a 20-fold increase in surface:volume ratio but a t 320OC. the effect disappeared. There was no increase in rate when the surface:volume ratio was increased. Unfortunately t h e error in rate measurements; together with the few measurements available, make it impossible to find, from the data, any general relation between the rate constant and the surface: volume ratio. Actually, if in a given reaction it had been found that the rate increased fourfold with a sixteenfold increase in surface this would have been interpreted as meaning that, in the unpacked bulb, the low-temperature heterogeneous reaction was occurring to the extent of about 20 per cent of the whole. THE INITIAL RATE
I n making a measurement of the initial rate of decomposition of a homogeneous gas reaction, the gas has first to be brought up to temperature and then tho steady-state concentration of radicals must be attained. On the basis of the original Rice-Herzfeld theory (theory 1) the steady-state concentration would take only a fraction of a second to attain. However, if the steady-state coneentration is dependent on a diffusion process from the wall, the time will be much longer and should be susceptible to measurement. Whenever an induction period is observed in a thermal decomposition, it should be studied by conducting the decomposition in vessels of different volumes and in the presence and absence of an inert gas such as helium. Furthermore, if the rate of the reaction is being followed by pressure-time observations, the results should be supplemented by mass-spectrometric analysis in order to be sure that one is not observing a false induction period. The decomposition of ethylene oxide has been (6) carefully studied and shows a well-marked induction period. Although the final products are methane and carbon monoxide, the decomposition almost certainly proceeds through a freeradical chain with acetaldehyde appearing as an intermediary. If the decomposiSee, for example, reference 20, page 1869, Table 11.
980
F. 0. R I C E AND K . F. HERZFELD
tion proceeds through acetaldehyde, pressure-time measurements would, of course, indicate an induction period. There is the further difficulty that the products of many reactions themselves act as inhibitors. For example, in a recent study of the thermal decomposition of n-pentane (E), the initial rate was obtained by drawing a tangent to the Ap-time curve a t time t = 0. In these experiments there was an initial high rate, which the authors ascribe to a marked inhibition by the products formed as the reaction proceeds. Further study of the initial rate of gas reactions supplemented by massspectrophotometric analysis is very much needed. In this way it would be possible to guard against misleading effects due t o isomerization and also it would be possible to identify the products and test if they had any effect on the initial rate. In addition, the measurements should be made with and without the addition of an inert gas such as helium. I S F L U E N C E O F INERT GASES
The effect of inert gases on the speed of gaseous decomposition has been studied by Hinshelwood and coworkers, mho found that for many reactions, such as the thermal decompositions of dimethyl ether (lo), methyl ethyl ether ( 5 ) , methyl propyl ether ( 5 ) ,and diethyl ether (7), the falling off of the rate at low pressures of the hubstrate is prevented by the presence of hydrogen, which brings the rate up to the normal value. This remarkable effect can hardly be due to the chemical reaction of hydrogen with the substrate or with the products of the reaction, because it is hard to imagine any reaction that would not result in a diminution of the number of molecules and hence a decrease in the measured rate of reaction. Hinshelwood himself (8) comments that it is “remarkable that the action of hydrogen is so specific and that helium, nitrogen and other gases do not have a similar effect.” The whole matter is somewhat complicated by a later report (13) that the lowpressure rate of diethyl ether decomposition is affected less by deuterium than by hydrogen. This result, however, is contradicted in a later paper (4). Heckert and Mack (6) found that the rate constants of the decomposition of ethylene oxide were not affected (within & l o per cent) by the following gases: carbon dioxide, carbon monoxide, nitrogen, methane, argon, helium, and neon. On the other hand, the presence of hydrogen caused a very considerable increase in the speed of the decomposition. L‘ernon and Daniels (25) found that the addition of nitrogen or hydrogen to ethyl bromide caused the rate to decrease at l o ~ vpressures. Quite recently Peri and Daniels, in an effort to clear up the mechanism of this puzzling gaseous decomposition, have studied the exchange reaction of ethyl bromide with bromine, hydrogen bromide, and deuterium bromide. They believe that the bromine eschange is a wall reaction but that the deuterium exchange is a chain reaction, starting and eliding on the wall. Taylor and Achilles (22) found that neither hydrogen nor nitrogen had any effect on the rate of decomposition of propylamine, and Busse and Daniels (3)
MECHANISM OF SOME CHAIN REACTIONS
981
found that, neither hydrogen nor carbon monoxide affected the rate of decomposition of nitrogen pentoxide. I t seems desirable to study the effect of both helium and hydrogen on the rates of thermal decompositions. Apparently helium and other inert gases are without effect, but hydrogen, in some decompositions a t least, has a very pronounced effect in raising the rate. The effect shows up a t low concentrations of substrate \\hen the addition of hydrogen raises the rate to the normal value. THEORETICAL
