Oct., 1052
Cl4
ISOTOPE EFFECT
IN T H E DECARBOXYLATION O F
approximation that the bond may be considered as a simple harmonic oscillator between the two atomR forming the bond. This is probably no worse an a proximation than others involved, mch as the arbitrarily cRosen frequency assignments. The calculated and experimental values are both considcrably larger than the reduced mass term by itself.
P. E. YANKWICH (University of Illinois).-I believe that we all agree that the statistical rate theory cannot permit a ratio of C14 and C1*intramolecular isotope effects which is sensibly greater than 2. It should be pointed out, however, that within this limitation we are still permitted considerable latitude in the choice of a detailed model, and, as Dr. Fry has shown, it is possible to construct reasonable models which are not in agreement with either the C18or C14experiments on some compounds. One of the compounds which has been studied by several groups of workers is unsubstituted malonic acid. There is apparent agreement on the values for the CIS isoto e effects and no agreement on the values obtained with Mr. E. C. Stivers and I have completed recently redeterminations of the intramolecular isotope effects in the decarboxylation of C1* and C14 labeled malonic and bromomalonic acids. The results for C14(expressed in the notation introduced by the Chairman) are: 100(k& 1) = 9.9 f 0.6 (malonic) and 11.6 f 0.6 (bromomalonic); the corresponding results with C18 are 2.8 i 0.3 and 2.4 f 0.4. The stable isotope
814.
-
THE
MALONIC ACIDS
901
results with bromomalonic acid leave much to be desired, but the very much greater than 2 experimental ratio of C14 to C'a isotope effects is shown clearly. I n the matter of agreement among various workers on the magnitudes of these effects, it is interesting to note that H. G. Thode and his co-workers report C'a intramolecular isotope effects which differ by almost 30% for two different samples of commercial malonic acid. The sample which gave the higher effect was analyzed carbon-by-carbon and found to be isotopically homogeneous. With the permission of the Chairman and of Dr. Thode, I would like to ask Dr. Thode if one of his reported values is to be favored over the other, or if the difference between them can be attributed to experimental error.
H. G. THoDE.-The difference in the C1*intramolecular isotope effect for two commercial Sam les of malonic acid reported by us (Lindsay, Bourns and bhode) and referred to by Dr. Yankwich, we believe is real. As suggested in our paper, this difference could be explained by a depletion of only 0.5% in the C1* content of the methylene carbon of the British Drug House malonic acid. We would favor the result obtained with Eastman Kodak Co. malonic acid since the C18 content of the methylene carbon waa checked in this case and found to be very nearly the same as that for the COZ from the completely oxidized malonic acid.
ISOTOPE EFFECT IN THE DECARBOXYLATION OF CY-NAPHTHYLAND PHENYLMALONIC ACIDS'j2
C14
By ARTHUR FRY^ AND MELVINCALVIN Radiation Laboratory and Department of Chemistry, University of California, Berkeley, California Rsceived March 6 , 1968
The isotope effects in the decarboxylation of a-na hthylmalonic a~id-1-C'~ and phenylmalonic acid-l-CI4 have been measured, both in solution and on the liquid acids near tfeir melting points. The carboxyl group containing CIS is lost as carbon dioxide about 10% more fre uently than is the C'ccontaining carboxyl group. Some aspects of the theoretical calculations of intramolecular isotope e8ects are considered. Neither the models considered here nor the previously proposed models of Bigeleisen give agreement between theory and experiment for both the C'8 and 0 4 cases.
Introduction In recent years the question of the effect of the substitution of isotopic carbon on the rate of chemical reactions has received considerable attention. A considerable portion of this attention has been directed toward determining the isotope effect in the decarboxylation of malonic acids. Yankwich and Calvin4 studied the decarboxylation of malonic acid-1-C14 and bromomalonic acid-l-CL4,and found rupture ratios for C1z-C12bonds to C14-C12 bonds of 1.12 f 0.03 and 1.41 f 0.08, respectively. The authors mentioned that the bromomalonic acid case was a single experiment on acid of doubtful purity.6 Since this time considerable work has been done (1) The work described in this paper was sponsored by the U. 8. Atomic Energy Commission. (2) This paper was abstracted from the thesis submitted by Arthur Fry to the Graduate Division of the University of California in partial fulfillment of the requirements for the Ph.D. degree, June, 1951. (3) Department of Chemistry, University of Arkansan, Fayettoville, Arkansaa. (4) P. E. Yankwich and M. Calvin, J . Chum. Phys., 17. 109 (1949). (5) The bromomalonic acid case has recently been checked and the ratio found to be around 1.1 rather than 1.4; P. E. Yankwich. E. C. Stivers and R. F. Nystrom, J . C h s n . Phya., 20,344 (1952).
