LOUISWATTSCLARK
2602
VOl. 67
THE KINETICS OF THE DECARBOXYLATION OF HEXYLMALONIC ACID IN THE MOLTEN STATE AND IN SOLUTION BY LOUISWATTSCLARK Department of Chemistry, Western Carolina College, Cullowhee, North Carolina Received M a y 22, 1963
Kinetic data are reported for the decarboxylation of hexylmalonic acid in the molten state between 110 and 160' and of hexylmalonic acid in three solvents: ethylene glycol, 1,3-butanediol, and 1,4-butanediol between 110 and 140". The parameters of the absolute reaction rate equation are calculated. The isokinetic temperature for the reaction series, calculated by the method of least squares, is found to be 214.5", about 109' above the melting point of the reactant.
The decarboxylation of malonic acid in the molten state and in solution has been the subject of many kinetic investigations during the past five decades. It has been shown that the rate-determining step of this reaction is the formation of an activated complex between solute and solvent molecules, the solute acting as an electrophilic agent, the solvent being the nucleophilic agent.lb An unlimited number of derivatives of malonic acid may be prepared according to standard procedures, all of which may undergo decarboxylation under suitable conditions. The existence of a large group of closely related compounds such as this, all capable of undergoing the same type of reaction, makes possible a study of the electronic and steric effects of various substituents on the decarboxylation of the molten material, and of the differences in the effects of various solvents on the decarboxylation of the derivatives. To date relatively few studies have been made on the decarboxylation of malonic acid derivatives. Data on the decarboxylation of cinnamalmalonic acid in various amines2 and phenols,a and of benzylmalonic acid in the molten state4 as well as in several fatty acids and phenolsa have been reported previously. In the present paper data are reported on the decarboxylation of hexylmalonic acid in the molten state as well as in three glycols: ethylene glycol, l,&butanediol, and 1,4-butanediol. Experimental Reagents.-The hexylmalonic acid used in this research was obtained commercially. It assayed 99.6% pure and melted a t 105-106' (cor.). After recrystallization from benzene it melted a t 105.5-106.5' (cor.) and assayed 99.8% pure. The solvents were reagent grade and were redistilled a t atmospheric pressure immediately before use. Apparatus and Technique.-The method of investigation consisted in introducing a fragile glass capsule containing a weighed quantity of the hexylmalonic acid into a reaction flask immersed in a constant temperature oil bath controlled to et0.05'. The thermometer used to read the temperature of the oil bath was graduated in tenths of a degree and was calibrated by the U. S. Bureau of Standards. All necessary corrections were applied to the thermometer in order to calculate the correct temperature. These corrections were (1) a steam point correction: (in applying this correetion the value of the boiling point of water a t the barometric pressure was needed. The barometric pressure was read, and three corrections were applied t o this reading (a) the temperature correction, ( b ) the latitude correction, and (c) the altitude correction); (2) a stem temperature correction in case the (1) (a) C.N.Hinshelwood, J . Chem. Soc., 17,156 (1920); (b) G.Fraenkel, R. L. Belford, a n d P. E. Yankwich, J . Am. Chem. Soc., 76, 15 (1954); ( e ) L. W. Clark, J . Phys. Chem., 67, 138 (1963); (d) L. W. Clark, i b i d . , 67, 526 (1963),a n d numerous previous papers in this series. (2) L. W. Clark, ibid., 66,836 (1962). (3) L. W. Clark, ibid., 67,1481 (1963). (4) L. W. Clark, ibid., 67, 138 (1963).
thermometer was not totally immersed in the oil bath; (3) the Bureau of Standards correction. The COZevolved during the course of the reaction was collected in a buret connected to a leveling bulb filled with an entraining liquid. This liquid consisted of a solution 20% by weight of sodium sulfate and 570 by volume of sulfuric acid, colored with methyl red. The solubility of COz in this solution is negligible. The vapor pressure of this solution had to be subtracted from the observed corrected barometric pressure in converting the observed gas volumes to STP. The vapor pressure was calculated using Raoult's Law and the activity coefficients of the two electrolytes. It was found to be 91.0% of the vapor pressure of pure water. The buret, which was calibrated by the U. S. Bureau of Standards, was surrounded by a water jacket through which tap water was allowed to flow. The temperature of the water in the water jacket was read by a calibrated thermometer. During the course of an experiment the water jacket temperature remained essentially constant, the greatest variation being but a few tenth's of a degree. Room temperature rarely changed more than f1' during an experiment. During a typical experiment dated February 5,1963, a sample of hexylmalonic acid weighing 0.3382 g. was introduced in the usual manner into the reaction flask immersed in the oil bath maintained a t 161.26' (cor.). This amount of sample (0.3382 g.) is that which is required to furnish exactly 40.0 mi. of COz a t STP on complete reaction. This value is obtained by calculation based not upon the molar volume of an ideal gas but upon the actual molar volume of COz a t STP, namely 22,267 ml. The reaction vessel was the same as that used in studying the decarboxylation of oxanilic acid and other unstable acids.6 The waterjacket temperature stayed a t 8.2 i 0.2", room temperature was 29.2 i 0.5'. The half-life of the reaction under these conditions was about 5 min. At the end of 1 hr. the final volume of the evolved COz was exactly 39.8 ml. a t STP. I n studying the decarboxylation of hexylmalonic acid in the various solvents, a three-necked, standard taper 100-ml. Pyrex flask, provided with a mercury seal stirrer and reflux condenser, was used as described previously.6 A GT-21 Motor controller was used to control the stirrer.
