CARBON ISOTOPE EFFECTS IN PYROLYTIC DECOMPOSITION OB ZINC OXALATE
1275
Carbon Isotope Effects in the Pyrolytic Decomposition of Zinc Oxalate
by Peter E. Yankwich and Petros D. Zavitsanos Noyes Laboratory of Chemistry, University of Illinois, Urbana, Illinois
(Receioed February 6 , 2964)
The CI3 isotope fractionation in the pyrolytic decomposition of anhydrous zinc oxalate (prepared from the dihydrate precipitating upon admixture of solutions of zinc nitrate and sodium oxalate) has been studied as a function of temperature. Between 282 and 500°, the intramolecular isotope effect observed a t complete reaction falls froin 0.79 to 0.36'%,, thus exhibiting normal magnitude and temperature dependence (the lead and manganous oxalate systems serving for comparison). A b initio calculations of the intramolecular isotope effect via the Wilson-Johnston method, and employing a three-particle model C-0-Zn, replicate the experimental results well. In one experiment a t 300", the intramolecular and both the intermolecular isotope effects were measured for 0-2Oj, and 2-4y0 decomposition. The intramolecular isotope effects a t complete and partial deconiposition are the same, as expected for this type of zinc oxalate. The pattern of intermolecular isotope effects is the same as observed in the manganous oxalate pyrolysis (dependent upon degree of decomposition) and may afford a useful probe for elucidation of mechanisms operating in early stages of such crystal decompositions.
Introduction This paper is a report on experiments designed to establish the magnitude and temperature dependence of the CIY isotope effects in the pyrolysis of anhydrous zinc oxalate. The kinetics and stoichiometry of the decomposition were subjects of an earlier report from this laboratory.' The current study is the third in a, series on isotope effects in thermal decompositions of metal oxalates, the previous investigations having dealt with the anhydrous salts of lead2and m a n g a n e ~ e . ~ Experimental Preparation of Zinc Oxalate Dihydrate. Aqueous solutions of equal volume of 0.10 M zinc nitrate and of 0.11 M sodium oxalate4 (reagent>grade cheniicals in deionized water) were brought to their boiling points and the former added rapidly to the latter; the mixture was stirred occasionally as it cooled to room teinperature. The precipitate is rather fine (particle size 2025 p ) , and uniform in dimension. The crystals were washed several times with distilled water, air-dried for 2-3 hr. at I lo", and stored over magnesium perchlorate m a drtsiccator. Apparatus and Procedure. The thermal decomposition apparatus and the procedures employed in both the kinetics and the isotope fractionation studies have
been described in detail in an earlier publication from this laboratory.] It is important to recall here the fact that each sample of anhydrous zinc oxalate was prepared from the dihydrate just before being brought to the decomposition temperature and in the decomposition apparatus. The sample size in the complete pyrolysis runs was approximately 0.25 mmole ; in thr single experiinerit where it was only partially decomposed, the sample consisted of 3.0 miiioles of zinc oxalate. Isotope Analyses. Carbon isotope analyses were carried out with a Consolidate-Sier isotope-ratio mass spectronieter ; the analytical procedures and methods for correcting the raw output data have been described in earlier publications from this laboratory. 2,5 ~
(1) P. E. Yankwich and P. D. Zavitsanos, J . Phgs. Chem., 68, 457 (1964). (2) P. E. Yankwich and J. L. Copeland, J . Am. Chem. SOC.,79, 2081 (1957). (3) P. E. Yankwich and P. D. Zavitsanos, Pure A p p l . Chem.. in
press. (4) Preparations ot zinc oxalate are designated A when precipitated by oxalic acid, C when precipitated by sodium oxalate. The two types of solids m a y exhibit different kinetic and isotope effect behavior.3 (5) P. E. Yankwich and R. L. Belford, J . Am. Chem. SOC.,75, 4178 (1953); i h i d . , 76, 3067 (1954).
