CARBON ISOTOPE EFFECTIN
THE
GASPHASE DECOMPOSITIOS OF OXALIC ACID
3135
Reversing Intramolecular Kinetic Carbon Isotope Effect in the Gas Phase Decomposition of Oxalic Acid
by Gabriel Lapidus,la Donald Barton,lband Peter E. Yankwich 4'oyes Laboratory of Chemistry, University of Illinois, Urbana, Illinois
61801
(Receiced M a r c h 28, 1966)
The intramolecular C13 kinetic isotope effect has been measured between 127 and 180" in the decomposition to carbon dioxide and formic acid of oxalic acid-h2 vapor at an initial pressure of 0.9 mm. This isotope effect, like that observed with oxalic acid-ds, and like the intermolecular hydrogen isotope effect, is small and is so strongly temperature dependent that it inverts within the experimental range. The carbon isotope effect for the ordinary acid decomposition appears to be simple above 156". The similarity of the inversion temperatures of the carbon and hydrogen isotope effects lends support t o the postulate that the inversion phenomenon arises in the accessibility to the reaction of more than one path, not in isotopic differential effects themselves.
Introduction Recently, we have reported on the hydrogen2* and carbonzb kinetic isotope effects in the vapor phase decomposition or^ oxalic acid. Though the hydrogen intermolecular isotope effect was measured comparatively, and the rarbon intramolecular effect competitively on (COOD)2, both exhibited similar characteristics: they were found to be relatively small, to have anomalously large temperature dependence, and, because of the latter, to invert in sense within the experimental temperature range. The deuterated acid was employed in the earlier carbon isotope effect study to eliminate or reduce to insignificance the possible influence of a statistical inverse isotope effect, should the ca. 1-mm initial pressure of the vapor lie well into the low-pressure region for the reaction. In this paper we report the extension of these experiments to ordinary oxalic acid, (C0OH)p.
Experimental Section Reagent. Fisher analytical grade anhydrous oxalic acid was purified further by vacuum sublimation at 110"; samples were stored in vacuo over magnesium perchlorate until used. Apparatus, Procedure, and Isotope Analyses. These were identical with those employed in the study of the oxalic acid-dz decomposition.2b Notation and Calculations. The isotopic rate con-
stant ratio sought was (k2/k3)H in the notation of Lindsay, NcElcheran, and Thode. ~
I
1
3
0
C1200H
+ HPOOH C1202+ HC1300H
ck2'H_ 0 ~~
1 3 0 ~
(1) (2)
Though the reaction was run essentially to completion, it can be shown that for product collection up to any time t
where ( X c ) t is the mole fraction of C1302 in carbon dioxide product collected up to t, and ( X F )is~ the corresponding mole fraction of HC1300H derived from measurements on carbon dioxide obtained by combustion (in a Pregl-like apparatus) of the formic acid product.
Results The results obtained at seven temperatures are collected in Table I. The first figure at each tempera(1) (a) Research associate, 1960-1963; (b) visiting assistant professor, 1960-1962. (2) (a) G. Lapidus, D. Barton, and P. E. Tankwich, J . Phys. Chem., 70, 407 (1966); (b) ibid., 70, 1575 (1966). (3) J. G. Lindsay, D. E. RIcElcheran, and H. G. Thode, J . Chem. Phys., 17, 589 (1949).
Volume 70. Xumber 10
October 1966
G. LAPIDUS,D. BARTON, AND P. E. YANKWICH
3136
L(kz/ks)H = -(0.32
f
0.26)8
+ (0.51
=k
0.59)
(6)
+
= -(o.070 1 0 . 0 5 7 ) ~
(0.150 1 0.296)
(7)
Within the respective temperature ranges, the mean deviations of the experimental points from the leastsquares lines are 10.08 in L for eq 5 and f0.04 in L for eq 6; from eq 4, one can calculate the apparent inversion temperature to be 145 1 8".
Table I: Intramolecular Isotope Effect in (GOOH)?(g) Decomposition Run temp, OC
126.6 I 2.4
I
2.2
2.3
2.5
(I0001T'K) Figure 1. Influence of temperature on (k2/k3)obed: -, oxalic acid& ((openrectangles encompass the average deviations; short horizontal bars indicate the extrema1 result,s a t each temperature); - - -, oxalic acid-d? (shaded rectangles, shifted 0.008 to right to avoid overlap, encompass average deviations).
