2597
DECARBOXYLATION OF MALONIC ACID
The Kinetics of the Decarboxylation of Malonic Acid and Other Acids in Neutral Solvents
by Louis Watts Clark Department of Chemistry, Western Carolina College, Cullowhee, North Carolina
(Received January 18, 1987)
Rate constants and activation parameters are reported for the following decarboxylation reactions: malonic acid in acetanilide, in ethylene glycol, in trimethylene glycol, in 1,3butanediol, and in 2,3-butanediol; oxanilic acid in 1-octanol; and oxalic acid in trimethylene glycol. The results indicate that the isokinetic temperatures for the decarboxylation of malonic acid and of oxanilic acid in neutral solvents containing only one functional group are equal to the melting point of the substrate. For reaction series involving polyhydroxy solvents, the isokinetic temperatures differ from the melting points of the substrates by integral multiples of 15”. The enol form of acetanilide appears to be the entity involved in the formation of the activated complex.
The fact that the rate of decarboxylation of malonic acid in quinoline-dioxane mixtures is proportional to the concentration of quinoline indicates that the reaction is bimolecular and suggests that the kinetics are governed by the formation of an activated complex involving the nucleophile and the substrate.l For bimolecular nucleophilic addition reactions, the enthalpy of activation is lower the greater the nucleophilicity of the solvent2 and the entropy of activation decreases as the steric hindrance increase^.^ This criterion for bimolecularity has been abundantly demonstrated from kinetic studies on the decarboxylation of malonic acid and other acids in pure solvents. For example, values of AH in kilocalories per mole and of AS* in entropy units per mole for the decarboxylation of malonic acid in quinoline and in 8-methylquinoline have been reported as 26.74 and -2.37 and 24.40 and - 10.47, re~pectively.~The methyl group in the 8 position on the quinoline nucleus increases the electron density on the nitrogen due to the +I effect and also hinders the approach of the nucleophile t o the electrophilic center due t o the steric effect. The first effect produces a decrease in AH* and the second a decrease in Ab’ Extensive studies on the decarboxylation of various a- and @-keto acids in acidic media have revealed an interesting linear free-energy relationship ; namely that the isokinetic temperature of each reaction series
*
*.
is equal to the melting point of the ~ u b s t r a t e . ~The isokinetic temperature is the temperature a t which the rate constants for all the reactions forming a particular reaction series are equal.6 The present investigation was undertaken with the view of determining whether or not such a relationship applies also to the reaction in neutral solvents. For this purpose the following systems were investigated : the decarboxylation of malonic acid in acetanilide, in ethylene glycol, in trimethylene glycol, in 1,3-butanediol, and in 2,3butanediol; of oxanilic acid in 1-octanol; and of oxalic acid in trimethylene glycol. The results of this investigation are reported herein.
Experimental Section Reagents. The malonic acid, oxanilic acid, and oxalic acid used in this research were reagent grade chemicals and were used as purchased. The solvents (1) G. Fraenkel, R. L. Belford, and P. E. Yankwich,
J. Am. Chem.
Soc., 7 6 , 15 (1954).
(2) K.J. Laidler, “Chemical Kinetics,” 2nd ed, McGraw-Hill Book Co., Inc , New York, N. Y., 1965,p 242. (3) L. P. Hammett, “Physical Organic Chemistry,” McGraw-Hill Book Co., Inc., New York, N. Y.,1940,p 204. (4) L. W. Clark, J. Phys. Chem., 62, 500 (1958). (5) L. W.Clark, ibid., 71, 302 (1967). (6) S. L. Freiss, E. S. Lewis, and A. Weissberger, Ed., “Technique of Organic Chemistry,” Vol. V I I I , Part I, 2nd ed, Interscience Publishers, Inc., New York, N. Y.,1961,p 207.
Volume 7 1 , Number 8 July 1967
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Table I: Apparent First-Order Rate Constants for the Decarboxylation of Several Acids in Various Neutral Solvents Temp (cor), Solvent
Substrate
hlalonic acid
Acetanilide
Ethylene glycol
Trimethylene glycol
lJ3-Butanediol
2,3-Butanediol
Oxanilic acid
1-Octanol
Oxalic acid
Trimethylene glycol
were reagent grade chemicals and were redistilled a t atmospheric pressure immediately before the beginning of each experiment. Apparatus and Technique. The apparatus and technique used in this research have been described previously.' In each decarboxylation experiment, a sample of the required acid was used which would yield 40.0 ml of COz a t STP on complete reaction. The amount needed was calculated on the basis of the actual molar volume of COZ a t STP (22,267 ml). The weights of these samples in grams were as follows: malonic acid, 0.1870; oxanilic acid, 0.2967; and oxalic acid, 0.1618. Approximately 90 ml of solvent was used in each experiment.
