PETERE. YASKWICH
694
AKD
RUDYH. H A S C H E M E Y E R
Vol. 67
TEMPERATURE DEPENDENCE OF THE CARBON ISOTOPE EFFECT IK THE DECARBONYLATION OF LIQUID FORMIC ACID BY PETER E. YANKWICH AND RUDY H. HASCHEMEYER h’oyes Laboratory of Chemistry, University of Illinois, Urbana, Ill. Received September 12, 1961
kinetic isotope fractionation in the decarbonylation of liquid formic acid was studied over the range (k12/k13) lay in the range 1.05-1.04. The observed temperature dependence was examined by the “gamma-bar” method of Bigeleisen and Wolfsberg, the “semi-empirical” method of Yankwich, Weber, and Ikeda, and several “two-center” approaches. Of the approximately 4.5% isotope effect, only a few tenths of a per cent is temperature independent; the calculated sums of the differences upon activation of the diagonal Cartesian force constants correspond especially well with the value expected for C-0 bond rupture, and indicate strongly that this rupture is a major component of the reaction coordinate motion. The
C13
59.8-100.0°;
Introduction A reinvestigation1 of the influence of temperature on the kinetic carbon isotope effect in the dehydration of formic acid by concentrated sulfuric acid2has shown that the temperature independent factor in the ratio of the isotope specific rate constants is very close to unity, and that the temperature dependence of the isotope effect, though large, is compatible with C-0 bond rupture being the major component of the reaction coordinate motion. The latter finding is consistent with the evidence recorded by Gel’bshtein, Shcheglova, and Temkin3 in support of the acidcatalyzed carbonium ion mechanism for the decarbonylation of formic acid in concentrated sulfuric and phosphoric acids. The research reported in this paper was undertaken in an effort t o expose possible similarities in the mechanisms of decarbonylation of formic acid in concentrated sulfuric acid and in the pure liquid state. The formic acid employed in the study contained C13a t the natural abundance level. Experimental Formic Acid.-Reagent grade formic acid (Mallinckrodt, “98-100~o’J) was dried for storage by distillation in vacuo at 25’, first from anhydrous copper sulfate, then from anhydrous magnesium perchlorate; before each distillation the acid stood in contact with the drying agent for two or three days. The dried formic acid was stored in vacuo over anhydrous magnesium perchlorate. Samples of the formic acid used 111 the experiments were 99.9% pure, or better, as indicated by titration with standard base, and by close agreement between specific rate constants for the decomposition a t several temperatures and those found with formic acid of this purity by Barham and Clark,4who investigakd the negative catalytic effect of water on the rate of decarbonylation. Apparatus and Procedure.-The reaction vessel conRisted of a 30-ml. Pyrex bulb fitted with a breakoff tube and side arm, both terminating in standard taper joints to permit connection t o the vacuum system. After the bulb was weighed and evacuated, 2-6 ml. of formic acid was distilled into it through the side arm, which was then sealed6; the bulb and contents were weighed. Reaction was initiated by placing the vessel in a constant (&0.05”) temperature oil bath. After 1-3y0 decarbonylation had occurred,B the bulb was removed from the oil bath and cooled in ice-water. (1) J. Bigeleisen, R. H. Haschemeyer, M. Tvolfsberg, and P. E. Yankwich, J . Am. Chem. Soc., 84, 1813 (1962). (2) G . A. Ropp, A. J. Weinbergber, and 0. K. Neville, ibid., 73, 5573 (1951). (3) A. I. Gel’bshtein,G. G. Shcheglova, and M. I. Temkin, Zh. Fiz. K h i m . , SO, 2267 (1956). (4) H . N. Barham and L. W. Clark, J . Am. Chem. Soc., 75, 4638 (1951). (5) It was established t h a t inappreciable isotope fractionation occurred under the conditions of this distillation transfer of part of the stock formic acid. (6) Times for 1% decarbonylation ranged from about 6 hr. a t 100’ t o 13 days at 60”.
