G. Scacchl J. F. Foucaut and M. ..awe Departement de Chimie Physique des Reactions Ecole Nationale Superieure des Industries Chimiques (I.N.P.L.) 1, rue Grandville 54042 Nancy (France)
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I I
Demonstrating Self-Acceleration or Self-Inhibition Phenomena in Chemical Reactions An experiment in alkane pyrolysis
In a course of homogeneous chemical kinetics, we often have to introduce the nhenomena of self-acceleration or self-inhihition in chemical reactions in discussion of the important notion of reaction order. The comparison hetween the different types of reaction orders can sometimes be exemplified by a simple experimental procedure to show self-acceleration and self-inhihition phenomena. However, we think it would he better to present first a more general approach to the problem-including the particular cases in which the reaction exhibits one or more orders. This approach is described in the first part of our paper. Then, in a second part, we describe an undergraduate laboratory experiment, the pyrolysis of an alkane, the results of which can he interpreted from the previous general remarks. General Remarks We base our discussiun on the simple reartion nyresented by the rlohal stoirhiumerrir equntlon: .4 = productts~,corresponding to a decomposition; an isomeriiation, or a polymerization of the single reactant A. The following results will extrapolate easily to the case of several reactants. Let us note that all the rates defined below are functions of concentrations and temperature. The temperature dependence will not he explicitly mentioned any more. The concentration dependence will he examined solely in this paper. lnitial Rate ro, Instantaneous Rate r , and Fictitious Instantaneous Rater *.
One can compare r and r* by plotting the ratio rlr* against the extent of reaction. If we obtain a horizontal straight line with an intercept on axis rlr* equal to one, the reaction is neither self-inhibited nor self-accelerated hy the products. If the experimental points rlr* are below or above this horizontal line, the reaction is, respectively, self-inhibited or self-accelerated. Initial Order no and "Order with Respect to Time" n Initial order no The function f can often be written ro = kocon@ (1) in which no is the initial order with respect to the reactant A (1,2, 3a). The slope of the straight line log ro against log co gives the no value.
"Order with Respect to Time" n I t is sometimes possible to link r and e by the simple relation r = kcn (2) in which n is the "order with respect to time" (1,2,3a). Then, we have
(3) logr=logk +nlogc But the relation (2) is, of course, valid a t point c = co (zero extent), therefore:
At only very small extents of reaction, the reactant system is exempt from reaction products (if the reactant is exempt and from them). Now, these latter, very often, complicate the log ro = log k + n log co (5) fundamental mechanism and thus have a kinetic effect on the reaction. When we want to clear up the mechanism of a From eqns. (3) and ( 5 ) ,we can deduce: chemical reaction. it is better. first. to studv its kinetics a t log r = log ro + n log (clco) (6) rnrtrnl tlmr r7rro extent,, the phenomena he~nggenerally muresim~lethan thme at any further instant.'l'hus the i n ~ t ~ a l The slope of log r against log (clco) gives the n value. rate ro is Hn important pieceif kinetic data. I t is a function of If r does not fit into a simple law such eqn. (2). the reaction the sole initial concentration co of the reactant. does not admit an "order with respect to time." Nevertheless, in this case, some authors define an "instantaneous order with ro = f [initial reactant concentration ca] respect to time," as the slope, at any instant, of the curve log r against log (clco). This "instantaneous order with respect If we consider the reaction a t anv extent (different from to time" varies, of course, during an experimental run. zero), it is possible to define an instantaneous rater. A priori Comparison between the Initial Order no and the "Order this rate is a function of the instantaneous concentration c of with Respect to Time" (or the "Instantaneou Order with the reactant A and, possibly, of concentration of products Respect to Time") n. r = g [instantaneousconcentration of the reactant Let us consider the particular case in which the reaction A A and, possibly, products concentrations] = product(s) admits a well-defined initial order no with reAt any instant, one can define a fictitious instantaneous rate spect to A. r*. It would he the instantaneous rate that the reaction would 1) If this reaction admits an "order with respect to time" have if the products had no kinetic influence. Thus, r* is a (constant) equal to the initial order no, log r varies linearly function of the sole instantaneous concentration c of the with log (clco) and the slope of the straight line is no reactant A and is linked to it by the function f that we have [straight line (I) in Fig. 11. The instantaneous rate deintroduced above, in the case of initial rates creases only because of the simple consumption of the r* = f [instantaneousconcentration c of the reactant A] reactant, according to the law 748 1 Journal of Chemical Education
Figure 1 . Comparison between the initial order no and the "order with respect to time" (or lhe "instantaneaus order with respeet to time") n.
~igure2. pyrolysisapparatus.
