LOUISWATTS CLARK
302
The Kinetics of the Decarboxylation of n-Hexylmalonic Acid, Cyclohexylmalonic Acid, and Oxamic Acid in Acid Media
by Louis Watts Clark Department of &?mistry, Western C a r o h a College, Cullowhee, North Carolina 88788 (Receiued June 19,1966)
Kinetic data are reported for the decarboxylation of n-hexylmalonic acid (mp 105O), cyclohexylmalonic acid (mp 180°), and oxamic acid (mp 210') in hexanoic acid and octanoic acid. Comparison of the results obtained in this research with previously published data on malonic acid (mp 135') and oxanilic acid (mp 150') indicates that the isokinetic temperatures for the various reaction series are the same as the melting points of the reactants and that the free energy of activation for the various reactions at the melting point of the reactant is a constant and is equal to approximately 31.1 kcal/mole.
Kinetic studies have been carried out previously on the decarboxylation of malonic acid in the molten state as well as in solution in a large number of fatty acids. The activation parameters for these reactions are listed in Table I and shown graphically in Figure 1. The slope of the line in Figure 1 is 408°K or 135°C. This is the so-called isokinetic temperature of the reaction series; ie., the temperature at which the rate constants of all the reactions conforming to the line are equaL2 It is also the melting point of malonic acid. This means that at its melting point, the rate of decarboxylation of malonic acid is not affected by the presence of acidic solvent^.^ The intercept of the isokinetic temperature line on the zero entropy of activation axis yields AF", the free energy of activation of all the reactions in the particular series at the isokinetic t e m p e r a t ~ r e . ~In Figure 1 this value turns out to be 31.1 kcal/mole. If AF*13b0 is calculated by means of the equation AF* = AH*
- TAS+
for the various systems shown in Table I, the result in every case is very close to the value of 31.1 kcal/mole as shown in the last column in the table. Kinetic data for the decarboxylation of several acids in the molten state are listed in Table 11. The free energies of activation of the various reactants at their respective melting points are shown in the last column. It is surprising to note that in spite of the The,Journal of Physical Chemistry
Table I : Activation Parameters for the Decarboxylation of Malonic Acid in the Molten State and in Several Fatty Acids" AH *, Solvent
Pivalic acid Melt Octanoic acid Propionic acid Isovaleric acid Hexanoic acid Pentanoic acid Benzoic acid 0-Mercaptopropionic acid Heptanoic acid Decanoic acid ( )-1,ZMethylpentanoic acid
+
a
kcal/ mole
38.7 35.8 34.83 33.6 32.56 32.5 32.2 30.4 30.3 29.7 26.6 26.45
*,
AS ell/ mole
18.3 11.9 8.9 6.1 3.57 3.2 2.4 -1.8 -1.9 -3.4 -11.0 -11.1
AF *iso,
koa]/ mole
31.2 31.0 31.19 31.11 31.10 31.20 31.20 31.14 31.08 31.1 31.1 31 . O
Reference 1.
wide variation in the values of the activation parameters and the range of melting points, the free energy of activation at the melting point is the same for each reactant and is equal to approximately 31.1 kcal/mole. (1) L. W. Clark, J . Phys. Chem., 68, 3048 (1964). (2) S. L. Freiss, E. S. Lewis, and A. Weissberger, Ed., "Technique of Organic Chemistry," Vol. VIII, 2nd ed, Part I, Interscience Publishers, Inc., New York, N. Y.,1961, p 207. (3) L. W. Clark, J . Phys. Che-m., 67, 526 (1963). (4) J. E.Leffler, J . Org. Chem., 20, 1202 (1955).
KINETICS OF
THE
DECARBOXYLATION OF ~-HEXYLAMLONIC ACID
303
Experimental Section
26
-
10
-5
I
I
0
5
I
I
1s
10
AS*, eu/mole.
Figure 1. Enthalpy V 8 . entropy of activation plot for the decarboxylation of malonic acid in the molten state and in several fatty acids. Slope of line: 408°K or 135°C.