~(~c~/= k $(3.20 ),~
* 0.14)e - (7.61 1 0.34)
1.00098 1.00198 1.00078 1.00388 I.00226 1,00061 1,00057 1.00268
146.4
0.99993
L(k2/k3)H
=
(4.37
* o.3a)e - (10.46
high temperakures The Journal of Physical Chemaktry
1 0.77)
1.00517f 0.00040 (1.00417f 0.00040)
0,99903
0,99938
155.6
160.0
0.99741 0.99795 0.99758 0.99629 0.99879
0.99760f 0.00062 (0.99825 0.00051)
0.99880 0.99737 0.99824 0.99738 0.99786
0.99793f 0.00047 (0.99782 f 0,00020)
170.0
0.99788 0.99788 0.99825 0.99791 0.99799
180.0
0.99858 0.99775 0.99795 0,99873 0.99738
(4)
(The point at 180" was considered deviant and ignored in the calculation of this equation.) The heavier solid lines represent the results for L ( h / k 3 ) derived ~ from Table I for the four lowest and the four highest temperatures; their equations are low temperatures
1.00606 1.00472 1,00505 1.00495 1.00484 1,00537
134.1
-
ture in t,he last column refers to the present experiments on oxalic acid-hz; the second figure (in parentheses) is for oxalic acid-d2.2b The appended errors are average deviations from the mean. All of these results are plotted in Figure 1 as L(k2/k3)4us. (1000/T); the open points represent the data for the ordinary oxalic acid; the shaded points represent results obtained with the deuterated acid and have been shifted 0.008 to the right to eliminate the overlap arising in the use of identical run temperatures in the two investigations. The mean precision of individual ( k 2 / k 3 ) ~ values is estimated to be *0.0005. Several least-squares fitted lines are drawn through the data plotted in Figure 1. The light dashed line through the oxalic acid-d2results has the equation4
(kn/ka)H
(5) (4) L ( z ) = 100 In (2); e = 1000/T("K).
*
0.9980~f0.0004o (0.99669f 0.00030)
CARBON ISOTOPE EFFECTIN
THE
GASPHASE DECOMPOSITION OF OXALIC ACID
Discussion The intramolecular carbon isotope effects and the intermolecular hydrogen isotope effects' in t'he decomposition of oxalic acid are similar in several respects: they are smail, apparently normal in sense5z6at low t,emperatures, and inverted at higher temperatures; further, the inversion temperatures are all similar within moderate experimental error [ ( k ~ / k ~ )139 , f 9"; ( k Z / h ) H ) 145 :k 8"; and (kZ/kB)D, 144 f 5'1; finally, in the region of reversal, the observed t'emperature dependence is enormous in comparison with the magnitude of bhe isotope effect' itself. It is very difficult' t,o see in the fact of smallness of an intramolecular isotope effect anything ot'her than a reflection of modest asymmetries in t'he force fields or configurations of the isotopically isomeric transit'ion states which :ire paired to generate such an isot'ope effect'. That :L hydrogen intermolecular and a carbon int'ramolecular isotope effect (the lat'ter, unlike the former, being , w t dependent upon the frequency shifts in the ground stat,e) exhibit similar rare and anomalous dependence upon t,eniperature must arise in some phenomenon other than similarity of the effects of D and C13 substit'ut,icin on the vibrations of oxalic acid molecules, which similarity would be a highly unlikely st.ate of affairs. Finally, the temperature dependence of an ordinary isotope effect' (be it simply kinetic or a combination of dynamic and equilibrium processes) bears a close relation to t'he magnitude of t,he the phenomen'ori of steep inversion is clearly excluded at t,he relatively low temperatures of these experiments,1° a.nd the temperature dependence one would expect, for even the largest isotope effect observed in t>his decomposition is minuscule in comparison with those found. Earlier,2bwe argued that carbon intramolecular isotope effect,s such as t,hose reported here were unlikely to arise in equilibria precedent to the rat'e-determining step or in other phenomena described adequately by simple isotope effect theory; nor was it likely that the huge temperature dependence found for eit,her the C13 or D cases be due to the stat,isticalinverse isotope effects described by Rabinovitch and his co-workers.l* Instead, we proposed2 t,hat these unusual isot'ope effects are due to accessibility to the reaction of at least, two deconiposit'ion paths; t,hat is, at least two pairs of isoCopically isomeric activated molecules yield products in this decarboxylation. It, was proposedzb that' the deviant 180" result for ( k z / k s ) D might be due to the final predominance of one pat'h over the other(s) as t'he temperature increased. The behavior of the higher temperature c1at.a for (k2/k3)H plotted in Figure 1 provide strong additional support for t'his notion, since
3137