Results Two decarboxylation experiments were carried out in each solvent a t three different temperatures over a 20" range. In each experiment measurements of the evolved COz were continued until the reaction was 7040% complete. Effective zero time volumes were determined by extrapolation of early volume readings back to zero time. This afforded plots of log V,/ ( V , - V , ) us. time which were straight lines passing through the origin. The pseudo-first-order rate constants for the various experiments were obtained by the method of least squares from the slopes of the logarithmic plots. The results are summarized in Table I. The Journal of Physical Chemistry
k X 104,sec-'
O C
Expt no. 1
Expt no. 2
Average
110.10 119.56 132.40 110.10 118.60 129.73 109.03 119.95 130.05 110.10 120.00 130.00 110.10 120.00 130.00 130.94 139.33 150.05 140.44 150.26 160.07
4.38 8.47 18.5 0.98 3.40 12.0 1.83 4.67 10.7 2.10 5.28 12.7 1.84 4.18 9.18 0.87 2.60 9.90 1.90 4.70 11.1
4.37 8.46 18.5 1.02 3.42 12.2 1.81 4.69 10.7 2.12 5.26 12.7 1.86 4.18 9.16 0.85 2.57 9.94 1.90 4.66 11.1
4.375 8.465 18.5 1.00 3.41 12.1 1.82 4.68 10.7 2.11 5.27 12.7 1.85 4.18 9.17 0.86 2.58 9.92 1.90 4.68 11.1
Activation enthalpies were calculated by the method of least squares from the lowest temperature of each reaction to the highest shown in Table I. Entropies of activation were calculated using the AH values and the corresponding rate constant at the midpoint of the temperature range in each case. The results are shown in Tables 11,111,IV, and V.
*
Table I1 : Activation Parameters for the Decarboxylation of Malonic Acid in Several Neutral Solvents A H *,
*,
Solvent
kcal/rnole
AS eu/mole
AF *ma, koal/mole
Ethylene glycol 1-Butanol" 1-Hexanol" 2-Ethylhexanol-1" Diisobutylcarbitol" Cy clohexanol" Acetanilide
38.33 27.2 26.0 24.8 24.8 23.0 19 85
22.86 -4.4 -7.6 -10.4 -10.7 -15.0 -22.66
29.1 29.0 29.1 29.05 29.16 29.13 29.1
a
L. W. Clark, J. Phys. Chem., 64, 508 (1960).
Discussion Activation parameters for the decarboxylation of malonic acid in seven neutral solvents are shown in Table 11. Those for the reaction in ethylene glycol (7) L. W. Clark, J . Phys. Chem., 60, 1150 (1956); 69, 3565 (1965).
DECARBOXYLATION OF MALONIC ACID
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6
Table I11 : Activation Parameters for the Decarboxylation of Malonic Acid in Several Polyhydroxy Solvents
*,
Solvent
1,3-Butanediol Trimethylene glycol Glycerol" 2,3-Butanediol
*,
AH kcal/mole
AS eu/mole
26.97 24.95 24.6 23.9
-5.54 -10.92 -12.2 -13.8
AF + d , kcal/mole
29.07 29.08 29.2 29.1
L. W. Clark, J . Phys. Chem., 60, 825 (1956).
Table IV : Activation Parameters for the Decarboxylation of Oxanilic Acid in Several Neutral Solvents
*,
Solvent
l-Octanol 1-Decanol" Bis(2-chloroethyl) etherb
*,
AH kcal/mole
eu/mole
AF *m", kcal/mole
42.61 36.3 21.4
27.65 12.8 -22.4
30.9 30.9 30.9
AS
" L. W. Clark, J. Phys. Chem., 68,3048 (1964). ibid., 66, 1543 (1962).
* L. W. Clark,
=
TIT T' - Ta
2R-
where CY and 6 have the above-described significance, R is the gas constant in calories, and T' and T are the upper and lower temperature limits, respectively, at which the rate constants were determined. When a single measuring technique is used over a small range of temperature, systematic errors may be nearly the same in all measurements and the degree of reproducibility may provide a basis for estimating CY for the purpose of calculating 6. On this basis the data in Table I for the decarboxylation of malonic acid in neutral solvents suggest a value of a! of 0.01. This does not, however, take random errors into consideration. Consideration of the precision and accuracy of the apparatus and technique appears to indicate that CY should not be much larger than the degree of reproducibility. From this we may conclude that CY cannot be larger than 0.05 and may perhaps be much smaller. If we set CY equal to 0.05and solve eq 1 for the reaction series shown in Table I1 we find that 6, the maximum possible error in AH *, is 1.14 kcal/mole. Petersen and co-authorss have pointed out that in a given reaction series, the range of AH values divided by twice the maximum possible error in AH must be greater than unity if any confidence can be placed in an observed linear AH *-AS* relationship. The fact that this ratio is considerably greater than unity (see Table VI) leaves little room for doubting that the linear relationship shown in Table I1 is indeed valid.
