REVERSING HYDROGEN ISOTOPE EFFECTON DECOMPOSITION OF OXALICACID
407
Reversing Hydrogen Isotope Effect on the Rate of the Gas Phase Decomposition of Oxalic Acid
by Gabriel Lapidus,' Donald Barton,a and Peter E. Yankwich Noyes Laboratory of Chemistry, University of Illinois, Urbana, Illinois
61803 (Received July 16, 1065)
The decomposition of oxalic acid-d2vapor at an initial pressure of 0.8 mm has been studied between 127 and 156'. The decomposition appears to be first order with respect to oxalic acid; observed Arrhenius parameters are: E = 34.5 i 0.9 kcal mole-' and log A (sec-l) = 14.3 f 0.5. Comparison of these results with those for oxalic acid reveals a small hydrogen isotope effect which inverts within the experimental temperature range and which has very great temperature dependence for its magnitude. The size of the temperature dependence seems explainable by combination of kinetic, equilibrium (between cyclic and noncyclic structures), and tunneling isotope fractionation effects. The magnitude of the observed isotope effect can be explained if there is impressed on this combination a virtually temperature-independent inverse isotope effect such as that described and observed by Rabinovitch and his co-workers.
Introduction Recently13we reported the results of experiments on the kinetics and stoichiometry of the decomposition of oxalic acid in the gas phase. The Arrhenius activation energy was found to be about 30 kcal mole-', and the preexponential factor was found near 10l2. After comparison of these results with those obtained from the related decompositions in a variety of solvents, 'we argued that they were consistent with a unimolecular mechanism proceeding via a cyclic activated complex and suggested that the rate-determining step was intramolecular hydrogen atom transfer from one carboxyl group to the carbonyl oxygen of the other. To permit more detailed exposure of the reaction mechanism, we have carried out experiments on oxalic acid-dzand report the results in this paper. Experimental Section Reagent. Fisher Analytical grade anhydrous oxalic acid was purified by vacuum sublimation at l l O o , labeled by three or four evaporations to dryness from deuterium oxide (99.5 atom % D; Stuart Oxygen Co.), dried in vacuo at 40°, and stored in a vacuum desiccator over magnesium perchlorate; the final product was at least 99.3 atom yo D in both carboxyl groups. Permanganate titrations showed the material to be pure within an analytical error of approximately 0.020/,.
Apparatus and Procedure. The apparatus and procedures were identical with those employed to obtain data on the decomposition of oxalic acid.3 Special care was used to establish identity of the reaction temperatures. Although no parallel study was carried out to determine the vapor pressure of oxalic acid-d2, we did observe from the material balance results that the vapor pressure of this substance at about 130' (the "injection" temperature) is slightly less than that of the ordinary acid. Blank experiments showed that the correction for decomposition upon injection was -1.3 f 0.4% here; a slightly lower correction, -1.2 f 0.3%, was applied to the data for the decomposition of oxalic acid.
Results As with the ordinary acid, the stoichiometry of the decomposition of oxalic acid-dz under these lowpressure, moderate-temperature conditions is simple. The formic acid-d2product found averages 99.5 f 0.5% of the carbon dioxide produced. Equivalence in amount of the carbon dioxide product and the oxalic (1) Research Associate, 1960-1963. (2) Visiting assistant professor, 1960-1962. (3) G.Lapidus, D.Barton, and P. E. Yankwich, J. Phys. Chem., 68,
1863 (1964).
Volume 70, Number 8 February 1066
G. LAPIDUS, D. BARTON, AND P. YANKWICH
408
Table I : Rate of Decomposition of Oxalic Acid-dl Vapor Run temp,
OC
126.6
Time, ma
Degree of decompn, cor
28 ,920 32 ,400 33 ,900
0.546 0.574 0.578
lo%, 880 -1
2.73 2.63 2.55 Av
134.1'
4,800 10 ,800 18 ,000 23 ,400 25 200
0.276 0,493 0.493 0.673 0.676 0.777 0.803 0.803
6.72 6.29 6.28 6.20 6.26 6.42 6.45 6.45 Av
146.4 (1000/T4K)
Figure 1. Temperature dependence of rate constants and rate constant ratios in the gas phase decomposition of oxalic acid and oxalic acid-&. Left ordinate: 10% (sec-1); right . points are for (COOH)2, solid ordinate: ( L H ) . ~ / ( ~ D ) ~ ~Open points for (C0OD)g. Vertical rectangles encompass average deviations from the mean; horizontal bars indicate maximum and minimum results observed. At 146.4', the points for k~ and k D are partly superimposed; for clarity, they are separated in the ovals a t either side of this point. Line A, -, k D from Table I; line B, -,LH from ref 3; line C, , k H with "first runs" correction applied to ( k ~at) ~ ~ 134.1' (point H); line D, ---, ( k ~ ) ~ ~ / with ( k ~original ) ~ ~ data ratio a t 134.1' (point F); line E, t (~H)Bv/(~)Bv with corrected (kH)Bv used to form ratio at 134.1' (point G).