Table I1 : Activation Parameters for the Decarboxylation of Several Acids in the Molten State AH*,
AB*
OC
kcal/ mole
eu/ mole
kcal/ mole
150 135 135 105 105
40.1 35.8 35.0 32.2 32.2
21.4 11.9 9.6 2.8 2.9
31.05 31.0 31.08 31.14 31.10
Mp, Reactant
Oxanilic acid. Malonic acidb Methylmalonic acidc n-Hexylmalonic acidd n-Butylmalonic acid*
AF%,,
a L. W. Clark, J. Phys. Chem., 66,1543 (1962). E.L. W. Clark, L. W. Clark, ibid., 70, 2523 (1966). ibid., 67, 138 (1963). d L. W. Clark, ibid., 67, 2602 (1963). * L. W. Clark, ibid., 68,
Reagents. The n-hexylmalonic acid and cyclohexylmalonic acid used in this research were obtained from Distillation Products Indust,ries, Rochester, N. Y. The cyclohexylmalonic acid melted sharply at 180" (corrected) and was used as purchased. The nhexylmalonic acid had a melting range of 103-106" when received. After recrystallization from benzene it was found to melt sharply at 105" (corrected). The oxamic acid was obtained from Matheson Coleman and Bell, Norwood, Ohio. It melted sharply at 210" (corrected) and was used as purchased. The hexanoic and octanoic acids were reagent grade. The samples used in the decarboxylation experiments were freshly distilled a t atmospheric pressure immediately before use. Apparatus and Technique. Details of the apparatus and technique have been described previously.6 In each experiment a weighed sample of the reactant was introduced in the usual manner into the reaction flask containing 95 ml of solvent. The weight used was that which was required to furnish exactly 40.0 ml of COz at STP on complete reaction calculated on the basis of the actual molar volume of COz at STP, namely, 22,267 ml. For n-hexylmalonic acid this is 0.3361 g, for cyclohexylmalonic acid, 0.3382 g, and for oxamic acid, 0.1600 g. All experiments were carried out in an atmosphere of dry COz.
Results For each reactant at least two decarboxylation experiments were carried out in each solvent at each
587 (1964).
These results suggest the possibility that compounds related to malonic and oxanilic acids may exhibit behavior in acidic solvents analogous to that of the parent compounds; i.e., (1) they may have isokinetic temperatures equal to their melting points, and (2) they may have the same free energies of activation at their melting points as does malonic acid, namely, 31.1 kcaI/mole. In order to test this hypothesis, three acids were selected differing widely in melting points (n-hexylmalonic acid, mp 105", cyclohexylmalonic acid, mp NO", and oxamic acid, mp 210") and their rates of reaction were carefully measured at several temperatures in two high-boiling fatty acids (hexanoic and octanoic acid). The results of this investigation, which are reported herein, leave no doubt as to the validity of the hypothesis which prompted it.
Table In: Apparent Firsborder Rate Constants for the Decarboxylation of n-Hexylmalonic Acid, Cyclohexylmalonic Acid, and Oxamic Acid in Two Fatty Acids -Hexanoic Temp,
OC Reactant
n-Hexylmalonic acid Cyclohexylmalonic acid Oxamic acid
acid-
-Octanoic Temp,
(cor)
k X 104, uec -1
(cor)
137.87 143.63 154.80 157.33 140.17 150.23 160.23 138.93 149.81 158.88
2.82 4.84 13.3 16.56 2.74 7.06 17.22 3.23 8.54 18.64
135.09 146.36 149.75 154.80 140.60 150.49 160.59 138.83 149.06 157.49
OC
acid-
k X IO', 8ec-1
2.06 5.90 7.97 12.4 2.32 6.30 16.15 3.11 7.81 16.38
(5) (a) L. W. Clark, J. Phys. Chem.,60, 1150 (1956); L. W. Clark, ibid., 70, 627 (1966).
