Pyrolysis of Zinc Oxalate: Kinetics and Stoichiometry
by Peter E. Yankwich and Petros D. Zavitsanos Kogcs Lnborator~/of Chemist, g , L'niversity of Illinois, Urbana, Illinois
( R e c e i w d Julg 8 , 1963)
The stoict1iometi.y of the pyrolytic decomposition of anhydrous zinc oxalate has been studied o ~ ~ ?the t ' temperature range 350-500°, and the kiiietics bctwecii 300 and 870'. The stoichiometry coimspoiids essentially to ZnC204(s) = ZiiO(s) CO,(g) CO(g). S o metallic zinc is produced, but carbon dioxide appears in slight excess. The kinetic results indicate that, there are three phases in the decomposition : (a) an initial accclcratory phasc ( a < ca. 0.04) during which reaction is due primarily to the growth of nuclei formed dutsiiig the dehydration of the Z I ~ C ? O . ~ . ~ Ifrom T & which the anhydrous starting material is prepared; (h) an intermediate acceleratory pcriod (0.04 < (Y < ea. 0.4) during which growth of ot~iginalnuclei predominates a t the heginning atid rcaotioii due to randomly formed nuclei predominates nea'r the end; and (c) a decay pcriod ( a > ca. 0.4) i n which the decomposition proceeds entirely through random nucleatioti. The results suggest that the same elementary processes are associated with nucleation aiid with nucleus growth.
+
Introduction 111 this paper we report the results of experiments on t,hc kiiictics atid stoichiometry of the thermal decompositioti of anhydivus zinc oxalate. This investigatioti is t'lic second i i i a series of studies of the tcmperature depcttid(wce of the stoiehiomctry and carbon isotope cf'fccts i l l thr pyrolyses of metal oxalates. The principal react,ioii occurring during: the pyrolysis of z i n c oxalat,c is
%riCz04(s)= %nO(s)
+ CO(g) + CO,(g)
Here, the production of a significant amount of the metal does not occiir2-S-a difference from the decomposition of the oxalates of ~ i i c k c l ,silver,' ~ mercury,8 atid lead.' While there have been a number of fragmentary stiidies"-'" of the decomposition kinetics, oiily t w o 4 ~ S ~seem i4 to have dealt with the pyrolysis over the whole range of decomposition. However, evcti this pair of investigations cannot be compared oolivc?iiictritly with each other, because Iluttig and 1,ehmatin dehydrated XiiC.L04.21-1&in contact with air, irliilc Iollimore, et al.,13 found m to he 1.51.8 a t 400'. IIuttig and I,ehmann2 conducted two experiments, at 360 and 405'; we have subjected their data to arinlysis and find m = l.t5 a t the lower tcmperature, 2 . 3 a t the higher. ( 2 7 ) -1. G . N . Thomas and 1.; C. Tompkirls, Proc. R o y . S ? c . (1,o~idori). 8209,550 (1951). (28) *J. G . N. Thnnitis arid 13.' C . Tompkins, ibid., A210, I 1 1 (1951). (29) 1'. LY. XI, Jacobs arid 1:. C. Toinpkins, in "Chernist,ry of the Solid State," W . 1C. Garner, I,:d.. Arademic Press, Inc.. New I'ork, N. Y., 1955. Chapter 7 .
