K. B. YERRICK AND M. E. RUSSELL
3752
The curve shown is a densitometer trace of the photographic plate. The response of the film i s not perfectly linear, but the relative intensities indicated by the trace should be sufficiently accurate to guarantee
that competitive absorption cannot account for the effectof the chelate on the photoreactions. Acknowledgment. This work was supported by the U. S. Atomic Energy Commission.
Kinetic Order Determination in the Thermal Decomposition of Dimethylmercury
by K. B. Yerrick and M. E. Russell Department of Chemistry, Michigan State University, East Lansing, Michigan
(Received February $8,196'4)
A kinetic order determination was made of the thermal decomposition of dimethylmercury in the temperature range from 275 to 330". The rate expression used to fit the experimental data is -d(DMM)/dt = kB(DMM) kb(DMM)2. The temperature dependence of the rate constants is k, = 2.6 X lo9 exp(-39,000/M') sec.-l and k b = 9.5 X exp ( -71,00O/RT) cc. mole-l set.-'.
+
Introduction The kinetics of the thermal decomposition of dimethylmercury has been examined by a number of ~ 0 r k e r s . l - l ~However, the kinetic order of this decomposition in the vicinity of 300' has not been studied in much detail, and the few determinations which have been done conflict with one another. Laurie and Long4 reported first-order kinetics in the temperature range 294 to 333O whereas Yeddanapalli, et u Z . , ~ in the temperature range 305 to 342') found their data were best correlated by using a three-halvesorder expression for the decomposition. The work of Russell and Bernstein8 yielded first-order kinetics for the cyclopentane-inhibited reaction (290 to 375") , but they did not perform an order determination for the uninhibited reaction. Since the mechanisms proposeda,6*8.1lJ4,15for the reaction depend upon the order, it seemed necessary to re-examine the kinetics over a wider concentration range than had been used previously. Accordingly, the initial concentration was varied about 10-fold at each of five temperatures in the range 275 to 330". The results of this study are consistent with neither first- nor three-halves-order kinetics but can be well correlated using a two-term rate expression. The Journal of Phy8kal Chemistry
Experimental A conventional high-vacuum system was used. The decompositions (static) took place in a Vycor vessel whose volume was 870 cc. and whose surface-to-volume ratio was 0.73 cm.-I. I n certain runs the surface(1) J. P. Cunningham and H. s. Taylor, J . Chem. Phys., 6 , 359 (1938). (2) B. G. Gowenlock, J. C. Polanyi, and E. Warhurst, Proc. R o y . SOC. (London), A218, 269 (1953). (3) L. M. Yeddanapalli, R. Srinivasan, and V. J. Paul, J. Sci. Ind. Res. (India), 13B, 232 (1954). (4) C. M. Laurie and L. H. Long, Trans. Faraday SDC., 51, 665 (1955). (5) L. H.Long, ibid., 51, 673 (1955). (6) S. J. W. Price and A. F. Trotman-Dickinson, ibid., 53, 939 (1957). (7) R. Srinivasan, J . Chem. Phys., 28, 895 (1958). (8) M.E. Russell and R. B. Bernstein, ibid., 30, 607, 613 (1959). (9) J. Cattanach and L. H. Long, Trans. Faraday SOC.,56, 1286 (1960). (10) R. Ganesan, J. Sei. Ind. Res. (India), 20B, 228 (1961). (11) R. Ganesan, 2. physik. Chem. (Frankfurt), 31, 328 (1962). (12) R. E. Weston, Jr., and S. Seltzer, J. Phys. Chem., 6 6 , 2192 (1962). (13) M.Xrech and S. J. Price, Can. J . Chem., 41,224 (1963). (14) A. 9.Kallend and J. H. Purnell, Trans. Faraday SOC.,60, 93, 103 (1964). (16) L. H. Long, J . Chem. SOC.,3410 (1956).
