K. D. Bartle, University of Leeds P. G. Butcher, CALCHEM
University of Leeds C. J. Harding,' and D. R. Roberts The Open University Walton Hall Milton Keynes, MK7 6AA. Great Britain
I
A Student Experiment for Measuring Rate Constants of Radical Recombination
The principles of chemical kinetics are often taught usinn examples of gas-phase reactions in preference to reactions in condensed phases. Results can then he compared with the predictions bf theories of reaction rates which &e not so easily applied to reactions in solution. In practice, student experiments in kinetics are often limited toreactions in solution. If gas-phase reactions are performed experimentally other benefits, such as the experience of using vacuum techniques and of handling gases are gained. However, these advantages are not usuallv obtained without cost: reactions with hieh activation eneigies require careful control of elevated ternperatures, and those with low activation energies normally demand sophisticated methods to measure concentrations of reactants, often radicals. For most reactions, the cost of the necessary equipment is likely to he prohibitive for a student experiment. The i m ~ o r t a nalkvl t radical recombination reactions have been stuiied by rotating sector and flash photolysis, as well as by molecular modulation spectroscopy (I),all expensive techniques. In 1972 Hiatt and Benson (2) reported a new method for measuring the ratios of rate constants for radical combinations which avoids expensive apparatus. We have adapted this method in a student experiment in which the rate con&ants of comhination of a himologous series of alkyl radicals are compared. 'The radical rectlmbination experiment ii one of the experiments devisd fnr a seron(l-level summer school uf the Own Uuiversitv (31.Summer schwls nf the Onm Univer~itv aim to provide an intensive period in which &dents practi; and devLlon skills which include experiment . exuerimental . (lvsign and intwpretatinn. Consequently the t,xperiments are cnrefullv idected and desirmd (for examr~lebee reterenue (411. The exberimmt descrihrh here i~~ustr'tes how a recent research dtw~lopmmt( a n he adapted to achieve these aims. The Radical-Buffer Method In the radical-buffer method of Hiatt and Benson, radicals are generated (for example . bv. the decomoosition of di-tertbutil peroxide) in the presence of two iodoalkanes, R1I and R21. The methyl radicals so produced may or may not he one of the radicals of interest; if not, their reaction with the iodoalkanes as in reaction (1)provides the radicals of interest. The method then relies on the estahlishment of equilibrium in reaction (1) being much more rapid than reactions between the radicals. Reaction (1) then acts as a buffer reaction for the radicals R1. and Ry.
The ratio of the concentrati~msof these radicals ran l)c estimated from the concentrations uf the iodualkanes and the equilibrium constant Klz for reaction 11).
' Author to whom correspondence should he addressed 742 / Journal of Chemical Education
Radicals produced in reaction (1)mav react hv comhination (reaction; (3) and (4)), by cross-comknation?reaction (5)), by disproportionation, and by hydrogen abstraction.
The amounts of the alkane products from reactions (3),(41, and (5) are governed by the relative rates of these reactions, the value of the equilihrium constant Klz, and the concentrations of iodoalkanes. Provided that the establishment of equilihrium in reaction (1) is rapid compared with the rates of reactions (3), (4), and (5) or any other reactions of the radicals RI. and Ry, the experiment may be interpreted quite s i m-~ l.v . For example, the ratio of the rate constants for reactions (3) and (5) is contained in ean. (6) which eives the relative rates of these reactions.
By assuming that the iodoalkane concentrations remain effectively constant throughout the experiment, we can integrate eqn. (6).
Here the subscript t denotes the concentration at some time t. The iodoalkane concentrations are the average concentrations throughout the experiment; these are assumed constant in the integration. In our experimentswe compare the rate constants for the comhination reactions (3) and (4). The ratio of these is
However, it is not alwavs easv (for ex~erimentalreasons) to determine the concentrations bf alkan; products, and in s~raph. The iamplmg dwice is eit her a Carlc 4.100 valvr w t w or a g h s rample hmp wrapped wth henrmg rape. Educational Aspects The experiment was designed s~ecificallvfor students with little knowledge of radical k a c t i o k , and so pro~,idesa useful intrtrlurrion to the ms-phase chemistrv uf radicals. We consider it to have other edkational advantages over more conventional experiments in kinetics: experimental planning based on the student's own observation plays an important part in the experiment; the experiment allows (indeed, forces) tht. student to emcentrate oh the chemistry rather than on kinetic equations; unlike must kinetic studies it does not require a large number of repetitive measurements; and by careful choice of the reactants the experiment can be adapted to become simple or sophisticated. As we desighed it, the experiment is completed in three sessions of 3% hr. In the first session students investigate qualitatively by gas chromatographic analysis the reactions which occur in the system. T h e second session is spent ~ l a n ning and performing a quantitative run, and finaliy the rate constant ratio is determined in the third session. In the qualitative investigation, the identification of products usually brings some surprises. In addition to the expected ~ r o d u c t (acetone s and combination ~ r o d u c t .. s )the .- presence i f alkenes and other alkanes leads t d t h e discovery of competine. d i s ~ r o ~ o r t i o n a t i oand n abstraction reactions. With iodoethane; disproportionation is by reaction (11).