Nonintctgral and temperature-dependent values of m have k~ccnobscrved in othcr decompositions. Thomas
and ‘ F o m p k i r ~ shave ~ ~ , ~reduced ~ both of thesc variations simultaneously by assuming that small nuclei grow less rapidly than large ones, that the growth rate changos a t some critical nucleus size, and that the activation energy for slow growth is larger than for normal growth. One obtains valucs for the length of t,he slow-growth period, t’, by forcing the data to fit some integral m’ cy
=
C’(t -
t’)m‘
(6)
from the variation of t’ with temperature, the activation rncrgy associated with the slow-growth process can he obtained. When our results are forced to fit eq. 6 with m’ = 1, B is the same (49 kea]. mole-’); the t’ are not only srnall (0. -400 sec.), but their variation with temperaturc corresponds to an activation energy for the slow?growth process much too small (ca. 20 kcal. mole-’). When t,he data are forced to m‘ = 2, E becomes 37 kcal./mole--I and the t’ negative,3o corresponding to an initial “fast-growth” period. The t’ in this case are small also (0-250 see.), but their scatter is so great as to rendcr meaningless the calculated associated activation onergy. In the casc of zinc oxalate, use of eq. G docs not lead to clarification of the kinetics as it docs for barium a ~ i d e * and ~ * ~other * decompositions. In three runs (300, 325, 370”) h~ is smaller than the minimum of r , for that part of the acceleratory phase which yields a linear plot of In a us. In t ; further, in all three eases these plots are everywhere concave downward, except for their linear segments. In terms of a power law representation, the values of m in these three runs are larger a t very low a than in the remainder of the acceleratory phase,” as are the k,, and smaller as a approaches unity. These observations suggest a model which can yield the observed temperature dependence of m. Equation 5 assumes that nuclcation is governed by a power laws2
N
=
No(kit)’/p!
(7)
where N is the number of (growth) nuclel formed up to time t, N o the number of germ nuclei, and kl the probability (see.-’) for one of the P successive events resulting i n the formation of a growth nucleus. If k2, the (linear) rate of growth of the nucleus, is invariant with time, and if it is the same in each of the X dimensions of nucleus growth (i.e., normal or isotropic nucleus growth is involved), then eq. 5 may be written in the form
CY
C8Cbk1’k2Xt”
=
(8)
where C , depends on the nature of the reagent and the concentration of germ nuclei, and Cb
’[
P!
=
I - - - - - - +XP
(P
+ 1)
X(X
- 1)p
2!(D
+ 2)
1
X(X - 1)(X - 2)p ___-
3!(P
+ 3)
($))
Now, suppose that more than one nueleationgrowth mechanism can operate in the acceleratory phase, that is, that mechanisms with different m Contribute to the observed decomposition. Then CY
=
C, [C&’kzXtm
+ Cb’kl’‘k~X’tm’’]
(10)
In general, a plot of In CY us. In t will have slope m a t low t and m’ a t large t. If the acceleratory phase is preceded by a short rapid growth phase (vide supra), and followed by a falling-rate phase (vide infra), the apparent slope of the plot in the intermediate acceleratory phase will depend upon the r, for the initial arid final phases; further, this apparent slope will change with temperature in a manner which depends primarily upon the p and X values which obtain in the initial and intermediate acceleratory phases, even if the activation energies associated with kl and k2 are the same in either and/or both of the phases.33 Decelemtory Phase. The zinc oxalate decomposed in these experinients is a rather uniform powder. The kinetics of the pyrolysis, a t least in the deceleratory phase of the reaction, might be well approximated by the contracting sphere model. I t is assumed that the solid consists of spherical particles of radius a , and that nucleus growth is uniform inward and proceeds with linear velocity k. Without accurate information concerning the uniformity of a, the experi(30) A similar situation has been observed for silver oxide decomposition: W. E. Garner and L. W. Reeves, T r a n s . F a r a d a y Soc., 5 0 , 254 (1954). (31) The d a t a are few, so reliable kinetic parameters caririot be calculated for these regions of low a. However, the m values are about 1.5 times, and tho k m values 1.5-2.0 times, those recorded i n Table I , part (i). (32) C . Bagdassarian, Acta phys.-chim. IIRSS, 20, 441 (1945). (33) An over-simplified example may be helpful at this point. Suppose t h a t a large number of nuclei are formed during the tiehyrlration process (once the pyrolysis starts, B = 0 for them), and that the activation energy for their foririatiori in the dehydratod material is greater than the ac!tivatiori energy for the growth process. With iricreasiiig t,empersture, an increasing nurnher of nurlei would be formed ( B f 0 for them) during the growth of those produced during the dehydration, and the apparent value of m i n t,hc interiiierliate acceleratory phase would inrrease with temperature. Of course, i f the falling-rate phase did not, overtake the acce1erator.v phnse xt sufficiently low a. there would be a conmve tc~itocirdinterniethte rcginri on the plot of In n us. 111 t instead of a linear region.