Volume 68, Number 6
J u n e , 196d
PETERE. YANKWICH AND PETROS D. ZAVITSAXOS
1276
I
Notation and Calculations. Isotope effects in oxalate decompositions are reported conveniently in the notation of Lindsay, McElcheran, and Thode6 c1200-
1
c1200~ 1 3 0 0 -
I ~ 1 2 0 0 -
k,
--+ C'202
I
I
+ C'20
+ 3-c1202+ -%~
I
1 3 0 ~ ~ 1 2 0
cl30
Let au be the mole fraction of C13 in carbon dioxide obtained from the combustion of the original zinc oxalate, ( X d ) $ be that in the carbon dioxide collected up to time I , and (X,)t be that of carbon dioxide obtained by combustion of chrbon monoxide produced up to time t. It can be shown that
1
I
1.40
I.60
I
1.80
/03/T K
that is, this ratio of isotopic rate constants results from the indicated quotient of mole fractions for any time t, any degree of decomposition, and, therefore, any increment of decomposition. Further
and
Figure 1. Influence of temperature on intramolecular carbon isotope effect. - - - -, eq. 4, ZnCz04;2 eq. 5, ZnCz04; shaded band, MnC204.a
rectangles encompass the average deviations, while the solid rectangle for the single run a t 400" has a length equal to the estimated mean precision of a single datum. The dashed and solid lines, respectively, are obtained from least-squares fitting of the data to equations of the form
(3)
where the subscript zero denotes, rigorously, the limit of zero time or infinitesimal degree of pyrolysis; practically, these equations yield results valid within limits imposed by the mass spectronietry if the products are collected up to about 5% reaction.'** In later tabulations, use will be made of two additional quantities: a' is the calculated mean of X, and Xd for the increment 0-294 decomposition; and a" is that calculated mean for the increment 2-4y0 decomposition. One would expect a' = a".
Results Complete decomposition isotope effect measurements were obtained at eight temperatures between 282 and 500"; values of ( / C ~ / I C , ) ~ I for , ~ ~ each run are listed in Table I. The computed average values of this rate constant ratio is shown in the last column of the table, the appended errors being average deviations from the mean ; the mean precision of individual (k21k3)obsd values is estimated to be k0.0003. Values of L(kz/lc,) = 100 In (kzlk3) calculated from the last colunin of Table I are plotted us. 6' = (1000/T) in Fig. 1; the open The Journal of Physical Chemistry
+
(4)
+ BZ
(5)
L(h/b)obsd
=
MI@ BI
L(h/k3)obiid
=
Md2
and
A single partial decomposition experiment was carried out a t 300"; product gases were collected for the first 2% and the second 2% reaction. I n Table I1 are collected the various C13 mole fractions observed and isotopic rate constant ratios calculated for the two parts of this experiment. The results are compared with those obtained with manganous oxalate, as are the values of the M's and B's for eq. 4 and 5, and several other quantities. The mean deviations of the experimental points from the least squares fitted (4) and ( 5 ) are k0.06 in L, or approximately 12% of the average isotope effect observed. The average value of the ratio CO,/CO for the product gases from the pyrolysis of anhydrous zinc oxalate ( 6 ) J. G. Lindsay, D. E. McElcheran, and H. G. Thode, J . Chem. Phys., 17, 589 (1949). (7) J. Bigeleisen, Science, 110, 14 (1949). (8) J. Y.-P. Tong and P. E . Ysnkwich, J . Phys. Chem., 61, 540 (1957).
CARBON ISOTOPE EFFECTS IN PYROLYTIC DECOMPOSITION OF ZINC OXALATE
Table I : Observed Intramolecular Isotope Effects in the Pyrolysis of Zinc Oxalate: ( a 0 ) C X lo8 = 10692 f 4 Temp., OC.
(xd)
x
106
Table I1 : Comparison of Isotope Effects Observed in Pyrolyses of Manganous3 and Zinc Oxalates MnCzOp
(X,) X 106
(kdkdobsd
10641 10639
1.0079 1,0079
(a0)c
282
10725 10723
10659 10658 10639 10638
1.0054 1.0065 1.0084 1.0073
10731 10714 10737 10729 10730
10660 10654 10684 10666 10656
1.0067 1.0056 1.0050 1.0059 1.0069
10707 10707 10711 10709 10707 10711 10709
10654 10669 10666 10660 10667 10656 10651
I .0050 1.0036 1.0042 1,0046 1,0037 1,0052 1.0054
1.0045f0.0006
400
10722
10675
1.0044
...