on malonic acid, both experimentally6-8 and theoretically.9-l The deaarboxylation of a malonic acid may be represented by the following equations where C* represents CI3or C14 k.1
+ +
RCH(COOH)1+ COz RCHzCOOH (1) C*OOH kz RCH( +c*oz RCH~COOH (2) COOH C*OOH k3 RCH< +coz RCH,C*OOH (3) COOH
+
For the labeled malonic acid molecule the rupture ratio C1z-C12/C1eC12is given by the ratio lcz/ks. In the terminology of Lindsay, Bourns and Thode,' this is an intramolecular isotope effect. (6) J. Bigeleisen and L. Friedman, ibid., 17, 998 (1849). (7) J. G. Lindsay, A. N. Bourns and H. C. Thode, Con. J . C h s n , 28, 192 (1951). (8)A. Roe and M . Hellmanr~,J . Chum. Phya., 19, €360 (1951). (9) J. Bigeleisen. ibid., 17,426 (1949). (10) K. Pitrer, ibid., 17, 1341 (1949). (11) A. A, Bothner-By and J. Bieeleisen. ibid.. 19, 755 (19Sl),
902
ARTHURFRYAND MELVINCALVIN
Bigeleisen's calculations5 lead to values for of 1.020 for C13 substitution and 1.038 for C14 suhstitut,ion. Pibzer's calculations'o are not, applicable to t,ho ratio X::,/k,,as was pointrd out by Bothncr-By a i d Biycleiscn. l L Actually Pitzer's calculations constitute an evaluation of k1/2k2. Bigeleisen and Friedmana studied the C18 isotope effect in the decarboxylation of malonic acid of normal isotope composition. The observed value corresponding to k3/kZ was found to be 1.020. For this Same ratio, Lindsay, Bourns and Thode7 obtained values of 1.021 and 1.026 on two different samples of malonic acid. The C13 experimental value reported by Yankwich, Stivers and Nystrom6 is 1.026. Yankwich and Calvin's4 value for k3/kz in the C14 case was 1.12. Roe and Hellmann* reported a value of 1.06. Yankwich, Stivers and Nystrom5 obtained a value of 1.099 for malonic acid and a slightly larger value for bromomalonic acid. The agreement among the values determined by the various workers in the C13 case is reasonably good, and the agreement between these values and Bigeleisen's calculated values is satisfactory. No such agreement is found between calculation and experiment in the C14 case. All of the CI4 values are higher than the calculated value, in some cases by a factor of two or three. A desirable way to check these large C14 values would be to study an acid which would be expected to give an even larger effect than malonic acid itself. Apparently, the bromo substituent in bromomalonic acid causes such an effect. From zero point energy considerations, a larger isotope effect would be expected with an acid which decarboxylates at a lower temperature. Another very desirable characteristic for a suitable malonic acid would be ease of purification of the malonic acid itself and of the substituted acetic acid derived from it. Blicke and Feldkamp12 have prepared a series of a-naphthylalkylacetic acids by hydrolysis and decarboxylation of the corresponding a-naphthylalkylmalonic esters. They state that addition of acid to an aqueous solution of the potassium salt of the malonic acid at room temperature results in the precipitation of the malonic acid as an oil which spontaneously loses carbon dioxide, forming the corresponding acetic acid. Such acids would be nearly ideally suited to a study of the isotope effect in the decarboxylation of the malonic acid. A large group is present such as i n bromomalonic acid; the acids apparently decarboxylate at room temperature; the substituted acetic acids produced are stable and readily purified. On investigation of the alkaline hydrolysis of a-naphthylmalonic ester it soon became apparent that the carbon dioxide evolution upon addition of acid was not due to decarboxylation of the malonic acid, but rather to carbonate caused by basic cleavage of the ester. l 3 k3/kZ
(12) F. F. Blicke and R . F. Feldkamp, J . Am. Chem. Soc., 66, 1087 (1944). (13) This basic carbonate cleavage reaction was studied in some de-
tail, and the results are to be published elsewhere.
Vol. 56
The free a-nnphthylmnlonic acid, however, did decarboxylate in solution a t relatively low temperatures, so it was decided to carry out isotope effect cxperimonts iisirig it. I A c r thc isotopc cffect in the decarboxylatiori of phenylmalonic acid was also studied.