If one aswmes that free-radical chains start and end at the wall, we can schematically devise two theories, in both of which it is assumed that the chainstarting mechanism is Free \\all
+ substrate
+
adsorbed H
+ RZ
The chain-breaking mechanism may occur in one of two ways, which v e shall call theory 2A and theory 2B. The original theory published in 1934 is referred to as theory 1. In theory 2 h \ve make the original chain radical, R2, relatively unstable with respect to the small-chain radical, R1, which is then present in relatively large concentration and the chain-breaking step is
+
+
Adsorbed H R1 -+ RIH free wall In theory 2B the original chain radical, Rz, is present in relatively high concentrations in the gas and the chain-breaking step is Adsorbed H
+ Rz
---$
R2H
+
free wall
In both cases the radicals must diffuse to or from the wall, but the result of the stationary-state diffusion is different in the two cases. In the situation described by theory 2A, at the stationary state there exist concentration gradients in the reaction vessel, R2 having the highest and RI the lowest, concentration near the wall; however, for long chains (>lo0 links) the concentration gradients are negligible. There are three cases which may be distinguished, as follows: (1) Most of the hydrogen atoms are on the wall and only a small fraction of the wall is covered. (2) Most of the hydrogen atoms are on the wall and most of the wall is covered. (5’) Most of the hydrogen is in the vessel and but little on the wall. The following discussion concerns case 1 and applies to both theory 2A and theory 2B. If there are no leaks, that is, no combination of hydrogen atoms or combination of radicals, the total number of hydrogen atoms is equal to the total number of radicals. If A is the area of surface, N the number of places on 1 sq. cm. divided by the hvogadro number, and z the fraction of the surface covered by hydrogen atoms, we have:
AN2
+ NHI
V([RiI
+ [Rd
(1)
982
F. 0. RICE AND K . F. HERZFELD
Since we have assumed that most of the hydrogen atoms are adsorbed on the
AN V
wall, we can neglect [HI in comparison with-r.
AN I V
=
[RII
We then have
+ [RzI
(3)
The starting and stopping of the chain is given by
A(l
- r)Bi[Ml
= k4A~[Ri.21
(4)
where R1,2 represents either R, or I%. Since we assume that the wall is mostly empty, 1 r = 1 and the starting and stopping is given by
-
kdMI = kdRi,*I
(5)
Eliminating z from equations 3 and 5 we obtain:
AN1~1 -V-k 4 [MI = [R1,zI ([Rll
+ [Rd
(6)
Dividing and multiplying by R: gives:
The chain reaction is given by
kz[RzI
=
ka[Ml[R11
Solving for R: we obtain:
The rate is given by
The foregoing applies to both theory 2.4 and theory 2B. I n theory 2A, R I , is ~ R1and the rate becomes
Therefore for case 1, when most of the hydrogen atoms are on the wall and only a small fraction of the wall is covered, according to both theory 2A and theory
MECHAWISM OF SOME CHAIN REACTIONS
983
2B the rate should be proportional to the square root of the surface:volume ratio. For this case when k z > k3[M],the rate is given by
I n theory 2B, R1,z becomes Rz and the rate is
For this case when kS < k,[M], the rate is given by
Notice that the theory predicts that such substances as ethane, dimethyl ether, and acetone follow an equation of the 0.5 order in the lower range of temperature. The foregoing case, as we have stated, arises when most of the hydrogen is on the wall and only a small part of the wall is covered. In this case it is necessary to have a large wall surface compared to the volume of the reacting vessel. The second case arises when most of the hydrogen is on the wall and a large part of the wall is covered. This case can arise only accidentally and increasing the surface:volume ratio by 10 or decreasing the pressure by 100 would bring it into case 1. We have not been able to treat this case except for theory 2B, because we have to make use of an equilibrium which is present only when the large radical is relatively stable. If a reaction follows the mechanism of theory 2B, the concentration of RS is uniform within the vessel, once the stationary state is reached. The effect of the wall may then easily be shown by considering a reaction vessel of volume 1’ in which there is thermodynamic equilibrium between the hydrogen atoms, the large radical Rs, and the substrate M. Note that ordinarily we could not write this relation between these stationary-state concentrations but must do so here because the chain-starting and chain-stopping reactions are the same. The equation representing this equilibrium is [HI[RsI
NMI
(16)
The role of the wall lies in taking hydrogen atoms out of the equilibrium and therefore increasing the equilibrium concentration of RP,which is the chain carrier. The rate of dissociation of the substrate, M, and the rate of the wall reaction do not enter into consideration. If one assumes as the chain
RS + RI Ri
+M
+ Mi +
RIH
Rate MRII
+ Rz
(17)
Rate k3[RJ[Ml (18)
984
F . 0. RICE AND K . F . HERZFELD
the total number of radicals present is
Combining equations 1 and 19 we obtain: (20) The adsorption equilibrium is [H](1 - Z) = K’x
(21)
Eliminating z from equations 20 and 21 we have:
Equations 16 and 22 permit us to eliminate [HI and to calculate [Rz]. If most of the surface is covered with hydrogen atoms (second case) K’
