R. P. JENSEN, E. M. EYRING, AND W. M. WALSH
2264
Rapid Reactions in Methanol-Water Solvents'
by Ronald P. Jensen,2 Edward M. E ~ r i n gand , ~ William M. Walsh Department of Chemistry, University of Utah, Salt Lake City, Utah 84112 (Received January 24, 1966)
Acid dissociation constants in water-methanol solvents ranging in methanol concentration up to 80 vol. % have been measured potentiometrically for the following dicarboxylic acids: maleic acid, citraconic acid, di-n-butylmalonic acid, and ethylisopropylmalonic acid. Temperature-jump relaxation method measurements of the rate constant, k , for the reacLO- + A2LOH, where HA- denotes the sample acid monoanion and tion HAL denotes either H or CH3,have also been carried out with these acids in the same solvents. Plots of log k vs. the reciprocal dielectric constant are linear up to 50 vol. % methanol. Over this linear portion we have applied Hiromi's electrostatic equation. This is a modification of earlier theoretical work by Laidler and Landskroener based on ITirkwood's calculation of the dependence of the activity coefficient on dielectric constant. This interpretation of our data points to a nonlinear symmetrical transition-state structure for the abstraction of a proton from the intramolecularly hydrogen-bonded monoanion.
+
+
Several kinetic studies of the rapid reaction
+
kza'
+
LALOA2L20 (1) in water and in deuterium oxide, where L represents a hydrogen atom when water is the solvent or a deuterium atom when D 2 0 is the solvent and LA- is the monoanion of a dicarboxylic acid having a ratio of dissociation constants K,,/K,, 2 lo4,have been carried out in this laboratory.*-' The results are consistent with the postulates that an intramolecular hydrogen bond exists in the monoanion of such acids. The measured deuterium oxide solvent kinetic isotope effect k23tH/k23tD'v 2 for the forward reaction and Brgnsted acid catalysis plots indicate a rate-determining proton transfer with L+ bonded equally strongly to A2- and LO- in the activated complex. I n the experiments described below, we have made temperature-jump measurements of the rate constants of equilibrium 1 for several simple acids in methanol-water solvents a t 25" ranging in coniposition from 0 to 0.65 mole fraction of methanol. We have also determined acid dissociation constants in the mixed solvents for maleic, citraconic (i.e., methylmaleic) , ethylisopropylmalonic, and di-n-butylmalonic acids and for 0-cresol sulfonephthalein (ie., cresol red). These data permit us to identify the transition state of reaction 1 as being a nonlinear symmetric configuration, thus demonstrating the utility of extending temperature-jump kinetic studies into mixed solvent media. The Journal of Physical Chemistry
Experimental Section Di-n-butylmalonic and ethylisopropylmalonic acids were obtained from basic hydrolysis of readily available substituted malonic esters. Both acids were recrystallized from water-acetone and melted sharply a t literature values. Maleic acid was obtained from the anhydride by hydrolysis in neutral aqueous solution and recrystallized from ether. Both the citraconic acid (J. T. Baker) and the cresol red (Eastman) were used as obtained. A check on purity was provided by the end points of the titrations, and in all cases errors were less than 1%. Solvents were prepared volumetrically from freshly boiled absolute methanol (Malinckrodt) and doubly dis(1) Abstracted from a Ph.D. Thesis submitted by R. P. Jensen to the Graduate School, University of Utah, Feb 1966. Acknowledgment is made to the donors of the Petroleum Research Fund, administered by the American Chemical Society, for support of this research and to the University of Utah Research Fund for an equipment grant. (2) American Chemical Society Petroleum Research Fund Fellow, 1963-1966. (3) To whom communications should be addressed. (4) J. L. Haslam, et al., J. Am. Chem. Sac., 8 7 , 1 (1965). (5) J. L. Haslam, et al., ibid., 87, 4247 (1965). (6) M. H. Miles, et al., J . Phys. Chem., 69, 467 (1965). (7) hf. H. hfiles, E. M.Eyring, W. W.Epstein, and M.T. Anderson,
in preparation. (8) For a bibliography, see L. Eberson and I. Wadso, Acta Chem. Scand., 17, 1552 (1963).