Procedure and Results The substituted malonic esters were prepared by condensation of dieth 1 oxalate with the substituted acetic ester, and decarbonyLtion of the resulting glyoxylate. The most satisfactory hydrolysis procedure wm found to be transesterification of the malonic ester with acetic acid catalyzed by hydrochloric a ~ i d . 1 ~ a-Na hth lmalonic acid and phenylmalonic acid were decarboxyYateJn the liquid state near the melting oints, and in dioxane1 N hydrochloric acid solution a t 728" and a t 87.5". The carbon dioxide evolved was collected as barium carbonate. The *naphthyl- and phenylacetic acids were purified, and sainples of them and of the starting malonic acids were oxidi ,ed by a wet combustion method, and the resulting carbon dioxide collected as barium carbonate. The 0 4 activitj, measurements were made using an ionization chamber and a vibrating reed electrometer connected to a Brown recorder. The ionization chambers were filled to a standard pressure with carbon dioxide generated in a vacuum system from the barium carbonate samples m t h concentrated sulfuric acid. The samples from each run were measured in the same ionization chamber and on the same instrument in as rapid succession as possible in order to minimize any variations in the procedure and instruments. At least two independent activity measurements were made on each Sam le. The specigc activities of the various samples are shown in Table I. The values given are averages of two or more activity determinations, and the indicated errors are average deviations of these measurements. The final two columns in Table I show the activity balance between the substituted malonic acid and its decarboxylac tion products. The activity balance is well within the error of the activity measurements for all of the runs on a-na hthylmalonic acid and is only 1.1% off in the most wid& deviating case with the henylmalonic acid. The average deviation of the activity Ealance from 100% is 0.46% for all runs.
Discussion The decarboxylation of phenylmalonic acid in solution has been shown to be first order with respect to the malonic acid. For malonic acid itself decarboxylation has been shown to be first order, both in the pure liquid and in solution.le The kinetics of decarboxylation of several other substituted malonic acids in solution has also been studied,'6v17 and in each case found to be first order in respect to the malonic acid. It therefore seems reasonable to assume that we are dealing with first order reactions here, and if so the specific activities of the products and reactants may be related t o the specific rate constants of equations (I), (2) and (3) by the following equations, where HOOCCH(R)COOH = M = MOat t = 0 HOOCCH(R)C*OOH = M* = Mo*a t t = 0 RCH2COOH = A, and RCH2C*OOH = A*
(14) This procedure was kindly suggested by Professor James Cason. (15) A. L. Bernoulli and W . Wege. Helu. Chim. Acta, 2 , 622 (1919) (16) (a) C. N. Hinshelwood, J . Chem. Soc., 117, 156 (1920); (h) J. Laskin, Tran. Siberian Acad. Agr. Forestry, 6 , No. 1 , 7 (1926); (c) G. A. Hall, Jr., J . A m . Cham. Soc.. 71, 2691 (1949). (17) A. L. Bernoulli and H. Jakubowicz, Helo. Chim. Acta, 4, 1018 (1921).
CY4 ISOTOPE EFFECT IN THE DECARBOXYLATION OF MALONIC ACIDS
Oct., 1952
903
TABLE I PHENYLMALONIC ACID-1-C'4 AND THEIRDECARBOXYLATION PRODUCTS Relative specific activity, drift rate, volts/min. X 109 cot 12 x a-Naphthylacetic acid a-Naphthylmalonic acid a-NaphthylObserved x 12= Observed X 13' acetic acid
ACTIVITIES O F ~-NAPHTHYLMALONIC ACID-1-C14,
SPECIFIC
R u n No.
+
Carbon dioxide
Temp., 'C.