mentally accessible qiiantity is an effective mean valuc? of (/cia) dcsigiiatcd by tlict subscript CS, Typically, cq. 2 Iiolds for tlio,lattcr part of tlic dcc:onipositioii,“L 0.35 < cy < 0.%jq01’ for thc lattci- part cxxccpt, for thc Iast,Rjo.?G < cy < 0.85. llic ra for (’(1. 2 arc lat1ic.r iricoiisist,ciit (‘l’ahlc I , part ii) : at, tlic lonwk a i d higlicst tcnipci,aturcs, t,hc cquatioii applics to ahoutJ tlic first, qiiart~eror third of the reaction ; a t the iiit~crinctliatc trmpcraturcs it describcs thc middle part of tlict dccomposition; at) no tompcraturc docs it s(’cin to be valid ticar the end of the pyrolysis, where is slioiild apply. The valiics for n rctrordcd i i i ‘l’nt)lc I, part iii, wcrc obtaiiicd from log log plots of cq. :agesof a dccomposition such as that of zinc oxalatc; two sccni paiticula.rly plausible. (a) jlt large a , t,lic: reaction interface has a vcry complicated shape, hiit tlic g m v t l i of niiclci t’ciids to produce rcgioiis in which iinreactetl mattrial is completely ciiclosed by the intorface. The formation of fissures a i d the collapsct of the interface, both of which are favored in tho piwelit sit,tiat,ion because gaseous products arc formed, can i.csdt i n the isolation of chunks of rc’agcnt i n which there arc iio nuclci; the decomposition of t,he reagent i n these chunks (which would be small) would he raiidom, leading to a firstorder relat,ion t)ct~weciicy atid t. (t)) liandom foimat,ioii of nwlri which thcn grow rapidly, i n vitlicr tivo or thr1:c dirnciisioiis, leads to first-ordor kinetics. 3R.a7 F;it,lici. (a) or (I)) is consist,t:nt, jvitli our car1ic.r argurncrits (!oriccriiiiig t,hv ac:c:clcrat,ory phase of the rcaction. Test oj the iZ vrnmi I:‘cpLation. Avranii*:3developed an c:xtc?nd(:ti ti.cat,inc.iit of solid statc reactions which, for w i i d o i n iiiicIc:Ltioii, t:tkrs ilit,o acbroulit tho iiigcistioii of pot.twtial iiiiclci by growing nuclci and tlic intcrsection aiid overlapping of‘ growing niiclri. I’.qriatioii 1 is m i :isyrnpt.otic forrn ohtainiiig at large f , large cy. The c:xpoiic,ni. t ~ tlcpciids , ~ on tlio prohat)ility of OOCIW-
reiicc of the energetic fluctuations which lead t,o nucleat h n , and on A. If I’ = 0 for small probability, and I-’ = 1 for largc prot)al)ility, t,heii, approximattly 7bA
zz
(A - 1’
+ 1)
(12)
:lccortliiig to the results i n ‘I’ahla I, part iv, the nqpnptotic form of tlie Avrami equation holds in t,hc early a i d inidtllc plinses of thc decomposition, rathcr than for large cy. F’urthcr, nA increases from about 1.1 to aboiit) 2.1 ovor tlic t,c:mpr:rature raiigc iiivost’igatcd. Since oiic would expect P to increase slightly \vit.li t,cinpcrature, the variatiou of 71* would seem to rrqiiirc: tli:it, A vary with teinperat,urc, or hc a n ef‘fectivo cornposite as suggested above. Although such corrclation Ieratorg and broad “middlc” phases is tcinptiiig, it docs not, scom so st,rongly justified as it would he wcrc tlic Xvrami eqiiation applicable, as it sliould he, for large CY. Kornicnko5 carried out a large number of cxpcriniciits at’ four temperaturcs hetlncen 368 arid 305 ’. Ilc rccords E = 43.8 (=1=2-4)kcal. molc-’ a,nd nA = 2 . Hiittig and Lehmanri’s data yield nA = 1.7-1.8 over r similar to those shown in Tahlc I, part iv. A ppnrent Activation E n e i y y and I’re-e:cponential Factor. Some of the rate constants in eq. 1-1 arc simple, others arc composite. I+om cq. 1 and 8, we havc
or worse (scc eq. 11). It would be difficult to intcrpret the prc-cxponential factor associated with k,, but the relatrd activation cncrgy is
The li in (I;/a)cs is related to k 2 ; since n-e do not havc good measurements of a (which is a mean cffcctivc quantity), we can interprct the E associated with ( k / a ) c s but riot the A . The 12, = k l of eq. 3, 7 , and 11 are all the same; this is the rate constant for nuclcation, arid refers to an elementary process- both the associated B and A are wcll defined. I n the asymptotic fovm of tlic Xvrami- Erofcyev equation, 714 should be 8 and k, would be equivalent to k,; howeverq n i t h nA < 3, k A is composite in a fashion similar to that of k , ~~~~~~