_._
---
.---
acid decomposed is demonstrable within a meancomposite analytical error (of titrations and manometry) of 1%; material balance can be proved to i1.4%. The Discussion of the kinetics results is based on data from 19 runs at temperatures between 126.6 and 155.6'; in each case the initial pressure of oxalic acid-dz vapor in the reactor was 0.82 f 0.02 mm (0.88 f 0.02 for oxalic acid). Examination of the data indicates that the rate is first order with respect to oxalic acid; the quality of the results is such that the accuracy of this order is approximately kO.1. Individual and average values of the apparent firstorder specific rate constants, k~ (sec-'), are shown in Table I and plotted as the solid points in Figure 1 ; the only correction applied to the input data is for the small decomposition during injection. Line A is the least-squares fit of these data; the related activation The J O U Tof~Physical Chemistry
1,500 2 ,700 4 200 7,200 13 ,440
0.255 0.375 0.544 0.738 0.898
900 1,800 2,400
6.38 f 0 . 1 3 19.64 17.42 18.71 18.61 16.97
Av
155.6
2.64i0.07
0.422 0.637 0.756
18.3 h 0 . 8 60.9 54.3 58.8
Av
58.7 =k 1 . 6
'Four additional runs a t 134.1' yielded k D values of 6.86, 7.17, 7.26, and 8.11 X loV6see-' for 0.10-0.17 decomposition. All four of these results are excluded from later consideration to maintain consistency with the oxalic acid results, in which similar data for low decomposition at this temperature were rejected.
parameters are listed in column A of Table 11; in column B of Table I1 are shown the corresponding quantities for k~ as reported in a previous paper13 and line B in Figure 1 is the least-squares fit of those results (open points). Comparison of the plotted average values of l c ~ with those for kR shows that the deviations from the fitted lines are greater in the case of the latter. The hachured points in Figure 1 are ( k ~ ) & ~ / ( kat~ ) ~ ~ each temperature, and line D is least-squares-fitted to those ratios; the large separation of point F from line E suggests that there may be an anomaly in the results reported earlier3for k~ at 134.1'. While a careful review of the data upon which the earlier publication was based does not preclude a different origin, we believe this possible anomaly could have arisen in an effect noticed not infrequently in
REVERSINGHYDROGEN ISOTOPE EFFECT ON DECOMPOSITION OF OXALICACID
Table II : Calculated Activation Parameters B
Log A(sec-1) E" AH*" AS*b
AF*' Mean dev of least-squares log k Estd inversion temp, H/D isotope effect
" Kcal
mole-'.
C (CO0H)r oor
A (COODh
(COOHI¶
1 4 . 3 i0 . 5 34.5 i0.9 33.7f0.9 + 4 . 3 f2 . 1 31.9 f 1 . 2
11.9 f 0.7 30.0 f 1 . 3 29.2&1.3 -6.6 f 3 . 0 31.9 f 1.8
12.7 i0 . 5 31.5 f 0.8 30.7 iz 0.8 -2.9 2.1 32.0 f 1.1
i0.038
io.065
f O .035
Ol'i
lated hydrogen kinetic isotope effect, its magnitude would depend upon the changes in bonding about the hydrogen atom incident upon activation. Maintenance of nearly constant total bond order about hydrogen would generate a small hydrogen kinetic isotope effect, perhaps as small as that observed here. However, no anomalous temperature dependence is expected on such a model, and certainly no inversion. If the hydrogen isotope effect is secondary instead of primary, a magnitude of 10-20% is entirely reasonable'; but, once again, one would not expect the temperature effects observed.