After being cooled, the reactiun vessel was connected t o a vacuum combustion systcm consisting of the following, in sequence: stopcock A; a trap, filled with glass wool and glass beads and cooled in liquid nitrogen’; stopcock B; a tubular combustion furnace packed with copper oxide wire; a collection trap cooled in liquid nitrogen; stopcock C; the vacuum manifold. First, the reaction vessel was cooled in liquid nitrogen and the combustion system evacuated; with all stopcocks closed, the breakoff seal was shattered. By manipulation of stopcocks A and B, carbon monoxide was “dosed” into the first trap, then through the furnace, and the product carbon dioxide collected in the second trap. The progress of the combustion of each “dose” was followed by means of a thermocouple gage; the next manipulative cycle was started when the pressure in the system had fallen to a low value, and the cycling of operations repeated until no significant pressure increase was noted upon opening stopcock A. With stopcock A closed, the contents of the reaction vessel were warmed to room temperature for a few moments, then re-frozen. Two or three freeze-thaw cycles were sufficient to liberate all the carbon monoxide product from the reaction solution. The carbon dioxide was distilled to the vacuum manifold through stopcock C (stopcock B closed) for manometric quantity determinations and final transfer to a mass spectrometer sample tube. Isotope Analyses.-The procedures employed have been described in detail in earlier publications from this Laboratory.*-ll Notation and Calculations.-The isotopic rate constant ratio eoiight was in the notation
k,z HC1*OOH-+- C1’0 IC13
HCI300H +C 1 3 0
+ HzO
(1)
+ HzO
(2)
Since the reaction was stopped at 3% decomposition or less, the following expression was employed in the calculation of result^^^-'^ (k12/k13)obsd
= (RF/&)
(3)
where Rp is the ratio (HC1300H/HC1200H) derived from measurements on carbon dioxide obtained by combustion (in a standard Pregl apparatus) of samples of the original dried formic acid,’j and Rc is the ratio (C1aO/C120) from measurements on carbon dioxide obtained from combustion of the samples of prod(7) This trap pre\,ented combustion of a small amount of formic acid “fog“ which apparently formed during the freeze-thaw cycles (vide i n f r a ) . (8) Carbon dioxide determinations by manometric measurement and estimates calculated from rate constants obtained from experiments with freshly dried formic acid were compared a t intervals during the use of a given sample of formic acid. The agreement was always within the estimated manometric errors, which is indicative of the constancy of composition of the stock formic acid over a period of several weeks. (9) P. E. Yankwich and R. L. Belford, J . Am. Chem. Soc., 76, 4178 (1953). (10) P. E. Yankwich and R. L. Belford, i b i d . , 76, 3067 (1954). (11) P. E. Yankwich and J. L. Copeland, %bid.,79, 2081 (1967). 112) J. Bigeleisen, Science, 110, 14 (1949). (13) J. Bigeleisen, J . Chem. Phus., 17, 425 (1949). (14) J. Y.-P. Tong and P. E. Yankwich, J . Phys. Chem., 61, 540 (1957). (15) These samples of carbon dioxide were purified by several distillations between traps a t 150 and 196O.
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-
March, 1963
CARBON ISOTOFTC EFFECT IN DECARBOXYLATION O F LIQUIDFORMIC ACID
uct carbon monoxide; for the formic acid used in these experiments, RF X 106 = 10923 f 2.
I
I
The correctedg-ll carbon isotope ratio for each sample is given in Table I, along with the value of (k12/ kl3)obsd to which it corresponds. The appended errors in the last column are average deviations from the mean; the mean precision of individual (klz/k13) obsd values is estimated to be 10.0003. Values of L(k12/k13) = 100 In (k12/k13) calculated from the last column of Table I are plotted vs. (1000/T) in Fig. 1; the solid vertical rectangles encompass the average deviations, while the open rectangle for the single experiment at 80.5” has a length equal to twice the estimated mean precision of a single datum. Least-squares fitting of the results recorded in Table I yields the equations
‘1
k’1
44-
Results
L(klz/kp.) = 2.531(103/T) - 2.834
-I
695
2.7
2.8
29
3.0
IOOO/T OK.
Fig. 1.-Influence of temperature on the intermolecular carbon isotope effect: -- , linear least-squares fit; - - - -, best 2center model.