410
10709 10705 10718 10707 10711
10666 10665 10663 10664 10665
1,0040 1.0038 1.0052 1,0040 1.0043
10704 10700 10698 10709 10715
10665 10657 10659 10675 10666
1.0037 1 ,0040 1.0037 1.0032 1.0046
1.0038It0.0004
10707 10696 10701 10705 10707
10669 10660 10675 10659 10661
1.0036 1.0034 1.0024 1,0043 1 ,0043
1.0036=!=0.0006
330
350
465
500
x
IO6
1.0069f0.0010
10691 f 3
First 27, reaction ( X d ) x lo8 (x,) x 105 (a’)x 106 (kZ/ka )obsd (k1/2k3)0bsd (ki/2kt)obsd
1.0060f0.0006
ZnCzOh
10692 f 4
A. Partial Decomposition a t 300”
1.0079i0.0000
10717 10728 10728 10716
300
1277
Second 2% reaction ( X d ) x 10‘ (X,) x 106 ( a ” ) x 10’ (kZ/ka)obsd (kl/2ka)obsd (kl/%%)obad
10648 f 55 10567 155 10608 f 55 1.0076 f 0.0010 1.0117 f 0.0052 1.0041 10.0052
10671 10591 10631 1.0076 1.0095 1.0020
10737 i 7 10658 13 10697 f 5 1.0074 10.0005 1.0031 i 0.0003 0.9957 1 0 . 0 0 0 7
10717 10639 10678 1.0073 1.0050 0.9977
B. Complete Decomposition Experiments 0.844 f 0.076 0.722 f 0.091 B1 -0.717 i 0.117 -0.612 f 0.141 0.263 f 0.026 0.240 f 0.029 Mz Bz .-0.061f0.062 -0.076 f 0 . 0 7 0 10685 f 4 ( 6 ) 10687 f 5 (34) (Xd Xm)/2(no. of experiments)
MI
+
1.0043 f 0 . 0 0 0 4
was found to be 1.10 f 0.02 in earlier experiments’ over approximately the range of temperatures encompassed by the results in Table I ; there was no sensible temperature dependence of this ratio. The astoichiometry of the pyrolysis evidently is small, and no correction for its possible effect was made because the mechanism for the effect is unknown.
Discussion The kinetics of the zinc’ and manganous3 oxalate pyrolyses exhibit an acceleratory phase, lasting only for the first 5-lOT’ decomposition, followed by a decay period in which the rate is approximately first order. A- and C-type samples4 of manganous oxalate displayed the same gross kinetic characteristics, but very
different isotope fractionation effects; (kZ/k3)obsd was normal in magnitude and temperature dependence in the pyrolysis of C-type samples, but enormous in both respects when A-type samples were decomposed. 30 simple explanation for these observations is available. The results shown in Table I indicate a carbon isotope effect of small magnitude and normal temperature dependence for the thermal decomposition of C-type samples of zinc oxalate. The comparison figures in part B of Table I1 indicate that the manganous and zinc oxalate complete decomposition isotope effects are very similar, those for zinc oxalate being somewhat the smaller. The data shown in part A of Table I1 illustrate the detailed similarity of the partial decomposition isotope effects for the two salt pyrolyses. Note that the intermolecular isotopic rate constant ratios ( k 1 / 2 k 3 ) o b s d and (k1/2k2)obsd not only are both significantly different from ( k z / & ) o b s d but also exhibit dependence upon the degree of reaction. (Significant dependence upon degree of pyrolysis is not expected below 5-6y0 dec~niposition.~J)In this regard it is important to compare ao, a’, and a”; a” and 010 are very similar, while a’ is definitely smaller. This may be an indica-. tion that isotopically lighter microcrystals of oxalate Volume 68, Number 6 June, 2.964
1278
~ ’ E T E RE.