2) Let us suppose that the experimental points log r against log (c/co) deviate from this line (I) If they are situated below (Curve I1 in Fig. I), the reaction slows down more strongly than we might expect from the law in eqn. (7). So, it is self-inhibited by one (or several) of the products formed during the transformation. If they are situated above (Curves 111, and Illb in Fig. 1)at least one of the products hasanaccelerating effect on the reaction. The rate either decreases (Curve 111.) during all the course of the reaction, or increases at the beginning, then decreases (Curve IIIb). The curves (11) and (111.) can he straight lines (if n exits) or not. However, in either case a t relatively small extents of reaction the slope of log r against log (clco) is higher than the value of the initial order no if the reaction is self-inhibited (Curve 11). smaller than no if one ofihe produds hasan accelerating effect on the reaction (Curves 111, and IIIb).
.
Thus, in the particular case (frequent) in which the considered reaction admits an initial order, Figure 1permits us, very simply, to show the existence of self-acceleration or self-inhihition phenomena in chemical reactions. The method using rlr* against extent of reaction is, of course, more general because it does not sumose .. the existence of a well-defined initial order no. We are eoine" to a .o d. v-these two methods of annroach to the .. example of the pyrolysis of an alkane, a reaction which admits an initial order no which is well-defined with resDect to the reactant.
(mn)
Figure 3. Pyrolysis of Po = 100 torr of neopentane. at about T = Cwve (I):pure hydrocarbon Curve (11):in the presence of 4 torr of methane Curve (Ill):in the presence of 4 torr of ikobutene.
798' K.
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Application to the Neopentane Pyrolysis (Undergraduate Laboratory Experiment) We study, by a physical method (pressure increase AP, a t constant volume), the kinetics of neopentane pyrolysis (neoC5H12). in gas phase, in a closed Pyrex* reaction vessel1, un0.8 em-'), uncoated, packed (surface to volume ratio s/u isothermal (about 520°C) and at initial alkane pressure P o from 20 to 350 torr. Neopentane (Phillips, research grade) was 99.9% pure. This alkane has been chosen for two reasons:
--
Its decomposition is simple; it is a chain radical reaction represented by the sole main primary stoichiometric equation Thus, the reaction extent a is directly linked with the pressure increasing AP: ' I t is puqsihlo to use t l w came reactur fur a great numhrr ,f experiments. No depoiit is ohscrved at thiq temperature.
The reaction is hardlv affected hv small amounts of oxveen. carbon trapped in liquid air, is enough. Experimental The spherical reaction vessel (about 250 ml) is placed in a thermoststed oven, whose temperature can be set at an accuracy of '14 degree. A vacuum is created to 10@tom) in the volume limited by S1,S4,Sg, and Vp, then neopentane is introduced, at a pressure of PI, into the volume limited by S1,Sp,S4, and SS.S3is already open; at initial time t = 0, S pis opened. Thus, the initial pressure Po is ohtained throughout the system. A few seconds later, S p and Sa are closed again; then the differential pressure transducer (or the differential liquid manometer) shows the evolution of A P = Pt - Powith respect to time (PCbeing the total pressure, in the reactor, at any time). Experimental Results and Interpretation
Study of Pyrolysis a t Initial Time Initial rate ro. The initial rate ro is given by the initial slope of the curve. A P = f(t). It is difficult to measure, graphically, an initial slope when the curvature of A P = f(t) is pronounced (Curve (I) in Fig. 3). In the particular case of neopentane pyrolysis, it has been shown that Volum 57. Number 10, October 1980 1 749
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0
1
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9
1
0
Exten! of rwclion w (in
%)
Figure 5. Self-inhibition phenomenon in the pyrolysis of neopentane. [PO = 100 torr: T = 798' K].
Figure 4. Effen of nwpentene inltial pressure Po onthe initial rate of pyrolysis ro at 798' K. 0 pure hydrocarbon after addition of 100 tan nitrogen
k1
Propagation
ka
ti
api p=(8) L ti The plot (for a given initial pressure Po) of (11~;)against AP; gives a slight curve and, by extrapolation a t APi = 0, leads to (tlAP)u=o, i.e. (llro), thence to ro corresponding to initial pressure Po. Finding an initial order no. Figure 4 represents the variations of log ro against log Po, at T = 798 K. Above ahout Po 140 torr, there is an initial order no rather well determined near 312. Therefore
--
ro = kdPo3/"
koeo3I2
(9)
Below about 140torr, the curve log ro against log Podeviates from the straight line having a slope of 312, the slope heing no more than about 1.1when Po 30 torr. The addition of 100 torr of ultrapure nitrogen (with less than 1ppm oxygen) notably reduces the initial rate of the pyrolysis of neopentane at 35 torr [cf., Fig. 41. This inhibiting effect of inert gas can only be amounted for if at least one rate constant of the termination processes depends on the pressure. In the case of hydrocarbon, this process can only be
+i-CaB
CH3. + neo CSHIZ+CHI Termination
it was possible to have a better value of ro thanks to the method of extrapolation, as follows. An ouernge rote i; is defined, corresponding to A?; during time
neo-CsH11'+CHd
+ neo-CsH~,.