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C2Hs + C2Hs C2H4 + C P H ~ (11) For the iodomethaneliodoethane pair, the production of ethane by reaction (11)raises problems in the estimation of kzzlkll. But these problems are not without benefit since they contribute to the interest in planning the experiment. Students have to decide whether a disproportionation product is identical to the product of one of the combination reactions, (3) or (4). Even when it is, comparison of rate constants kP2 with kll-is still possible using eqn. (10) (2). A second ~ r o b l e m the student has to face arises from the presence of methyl radicals produced by the initiator. I n some systems, for example ethyl-propyl, the combination of methyl with propyl leads to the same product as the combination of ethyl radicals. CHs + C3H7. CIHIO CPHS+ CZHS CIHIO
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CH3. + RI = CH31+ R. (12) Again, the student has to decide whether eqn. (12) presents a problem. In fact, if rapid equilibration in eqn. (12) is assumed, as in e m . (1). it does not. At this stage-in the experiment, armed with the data from the qualitative investiaation and havine considered the various problems which m& arise, the studint plans in detail how heir i*, d~terrninethe ratio of rate constants. The olan is tested by using an interactive computer program deiigned to examine the conclusions of the qualitative experiment. This program from the CALCHEM project (5) provides an adaptive tutorial dialogue on the relevant background and detail to be considered when oerforminz the ex~eriment.The nrogram is written in the STAFauth; language (6)which&&s not only free format i n ~ uto t the student but also assesses the student's progress thiough the program so that remedial tuition can be aiven where necessarv. h carefully plannpd and rotttrdlrii run then yields the analytical data fur eqn. (8) or (101. Kt:, is calculated from tables of thermochemical data (e.g. see reference (2)). The calculation provides valuable experience in the manipulation and use of thermodynamic data.As a check on the student's method of working towards a value of K12 a second interactive computer program is available. This time, written in BASIC, it provides a systematic check of the student's data and method if an error is found in the value calculated for KI2. Finally the relative values of the rate constants provide an interesting discussion. I t is possible to compare values of rate constants with the predictions of collision theow and consider the possibility of low steric factors. In the context of the Course (31, the observation of similar rate constants for combination uf t he larger radicals provides some justification for assumptions that are made in polymerrzariun kinetics. Results and Discussion In the course of two years the experiment was completed by over 400 students. Their results (more than 200 rate constant ratios) are summarized in Table 1. The most striking feature of these results is the similaritv between rate constants for all pairs of radicals rxrepr those which include mrthyl. The rate wnstnnr fur the recom1)inn. t orders of tioo i f these radicals is found to he i ~ t x ~ uthree magnitude smaller than thr rate constant for cnml~inariunof mrthgl radicals. An absolute value for combination of methyl radicals. d a b o u t 3 X 10'" l mole-I s-' (71 is very close to the predictionofcollision theurs. On the basisof this theorv. ..the results of these experiments could only be rationalized by assuming steric factors of about for all radical pairs excluding methyl. The increase in size of the radicals does not seem to provide a sufficient basis for this large and abrupt change in the steric factor. Table 1. Summary of Results for Ratios of Rate Constants kdkm Rr
CHs C2Hs CnH,. CaHs
CsH-r
C2Hs
3.62 X
(37)
... ... ...
C&b
2.61 X (SO) 0.77 X lO-'(6) 0.75(15) 1.12(13) ... 2.24(35) ... ...
CsHn ... 0.87(2) 0.62(12)
1.56(34)
The numbers in parenmeres denote me number of determinations made on that oys-
tem.
Volume 55, Number 11, November 1978 / 743
Table 2.