Liquid 1 2
163.0 163.0
1567 f 3 1601 f 18
140.0 f 1.4 144.0 f 0 . 4
1680 f 17 1728 f 5
250.0 f 0 . 3 255.4 f 0 . 5
3250 f 4 3320 f 6
3247 3329
Solution 3 4 5 6 7
100.5b 72.8 72.8 87.5 87.5
1543 f 3 1561 i 13 1150f 1 1149f 1 1543 i24
141.710.1 143.011.0 105.0 i 0 . 4 104.6 1 0 . 0 141.2 f 1 . 2
1700f 1 1716f12 1260 f 5 1255 f 0 1694 f 14
251.0f1.8 251.0f.2.4 184.2 f 2 . 0 184.3 i 1 . 9 250.0 f 2.4
3263f23 3263f31 2395 f 26 2396 f 2 5 3250 f 31
3243 3277 2410 2404 3237
Phenylacetic Acid Observed x 8"
cos + 8 x
Phenylmalonic acid Observed x 95
Phenylacetic acid
Liquid 1527 f 9 1492 f 1
163.0 163.0
1
2
205.3 f 0 . 1 205.3 f0.0
1642 f 1 1642 f 0
Solution 1465 f 14 209.1 f l . 1 1673 f 9 3 72.8 1468 f 10 206.1f2.1 1649f17 72.8 4 a Factor to convert to specific activity of the single labeled carbon atom. perature unknown, -85-95". A*
A +A *
=
Mo*(l - e-(kz+ka)l)
ka kz
+ IC3 Mo(l - e-kif) + Ma* ( 1-
e-(kA-kdl)
(5)
When the reaction is complete, t = m , and equations (4)and ( 5 ) become, after rearrangement
By combining equations (4) and ( 5 ) at any time whether th8 reaction is complete or not, we obtain equation (8). A*
+
The values C*02/(C0, C*02), A*/(A* A) and Mo*/(Mo* Mo) are the molar specific activities of the carbon dioxide, the substituted acetic acid and the substituted malonic acid, respectively. These are the values given in Table I. For ease of tabulation and convenience of reference, the percentage isotope effect may be defined as 100 (k3/kz - 1). The percentage isotope effect values may then be calculated from the data in Table I using equations (6), (7) and (8) with the results shown in Table 11. The agreement among the calculations by the three different equations furnishes a measure of the internal consistency of the data. Only two of these three values are inde-
+
*
3173 f 18 3163 f 18
3169 3134
350.2 f 2 . 4 3152f22 3138 350.2f2.7 3152f24 3117 Bath temperature, actual decomposition tem-
TABLE I1 CI4 ISOTOPE EFFECT IN THE DECARBOXYLATION OF 01NAPHTHYLMALONIC A c I D - ~ - CA ~ ND ~ PHICNYI,MAT,ONIC Acrn1-C'4 Per cent. isotope effect 100(ka/kz - 1 ) Cdz and monoacid, equation 7 8 or-Naphtbylmalonio acid-I-C" COz and diacid,
Tonip., cquation Run No. OC. 6
Liquid 1 163.0 2 163.0 Average 163.0
A *n
+
368.6 f.2 . 0 351.4 f 2.0
7.4 7.4
Solution 3 100.5" 11.5 4 72.8 9.0 5 72.8 8.3 Averago 72.8 6 87.5 8.5 7 87.5 10.6 Average 87.5 Average all Eoln. runs Tiquid
Monoacid and diacid, equation
Averace I
7.0 8.5
7.2 7.9
'7.2 f 0 . 2 7.9f00.6 7.6 f 0 . 5 10.2 f 1 . 3 9.9 f 0 . 9 9.Gf1.4 9.8 f1.2 9.2f0.7 0 . 8 f0.8 9 . 5 f 0.8 9.7 f1.1
8.8
10.2
10.9 11.0
9.9 9.6
10.0 8.0
0.2 9.8
Phenylmalonir acid-1 -C14
1 163.0 7.8 7.3 7.5 '7..5 f 0 . 3 2 163.0 12.0 8.0 1 0 . 1 10.0 f 2 . 0 Average 163.0 8.8 f 1.8 Solution 3 72.8 15.1 13.2 14.2 14.2 f 1.0 4 72.8 14.7 9.8 12.3 12.3 f 2 . 4 Average 72.8 13.2 f 1.7 Bath temperatsure, actual decomposition temperature known, -85-95".
pendent, however, and the average values and the indicated errors are calculated on the basis of equations (6)and (7) only.
ARTHURFRYAND MELVINCALVIN
904
The C14isotope effects in the decarboxylation of liquid a-naphthylmalonic a~id-1-C'~ and phenylmalonic a~id-1-C'~ a t 163.0' are thus seen to be 7.6 f 0.5 and 8.8 f 1.8%. The corresponding values in solution between 72.8 and -95' are 9.7 f 1.1 and 13.2 =t1.7%. The precision of the measurements is not great enough to show a significant temperature coefficient of the isotope effect in the solution experiments. However, there is a significant difference in the isotope effect between the liquid acid at 163.0' and the acid in solution at 72.8 to 95", and part of this is probably a temperature effect. These values are in the same range as the other C14work previously mentioned and are much higher than Bigeleisen's calculated upper limit of 3.8%.9 That these calculations do not represent an actual upper limit may be demonstrated by making similar calculations using a different model from that used by Bigeleisen.9~~8If we assume that the only vibrations which need be considered in malonic acid are the stretching vibrations of the carbon-carbon bonds, we may picture the reaction in the manner kz - - C*]$ + c* + c-c
c J_
[C-c
c*=
ka [C * * . C - C * ) $ + C + C - C *
.