Volume 71,Number 2 January 1987
LOUISWATTSCLARK
304
TabIe 1V : Comparison of Activation Parameters for the Decarboxylation of Several Unstable Acids in the Molten State and in Solution n-Hexylmalonic acid, m p 105OAH AS AF*ma, eu/ kcal/ kcal/ mole mole mole
Y Solvent Melt Hexanoic acid Octanoic acid 5
+,
32.2O 31.24 30.75
*,
2.8 0.54 - 1.0
31.14 31.1 31.14
-mp
Malonic acid,
AH*#
kcal/ mole
Cyclohexylmalonic acid,
AS*, A F * ~ , AH*, eu/ ked/ kcaV mole
mole
35.8" 11.9 32.5' 3.2 34.83" 8.9
-mp
Oxanilic acid,
150°-mp AS*, A F * I ~ Q ~ AH*, , eu/ kcal/ kcal/
135"-
mole
mole
mole
31.0 31.2 31.19
40.1" 21.4
31.05
36.73" 13.3
31.1
mole 31.82 33.7
18O0-
AS+, AF*iso', eu/ kcal/ mole mole 1.94 5.61
31.09 31.16
Osamic acid, m p 210°.-.
y AH*,
AS+,
AFd+o0,
kcal/ mole
eu/ mole
kcal/ mole
30.5 30.5
-1.25 -1.25
31.1 31.1
Reference 1.
constant temperature selected. Each reaction was measured at three or four different temperatures over a 20" range. All the reactions gave good first-order kinetics in both solvents over the greater portion of the reaction. Average rate constants, calculated in the usual manner from the slopes of the logarithmic plots, are shown in Table 111. The parameters of the absolute reaction rate equation based upon the data in Table I11 are shown in Table IV. Included for comparison are corresponding data previously published for malonic acid and oxanilic acid.
Discussion In Table IV it will be observed that for the first three reactants the acidic solvent lowers both the enthalpy and entropy of activation of the decarboxylation reaction. This is consistent with the proposed mechanism of the reactions since the fatty acids are weaker acids (and therefore stronger bases in the Lewis sense) than malonic acid. It will be observed also that, in the molten state and in identical solvents, the substituent on malonic acid lowers both the enthalpy and entropy of activation of the reaction. The effect of the cyclohexyl group, however, is less than that of the n-hexyl group. In octanoic acid the enthalpy of activation for the decarboxylation of oxamic acid is considerably less than that for the oxanilic acid reaction. The reverse is true for these two reactions in basic solvents.' The most interesting feature of Table IV is the comparison of the free energies of activation of the various reactions at the melting points of the reactants (the third column in each section). For each of the five reactants shown, in the molten state (where data are available) as well as in the fatty acids, it will be observed that the free energy of activation at the melting point of the reactant is constant (equal to approximately 31.1 kcal/mole) as was noted previously in the case of malonic acid (see Table I). In the case of the d e carboxylation of oxanilic acid, oxamic acid, and malonic acid and its derivatives, in the molten state and in The J o u d of Phyaical Chemistry
solution in fatty acids, these results indicate that the isokinetic temperature is the same as the melting point of the reactant and that the free energy of activation at the melting point is constant (equal to approximately 31.1 kcal/mole). It is interesting to note that the melting points of the acids shown in Table IV (as well as in Table 11) increase by integral multiples of 15". It has been noted previously that numerous reaction series formed by the decarboxylation of a large number of compounds in various homologous solvents exhibit isokinetic temperatures beginning at 105" and increasing by integral multiples of l!ioa8 These results indicate that the numbers associated with these melting points and isokinetic temperatures are natural constants pointing to some sort of fundamental interrelationship of chemical reactivity. High melting points are indicative of strong attractions between the units composing the crystal lattice. Similarly, high isokinetic temperatures would be expected to be associated with strong mutual attractions between the electrophile-nucleophile pairs of the transition state. The reactants listed in Table IV and Table I1 may be regarded as belonging to either of two groups of compounds: (1) a-keto acids (oxamic and oxanilic acids) and ( 2 ) p-keto acids (malonic acid and its derivatives). It is interesting to speculate whether or not the results of the present research may apply to other a- and @-ketoacids. If so, then a compound such as o-nitrophenylpyruvic acid (mp 120") should have a free energy of activation at 120' of 31.1 kcal/mole and an isokinetic temperature of 120" in acidic solvents. Unstable acids belonging to other homologous series (e.g., a-amino acids) should show analogous behavior; Le., the free energy of activation at the melting point should be constant (but not necessarily the same as (6) G. Fraenkel, R. L. Belford, and P. E. Yankwich, J. Am. Chem. Soc., 76, 15 (1954).
