TEMPERATURE COEFFICIENTS OF T H E DECOMPOSITION OF ACETONE DICARBOXYLIC ACID I N WATER*
BY EDWIN 0 . WIIG
The decomposition of acetone dicarboxylic acid in aqueous solution has previously been studied' at 40°, joo, and 6ooC. The reaction was found to be unimolecular and may be represented by the equation
+
CO(CH2COOH)z--+(CH3)zCO 2 Con, the rate of reaction having been followed by measuring the volume of carbon dioxide liberated. The object of the present work was to measure the velocity of decomposition down to 0°C. in order to test, over a wide range of temperatures, the Arrhenius equation expressing the relation between absolute temperature and the velocity constant. Materials and Procedure The acetone dicarboxylic acid was prepared and purified as described in the earlier work. The water in which the acid was dissolved was ordinary laboratory distilled water which had been boiled vigorously to remove carbon dioxide. The aqueous solution of acetone dicarboxylic acid was placed in an 8" Pyrex test tube which was immersed in a thermostat. At oo the Pyrex test tube containing the reaction mixture was placed in a thermos bottle containing ice and water, and this bottle was kept in a jar of ice water. The rate of decomposition was followed by titrating the undecomposed acetone dicarboxylic acid with N / I O NaOH. Since carbon dioxide is one of the products of decomposition and would be titrated by the alkali, it was necessary to remove it. This was accomplished by bubbling a stream of nitrogen or oxygen gas rapidly through the solution. The velocity constant obtained at 4oOC. by this method checked very well with that previously determined gasometrically, the two values for k x 1 0 4 being 57.6 and 5 7 . 0 respectively. This indicates that the method used is satisfactory. Results The results obtained are summarized in Table I, the data for 50' and 6ooC. having been taken from the previous work. The value of k, the velocity constant, was calculated from the well known equation for a mono-molecular reaction, The velocity constant increased slightly in any one experiment but was constant between j o % and 7570decomposition. The values of k *,Contribution from the Laboratories of General Chemistry of the University of Wisconsin. Presented a t the Seventy-Seventh Meeting of the American Chemical Society, Columbus, Ohio, April 29-May 3, 1929. 1 J. Phys. Chem., 32, 961-81 (1928).
ACETONE DICARBOXYLIC ACID IN W A T E R
597
given in the table are the average of the velocity constants obtained between soyo and 7 5 % decomposition in three experiments, except at o°C. in which case k is the average obtained from two experiments.
TABLE I Effect of Temperature on the Reaction Rate Initial Concentration of Acetone Dicarboxylic Acid = 68.5 mols. per liter Temp. "C.
K
x
Temperature Coeff.
104
60
5 48
50
185
40
57.6
30
16.3
20
4.35
IO
I .08
Critical Increment (E)
. . . . . . . . . . . . . . 2.96 . . . . . . . . . . . . . . . 23,100 . . . . . . . . . . . . . . . . 3 . 2 5 . . . . . . . . . . . . . ..23,600 ...............3.53..............
,23,700
. . . . . . . . . . . . . .. 3 . 7 5 . .. . . . . . . . . . . ..23.200
. . . . . . . . . . . . . . .4 . 03 . . . . . . . . . . . . . . .22,900 . . . . . . . . . . . . . . .4.39.. . . . . . . . . . . . . .22,600
0
0.246
The value of the critical increment, E, was calculated from the Arrhenius equation l n- k E -d= dT RTZ using the integrated form 1.98 Tz X TI X 2.303 log kp/ki, E = Tz - Ti where kp and kl are the velocity constants a t the absolute temperatures Tz and Ti and E is expressed in calories. The values of E vary somewhat but are about within the limits of experimental error, the maximum deviation from the mean value of E being about 3%. The fact that the value of E has been found t o be constant within the limits of experimental error over the temperature range oo to 60°C. indicates that the Arrhenius equation holds true.
-S The rate of decomposition of acetone dicarboxylic acid in aqueous solution has been measured at 0, IO, 20, 30, and 4oOC. 2. The critical increment, E, has been calculated from the temperature coefficients obtained. 3. The value of E was found to be constant within the limits of experimental error over the temperature range oo to 60°C., indicating the validity of the Arrhenius equation. I.
Madison, Wisconsin