~
~
I t , I. Ilazouk. J . C h ~ mSoc.. . S X (1949). (35) \V. D. Spencer a n d 13. Topley, ibid., 2W3 (1929). (3(i) Strictly speakilkg, this convlusiori i s valid for small pxrt,ic:les over i i wide range o f a. but oiil5- for large a i f the uart.ic.les are 1:irj:e. The r)riil)Ierii h>tsheeii exttniiried in det:iil by .\la1111)el.~’~ (34) R. ,J, Gregg aiid
(37) K. L. hIariipel, % . p h i / 8 i k . Chr,m., 8187, 3 3 , 235 (19.40). (38) At large n . n,, = 1, h u t t,his is equivalent to first-ortier kiriet ics.
PYROLYSIS O F ZINC OXALATE
The most striking feature of the data collected in Table I1 is the similarity among the calculated activation energies, this in spite of the varying makwp of the k’s with which they are associated. This similarity suggests strongly that El and EQ are nearly the same; in turn, this fact suggests, though less strongly, that the elementary processes associated with nucleation and nucleus growth are the same. However, it may be that these possibilities are less important than the demonstration that rather good and rather poor representations of the kinetics have associated with them similar activation parameters, a situation which would seem to reduce the sanctity occasionally accorded these parameters. The values for the pre-exponential factors colleci,ed in Table I1 shed little light on the matter at issue. The A for k , is above the range of lattice frequencies; it lies in the optical range and corresponds to a frequency of the order of tens of thousands of crn.-l. If the well defined A values are reasonably accurate, and if the complexity of IC, is similar to that of k , in eq. 13, the pre-exponential factor in liz must lie in the range 1011-1C~12, in the low range of lattice frequencies. The activation energy and pre-exponential faclor calculated from KornieGko’s results are both slightly smaller than those shown in Table I1 for k,. This agreement is interesting because it indjcates similarity between the characteristics of our samples (which were dehydrated a t a lower temperature just before the pyrolysis run) and Kornienko’s (which were dehydrated during the early minutes of the pyrolysis). Analysis of the data of Huttig and Lehmann s h o m
463
the several activation energies to be somewhat lalwer than those in Table 11, but still confined to a narrow range (30-34 kcal. ‘mole-I), a difference‘ which could arise in the method of preparation of the salt
Conclusions The stoichiometry of the in vacuo pyrolysis of anhydrous zinc oxalate is not significantly dependlent upon temperature, a difference from the lead system.’ Our kinetics results indicate that random nucleation processes are involved in all phases of the pyrolytic decomposition of anhydrous zinc oxalate. In an initial acceleratory phase ( a < 0.04) the reaction proeeeds primarily, however, through the growth of nuclei formed during the dehydration of the zinc oxalate dihydrate. There follows an intermediate acceleratory period (0.04 < a < ca. 0.4) during which growth of the original nuclei predominates at the beginning and reaction due to the randomly formed nuclei near the end. Finally ( a > ca. 0.4), the decomposition proceeds entirely through random nucleation followed by very rapid reaction. Some of the features of these kinetics have been observed in earlier studies, but they have involved contact of the dehydrated oxalate with air, or have obscured the initial phases of the decomposition by dehydrating the sample material at the pyrolysis temperature. Acknowledgment. This research was supported by the C . S. Atornic Energy Commission.
Volume 68, Sumber 3
March, 16164