Comparison of Rate Constants for Radical Combination k
Radical pair
C2Hr
+ C2Hs
1 mole-' s-'
2.5 X 1O1O 4.6 X 10' 4 X lo8 7.8
x lo9
Methodd
Reference
RS
(131 (2) (14) (1) (15)
RB P MMS
1 X 10'" 1.6 X lo8
VLPP
3 x lo= 2.5 X 10' 3 X lo8
VLPP
RB
MMS
RB
(18) (1) (191
a ns = ,&tine secmr. Ra = radica~-bu~~er, P = pyro~eis. MMS = ~ O I W I Wmadulatkan spechoocopy. VLPP = very low pressure pyrolyeir. ST =shock tube. Student9 01 ST294. The authm state that k may be twenty-fold overestimated.
"
tained between the results of the radical-buffer technique and very low pressure pyrolysis using modified thermochemistry of the tert-butyl radical (10). Similarly, using the recent examination of the thermochemistrv of the n-oroovl radical (11). we find that our value of the ratk constant'fori-propyl combination is about 1X 10'0 1mole s-I which seems more likelv than the result of the rotating sector technique (12). The possibility of errors in 'known' thermodynamic data can lead to useful discussion of the problems of estimating data for reactive species such as radicals and the danger of using erroneous data, especially via calculation of equilibrium constants, to establish values of rate constants. Finally we note that in view of these uncertainties, the ratios of rate constants for radicals larger than methyl are not much different from unity. In the context of our Course (3) this observation if extrapolated to radical reactions in the liquid phase, provides some justification for the usual assumption: that rates of propagation reactions in radical polymerization are independent of radical chain length. Literature Cited
Recognition of this problem leads to a consideration of the validitv of the radical-buffer method. The introduction of the radicLbuffer technique in 1972 led to a widespread view that the rate constants for combination of ethvl(2) and iso-oro~vl ( 8 ) radicals had values of about 4 X ids 1&olec1 s-i w h i e those for tert-hutyl(9) were much lower. More recent investigation (1)of these rate constants by direct methods suggests that they are not as low as was thought a few years ago. The extent of the disagreement is illustrated in Table 2 which includes our results where they can be estimated by direct comparison with the well established value for methyl combination. The imoortance of accurate measurement of radical combination rate constants has clmphasized the dticrepancie in l ' a t h 2 nnd drawn attention to the rhermorhemistrv of the radicals since this is the most likely source of error in the radical-buffer method. For example, good agreement is ob-
744 / Journal of Chemical Education
(11 Parkes. D. A..sndQuinn.C.P. C h e m Phys Lett., 33.483(19751. (2) Hiatt.R., and Benrun.S. W. J. A m e r Chpm Soc.. 94.25(19721. (31 W294. ThePnnctplesufChemicslPraerses, AnOpon University recond-laveleourse prcducod by the Facultie. of Science and'rechnulugy. (0 Mason. J., J.CHEM. EDUC..52. 214 (1975). (5) CALCHEM. (computer-mistedlearning in chemistry).Director: Professor P.B. Amcough, Department 01 Physical Chemistry, UniversityofLeeds.Leeds. England. (6) STAF.(afranrF~rableaufhoringsyrtem).CALCHEM, 197516. (71 James,F. C.,andSimuns. J. P.,inlsmot J. Chem K m n , 6,887 1194). (81 Hiatt.H..andBenrun,S.W..lntsrn.J. Chem K ~ n a t . .4.151 (19721. (91 McMillen, 0. F. Gulden. D. M.. and Benson S. W., J. A m e i Chrm Soc, 94. 1403 (19721. (101 Chuo. K. Y..Beadle.P.C.,Piszkiewicz,L. W..andGuldon,D.M.,lnfemaL. J. Chem. Kinel.. 8.15 119761. 1111 Marshall. K.M. sndRahman. L.,JC.S Chem. Cummun. 614 (19761. (121 Motcalf, E. L.,J Chsm.Sur.,3560 11969). (131 Shepp,A..and Kutschke. KO.,J. Chem Phya.. 26.102U(19571. (141 Hughes. D. C.. Marshall. R. M..sndPurnell.J. H.. J.CS Far. I. 70,594 (19741). (15)Gu1den.D. M..Choo, K. Y..Perona,M.J.,sndPiszkiowicz,I. W.,inlcrnot.J. Chzm. K k e l . , 8,881 (19761. (16) Metcalf E. L a n d Trotman-Diekenson,A. F., J. Chem S o r . 4620 11962). (171 Tssng, W.. J. Chem.Phy8..43,352 (19651. 118) Golden, U. M., Pir~kiewicr. 1. W., Perom. M. J..and Beadle, P. C., J. Amrr Chrm. Soe, 96.1645 119741. (19) Bartlo. K. D , unpublished results.
