LOUISWATTSCLARK
3048
where S is the value consistent with eq. 4, $.e., on a common logarithm basis. Acknowledgments. The authors wish to express their
sincere appreciation to 511. D. Armstrong, John Byrnes, Walter Stevens, and Ralph Whitfield who performed the experimental e.ni.f. measurements.
The Kinetics of the Decarboxylation of Malonic Acid and Other Acids-
A General Relationship
by Louis Watts Clark Department of Chemistry, Western Carolina College, Cullowhee, North Carolina
(Received J u n e I$, lQG4)
Kinetic data are reported for the following decarboxylation reactions : malonic acid in benzoic acid, pivalic acid, octanoic acid, heptanoic acid, and dl-2-inethylpentanoic acid ; n-butylmalonic acid in hexanoic acid and octanoic acid; n-hexylnialonic acid in o-cresol; and oxanilic acid in o-cresol, octanoic acid, benzoic acid, and decanol. The activation parameters for these reactions were calculated and compared with corresponding data obtained previously. A general kinetic relationship was indicated.
A plot of enthalpy us. entropy of activation for a series of related reactions often yields a straight line, the slope of which is designated as the isokinetic temperature. This is the temperature at which the rate of reaction is equal for all the reactions conforming to the line. I n the case of the decarboxylation of oxanilic acid in the molten state and in a dozen polar solvents (ethers and amines) the isokinetic temperature determined graphically was found to be 423"K2 For the decarboxylation of malonic acid in the molten state and in 11 polar solvents (acids, cresols, nitro compounds) the isokinetic temperature was found graphically to be 407°11.3 These values corresponded closely to the melting points of the two reactants (oxanilic acid melts a t 150", which is 423"K.,malonic acid a t 135.6",4which is 409°K.) It was subsequently pointed out by a referee that the isokinetic temperatures for these two reaction series, calculated by the method of least squares, were slightly different from those reported, namely, 418°K. for the oxanilic acid reaction and 414°K. for the malonic The Journal of Physical Chemistry
acid reaction. These revised values still did not differ appreciably from the melting points of the two reactants. I n view of these circumstances it was decided to perform additional experiments in order to try to establish more accurate values for the two isokinetic temperatures. Accordingly, the following experiments were carried out in this laboratory: (1) The decarboxylation of malonic acid in benzoic acid, pivalic acid, octanoic acid, heptanoic acid, isovaleric acid, and d2-2-niethylpentanoic acid ; ( 2 ) the decarboxylation of n-butylmalonic acid in hexanoic acid and in octanoic acid ; (3) the decarboxylation of n-hexylmalonic acid in o-cresol; and (4) the decarboxylation of oxanilic acid in o-cresol, octanoic acid. benzoic acid, and n-decyl alcohol. The data obtained in this research were com~~~~~
~
(1) 5.L. Friees, E. S. Lewis, and 4.Weissberger, Ed., "Technique of Organic Chemistry," Vol. VIII, Part I, "Investigations of Rates and Mechanisms of Reactions," 2nd Ed., Interscience Publiohers, Inc., New York, N. Y . , 1961, p. 207. ( 2 ) L. W. Clark, J . Phys. Chem., 66, 1543 (1962). (3) L. W.Clark, ibid., 67, 526 (1963) (4) T. Salzer, J . Prakt. Chem., 61, 66 (1900).
KINETICSOF
THE
DECARBOXYLATIO:~ OF MALONIC ACID
bined with others obtained previously revealing an unexpected general relationship. The results of this investigation are reported herein.
Experimental Reagents. (a) Reactants. The four reactants, nialonic acid, n-butylninlonic acid, n-hexylmalonic acid, and oxanilic acid, assayed a t least 99% pure by neutralization equivalents. This degree of purity also was verified by measuring the volume of COz evolved on complete reaction. Their melting points agreed with those cited in the literature. ( b ) Solvents. Reagent grade benzoic acid, 100yo assay, was used dirlectly from the container without further treatment. The other solvents were reagent grade or highest purity chemicals. A fresh sample of each liquid was distilled off a t atmospheric pressure immediately before use. Apparatus and Technique. The apparatus and technique have been described in detail previously.6 The use of a completely transistorized temperature control unit enabled the temperature of the oil bath to be kept constant to *0.005". The evolved COZ was collected in a 50-ml. buret calibrated by the U. S. Bureau of Standards. The temperature of the water surrounding the buret was controlled by j=O.O5", using a water circulator, heater, mercury thermoregulator, and electronic relay. I n each decarboxylation experiment a sample of reactant was weighed out in a fragile glass capsule. The weight of samplc: was that required to furnish 40.0 rnl. of COZ a t STP on complete reaction, calculated 011 the basis of the actual molar volume of COZ a t STP, namely, 22,267 ml. About 60 ml. of solvent was used in each experiment. Results The decarboxylation reactions of all the reactants in all the liquids studied in this research gave good firstorder kinetics over the greater part of the reaction. Each reaction was generally studied over a 20" range of temperature, a t three or four different temperatures. Two experiments were ordinarily carried out a t each temperature. Variations between the two values of the rate constant as measured in the same solvent a t the same tlemperature were usually no more than 1%. The average values of the rate constants for the reactions in the various solvents a t the different temperatures studied are shown in Table I. The apparent first-order rate constants were calculated from the slopes of the experimental logarithmic plots. Table I1 shows the parameters of the absolute reaction rate equation6calculated from the data in Table I.