2 C H i (+M) % c & ~ (+M)
(14) (15) (16)
The calculation2leads easily to the initial rate ro of methane production3 k 112 (neo-CgH12)0~/~ ro = k~
(2)
Cumparing rxperimrntal and theoret&l :"ilia1 urdtrs points out the great ituporranre u i t h ~ notion s uf initial order ia.r the building uf a complex reaction mechanism.
Study of Pyrolysis during the Reaction Since the reaction has s n initial order no = 312 (above 140 tom, a t
798' K), the study during the readion can be observed according to the two approaches described in "General remarks." Study of Variations (rlr*). The initial order heing near 312, the fictitious instantaneous rater* is written
--
2 CH3. (+MI 4 CzHd+M)
(10)
because terminations involving H. atoms are negligihle under our experimental conditions of pressure and the radicals heavier than C H r do not require a third body in order to combine. Thus it is s h a m , in a simple way, without analysis, that process (10) is one of the main termination processes-if not the only one-in the pure neopentane pyrolysis. According to the rules "8,M" (3b,5), this termination implying 2 C H r is compatible with the initialorder no = 312, found experimentally (unimolecular initiation and himolecular termination between two radicals "8"). Remark. The detailed study of neopentane pyrolysis (6)has made it possible to propose, at initial time, and about 500°C, the chain radical mechanism as follows: Initiation
k
neo-CsH1z A
C H+ (CH3I3C. ~
k
+ k H. + neo-CsHlz &HZ + neo-CsHn (cH~)~c.AH. i - C ~ B
750 1 Journal of Chemical Education
in which P is the partial instantaneous pressure of neopentane, i.e., P=Po-AP. At any time, r* can be calculated, taking into account e m . (9)
l'he tangent to thecurve 11'= f t l , gives, ar all pmntr, the instantaneous rater Thus, the ratiu ( r r ' ) , ran be pbtted arainrt the renmonexrenr a. Figurr .',shows, for 1'0 = 100 twr and T = 7Yb" K, that (rlr*) is a decreasing function of reaction extent; the neopentane pyrolysis is, therefore, self-inhibited hy one of the products formed. Findingn Possible "Order with Respect to Time" n. Let us examine if the experimental instantaneous rater can be represented by ~
r = k'Pn (in which P = Po- AP)
(11)
(12) (13)
..
2This calculation is based on the suooosition that the free atoms and radicals hare reached their quasi-steady state. 'This mw is the qanw os that of formation o i isohurene or con. sumprwn c,tncopenrnnc if the chains nrr I h g .
Figure 6 shows the variations of log r against log (PIPo).The resulting curve clearly diverges from a straight line; so, the neopentane pyrolysis admits no "order with respect to time" n. The "instantaneous order with respect to time," that is to say, the slope of the curve, a t any time, decreases from s very great value a t very small extent ("n" = 60) to a value nearing 5, a t about 10%extent. But, anyhow, this "instantaneous order with respect to time" remains suoerior t o the initial order nn = 312 (as lone as the extent remains small). According to Figure 1; that shows a k f - i n h i b i t i o n of neopentane pyrolysis. Here, again, is the conclusion of the study of variations (rlr*). I d e n t i f y i n g the Self-inhibitor In this study it is logical to begin with envisaging the kinetic effect of the two main primary produck, CHa and i-c~Hs.'Forthat, just add some percentage of one or the other of those products when starting the pyrolysis a t a given initial pressure Po of neopentane. Curve (11) in Fieure 3 shows the curve LIP = f(t) for the case of the pyndgsis at PI#= LIIO torr of nQopQlltane,in the presence of 4 torr rn+rhonr. Cmyvariim with the h a s i c C ~ r vII) ~ shuw that the initial rnteb are p r x t i ~ ~ 1 1the y i a m e Su,methane ir r w r the .elf-inhihitor in the reaction. On the other hand, adding 4 tom isobutene to 1M) torr neopentane considerably slows down the initial rate (Curve (111) in Fig. 3). Therefore. isahutene is resoansihle for the self-inhibition in the nvrolvsis. observe that CU~V;(III)is verv, sliehtlv .. , bent cornoared i i i h t h i hnsir ( ~ Y 11,. P This is [