(7) L. W.Clark, J. Phy.3. C h m . , 65, 1460 (1961). ( 8 ) L. W. Clark, ibid., 70, 1597 (1966).
KINETICSOF THE DECARBOXYLATION OF n-HEXYLMALONIC ACID
for the keto acids) and isokinetic temperatures in acid media should be equal to their melting points. If such results are established a great deal of insight will be gained in regard to chemical reactivity. Furthermore, the rates of a vast number of reactions of theoretical as well as practical interest under all kinds of conditions may be c:dculated without recourse to experimentation. In the case of the decarboxylation of the high-melting cyclohexylmalonic acid (mp 180') in the fatty acids, klsoo may be calculated by use of the absolute reaction rate equation4 assuming an average value of A F * ~ to be 31.1 kcal/mole. When this is done, the rate constant at 180" turns out to be 0.0094 sec-' corresponding to a half-life of 73 sec. Similar calculations for oxamic acid (mp 210") yield k2100 equal to 0.086 sec-l corresponding to a half-life of only 8 sec. These results evidently would apply also to the decarboxylation of the molten acids at their melting points. These rates are too rapid for accurate measurement with the apparatus employed in this research. It should be pointed out that the decarboxylation of malonic acid in a l c o h o l ~ , ~cresols," J~ and aniline and its derivatives12 forms three separate reaction series all having the same isokinetic temperature as that for the reaction in fatty acids (namely, 135") but with different values of AF' (see ref 4). However, not all reaction series involving decarboxylation show isokinetic temperatures corresponding to the melting points of the substrates. For example, the isokinetic temperature of the reaction series formed by the decarboxylation of oxanilic acid (mp 150") in ethers is 135" (see Table IV). Similarly, the isokinetic temperature of the reaction series consisting of the decarboxylation of n-butylmalonic acid (mp 105") in cresols is 150" (see Table VI). The interesting fact remains, however, that the various isokinetic temperatures
305
shown by all the reaction series under discussion appear to differ from one another by integral multiples of 15". It is hoped that a theoretical explanation of these puzzling results will soon be forthcoming. ~
Table V : Activation Parameters for the Decarboxylation of Oxanilic Acid in Ethers" AH
Solvent
A S f,
AF
*l~o,
eu/mole
kcal/mole
28.3 31.3 32.6 35.6 36.8 40.1
-6.6 0.7 4.0 11.1 14.2 22.1
31.0 31.0 31.0 31.07 31.0 31.0
n-Amyl ether
~ ~8-Chlorophenetole ~ Phenetole Anisole Dibenzyl ether %-Hexylether a
*,
kcal/mole
L. W. Clark, J . Phys. Chem., 66, 1453 (1962).
Table VI : Activation Parameters for the Decarboxylation of n-Butylmalonic Acid in Cresolso AH
Solvent
Phenol p-Cresol m-Cresol 0
*,
kcal/mole
36.2 24.0 29.7
A S f,
AF *iw0,
eu/mole
kcal/mole
13.0 -15.8 -2.3
30.7 30.7 30.7
L. W. Clark, J. Phys. Chem., 68, 587 (1964).
Acknowledgment. Acknowledgment is made to the donors of the Petroleum Research Fund, administered by the American Chemical Society, for support of this research. (9) L.W.Clark, J. Phys. Chem., 64, 508 (1960). (10) L. W.Clark, ibid., 64, 677 (1960). (11) L. W. Clark, ibid., 67, 526 (1963). (12) L. W.Clark, ibid., 62, 79 (1958).
Volume 71, Number 2 January 1067