(4)
spondence between experimental results and those obtained from calculations often can be achieved if molecular fragment masses are used with the Slater2I TABLE I CORRECTEDISOTOPE RATIOS OF EXPERIMENTAL SAMPLES; two-center coordinate; on this basis, T I F = 1.0062 for the isotope effect under consideration.22 To apply INTERMOLECULAR ISOTOPE EFFECTS CALCULATED the Slater coordinate notion t o TDF, one assumes that Expt. Decarb., A V. Temp., OC. Bo x 106 (k1dklS)obsd (kl?/klS)obsd no. % the transition state differs from the normal state only 16 1.0 10426 1.0492 59.8 by loss of a single vibration, the C-0 stretch in the 10432 1.0486 17 1.0 case at hand; further, the isotopic frequency shift in 1.0491 10427 23 3.0 that vibration is assumed given by the diatomic re24 2.1 1.0493 10425 duced mass relationship. The normal mode frequency 1.0489 1.0490?c0.0002 25 1.7 10429 most nearly characteristic of the C-0 bond in formic 1.0469 10449 69.5 13 1.0 acid has a value in the range 1393-1200 cm-I 23-z6; the 1.0451 10466 14 1.0 TDF calculated for loss of a frequency in this range is 1.0464 1 . 0 4 6 1 1 .0007 10454 15 1.0 too small to produce agreement with the experiments 1.0446 10472 34 2.4 ... 80.5 for TIF = 1.0062,26 The best fit which can be secured 10495 7 1.6 1.0423 89.0 1.0420 10498 28 1.6 with this model requires that the frequency “lost” 10497 29 1.6 1.0421 1.0421f .0001 be 1330 cm.-l; (k12/k1J calculated for this frequency 10516 4 2.0 100.0 1.0402 is shown in Fig. 1, 10526 5 2.0 1.0392 A theoretical analysis of small isotope effects can be 10507 1.0411 18 1.3 made without detailed knowledge of the vibrations of 10511 1.0407 20 1.3 the isotopic normal molecules and the transition states 10509 1.0409 1 . 0 4 0 4 3 ~ .0006 1.3 21 by use of the “gamma-bar” method of Bigeleisen and Wolfsberg20; the natural logarithm of TDF is given by the standard error of the equation being 0.06 and the average deviation from the least-squares curve 0.04 in In (TDF) = 0.1464(106/T2)7X both cases. A line corresponding to eq. 4 is drawn 3n - 1 1 through the plot of results in Fig. 1. (ajj - a*jj) (6)2’ j mij mzj Discussion The value of T to be employed in a particular calculaThe slope of the least-squares line in Fig. 1 is about tion is estimated from an approximate knowledge of twice that which would be associated, in this temperathe frequencies of the normal and activated molecules. ture range, with an isotope effect having a temperaIf it can be assumed that the principal change in vibrature-independent factor (TIF) l6 of normal magnitude; tion frequencies upon activation is associated with the apparently, TIF here, as in the decarbonylation in concentrated sulfuric acid,l lies very near unity (upper (21) N. B. Slater, Trwns. R o y . Soc. (London), 2468, 57 (1953). (22) The original Slater calculation, which employs only the C and 0 limit, TIF = 1.0045). Small-vibration theory, as atomic masses, leads t o TIF = 1.0227. The dependence of L(k1z/k13) on customarily applied to the transition state, affords no temperature is as 1/T a t “low” temperatures and as 1/T2 at “high” ternperagenerally satisfactory explanation of such TIF values.1’ tures.20 Equations 4 and 5 yield, respectively, 0.9721 and 1.0045 as minimum and maximum values for TIF. Bigeleisen and Wolfsbergzo have found that corre(23) L. G. Bonner and R. Hofstadter, J . Chem. P h y s . , 6, 531 (1938). L(k12/k13) = 0.483 (1O6/T2)f 0.446
(5)
1- -1
(16) (kiz/kls) = (TIF)(TDF). (TIF) is the ratio (VIZL/VI~L) of {he imaginary frequencies associated with the reaction oodrdinate motion; ( T D F ) , the temperature dependent factor, arises in the mass dependence of the genuine vibrations of the normal and activated species. (17) However, introduction of an abnormally large bend-stretch interaction force constant, after Johnston, et aZ.,l8results in T I F values much nearer unity than seems normal.1s (18) H. S. Johnston, W. A. Bonner, and D. J. Wilson, J . Chem. P h y s . , 26, 1002 (1957). (19) M. Wolfsberg and P. E. Yankwich, unpublished calculatlons. (20) J. Bigeleisen and M. Wolfsberg, Adean. Chem. Phys., 1, 15 (1958).
(24) R. Hofstadter, ibid., 6, 540 (1938). (25) J. K. Wilmshurst, ibid., 26, 478 (1956). (26) At the mid-temperature of the experiments, and with w = 1200 Cm. -I, (klz/kiS)calcd = 1.0392, while (klZ/klS)obsd = 1.0446. (27) n is the number of atoms in the molecule, m is the mass of a n atom in a.rn.u., the subscripts 1 and 2 refer t o the light and heavy isotopic species, respectively, and the ajj are diagonal Cartesian force constants in md. H.-1; 7 is a suitably weighted average value, for the particular reaction under discussion, of the quantity :lZU(ui)/ui, where ui = hcwi/loT, and U(ui) is the function of Bigeleisen and Mayer.28 (28) J. Bigeleisen and M.G. Mayer, J . Chem. P h y s . , 15, 261 (1947).