Results 1. The Decarboxylation of Hexylmalonic Acid in the Molten State.-Samples of hexylmalonic acid weighing 0.3382 g. were decarboxylated as described a t eight different temperatures between 110-160°. Two or three experiments were carried out a t each temperature. Two or three experiments were carried out a t each temperature. Smooth first-order kinetics prevailed over the first 90% or so of the reaction. Averagevalues of the first-opder rate constants, calculated from the slopes of the experimental logarithmic plots, are shown in Table I. The plot of log k / T us. 1 / T is linear for this reaction (see Fig. l),indicating that the enthalpy of activation is constant over the entire range of temperature. 2. The Decarboxylation of Hexylmalonic Acid in Several Glycols.-Samples of hexylmalonic acid as before were decarboxylated in each solvent a t four dif( 5 ) L. W. Clark, ibid., 66, 125 (1962).
(6) L. W. Clark, {bid., 60, 1150 (1956).
KIXETICS OF DECARBOXYLATIOLU. OF HEXYLNALONIC ACID
Dec., 1863
2603
TABLE I F I R S F O R D E R RATECONSTANTS FOR THE DECARBOXYLATION OF HEXYLMALONIL ACIDI N THE &fOLTEN STATE Temp., "C. (cor.)
110.62 120.74 130 72 138.90 141.12 149.10 151.94 161.26
IC
x
104, sec. -1
0.150 0.470 1.32 2.94 3.79 7.85 10.1 23.3
Av. dev.
i
0.002 .005 .01 .01 .02 .02 .04 .08
-7.2
,
-7.0
1 r
-6.8
-6*6
g 1-::; 6.0
-5.8
-5.4/ -5.6
ferent temperatures over about a 30" range of temperature. Two experiments were conducted a t each temperature in each solvent. Excellent first-order kinetics were observed in every experiment over more than three-fourths of the reactiol?. Table I1 lists the average values of the first-order rate constants for the reaction in the various solvents a t the different temperatures studied.
Ethylene glycol
1,3-Butanediol
1,4-€3utanediol
Temp., O C . (cor.)
111 12 120.40 129.10 139.32 110.84 120.04 129.00 139.12 110 84 119.86 129.00 139.37
k X 104, sec.-l
Av. dev.
2 04 i 0.02 4 29 .03 8.34 .04 17.7 .1 3.08 .02 6.10 .02 11.6 .07 23.2 .I 3.27 102 6 37 .02 11.9 .05 24.6 .1
3. Activation Parameters for the Reaction.-By applying the method of least squares to the data in Tables I and I1 the ,activation parameters for the reaction were calculated using the absolute reaction rate equation'
The values thus obtained are shown in Table 111. TABLE I11 ACTIVATION PARAMETERS FOR THE DECARBOXYLATION OF HEXYLMALONIC ACID ALONEASD I N SOLUTION Solvent
AH*, kcal./mole
AS*. e.u./mole
Melt Ethylene glycol 1,3-Butanediol 1,4-Butanediol
32 2 23.4 21.6 21.3
+2.8 -15.2 -18 9 -19 6
Discussion A comparison of the activation parameters for the decarboxylation of molten hexylnialoiiic acid with those previously obtained for the parent acid and another derivative, benzylmalonic acid, is shown in Table IV. In the case of both malonic acid derivatives shown in (7) S. Glasstone, K. J. Laidler, and H. E y n n g , "The Theory of R a t e Processes," McGraw-Hi11 Book Company, Inc., New York, IV. Y., 1941, p. 14.
!-L
1
1
234
238
1
1
1
1
1
242
246
250
254
258
1,/T X 106.
Fig. 1.-The
decarboxylation of hexylmalonic acid in the molten state.
TABLE IV ACTIVATION PARAMETERS FOR THE DECARBOXYLATION OF HEXYLMALONIC ASD ITS DERIVATIVES Reactant
TABLE I1 APPARENTFIRST-ORDER RATECONSTANTS FOR THE DECARBOXYLATIO~Y OF HEXYLMALOSIC ACIDIN SEVERAL GLYCOLS Solvent
1
a
Malonic acid" Hexylmalonic acid Benxylmalonic acid" See. ref. 4.