yield a large fraction of the initial gaseous products collected. In such a situation, the intraniolccular isotopic rate constant ratio (kzlk3)obsciis consistently defined by eq. 1, but cy0 in eq. 2 and 3 should perhaps be replaced by some other quantity; it is not obvious that the appropriatr rrplacenient is a’ or a”, depending upon the segment of decomposition observed. Thcsc considerations lrad us to the conclusion that only ( k Z I I ~ 3 ) o b s dfroni the present exprrinimts can be treated even approximately by current isotope rffect theory . i2b initio calculation qf the intramolecular isolope e$’ect. In gcncral, we can write
YANKWICH ANI) PETHOS D. ZAVITSANOS
Table 111: C-O-Zri, Isotope Effect Calculated by Wilson-Johnston Method (ml = 12, m2 = 16, m3 = 65.4, m’l = 13, m‘2 = 16, m‘3 = 65.4
T~~ $12
fl2
=
Kormal hfolecules 1.38 .I.; ~2~ = 1.87 b.; 6 = 180” 6.0 mdynes/.&.; J23 = 3.0 mdynes/.i.; fq/r12r23 = 1.0 rndynelk. =
Activated Complexes r12 = 1.47 b.; r23 = 1.87 b.; 4 = 180” = j 2 3 = fi = 4.0 mdynes/A.; J q / r l ~ r 2 3= 0.25 mdyne/A. Reaction coordinate: Q = ( q 1 2 / d 2 ) - ( q 2 3 / v ‘ 2 ) Results Observed :
TIF is the ratio ( v ~ ~ ’ v sof~ )the imaginary vibration frequcncic)s associated with the reaction coordinate ; TDF, the temperature-dependent factor, arises in the mass depcndence of the genuiric vibrations of the nornial and transition-state species. The sniall size of the intrainolecular isotope effect and its nioderate teniperature dependence indicate that TIF is nearly unity, i.e., that the contribution of the reaction coordinate to the observed isotopr fractionation is sniall. Equations 4 and 5 are of the form I,(kz/k3) = I, (TDF) L(T1F). The dependence of L ( k z k 3 ) , or L(TI)F), on temperature is expected to br as 1 / T at “low” tenipcratures and as 1 IT2 at “high” teniperatures. Thesr being extrenial situations, it seems likely that B1 represents a niini~nunivalue for L(TIF), and Bz a niaxiniuni. Since tenipcratures a hundred degrees on either side of 400’ are rclatively high (at least for stretching vibrations of systenis like Zn-0 C, 0-C-C, etc.) in the case of a metal oxalate, it seenis likely that 1 3 2 should br a good approximation to L(T1F). As inferrcd in the paragraph above, Bz is close to zero. Examination of the intraniolecular isotope effect using the “ y b a r ” riirthod of Bigeleisen and Wolfsbergs suggests that a good approxirnatioti to the reaction coordiriatr is an asymmetric stretching vibration involving a t least t~hrec centers, such as 0-(2-0 or
+
c--0-Zn.
The thrcc-particle systcni C -0-Zn was investigatrd, vibration frequencies wing obtained by niatrix nirthods.10 ‘I%(> asyiiiiiietric stretching vibratioii was takcw as the reaction coordinate, and the frequency associatrd with this niotion was driven to zero i n the activatrd coniplexes by setting the bond-stretching force constants equal to c>ach other and to an interaction force constant, f,, as suggrsted by ,Johnston, Bonner, and Wilson. l I ‘I’hc input parainrters for this calculation and thc results arc shown i n Table 111.
L(T1F) L(TI)F) a t 282’ at 500’
Calculated
eq. 5
0.105 0.800 0.448
-0.076f0.070 0.779 f 0.094 0.401 f 0.049
The agreernerit for T D F is satisfactory, but the calculated T I F is high. For this model, which is niore successful than any other three-particle systcni studied, a better TIF is secured a t the cost of any correspondence between the observed and calculated temperature dependence, a result hardly to be desired. Especially sirice this niodel requires (kl:/2kz)= 1, a more complicated system apparently would have to be devised were better agreement between calculation and experinwrit desired. Even so, it is striking that an approach which assumes essentially an ideal gas systeni yields such good results when applied to the decompositions of crystals. It, appears that, the iiiterniolecular isotope effects in the zinc oxalate pyrolysis may provide a useful probe for details of the mechanism of thc early stages of the decomposition. Even when anomalous observations on the intraniolecular isotope effect are absent, the iriterrnolecular isotope effects appear to depend in a complicated manner on the degree of decomposition. .4ddit,ional experimentation on this and similar systems is in progress in this laboratory.
Acknowledgments. We are indebted to Dr. Geneva Relford for generous assistance in programming certain of t.he theoretical calculations, and to Alrs. Ihila Ihnen for all rnass spectrometric analyses. This research was supported by t.he United States Atomic Energy Comniissiori. (9) J. Rigeleisen and h l . Wolfsherg, Admn. Chem. Phys., 1, 15
(1958). (10) E. A. Wilson, Jr., J. C. Decius, arid 1’. C . Cross, “Molecular Vibrations,” McGraw-Hill Rook Co., Inc.. New York. N. Y., 1955. (11) H. S. Johnston, W. -4.Ronner. and D. J. Wilson, J . Chem. Phys.. 2 6 , 1002 (1957).