*
Table V: Activation Parameters for the Decarboxylation of Oxalic Acid in Trimethylene Glycol and in 1,4-Butanediol
*,
Solvent
Trimethylene glycol 1,4-Butanediola a
A S *,
AH kcal/mole
eu/mole
AF *ios", kcal/rnole
31.1 25.5
-1.06 -15.8
31.5 31.47
*
L. W. Clark, J. Phys. Chem., 70, 1597 (1966).
and in acetanilide are based on the data in Table I. The range of AH values covered by this reaction series is 15.5 kcal/mole, yet the free energy of activation at 135" (the melting point of malonic acid) is the same in each solvent. In other words, the data in Table I1 indicate that the isokinetic temperature for the decarboxylation of malonic acid in neutral solvents, like that for the reaction in acid so1vents16is equal to the melting point of the substrate. Petersen and co-authorsa have shown that when AH and AS* are measured for a series of reactions using the same two temperatures T and T' throughout the series, the error in AX* is directly proportional to the error in AH*. The maximum possible error in AH* can be decreased by lowering the temperature of measurement, by increasing the temperature range, or by decreasing CY, the maximum fractional error in the measured rate constant. The maximum possible error in AH 6, can be calculated by the formula
*
Table VI: Validity Tests of Two Linear AH Plots According to Petersen, et da Reaction series
(1) Malonic acid in neutral solvents (Table 11) (2) Oxanilic acid in neutral solvents (Table IV)
See ref 8.
dAH*, kcal/rnole
* us. AS * 26,'
kcal/mole dAH */a
18.48
2.28
8.1
21.21
2.28
9.3
6 = the maximum fractional error in AH
*.
*
*,
The presence of acetanilide in the reaction series shown in Table I1 composed otherwise of hydroxylic solvents is surprising and suggests that the species involved in the formation of the activated complex is the enol ( 8 ) R. C. Petersen, J. H.Xlarkgraf, and S. D. Ross, J . Am. Chem. Soc., 83, 3819 (1961).
Volume 71, Number 8 J u l y 1967
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It is interesting to note in Table I1 that the enthalpies as well as the entropies of activation for the decarboxylation of malonic acid decrease with increase in the complexity and branching of the alcohol. This trend is consistent with the proposed mechanism.' It is also interesting to note that the values of A H and A S for the reaction in ethylene glycol are considerably greater than corresponding values in the monoalcohols. The -I effect of a hydroxyl group on a carbon atom adjacent to another hydroxyl group evidently lowers the electron density on the hydroxyl group which takes part in the formation of the activated complex. The high concentration of hydroxyl groups in a single small molecule will increase the probability of the formation of the activated complex; this is reflected in the high positive entropy of activation for the reaction in ethylene glycol. Evidently ethylene glycol is the only glycol that fits into the same reaction series as the monoalcohols. This is perhaps an example of the commonly observed phenomenon that the first member of a homologous series exhibits eccentricities. Table IV lists the activation parameters for the decarboxylation of oxanilic acid in several neutral solvents. Those for the reaction in 1-octanol are based upon the data in Table I. A study of the data in Table IV and in Table VI indicates that, as in the case of malonic acid, the isokinetic temperature for the decarboxylation of oxanilic acid (mp 150") in neutral solvents is equal to the melting point of the substrate. Evidently not every reaction series involving decarboxylation in neutral media bears a simple melting point-isokinetic temperature relationship as is observed in the case of malonic acid in simple hydroxylic solvents and of oxanilic acid in alcohols and ethers. The data in Table I11 reveal that for the reaction series formed by the decarboxylation of malonic acid in several polyhydroxy solvents the isokinetic temperature is not 135" (the melting point of malonic acid), but instead is 105". (The activation parameters for the decarboxylation of malonic acid in l13-butanediol, in trimethylene glycol, and in 2,3-butanediol, shown in Table 111,are based upon the data in Table I.) Although the two reaction series (Table I1 and Table 111) have different isokinetic temperatures, nevertheless the free energy of activation a t the isokinetic temperature ( A F " ) is the same in each case, namely, 29.1 kcal/mole. A similar coincidence in AFO values in the case of different reaction series having different
*
The Journal of Physical Chemistry
*
isokinetic temperatures was observed in the study of the decarboxylation of different acids in acidic media.5 It is interesting to note that the difference between the isokinetic temperatures of these two reaction series (Tables I1 and 111)is an integral multiple of 15°.5 Kinetic data on the decarboxylation of oxalic acid (mp 195") in simple alcohols are not available. If such a study is carried out, it is reasonable to anticipate, on the basis of the present results, that the isokinetic temperature will be found to coincide with the melting point. The activation parameters for the decarboxylation of oxalic acid in two polyhydroxy solvents-1,3butanediol and 2,3-butanediol-are shown in Table VII. It will be observed in the last column that the free energies of activation for the two reactions are equal a t 165". This is 30" below the melting point of oxalic acid. Thesesame two solvents are included in Table 111, involving the decarboxylation of malonic acid, and belong to the reaction series which has an isokinetic temperature of 105", 30" below the melting point of malonic acid.