THERMAL DECOMPOSI~rIONO F D~METHYLMERCURY
to-volume ratilo of the vessel was increased to 10.1 c m - I by packing it with short lengths of Vycor tubing The reactor was conditioned to a reproducible state'' by performing a large number of preliminary decompositions prior to making the kinetic measureiiieiits The temperature in tht. vessel was measured using eight thermocouples placed next to the vessel at various points; the mcan of these eight readings was designated as the tenipera,ture of the run. The average deviation from the niean of these readings was typically k0.1". The drift of any thermocouple with time mas less than 0.4" for the longest reaction times used. The average deviation of a single run temperature about the mean of all runs a t that temperature wafi less than jzO.2". Samples of dimethylmercury (DMnI) were kindly furnished by C. H. Brubaker, Jr., and R. B. Bernsteiri; each sample was prepared by the method of Gilnian and Brown.I6 The Brubaker saniple was fractionated in an efficient column, mixed with the Bernstein sample, and this mixture was fractionated in the same column. The fraction boiling between 91.5 and 92.0" (740 mm.) was collected, passed over P20b,distilled in uucuo, and stored in the dark a t -78". The infrared spectrum of this material agreed with the literature." A weighed amount of D S N was introduced into the reaction vessel, and the reaction was allowed to proceed until approxiniately 15% of the reactant had decomposed. The reactor contents were passed through two traps at -194', and the product volatile a t this temperature (pure CH[S was discarded. The remaining substances were warmed to -97", and the products volatile a t this temperature (hydrocarbons containing two to four carbon atoms) were also discarded. The residual material was warmed up, distilled into a weighing bulb, and weighed as DJG\II. The infrared spectrum of this residual material was identical with the spectrum of DMRI. In separate experiments, performed at 230°, it was shown that less than 0.3% of the DhlM was lost using the above technique. In certain experiments the total pressure was increased by the addition of COZ (Matheson Chemical Co., Bone Dry grade, stated purity >99.9'%) shortly after the DMM had been introduced into the reaction vessel.
Results and Discussion Table I gives typical experimental data obtained a t the two extreme temperatures used in this study, (All of the points are included for 275.5", and half of the points are included for 330.2". At 330.2' the selection was done by chioosing every other point in the order of increasing concentration.) The calculated rate constants assuniiiig first order (kl*) and three-
3753
-
Table I : Effect of Concentration on the Thermal Decomposition of Dimethylmerc ury (DMM)O
x
106,
moles/cc."
reaction time X 1 0 - 3 , sec.
f fraction decomposed
see. -1
k*Q/z X 103, (cc./mole)'/t 8ec. -1
0.60 0.60 0.81 0.86 0.94
0.86 0.48 0.43 0.38 0.38
15 16 24 29 42 62 71 78 93 113 123
32 31 38 32 33 38 40 41 43 48 51
ki* X 106,
Temp. 275.5'
0,526 1.636 3.848 5.454 6.786
313.7 217.6 220,7 187.2 185.8
0.170 0.122 0.163 0,149 0.160 Temp. 330.2' 11.16 0.149 8.44 0.122 7.44 0.163 5.82 0.153 4.20 0.162 2.94 0.165 2.22 0.146 2.04 0.147 1.74 0.149 1.44 0.150 1.44 0.162
0,220 0.270 0,434 0.845 1 ,792 2.821 3.401 3.917 4.942 5.907 6.436
(DMM)o
=
initial concentration of the dimethylmercury.
halves order (ICa/**) are given for each of the experimental points. The systeiiiatic drift in the calculated first- and three-halves-order constants shows that neither order is very satisfactory. Other oneterm rate expressions, such as second-order, yield rate constants which are also functions of the concentration. The rate expression which was used to correlate the experimental data in this study is -
d (DM M) dt
=
k,(DMRil)
+ kb(DMRII)2
(1)
Equation 1 can be approximated, a t small values of j (fraction decomposed), by
- A(DRIM) (DMM)o - (DMM) At
-
t
k,(DAIJ!I) where (DJIRII) = [(DMSI), stituting in eq. 2 the relation (DMIT)
=
+ ICb(DMM)'
+ (DMM)]/2.
(2)
By sub-
(1 - f)(DMM),
and noting that f / ( l - f/2) is approximately equal to f/2), we obtain
,f(1
+
~
(16) H. Gilman and R. E. Brown, J . A m . Chem. SOC.,5 2 , 3314 (1930).
(17) H. S. Gutowsky, J . Chem. Phv/s., 17, 128 (1949).