AS*,
AH*, kcal./mole
e.u./mole
35 8 32.2 29 4
+11.9 +2.8 -2.6
Table IV, the AH* of the reaction is lowered by the presence of a single substituent group on the central methylene group of malonic acid. The lowering is greater for the benzyl group than it is for the n-hexyl group. Since the benzyl group has a much greater tendency to release electrons than does an alkyl group, all malonic acid derivatives containing a single alkyl group may be expected to have activation enthalpies intermediate between those for malonic acid and benzylmalonic acid. In the case of the two derivatives shown in Table IV it will be seen that the entropy of activation of the reaction decreases with increasing size of the substituent group. The velocity constants of the reaction in the three glycols a t the temperatures studied are may times greater than those of the free acid as shown by Tables I and 11. For example, a t 130°, the rate of reaction in 1,3-butanediol is 10 times as fast as it is in the molten state. Stated another way, at 130" the half-life of the decarboxylation of the free acid is 90 min., whereas in 1,3-butanediol it is 9 min. The velocity constants, at any given temperature, increase as the distance between the two hydroxyl groups increases, The enthalpies of activation of the reaction in the glycols are very much smaller than that of the free acid as shown in Table 111. For example, for the reaction in 1,4-butanediol A H + is 10.5 kcal./mole lower than it is for that in the free state. Studies have been made previously on the decarboxylation of malonic acid in the molten state4 and in glycerol.8 These studies show that for the reaction in glycerol AH* is 11.2 lical./mole lower than it is for that of the molten acid. Figure 2 is a plot of AH* us. AS* for this reaction series. A good linear relationship appears to obtain for the four sets of parameters. Tne equation for this line, obtained by the method of least squares, is ( 8 ) L.
W.Clark, J. Phys. Chem., 60, 826 (1956).
LOUISWATTSCLARK
2604
32
d 30
5;
fi
I ++
28 26
2 24 22 I
~
1
- 15
~~
I
I
- 10
-5
I
I
0
designate the range of AH* values for a particular reaction series by dAH*. Evidently, therefore, the ratio dAH*/26 is a measure of the reliability of the given series of measurements. This ratio must be at least equal to unity if any observed AH* - AS* relationship can he assumed to be valid, and it must be much greater than unity if any details of the relationship can be inferred with confidence. The maximum possible error in AH*, which we have called 6, may be calculated by the following formula as shown by Petersen and co-workers12
AS*, e.u./mole.
T'T 6=R-----ln-
Fig. 2.-Enthalpy-entropy plot for the decarboxylation of hexylmalonic acid in the molten state and in several glycols.
AH* = 487.7AX*
+ 30,830
The slope of the line is thus seen to be 487.7"K., corresponding to 214.5"C. This slope is the so-called isokinetic temperature. The isokinetic temperature is the temperature a t which the rate of reaction is equal in all the solvents conforming to the Since the melting point of hexylmalonic is 106", the isokinetic temperature for this reaction series is about 109" above the melting point of the reactant. This may be compared with results obtained previously for the rearrangement of triphenylmethylazide in several solvents. lo The isokinetic temperature for the reaction series was found to be 194". Since the melting point of the reactant is 65", the isokinetic temperature in this case is 129" above the melting point of reactant. I n the present reaction series the isokinetic temperature is about 90" above the midpoint of the temperature range used in this research. An analysis of 81 reaction series reported in the literature showed that 32% have isokinetic temperatures more than 100" above the midpoint of the experimentally investigated temperature region.ll Petersen and co-workers12 have shown that the positive demonstration of any kind of linear relationship between the enthalpy and entropy of a reaction taking place in different solvents is extremely difficult due to the nature and magnitude of the experimental errors. When AX* and AH* are measured for a series of reactions using the same two temperatures T and T' throughout the series, the error in AS* is directly proportional to the error in AH*. iZ AH* - AX* plot which is linear with each point lying on the line is very likely a demonstration of experimental error according to these authors. For any given reaction the maximum possible error in AH* can be readily calculated on the basis of the maximum possible fractional error in the rate constant. If we designate the maximum possible error in AH* in the positive direction by 6, then 26 will be the total maximum possible error in AH*. We may (9) S. L. Friess, E. S. Lewis, and A. Weissberger, Ed., "Technique of Organic Chemistry, Volume V I I I , P a r t I, Investigations of Rates and Mechanisms of Reactions," 2nd Ed., Interscience Publishers, Ino., New York, N. Y., 1961, p. 207. (10) W. H. Saunders, Jr., and J. C. Ware, J . A m . Chem. Soc., 80, 3328 (1958). (11) J . E. Leffler, J . Org. Chem.. 2 0 , 1202 (1955). (12) R. C. Petersen, J. H. Markgraf, and S.D. Ross, J . A m . Chem. floc., 75, 3819 (1961).
Vol. 67
(1
T' - T
+ a)
(1 - a )
where a is the maximum possible fractional error in the rate constant and T' and T' are the upper and lower temperature limits, respectively. If a