Table VI1 : Activation Parameters for the Decarboxylation of Oxalic Acid in 1,3-Butanediol and in 2,3-Butanediol
*,
kcal/mole
AS eu/mole
A F fm', kcal/mole
l,3-Butanediol" 2,3-Butanediol"
29.3 22.63
-4.9 -20.2
31.44 31.48
AH
a
*,
Solvent
See footnote a of Table V.
Table V lists the activation parameters for the decarboxylation of oxalic acid in another group of polyhydroxy solvents (those for trimethylene glycol are based upon the data in Table I). It will be observed that this reaction series has the same isokinetic temperature as that shown in Table I11 which involves the decarboxylation of malonic acid in several polyhydroxy solvents. Both include the same solventtrimethylene glycol. The isokinetic temperature in this case is 90" below the melting point of oxalic acid (90" is an integral multiplet of 15"). Although the isokinetic temperatures for the decarboxylation of oxalic acid in the two sets of solvents shown in Tables V and VI1 differ by 60", their AF" values are equal31.5 kcal/mole. We have seen that reaction series formed by the decarboxylation of certain dicarboxylic acids and their derivatives in solvents composed of monocarboxylic acids and of monoalcohols show isokinetic tempera-
DECARBOXYLATION OF MALONIC ACID
tures equal to the melting point of the substrate. These melting points (and isokinetic temperatures) differ from one another by integral multiples of 15". The isokinetic temperatures of reaction series formed by the reaction in polyhydroxy solvents differ from the melting points of the substrates by integral multiples of 15". The existence of a multiplicity of isokinetic temperatures related to one another by 15" intervals cannot be denied, although their significance is not immediately evident. The numbers are evidently natural constants pointing to some sort of fundamental interrelationship of chemical reactivity. It is hoped that an explanation of the phenomenon will soon be advanced. It is interesting to compare the relative rates of decarboxylation of malonic acid and oxalic acid in the two solvents ethylene glycol and trimethylene glycol (Table VIII). It will be observed in Table VI11 that in trimethylene glycol at 105", malonic acid reacts 24 times as fast as does oxalic acid, whereas in ethylene glycol at this same temperature, oxalic acid reacts 2.5 times as fast as does malonic acid. Also, in trimethylene glycol, malonic acid reacts twice as fast as it does in ethylene glycol a t this temperature and oxalic acid reacts 30 times as fast in ethylene glycol as it does in trimethylene glycol. In every case, the reaction having the lowest enthalpy of activation proceeds at the faster rate. The substrate with two adjacent carboxyl groups reacts faster in the glycol
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Table VI11 : Activation Parameters and Rate Constants a t 105" for the Decarboxylation of Malonic Acid and Oxalic Acid in Two Polyhydroxy Solvents AH
System
Malonic acid in ethylene glycol Oxalic acid in ethylene glycol" Malonic acid in trimethylene glycol Oxalicacidintrimethylene glycol
*?
kcal/ mole
36.6
AS*, eu/ mole
18.44
A F * ~ ~ ~klaso ~ .x kcal/ 104,
mole
8ec-1
29.62
0.60
17.6
- 30.0
28.95
1.47
24.95
- 10.92
29.08
1.2
31.1
-1.06
31.5
0.05
L. W. Clark, J. Phys. Chem., 67, 1355 (1963).
containing two adjacent hydroxyl groups, whereas the substrate with two carboxyl groups separated by a methylene group reacts faster in the glycol with two hydroxyl groups separated by a methylene group. These results indicate that structural interrelationships are important in the formation of the activated complex.
Acknowledgment. Acknowledgment is made to the donors of the Petroleum Research Fund, administered by the American Chemical Society, for support of this research.
Volume 7 1 , Number 8 Julg 1967