Volume 68,Number 12 December, 1964:
K. B. YERRICK A N D 11. E. RUSSELL
3754
The first-order rate expression kl*t
=
-In (1 - f )
(4)
can be approximated, for smallf, by kl*t = f(1
+ f/2)
(5)
Combining (3) and (5) gives kl*
=
k , $- kb(1 - f/2)(DMILI)o
(6)
Thus, if f is small and constant, a plot of a pseudofirst-order rate constant (ie., one calculated using eq. 4) us. the initial concentration of dimethylmercury will yield a straight line. Figures 1 and 2 are plots of the datal8 a t each of the five temperatures studied. The linear nature of these plots is evident.
Equation 9 can be rearranged in the form
+
Since (1 - k,t/2! (l~,t)~/3 ! ...) is approximately equal to 1, eq. 10 was used to evaluate k , and k b by an iterative procedure. These values were then used to correct the experimental data to constant a , and the iteration mas repeated. The values of k , and kb obtained by this procedure (unpacked vessel) are plotted
70
50
c
30
0
: 10 y
28
I
I
I
I
b rl
*Y
24-
-
2.0 -
-
T: 275OC.
18
-
16
-
14
-
12
-
c
Y 5 X
10 t Y
B 041 0
I
I
2.0
4.0
I 60
I 1 80
6-
(OMM), x IO6, (MOLES cc-'1
Figure 1. Pseudo-first-order rate constants as a function of initial DhIM concentration at 275.5, 289.2, 319.2, and 330.2'.
The method used l o evaluate the rate constants k, and kb was to rearrange the integrated form of eq. 1 into an equation which yielded k , and k b by aniterative procedure. Integration of (1) gives
The Journal of Physical Chemistry
4
0
I 2.0
I
I
4.0 60 (DMM), x IO6, ( M O L E S c c - ' )
8.0
Figure 2. A comparison of pseudo-first-order rate constants as a function of initial DMRI concentration for the packed and unpacked (open circles) vessel a t 303.7".
(18) The dat,a plotted are uncorrected for variations in .f However, the maximum variation in f was from 0.122 to 0.185. The variation of 1 - fj2 is then from 0.91 t o 0.94, which will not affect the slopes significantly.
DEcoMPosITIox O F DIMETHYLMERCURY
3755
in Fig. 3. A least-squares treatment of these points gives the Arrhenius equations
The data used by Laurie and Long4 for their order determination are compared with our data in Fig. 2. Extrapolation of their points (mean temperature 305.5") to 303.7" gwes agreement with our data within the experimental error of both sets of data. The determination of order by Yeddanapalli, et u Z . , ~ was conducted at a temperature higher (342") than that used in the present study, but using k , and ICb (calculated a t 342" from eq. 11 and 12) in eq. 7 yields calculated values of (DMXI)o/(DMM) which deviate by less than 2% from the experimental values of ref. 3. I t is of some interest to note the observations of previous investigators with respect to the effect of temperature on the kinetic order of the reactioji. Yeddanapalli, et a?., 3 reported that at 305 and 323" there was little to choose between first- and threehalves-order kinetics. On the other hand, at 342" the three-halves-order constants were decidedly more consistent than first-order constants. Laurie and Long4 observed that the reaction appeared to be first order in the range 294-332") but at 343" the order appeared to increase to nearly three-halves. These observations are qualitatively consistent with eq. 1. At low temperatures the first term in this expression would predominate because k, has a much lower activation energy than kb. Thus, the data would appear to correlate better with a first-order expression rather than a higher order. At higher temperatures, however, the contribution of the second term in eq. 1 increases, and, thereby, the apparent order of the reaction increases. These effects can be seen also from the calculated first- and three-halves-order rate constants in Table I. Since the submission of this study for publication, a comprehensive study of the decomposition in the vicinity of 400" has been published by Kallend and P ~ r n e l 1 . I ~Their proposed inechanisin gives the rat e equation
THERMAL
IC,
=
IC,,
2.6 =
x 109 exp(-39,000/RT) sec.-l
(11)
9.5 X 1026exp(-71,000/RT) cc. mole-1 sec.-l
(12)
The effect of surface on the reaction was examined by making runs in a packed vessel at) 304" and cornparing them with runs made in the unpacked vessel at the same temperature. The results are plotted in Fig. 2. Calculation of IC, and kb from these data shows that each increased 40% over its value for the unpacked vessel whereas the surface-to-volume ratio increased by a factor of 14. From this we can conclude that the heterogeneous component in the unpacked reactor is less than 5% of the total.