Earlier Experiments on Isotopic Oxalic Acids. 145 f 13"
' Kcal mole-'
139 i9"
OK-1.
gas kinetics studies4: the nine runs at 134.1' using oxalic acid as reagent were the first carried out in the apparatus; any failure to season or age the reactor or condition its surfaces could have resulted temporarily in a rate being observed which was different from that which would have been observed after an appropriate number of experiments had been completed in the apparatus. Problems of this kind must contribute to the much lower accuracy of isotope effect results based on isotope comparative experiments (as here) as opposed to isotope competitive experiments. For purposes of discussion, we assume that the smallest temperature dependence of ~ C H / ~ D implied by our combined data is that based upon the results at temperatures other than 134.1°, line E.6 The best use of the other seven nonsuspect sets of data can be made by adoption of the corollary that the true value of (kH)BV/(kD)BV a t 134.1' is shown by the dashed point G, which is equivalent to the notion that the correct value of k H at this temperature is approximately as shown by the circular point H.6 I n column C of Table I1 we give the Arrhenius parameters and the transition state theory activation quantities calculated using this interpolated (kH)BV; these are closer to those in column A than are those in column B, and the lessened differences seem appropriate for the level of the apparent hydrogen isotope effect, which is rather small.
Discussion In Our
409
paper3 we suggested that the acid decomposition proceeded via a cyclic activated complex, there being intramolecular hydrogen atom transfer from one carboxyl group to the carbonyl oxygen of the other. Whatever the Sense of the re-
The only previous comparison of the rates of decomposition of hydrogen isotopic oxalic acids is in the work of Lutgert and Schroer,8 who determined ka: for solutions in ordinary water, k~ in DzO, and both in ordinary dioxane. The water solution experiments were carried out a t five temperatures between 132.2 and 173.6'; the results correspond to a reverse isotope effect at low temperatures which decreases with increasing temperature (and would be expected to invert in the neighborhood of 300'). Experiments in dioxane were a t only two temperatures: kH/kD = 0.974 a t 120.0', and 0.997 at 152.5'. Though the results are few, a reverse isotope effect is indicated which appears to approach inversion to normal a t about 155'. Temperature Dependence of Kinetic Isotope Effects. I n the remainder of this Discussion, we examine the possible sources of a hydrogen isotope effect as strongly temperature dependent as that represented by line E. One would expect inversion of the isotope effect were large temperature dependence coupled with small magnitude; but, as will be shown, the limitations imposed by a conventional theoretical description are severe in this regard. Any explanation or model (4) E.g.: D. Brearley, G. B. Kistiakowsky, and C. H . Stauffer,
J. Am. Chem. SOC.,58,44 (1936); D.H.R. Barton and P. F. Onyan, Trans. Faraday Soc., 45, 725 (1949); J. B. Peri and F. Daniels, J. Am. Chem. SOC.,72, 424 (1950); F. 0.Rice and K. F. Herzfeld, J. Phys. Chem., 55, 975 (1951). ( 5 ) It seems only fair to examine the situations which would obtain were this assumption made, in turn, a t each one of the other reaction temperatures (as if the first runs had been made a t some temperature different from 134.1'). It is apparent from Figure 1 that elimination of any other point would suggest a best-fit line of slope equal to or greater than that of line D. I n any case, the temperature dependence over the short experimental range of 29O is so large as to imply the inversion of the isotope effect even had it not been observed directly. (6) That is, instead of using a pair of rate data for computation of the isotope effect, we employ an interpolated value of the isotope effect to calculate the numerator of the isotopic rate constant ratio. (7) A secondary hydrogen isotope effect of this size in this reaction would seem to imply important changes upon activation in the adjacent C-0 bond. (8) I. Lutgert and E. Schroer, z. Physik. Chem., ~ 1 8 7 133 , (1940).