3049
Table I : Apparent First-Order Rate Constants for the Decarboxylation of Several Reactants in Various Solvents
Reactant
Malonic acid
Solvent
Benzoic acid
Pivalic acid
Octanoic acid
Heptanoic acid
dl-2-methyl pentanoic acid
Isovaleric acid
n-Butylmalonic acid
Octanoic acid
Hexanoic acid
n-Hexylmalonic acid
o-Cresol
Oxanilic acid
o-Cresol
Octanoic acid
Decanol
Benzoic acid
Temp., 'C. (cor.)
137.11 145.78 154.66 142.06 151,21 160.50 139.69 150.06 159.84 139.09 149.70 159.11 139.94 149.70 159.32 139.94 150.75 159.67 137,87 147.78 157.77 135.61 147.78 155.49 135.11 136.75 144.05 151.36 155.70 128.63 138.91 148.13 140.73 150.34 159.46 130.66 140.72 150.45 131.32 140.97 151.76
k X 104, aec.
-1
2.12 4.68 10.16 2.23 6.26 17.15 2.83 8.10 22.5 2.98 7.58 16.7 3.35 7.18 14.9 3.17 8.93 20.3 2.32 5.98 12.9 1.94 6 40 13.25 3.79 4.37 7.63 13.6 18.8 0.705 2.62 7.98 2.78 7.22 18.67 1.21 3.71 10.44 0.94 2.53 7.23
Activation parameters for the decarboxylation of various reactants in a wide variety of solvents, based upon previously reported results, are brought together in Table 111. All the data in Tables I1 and I11 are shown graphically in Fig. 1.
(5) L. W. Clark, J. Phus. Chem., 60, 1150 (1956). (6) S. Glasstone, K. J. Laidler, and H. Eyring, "The Theory of Rote Processes," McGmw-Hill Book Co., Inc., New York, K. Y., 1941, p. 14.
Volume 68. Number 10 October, 1.966
3050
LOUISWATTSCLARE
~~~
Table I1 : Activation Parameters for the Decarboxylation of Several keactants in Various Solvents Based on Present Research AS*, e.u./ mole
AH*,
Reactant
kcal./ mole
Solvent
Malonic acid
Octanoic acid Benzoic acid Heptanoic acid Isovaleric acid dl-2-Methylpentanoic acid Plvalic acid n-Butylmalonic acid Hexanoic acid Octanoic acid n-Hexylmalonic acid o-Cresol Oxanilic acid Benzoic acid o-Cresol Hexanoic acid n-Decyl alcohol
-16
-8
0
16 24 32 A S*, e.u./mole.
8
40
34.8 30.4 29.7 32.56 26.45
-11.1
38.7 33.2 32.7 25.9 33.3 41.0 36.73 36.3
+18.3 +5.1 +3.8 -11.4 $4.7 +23.9 $13.3 +12.8
48
+8.9 -1.8 -3.4
+3.57
56
64
Figure 1. Enthalpy-entropy of activation plot for the decarboxylation of oxanilic acid, oxamic acid, malonic acid, n-butylmalonic acid, n-hexylmalonic acid, and benzylmalonic acid in the molten state and in solution.