the graph in that region is, within experimental error, what one would expect for a simple isotope effect. One kind of decomposition path duality would be provided by combination of a homogeneous and a heterogeneous mechanism.12 If these differed only in the association of an adsorptive effect with the latter ( L e . , were the two paths different physically but not chemically), no isotopic phenomenon as extreme as those reported here and in the earlier investigations would be observable. The work of Klein, Simborg, and Szczepanik13 on double isotopic differential effects in adsorption chromatography permits the estimate that a simple adsorption C13 isotope effect for a molecule like oxalic acid would contribute to L(k2/k3) a term of the order of *0.03; for L ( k H / k D ) the corresponding term mould be f5. When it is recognized that these terms, which arise in isotopic exchange equilibria, must have normal temperature dependence appropriate to their sizes, it is apparent that they are too small by two orders of magnitude to account for the experimentally found inversions. Of course, a physical effect of adsorption (above) may be impressed upon a chemical effect of adsorption, but the latter would be large in comparison with the former and classifiable among the chemical phenomena to be described. Another kind of decomposition path duality is provided by accessibility to the decarboxylation of two different reaction coordinates. I n the report of the
A-1 ( 5 ) The normal sense of the hydrogen isotope effects, which are intermolecular, is k~ > kn. Normal sense for the intramolecular carbon isotope effects is more a matter of definition, especially where the bifunctionally symmetric reagent molecule is as simple as oxalic acid; an accurate translation of the word here is: "having the same sense as observed earlier by Lindsay, h'lcElcheran, and Thode.3" Bigeleisen and Wolfsberg6 have described the conditions under which intramolecular isotope effects in similar reactions might be expected to have different senses, but their analysis does not contain the situation reported here. (6) J. Bigeleisen and h l . Wolfsberg, J . Chem. Phys., 21, 1972 (1953); 2 2 , 1264 (1954).
(7) J. Bigeleisen and hl. Wolfsberg, Adcan. Chem. Phvs., 1, 15 (1958). (8) P. E. Yankwich and H. S. Weber, J . Am. Chem. SOC., 78, 564 (1956).
(9) E'. E. Tiankwich and R. 11.Ikeda, ibid., 81, 1532 (1959). (10) H.'C. Urey, J . Chem. SOC.,562 (1947). (11) F. W. Schneider and B. S. Rabinovitch, J . Am. Chem. SOC.,8 5 , 2365 (1963). (12) G. Lapidus, D. Barton, and P. E. Tankwich, J . Phys. Chem., 68, 1863 (1964). (13) P.D. Klein, S. W. Simborg, and P. A. Sacaepanik, Pure A p p l . Chem., 8 , 357 (1964).
Volume 70, 'Vumber 20
October 1966
3138
G. LAPIDUS,D. BARTON, AND P. E. YANKWICH
kinetics of the oxalic acid-hz decomposition, the proposed transition state (A-1) was achieved by intercarboxyl hydrogen transfer from oxygen to oxygen. The break-up of this entity would require rapid transfer of hydrogen to carbon to form the reaction products. Another monocyclic transition state (B-1) which must be considered2bis formed via direct motion of hydrogen to carbon
+4
t
1
"t I t
------
I
---
?
B-1 2.4 (IOOO/T"K)
2.3
2.2
The dihedral angle between carboxyl groups in B-1 would be expected to be near go", while that in A-1 should be close to 0". The gaseous oxalic acid molecule appears to have a dihedral angle no more than 30" different from 0°.14 Since a planar skeletal configuration would favor intercarboxyl hydrogen bonding, one can derive from the transition states just described extremal relatives which differ from them in that energetically and geometrically symmetric 0-H .O hydrogen bonding has been achieved
A-2
B-2
Though these extreme bicyclic forms are highly unlikely to occur, less symmetrical hydrogen bonding could give rise to states intermediate to A-1 and A-2, and B-1 and B-2, respectively. Thus, one can envision a continuum of forms lying between the monocyclic and bicyclic extremal configurations of each basic transition state type, A or B. Bigelejsen and Wolfsberg' have given simple formulas16 which can be employed to estimate values of intramolecular carbon isotope effects using a minimum of detailed structural and force-field information. Estimated values of L ( h / k 3 ) ~are plotted vs. 0 in Figure 2 ; the input structural parameters were based on the results of Shibata and Kimura,14 while force constants were taken from a variety of sources.16-18 The vertical width of the shaded bands, which is about 0.4 in L, reflects the span of reasonable choices for various force constants; the vertical width of the open bars representing the experimental results in Table I is proportional to the average scatter of the data. The Journal of Physical Chembtry
Figure 2.