Volume 70,Number 2 February 1966
410
which fails for line E must fail for a plot of higher slope, such as D. The ratio ~ H / I C D is the product of a temperatureindependent factor (TIF) arising in the reaction coordinate motion and a temperature-dependent factor (TDF) due to the mass dependence of the genuine vibrations in the normal molecules and activated complexes; it is to the latter that one must look first for an explanation of a kinetic isotope effect which reverses with increasing temperature. Except for the missing terms due to the reaction coordinate, T D F has the form of an isotopic exchange reaction equilibrium constant. U r e ~ in , ~ his Liversidge lecture, mentions that reversal (with respect to unity) of such equilibrium constants, though not general, is not uncommon. The reversal "will occur if the difference in the sum of differences of (isotopic) frequencies has the same sign as the differences in the sums of the fractional differences of frequencies"-a condition rather difficult to predict. I n attempting to account for earlier observations on the kinetics of the decomposition of ordinary oxalic acid in the gas phase,3 it was proposed that the reaction was unimolecular and that the mechanism involved intramolecular hydrogen transfer through for~ mation of a cyclic activated c ~ m p l e x . ~ I~n- ~this regard, it is important to note that there are apparently reversing isotope effects in several equilibria which involve hydrogen bonding not dissimilar to that proposed for the transition state of the oxalic acid decomposition. The ratios of the isotopic association constants for the monomer-dimer equilibria in the gas phase for the following pairs of carboxylic acids all show temperature dependence which should lead to reversal of the isotope effect: CH&H&OOH-CHaCHzCOOD,15v16CH3COOH-CD3COOD,17 and CFsCOOH-CF3COOD1*; the senses with respect to unity of KH/KD a t low temperature and estimated inversion temperatures (t°C) are, respectively: >1 (70°), 1 (265'). The largest temperature dependence is exhibited by the propionic acid equilibria; across a 303 span centered on the inversion temperature (similar to the conditions of our experiments), K H / K Dfalls from 1.08 to 0.94. Even this large change with temperature is much smaller than that observed in the decomposition of the isotopic oxalic acids. Some appreciation for the magnitude of the variation with temperature of k H / k D can be gained by comparing it with that of the most strongly temperature-dependent equilibrium constant tabulated by Ureyg for hydrogen-deuterium exchange. For the exchange of these isotopes between potassium hydride and water vapor, the ratio of equilibrium constants at 127 and The Journal of Physical Chemistry
G. LAPIDUS, D. BARTON, AND P. YANKWICH
156' is 1.13; for k ~ / reported k ~ here, the corresponding ratio is 1.28 for line E and 1.48for line D. Similar equilibrium constant calculations for hydrogen-deuterium exchange between noncyclic, monocyclic, and bicyclic oxalic acid molecules (cyclization being through hydrogen bonding of oxygens in different carboxyl groups) have been carried out in our laboratory.l9 Single cyclization can contribute to the observed IG&D a factor of 1.100 at 127' and 1.095 at 156O, while double cyclization can contribute factors of 1.210 and 1.199, respectively; the ratios of these factors at the temperature extremes of our experiments are 1.0046 for single cyclization and 1.0092 for double cyclization-both far too small to explain the temperature dependence of k ~ / k ~ . Another source of large temperature dependence in a hydrogen-deuterium kinetic isotope effect is hydrogen tunneling; a classic example of the application of this approach is contained in the paper of Sharp and Johnston20 on the reaction of methane with trifluoromethyl radical. Though unimolecular instead of bimolecular, the model proposed for the oxalic acid transition state is similar in many respects to that studied by Sharp and Johnston. Tunnel effect factor calculations depend not only upon the molecular model but also upon the choice of computation method. Typically, for a hydrogen transfer of the type considered here, hydrogen tunneling might contribute the factors 2.04 and 1.89 to JCH/ICD at 127 and 156O, respectively; their ratio is 1.08. If the ordinary kinetic isotope effect contribution to k ~ / isk a~factor of 2.00 at 127' (a reasonable value for an intramolecular hydrogen transfer),'g the ratio of such contributions a t 127 and 156' would be about 1.05, typically. If we combine the effects of single cyclization (Le., assume that a (9) H. C. Urey, J. Chem. Soc., 562 (1947). (10) K. J. Pedersen, J. Am. Chem. Soc., 51, 2098 (1929); 60, 595 (1938). (11) A. Dinglinger and E. Schroer, Z . Physik. Chem., A179, 401 (1 937). (12) M. R. F. Ashworth, R. P. Daffern, and D. L. Hammick, J . Chem. SOC.,809 (1939). (13) F. H. Westheimer and W. A. Jones, J . Am. Chem. SOC.,63, 3283 (1941). (14) J. A. King, ibid., 69, 2738 (1947). (15) M.D.Taylor and J. Bruton, ibid., 74, 4151 (1952). (16) R. C. Herman and R. Hofstadter, J . Chem. Phys., 7, 460 (1939). (17) A. E.Potter, Jr., F. Bender, and H. L. Ritter, J. Phys. Chem., 59, 250 (1955). (18) M. D.Taylor and M. B. Templeton, J. Am. Chem. Soc., 78, 2950 (1956). (19) W. E.Buddenbaum and P. E. Yankwich, unpublished calculations. (20) T. E. Sharp and H. S. Johnston, J. Chem. Phys., 37, 1541 (1962).