Discussion It is surprising to note that all the points representing the reactions shown in Tables I1 and I11 lie on the same isokinetic temperature line (see Fig. 1). These include parameters for the decarboxylation of oxamic acid in five solvents, of oxanilic acid in the molten state and in 16 solvents, of nialonic acid in the molten state and in 21 solvents, of n-butylmalonic acid in the molten state and in six solvents, of n-hexylmalonic acid in the molten state and in one solvent, and of benzylmalonic acid in the molten state and in two solvents-a total of 56 reactions, representing six reactants, and covering a wide range of solvent types. These results are based upon more than 500 kinetic experiments, carried out by a single investigator, extending over a period of approximately 8 years. The fact that all these reactions conform to the same The Journal of Physical Chemistry
Table I11 : Activation Parameters for the Decarboxylation of Several Reactants in Various Solvents-Previously Reported Resuli,s AH*,
Reactant
kcal./ mole
Solvent
Oxanilic acid
Bis(2-chloroethyl) ether" n-Butyl ether" n-Amyl ether' P-Chlorophenetole" Phenetolea Anisole" Dibenzyl ether N,N-Dimethylaniline" Melt" n-Hexyl ether" o-Ethylaniline" o-Toluidine" 8-Methylquinolineb Oxamic acid $nilhe" Quinolined 8-Methylquinolined Dimethyl sulfoxidee Triethyl phosphatee Malonic acid Melt' Propionic acid' Hexanoic acidi m-CresoP n-Butyric acid' n-Valeric acid' P-Mercaptopropionic acid' p-CresoIf Nitrobenzene' Phenol' Decanoic acid' o-Cresol' o-Xitrotoluene' 2-Nitro-m-xyleneO Benzaldehydeh p-Chlorophenetole* Benzylmalonic acid Melt! n-Butyric acid3 Decanoic acid' n-Hexylmalonic acid hIeltk n-Butylmalonic acid Melt' Phenol' m-Cresol' p-Cresol' o-Cresol'
.
21.4 25.1 28.3 31.3 32.6 32.6 36.8 37.6 40.1 40.1
45.5 47.8 35.6 59.7 47.0 36.0 37.7 40.9 35.8 33.6 32.5 32.3 32.3 32.2 30.3 29.8 28.1 27.3 26.6 24.2 23.5 30.0 27.9 27.8 29.4 23.0 26.9 32.0 32.2 36.2 29.7 24.0 21.3
AS*, e.u./ mole
-22.4 -13.9 -6.6 +0.7 f4.0 +11.1 +14.2 +15.3 +21.4 +22.1 +34.3 $39.9 +lO.O +68.0 f37.5 +12.2 f14.9 +24.7 +11.9 +6.l f3.2 4-3.2 f2.5 +2.4 -9.9
-2.4 -7.2 -8.9 -11.0 -16.5 -17.9 -3.12 -7.0 -7.9 -2.6 -18.9 -9.0 +2.4 +2.9 +13.0 -2.3 -15.8 -22.8
a See ref. 2. L. W. Clark, J . Phys. Chem., 65, 542 (1961). ' L. W. Clark, ibid., 65, 180 (1961). L. W. Clark, ibid., 65,
659 (1961). L. W. Clark, ibid., 65, 1651 (1961). 'See ref. 3. L. W. Clark, J . Phys. Chem., 62, 368 (1958). * L. W. Clark, ibid., 64, 677 11960). L. W. Clark, ibid., 65, 2271 (1961). L. W. Clark, ? b i d . , 67, 1481 (1963). L. W.Clark, ibid., 67, 2602 (1963). ' TJ. W. Clark, ibid., 68, 587 (1964).
'
'
kokinetic temperature line is strong evidence that they all take place according to the same mechanism.'
ACID
3051
This mechanism has been shown to consist of the formation of an activated complex, a carbonyl carbon atom of the reactant, coordinating with a pair of imshared electrons on one of the nucleophilic atoms of the solvent, facilitating cleavage.8 An interesting feature of the results shown in Fig. 1 is the large variety of reactions composing a single reaction series. These include: (1) the decarboxylation of oxamic acid and oxanilic acid (and presumably their derivatives) in the niolten state and in a wide variety of polar solvents (ethers, amines, alcohols, acids, cresols, triethyl phosphate, dimethyl sulfoxide, etc.), and (2) the decarboxylation of malonic acid and of all monoalkylated derivatives of malonic acid in the molten state and in several types of polar solvents (acids, cresols, nitro compounds, ethers, aldehydes, etc.). Inasmuch as oxarnic acid and oxanilic acid belong to the type of a-keto acids, and inalonic acid and its derivatives belong t o the type of @-ketoacids, it may be expected that the decarboxylations of a- and @-keto acids in tlie molten state and in many polar solvents likewise belong to this reaction series It has been found that the decarboxylation of malonic acid in alcohols forms a new reaction series as shown by the fact that the isokinetic temperature line for this group of reactions lies below and parallel to that for the reactions in acids, nitro conipounds, cresols, etc. A third parallel line is formed by the group of reactionis in aniline d e r i ~ a t i v e s a, ~fourth for the reaction in picolines.l0 (Compare ref. 7, p. 1208). On the other hand, the decarboxylation of oxamic and oxanilic acids in all types of polar solvents apparently constitutes only a single reaction series, all points lying on the same isokinetic temperature line. It inay be expected that other a-keto acids will follow the same pattern as oxamic and oxanilic acids, and other @-ketoacids that of malonic acid. The equation of the line in Fig. I, obtained by the method of least squares, is