2.5
Intramolecular carbon isotope effects predicted for 4
various transition states: (A) reaction coordinate, 0 . . H . 4
eo;
(B) reaction coordinate, 0 . . H . *C;(1) extreme monocyclic configuration, no 0 * H * O bridging outside of reaction 4
coordinate; (2) extreme bicyclic configuration, 4
symmetrical 0 * H .O bond system in addition to reaction coordinate. Arrows indicate depression of L ( k z / k 3 )with increasingly symmetric hydrogen bonding in the nonreaction coordinate cycle. The open bars are the apparent low-temperature and high-temperature isotope effects represented by eq 5 and 6 . 9
The shift from a monocyclic toward a bicyclic transition state depresses L(k2/k3). No such shift in an activated complex of the A type produces correspondand the resulbs observed a t ence between ( h / k & ~ the higher t,emperatures, because total symmetry of such a complex reduces (k2/k3)A to its absolute minimum value 1.oooO. In an activated complex of the B type, however, a bicyclic configuration involving an O - H . . O bond system just a little stronger than characteristic of carboxylic acid dimers is capable of bringing (kz/ky) into correspondence with the experimental findings at the higher temperatures. 19,20 ~~
(14) S. Shibata and M. Kimura, Bull. Chem. SOC.Japan, 27, 485 (1954). (15) For a recent detailed application, see A. J. Kresge, N. N. Lichtin K. N. Rao, and R. E. Weston, Jr., J. Am. Chem. Soc., 87,437 (1965): (16) E. B. Wilson, Jr., J. C. Decius, and P. C. Cross. "Molecular Vibrations," McGraw-Hill Book Co., Inc., New York, N. Y., 1955, pp 175, 176. (17) L. Jenorsky, 2. Chem., 3 , 453 (1963). (18) M. J. Stern and M. Wolfsberg, J. Chem. Phys., 39, 2776 (1963). (19) Though there is considerable uncertainty in the selection of all the force constant shifts, a force field equivalent to a structure about 0.2 of the way between B-1 and B-2 ( L e . , B-1.2) reproduces the hightemperature results.
CARBON ISOTOPE EFFECTIN
THE
GASPHASE DECOMPOSITION OF OXALICACID
To reproduce the isotope effects observed in the inversion region, there must compete with the hightemperature path one or more others with which are associated isotope effects of the sense and magnitude of those characteristic of models near A-1; in no other way can one obtain the drastic temperature dependence observed in the region of reversaLZb We have not carried out calculations more sophisticated than the above, and these simple results do nothing to establish that a possible heterogeneous mechanism involve transition states like those of types A or B. However, the importance of planarity to the suggested models increases in the order B-1 B-2 --t A-1 A-2; further, a heterogeneous mechanism dependent upon adsorption would decrease in importance with increasing temperature. These two considerations interact to lead one to the conclusion that a path through an activated complex like A-1 might well be favored on a surface, while a path through a transition state configuration approximately B-1.2 is more likely to be typical of reaction in the body of the gas. The original kinetics investigationszatlZ covered t,he short temperature range 127-157 O while the carbon isotope effect experiments extend to 180"; there is in the former thus no reflection of the kinetic complexity postulated to account for the results reported here. The present i--esults support the conclusion that the
-
-
3139
large temperature dependences which lead to reversal
of the carbon and hydrogen isotope effects arise not in isotopic differential phenomena but in mechanistic complexity. 21
Acknowledgments. Mrs. Nancy Neilson performed the mass spectrometric analyses. The assistance of 1Llr. James E. Harmon and Mr. Lawrence E. Kraut in bringing this and the two preceding publications2 to the submission stage is deeply appreciated. This research was supported by the U. S. Atomic Energy Commission, COO-1142-66. (20) The structures A-1 and B-1 are conventional in that bonds affected by the reaction are shown with orders halfway between those characteristic of the reagent and the product states. Transition states more reagent-like yield isotope effects closer to zero for both types of structures. Transition states more product-like and having the A-type reaction coordinate yield isotope effects larger than those shown for A-1. For the B-type reaction coordinate, increasing the product likeness of the transition state moves the predicted value of L(kz/ka) downward from the band shown for B-1 toward a limit lying somewhat above the band for B-2; the vicinity of this limit is indicated by the light dashed line in Figure 2. (21) The fact that both the carbon and the hydrogen isotope effects exhibit inversion with increasing temperature is likely an accident; there is no a priori expectation that the sense of a hydrogen intermolecular isotope effect and that of its carbon intramolecular re1at)ive will correspond. The fact that the inversion temperature for ( k ~ / k Dand ) those for the (kzlks) are similar is likely another accident; such similarity requires symmetry in the senses and relative magnitudes of the two kinds of isotope effects, a situation likely to be unusual of occurrence.
Volume 70. Number 10
October 1066