REVERSING HYDROGEN ISOTOPE EFFECT ON DECOMPOSITION OF OXALIC ACID
monocyclic form af oxalic acid is the actual reactant), hydrogen tunneling, and kinetic isotope fractionation, we would estimate kH/kD = 4.49 a t 127' and 3.94 at 156', the ratio of these figures being 1.14. It is possible to increase somewhat the temperature dependence of this estimated isotope effect, without altering similarly its average value near 140', by adjusting the parameters of the molecular model and the method of calculating the tunnel effect. However, even extreme variations of these kinds are capable only marginally of lifting the temperature dependence so high that the ratio of ~ H / I C D a t 127 and 156' is in the neighborhood of 1.2. A complex model such as this, however, yields an estimated isotope effect of large magnitude and provides no explanation for the observed isotope effect being small. To rationalize the experimental results we require that the temperature dependence of the complex model described above be preserved, while some temperature-independent phenomenon depress its magnitude so that a small isotope effect, inverting over a limited temperature range, would be observed. Our experiments on the oxalic acid decompositions were carried out a t a single pressure for each of the isotopic compounds, these pressures being in the neighborhood of 1 mm. We know nothing of the relative collision efficiencies of oxalic acid vs. carbon diformic acid, but it may be that they are so oxide similar as to mask effectively apparent second-order behavior of the kinetics as determined from decomposition measurements a t different time intervals where the pressure is this low. Recently, Rabinovitch and his associates21-26have detailed some effects of frequency lowerings and of differential quantal effects on nonequilibrium falloff behavior (and on other characteristics) of thermal systems. The effect of possible interest in the present
+
41 1
discussion is statistical-weight inversion of an intermolecular kinetic isotope effect. The system studied by Schneider and RabinovitchZ6was the isomerization of methyl-& isocyanide. It was observed that the inverse isotope effect could be large, a factor of 0.28 in k H / k D and, important to our discussion, that the temperature dependence of this effect was very small. We have not yet carried out detailed calculations for the oxalic acid intermolecular isotope effect using the techniques of Rabinovitch and his co-workers, but a phenomenon with the characteristics they describe seems required to explain the gross features of our observations and is consistent with them. As indicated above, such an explanation is plausible only if at about 1 mm the oxalic acid decomposition is well over into the falloff region. As yet, there is no evidence on this point. Carbon-13 isotope effect results which we have obtained2'jmay permit a stringent test of the notions discussed above even in the absence of information about the low-pressure kinetics of this reaction; such a test is presently under way.
Acknowledgments. We are indebted for much helpful discussion to our colleagues Prof. R. A. Marcus and Drs. L. B. Sims and W. E. Buddenbaum. This research was supported by the U. S. Atomic Energy Commission. (21) B. S. Rabinovitch, D. W. Setser, and F. W. Schneider, Can. J . Chem., 39, 2609 (1961). (22) B.8. Rabinovitch and J. H. Current, ibid., 40, 557 (1962). (23) F. W. Schneider and B. 9. Rabinovitch, J . Am. Chem. SOC., 84, 4215 (1962). (24) J. H.Current and B. S. Rabinovitch, J . Chem. Phys., 38, 1967 (1963). (25) F.W.Schneider and B. S. Rabinovitch, J . Am. Chem. Soc., 85, 2365 (1963). (26) G. Lapidus, D. Barton, and P. E. Yankwich, unpubliihed experiments.
Volume 70,Number 2 February 1966