kinetic temperature may be calculated by substituting this value of AF* in the absolute reaction rate equation6
KINETICS OF
THE DECARBOXYLATION O F &IALOSIC
AH* = 422.0AS*
k
KT . h_e - A F * / R T
The rate constant thus calculated turns out to be 8.55 X sec. -I. In the case of a reaction taking place at a temperature below 149", the reaction having the lowest enthalpy of activation will have the highest rate, whereas, above 149'; the reaction having the highest enthalpy of activation will have the highest rate. Petersen, et al.," have analyzed the effect of experimental errors on the validity of an observed linear enthalpy-entropy of activation relationship, and they reached the conclusion that "the positive deinonstration of such a phenomenon is extremely difficult due to the inherent nature and magnitude of experimental errors." They applied their niethod of evaluation to many published examples but failed t o find a single clearly valid case. They thought that the major part of any observed linear enthalpy-entropy of activation relationship is very likely the result of experimental error in most, if not all, previously published examples. In view of this sweeping indictment one is prone to ask whether or not the results shown in Fig. 1 niay be considered valid. Petersen, et al., pointed out that only unless the observed range of AN* values in a given series is greatei than twice the maximum possible error in AH* can any validity be assumed in the observed AH*-AX* relationship, and only unless the range is much greater than this can any details of the relationship be inferred. Now the range of AH* values represented by the reactions in Fig. 1 is nearly 40.0 kcal./niole. The error in AH* of the reactions included in Fig. 1 can be readily calculated by recourse to the formula proposed by Petersen and co-workers'
6=2R-
+ 31,000
The slope of the line, which is designated as the isokinetic temperature, is thus 422.0"K. or 149°C. I t is now evident that the fact that this value is within 1" of the iiielting point of oxanilic acid is only a coincidence. The free energy of activation a t the isokinetic temperature for all the reactions belonging to this reaction series is given by the last constant in the above equation, namely, 31,000 cal. The specific reaction velocity constant for all the reactions in the series at the iso-
=
T'T T'-Ta
where 6 is equal to the maxiinuni possible error in AH*, a is the iiiaxiiiiuiii fractional error in the rate constants, R is the gas constant in calories, and T ' (7) J. E. Leffler, Y.Org. Chem., 20, 1202 (1955). (8) G. Fraenkel, R. L. Belford. and P. E. Yankwich, J . Am. Chem. Soe.. 76, 15 (1954).
(9) L. W. Clark, J . Phvs. Chem., 62,79 (1958). (10) L . W. Clark, ibid., 60, 1583 (1956). (11) R. C. Petersen, J. H. Markgraf, and S. D. Ross, J . Am. Chem. Soc., 83, 3819 (1961).
Volume 68, N u m b e r 10
October, 1964
3052
and T are the upper and lower temperatures, respectively, a t which the rate constants were determined. What is a , the maximum fractional error in the rate constants, of the 56 reactions represented by the points in Fig. l'? This we can only estimate. Each reaction has been carried out a t least twice a t each temperature, and often five or more temperatures have been studied for one reaction. Every effort has been made to reduce experimental error to a minimum. Reagents of the highest purity have been used. Temperature control has been h0.1" in the earlier experiments, and about *0.005" in the later ones. Reproducibility of the experiments has been of the order of about 1%. I n view of these factors, an assumed value of a of 0.05 should not be too small. We may exaggerate this value and set a equal to 0.1 or 10 times the reproducibility of k for the sake of removing any question as to the reliability of the calculations. If we let typical
The Journal of Physical Chemistry
LOUISWATTSCLARK
values of T' and T be 423 and 413"K., respectively, and set a equal to 0.1, the value of 6 turns out to be 7 kcal./mole. Twice this amount is 14 kcal./mole, as compared with 40 kcal./mole for the range of AH* values. Since the range of AH* values covered by the reactions in Fig. 1 is very much greater than twice the maximum fractional error in AH*, the linear relationship represented by the data in Fig. 1 must be considered valid. Acknowledgments. Acknowledgment is made to the donors of The Petroleum Research Fund, administered by the American Chemical Society, for support of this research. Thanks are due also to Western Carolina College for the use of its punch card equipment and computer facilities, and to William Cowan, the programmer, who wrote the Fortran program used in this research.