RAPIDREACTIONS IN METHANOL-WATER SOLVENTS
2265
These constants are related to the thermodynamic acid dissociation constants KaT by the relation15
tilled, freshly boiled water. Solvents were stored in polyethylene bottles protected from atmospheric C02 and moisture, and delivered from these containers by siphon. Experiments conducted using freshly prepared solvent as well as solvent that had been stored up to 60 days showed no significant differences. Solvent compositions are designated herein as volume per cent defined by the relationg vol. % CH,OH = [VCH~OH/(~CH,OHVHz0) ] x 100. Carbonate-free KOH was prepared by a method based on that of Armstronglo and was standardized against potassium hydrogen phthalate with potentiometric determination of the end point. Our temperature-jump and potentiometric titration techniques were essentially the same as previously des~ribed.~.6The validity of glass electrode determinations of hydrogen ion activity in methanol-water
with an analogous relation for the second dissociation constant. Large values (>>lo4) for the ratio KaIM/KaZM have been attributed to intramolecular hydrogen bonding in the monoanion of an acid.16 It is interesting to note that the increase in the ratio KaIM/ KalMas the per cent methanol in the solvent increases is much more pronounced for those acids for which intramolecular hydrogen bonds in the monoanion have been postulated. (See Table 11.) Kinetic Data. The complete reaction scheme for our sample system in basic methanol-water media is given by relationship 3 which is shown below
+
0
+ HIn- + He0 + CHsO-
HA-
HA-
0
+ In2- + H20 + CHsOH HA-
. It
\ A*-
0
+ HIn- + H20 + CHaOH
(3)
+ HIn- + OH- + CHsOH 0
media has been established.ll Our electrodes were required to perform stably in aqueous media over the pH range of 3-11 before being accepted for work in mixed media. A glass electrode was equilibrated for at least 24 hr in a given mixed solvent prior to actual use. When not in use, electrodes were stored in solvent having the same composition as that in which they were equilibrated. Each glass electrode was standardized in buffered solvents of the same methanolwater composition as those in which it was used. We ~ employed the buffers proposed by Bates, et U E . , ~ and Deligny and Rehbach.I3 In conducting temperaturejump experiment,son methanol-water solutions, the decreasing heat capacity with increasing methanol contentf4required lower voltages for the higher methanol content solvents to induce equivalent temperature jumps. The high methanol-water content solutions are especially susceptible to cavitation; hence temperature jumps as small as 5” were frequently employed. In all cases the initial temperature was adjusted to yield a final temperature of 25’.
Results and Discussion Equilibrium Data. In Table I we have assembled mixed acid dissociationconstants KaMfor the acids used.
where HA- is the monoanion of a dicarboxylic acid and HIn- is the monoanion of cresol red. Such a scheme would lead to a spectrum of relaxation times; however, over the time range being examined to sec) only one relaxation was, in fact, observed. Equilibria @ f-) 0, 0 cf 0,and 0 c-) 0 involve proton exchange between nonintramolecularly hydrogen bonded species and hence should have rate constants characteristic of diffusion-controlled processes.’’ Such reactions would have relaxation times of the order of 1 psec or less and hence would not be observed. We are (9) C.Carr and J. A. Riddick, I d . Eng. Chem., 43, 692 (1951). (10) D. M.G.Armstrong, Chem. I d . (London), 1405 (1955). (11) A. L. Bacarella, et al., J . Phy8. Chem., 62, 856 (1958). (12) R. G. Bates, M. Paabo, and R. A. Robinson, ibid., 67, 1833 (1963). (13) C. L. Deligny and M. Rehbach, Rec. Trav. Chim., 79, 727 (1960). (14) “International Critical Tables,” Vol. 5, 1st ed, 1929, p 116. (15) A. Albert and E. P. Serjeant, “Ionization Constants of Acids and Bases,” Methuen and Co., Ltd., London, 1962. (16) D. H.McDaniel and H. C. Brown, Science, 118, 370 (1953). (17) M.Eigen and L. DeMaeyer, “Technique of Organic Chemistry,” Vol. VIII, Part 11, 5. L. Friess, E. 9. Lewis, and A. Weissberger, Ed., Interscience Publishers, Inc., New York, N. Y., 1963, Chapter 18.