696
PETER E. YANKWICH AND RUDY H. HASCHEMEYER
normal mode which becomes the reaction cotirdinate, the most important component of T arises in that single frequency. In their original application of this method,2oBigeleisen and Wolfsberg calculated T I F using molecular fragment masses; TDF was then computed using an estimated single critical frequency and sum of force constant differences by means of eq. 6. The resulting k/k’ was then compared with experiment. We shall employ a somewhat different approach. First, let TIF be calculated using molecular fragment masses, and TDF then computed from the experimental values of k/k’. Second, let there be assumed a range of values for a single critical frequency and, therefrom, appropriate ranges of -729 over the span of temperatures covered by the experiments. Third, let the experimental TDF be matched at the mid-temperature, this resulting, for each assumed frequency, in an estimate of
Finally, one can test the applicability of the method thus employed by comparison of the values of A, with force constants typical of the C-0 bond stretch and related bending vibrations, and by comparison of the slope of a plot of L(klZ/kl3)oalod us. 1000/T with that of the experimental plot. The plots of such calculated L(klZ/kl3) differ insignificantly from that for the “best” 2-center model, shown in Fig. 1; for assumed frequencies in the 1100 to 01200 cm.-‘ range, the values o$ A, are 5.1-5.3 md. A.-l, whereas values of 6-7 md. A.-l seem more reasonable. Improvement of the calculated A, would require the assumption of frequencies much higher than those characteristic of the C-0 stretching vibration, T I F being taken as 1.0062; to secure better slope agreement, one would have to use a different (and smaller) TIF. An experimental estimate of TIF can be obtained by employing the semi-empirical method described in earlier p u b l i c a t i o n ~ ~from ~ ~ ~ l this Laboratory. If formic acid is treated as a three particle system, the experimental temperature dependence corresponds to TIF = 1.0014 i 0.002. Repetition using this TIF of the “gamma-bar” method calculations described above does not improve significantly the agreement between calculated and observed slopes of the plot of L(klz/klJ us. (1000/T); but, the A, values, again for frequzncies in the 1100-1200 cm.-‘ range, are 5.9-6.1 md. A.-1, a definite improvement. Another experimental estimate of TIF can be obtained by eliminating A, between a pair of expressions (29) In the computations, the following weighting was employed
with Wretch =s 3vbend. (30) P. E. Ysnkwioh and H. S. Weber, J . Am. Chena. Soc.. 78, 564 (1956). (31) P. E. Yankwioh and R. M. Ikeda, ibid., E l , 1532 (1959).
Vol. 67
(klz/k~)= (TIF)(TDF), where TDF a t two different temperatures is computed from eq. 6; similarly, TIF can be eliminated to yield values for A,. To illustrate this procedure, calculations were carried out for average stretching frequencies (corrected for loss of bending vibration^)^^ of 800, 1000, 1200 cm.-l; in the same order, the values of A, (in md. 8.-l)and TIF are: 6.4, 1.0021; 7.1, 1.0001; 7.8, 0.9982. The values of these parameters are in reasonable agreement with expectation except at the highest frequency. This application of the “gamma-bar” method seems to require a low C-0 frequency to explain the observed isotope effect, while the “best” 2-center model involves a high C-0 frequency estimate. The former situation is due undoubtedly to the fact that values for 7 must be assumed for two temperatures according to some simple idea; in the discussion above, 7 was evaluated on the asumption that the C-0 stretching vibration was the major component of the reaction coordinate motion, due regard being had for the fact that bending motions are “lost” when C-0 bond rupture occurs. A more sophisticated estimate of the values of T involves the same additional complications as are associated with solution of the small vibration problem for multiple-particle representations of the normal molecules and activated complexes, or the Monte Carlo approach which is the basis of the “semiempirical” method. In its higher approximations, the “gamma-bar” method is equivalent to the “semiempirical” method; unlike other “single frequency” approaches to the explanation of small isotope effects, the simplest “gamma-bar” method application yields for many systems results in agreement with experiment which do not require an arbitrary estimate of TIF. The several calculations described above have involved very similar models for the reaction coordinate motion; in one extreme it was assumed that the motion consisted entirely of the C-0 bond stretch (which disappears upon activation) ; in the other, that bondstretch was assumed to be “the most important component” of the motion. A more detailed specification of the reaction coordinate would require additional assumptions. The utility of the “gamma-bar” and “semi-empirical” methods lies in the fact that TIF need not be known or assumed in order to win useful information from the temperature dependence of experimental kinetic isotope effects. Comparison of the results reported here with those obtained for the decarbonylation in concentrated sulfuric acid1 shows only that in both situations the major component of the reaction coordinate motion is as indicated above. In neither case do the calculations provide an explanation for the fact that TIF differs so little from unity. Acknowledgments.-This research was carried out under the auspices of the U. 5. Atomic Energy Commission, Mrs. Beverly Thomas and Mrs. Eulah Ihnen performed the mass spectrometric analyses.