E',
(OK")
Figure 3. Arrhenius plots for k, (open circles) and kb (full circles).
A possibility exists that the increase in kl* as coiicentration increases might be attributed to the falling off region of unimolecular reactions. However, this can be refuted by examining the two points at 330" in Fig. 1 iii which the pressure was increased approximately 100-fold by the addition of CO,. The increase in ICl* is small aiid within the scatter of the data. Moreover, the large number of atoms in DMM would seem to preclude such a large effect at this temperature and pressure,1sand the shape of the curve is not what one would expect for a uniinolecular fall-off.
-
-d(DMM) -dt where action
k.1
=
2kl[DhI-11]
+ B[DMAI]'/'
(13)
is the rate constant for the elementary re(CHS),I-Ig ---j. CH3
+ CH3Hg
and B is a combination of several rate constant,s in their postulated mechanism. Their data are found to fit this expression rather well. The results of the present study differ from those crf Kallend and Purnell in several respects. They ob(19) A. F. Trotman-Dickinson, "Gas Kinetics," Auttermorths Scientific Publications, London, 1955, p. 69.
Volume 68, Xumber 1 2 December, 1968
3756
tained good material balances on carbon and hydrogen whereas data near 300°, even a t low extents of reaction, show poor material balances (e.g., in a runzo for which j was 0.066, the amount of carbon and hydrogen in the recovered products was approximately 60% of the total in the decomposed diniethylniercury). Our rate expressioii also differs from eq. 13. h plot of ICl* us. (DXLI)o’’zdoes not yield a straight line as it should if their expression is valid a t 300”. Furthermore, k , should equal 2kl if the results of ref. 14 were applicable in the temperature range of this study. The difference between IC, and 2kl is quite large (e.g., at 305”, 2kl is equal to 3 X set.-' and IC, = 4.4 X set.-'). We feel the differences cited above are probably due to the two different temperature ranges examined in these two studies. The nature of the hydrogen and carbon “lost” has been the subject of some speculation. Several workers’ 3 , 4 have assumed that a hydrocarbon polymer deposits on the walls of the reaction vessel. Some experiments by one of usz1indicate another possibility. A calculation of the empirical formula of the “lost” carbon and hydrogen was made from the results of two runs carried out at lows (0.066 and 0.074). The values obtained were CH2 47 and CH254. In another series of experiiiients a material balance on the mercury was made, and it was found that about half of the mercury from the decomposed dimethylinercury was not recovered. This indicates that the “polymer”
The Journal of Physical Chemistry
K. B. YERRICKA N D :\I. E. RUSSELL
contains mercury A substance which has been proposed as a possible product2l 4 in the pyrolysis is (CH3HgCH2),. This substance has a carbon-hydrogen empirical foriiiula of CH2 and also contains mercury. If this compound were relatively nonvolatile the loss of carbon, hydrogen, and mercury could be explained. However, attempts by us to isolate (CH3HgCH2)2 have not been successful. The “polymer” may well be a complex mixture which gave the empirical formula of CH26 by coiiicideiice for the two runs mentioned. We are unable to postulate a mechanism which is consistent with our data. The very large pre-exponential factor of ICb suggests that it is at least the product of two elementary rate constants. It also should be noted that the Arrhenius plots of k , and k b show coiisiderable scatter. This may indicate that IC, and kb are each a collection of elementary rate constants and their Arrhenius plots might well be curved. A situstion like this was found by Palmer and Dormis’222 in their examination of the kinetics of ethylene decomposition. Acknowledgment. We wish to thank Professors R. B. Bernstein and C. H. Brubaker, Jr., for furnis!iing the dimethylmercury used in this study. (20) M E Russell, P h D Thesis, Universitl of Michigan, 1958 (21) M E Russell, unpublished work, L-niversit> of Michigan ( 2 2 ) H P Palmer and F L Dormish, J Phys C h e m , 68, 1553 (1964).