Volume 70, Number 7 Julu 1966
2266
R. P. JENSEN,E. M. EYRING, AND W. M. WALSH
~~
Table I: Mixed Acid Dissociation Constants' in Methanol-Water Solvents at 25' VOl. y* CHaOH
Acid
Di-n-bu ty lmalonic
0 25
40 70 80
Ethylisopropylmalonic
0 25 40
70
80 Maleic
0
Citraconic
Cresol red
Insol. Insol.
(1.79 i 0.11) x 10-3 (4.27 i 0.13) X 10-4 (2.06 f 0.04) x 10-4
4.36 (5.35 (1.00 (1.52 (6.90
x x
10-10 10-11
9.34 x 10-3b (3.10 f 0.18) X 10-8 (4.37 f 0.40) x 10-3 (6.44 0.11) x-10-4 (4.21 f 0.49) x 10-4
7.94 x 10-9b (1.38 f 0.10) x (2.19 f 0.24) x (3.21 f 0.17) x 0.07) X (1.52
10-9 10-10 10-11 10-11
25 40 70 80
1.20 (4.73 (4.64 (2.95 (2.88
0 25 40 70 80
5.14 (1.19 (2.36 (5.56 (3.06
0 25 40 70 80
x
10-2c
f 0.03)
f 0.26)
x 10-7c f 0.05) f 0.12) f 0.08) f 0.08)
x x x
10-8 10-3 10-3
5.95 (1.65 (4.66 (6.34 (3.00
x f 0.48) x f 0.11) x f 0.12) x (6.16 f 0.40) x (3.07 f 0.11) x (7.00 f 0.33) x (2.91 f 0.12) x (1.46 f 0.02) x
10-3 10-3 10-4 10-4
7.15 x 10-7d (2.49 i 0.19) x (5.99 f 0.56) X (1.13 f 0.04) X (6.31 i 0.53) x
f 0.76) X 10-3
f 0.22) f 0.26) i 0.19)
x
10-3
f 0.05)
Averages of 10-20 values tabulated with mean deviations. See ref 6. Ashton and J. R. Partington, Trans. Faraday SOC.,30,598 (1934).
then concerned only with reactions involving abstraction of a proton from the hydrogen-bonded monoanion. Since investigations in water and D204-'indicated that in such a reaction the rate-determining step is cleavage of the intramolecular hydrogen bond, we propose the following 5t9 the most probable representation of the observed relaxation
HA-
X 10-Eb
f 0.71) X 10-9 f 0.08) X 10-9
+ HIn- 4- LO-
x lo-' x lo-* x 10-9 x 10-0 10-7 10-8 10-8 10-9
10-9 10-9 10-10 10-10 10-10
W. H. German, et al., Phil. Mag., 22,790 (1936).
H. W.
Table 11: Ratios of Mixed Acid Dissociation Constants for Water and 80 Vol. % Methanol Acid
Ha0
(KaiM/KarM) 80
Fumaric Maleic Succinic Diethylmalonic
32 204,000 23 850,000
41 1,820,000 30 3,160,000
(KniM/KaaM)
matical techniques'g leads to the following expression for the rate of proton abstraction by lyate ion
O where L is taken hereafter to represent H or CHa. In equating the two bases OH- and CHaO-, we are assuming the difference in their basicities is not important; for OH- in water pKb = -1.74 and for CHaO- in water pKb = -0.86.'* Application of known matheThe Journal of Physical Chemistry
(18) J. Koskikallio, S m e n Kentistilehti, JOB, 111 (1957). (19) G. W. Castellan, Ber. Busenges. Physik. Chem., 67, 898 (1963).
RAPIDREACTIONS IN METHANOL-WATER SOLVENTS
2267
Table I11 : Relaxation Spectra‘ of Di-n-butylmalonic Acid in 0.05 -44 Ionic Strengthb Methanol-Water Solvents for the Reaction HA-
+ LO- --%A2- + LOH ha,’
In applying ecl 5 to our rate data, we utilized values for K , = ULOH, + ULO - reported by I
