3490
M. MILES, E. EYRING, W. EPSTEIN, AND nf. ANDERSON
Deuterium Oxide Solvent Isotope Effects on Fast Reactions of Substituted Malonic Acids’
by Melvin H. Miles,2 Edward M. Eyring, William W. Epstein, and Michael T. Anderson3 Department of Chemistry, University of Utah, Salt Lake City, Utah 84118
(Received A p r i l 18, 1966)
Acid dissociation constants have been determined by potentiometric titrations, and rate constants have been determined by the temperature-jump relaxation method in D20 for a series of seven substituted malonic acids that had been studied previously in water using OD- --t A-2 D20 where DAthe same techniques. The reaction of interest is DArepresents the monoanion of a malonic acid in D20 solvent. The slope of a Brfinsted plot of the data indicates that in the transition state the proton is about equally bonded to the A-2 dianion and the OH- ion. The reaction is slower in D20 than in water, indicating a rate-determining proton transfer. These results are discussed in terms of an intramolecular hydrogen bond postulated to exist in such malonic acid monoanions.
+
Introduction The expected value for the ratio of the ionization constants K1/K2 for dicarboxylic acids is 4 from statistical considerations. Striking departures from this statistical value which have been observed for some dicarboxylic acids have been interpreted in terms of electrostatic eff ects5 or by postulating the existence of an intramolecular hydrogen bond in the monoanion.6 Reaction rate studies by the temperature-jump method have been interpreted in terms of intramolecular hydrogen bonding in highly substituted malonic acid monoanions;’~~ in fact, the experimental rate constants for the following reaction in water HA-
+ OH- k23: A-2 + 1120
(1)
where HA- represents the monoanion of several homologous series of dicarboxylic acids, appear to be an excellent index to the relative strength of this Kinetic isotope effects are reported here to test the proposal that the rate-determining process in reaction 1 involving malonic acids is a proton transfer. Further, a Brflnsted plot is used to characterize differences in the bonding of this proton to the solvent in reactant and activated states.
Experimental Section Synthesis. The methyl(1-methylbuty1)-, diethyl-, The Journal of Physical Chemistry
+
ethylisoamyl-, ethylphenyl-, and ethylisopropylmalonic acids were prepared by base hydrolysis of the readily available substituted malonic acid esters. Diisopropylmalonic Acid. To a solution of 33 g (0.25 mole) of dimethyl malonate in 400 ml of dry benzene was slowly added 11 g (0.27 mole) of sodium hydride (as a 56% mineral oil dispersion). The reaction mixture was heated until hydrogen was no longer evolved, and 43 g (0.30 mole) of isopropyl iodide was added. The reaction mixture was refluxed for 12 hr and washed with water to remove the precipitated sodium iodide. The solution was dried by distilling (1) This research was supported in part by the Nationd Institute of Arthritis and Metabolic Diseases (Grant AM-06231) and the University of Utah Research f i n d . (2) This is an essential portion of a the& submitted to the Chemistry Department, University of Utah, in partial fullilment of the requirements of a Doctor of Philosophy Degree, 1966. (3) National Science Foundation Undergraduate Research Par-
ticipant. (4) J. F. King, “Technique of Organic Chemistry,” Vol. XI, Part I, A. Weissberger, Ed., Interscience Publishers, Inc., New York, N. Y., 1963, pp 318-321. (5) H. M. Peek and T. L. Hill, J . A m . Chehen. Soc., 7 3 , 5304 (1951). (6) L. Eberson and I. Wadso, Acta Chem. Scand., 17, 1552 (1963). (7) M. Eigen, Angew. Chem., 7 5 , 489 (1963). (8) M. H. Miles, E. M. Eyring, W. W. Epstein, and R. E. Ostlund, J . Phys. Chem., 69,467 (1965). (9) J. L. Haslam, E. M . Eyring, W. W. Epstein, C;. A. Christiansen, and M. H. Miles, J . A m . Chem. Soc., 87, 1 (1965).
DEUTZRIUM OXIDESOLVEVT ISOTOPE EFFECTS
3491
Table I: Mean Values for Mixed” Ioriization Constants in Water and DtO a t 25.0 f.0.1” Determined in 0.100 F KCl Solutions* (Estimated Error. is k0.06 pK Unit. for pK1 and k0.03 p K Unit for p&) Malonic wid
Isopropyl Methyl (l-inet,li,vL butyl) Diethyl Ethylisoarnyl Ethylpheilyl Ethylisopropyl Diisopropyl
pKiH
PKP
2.79 2.79
3.32 3.42
2.09” 2.09” 1.6c l.gc 2.06’
2.67 2.67 2.00 2.37 2.71
_ _
- PKlH
-
pKP
PKP
0.53 0.63
5.57 6.64
6.07 7.14
0.50 0.50
600 7,100
0.58 0.58 0.4 0.5 0.65
7 . 06c 7.31 7.10’ 8.07’ 8.58’
7.50 7.68 7.45 8.42 8.93
0.44 0.37 0.35 0.35 0.35
93,000 170,000 320,000 1,500,000 3,300,000
PKlD
PKZD
pK2H
K:H/K*H
By ‘‘mixed’’ we mean K = 10-pHA/HA where HA is the concentration in moles per liter of the protonated form of the acid, etc. Superscript H ident’ifiesresults obtaiced by potentiometric titration with a glass electrode in solvent water; superscript D identifies the solvent as DzO. Slight discrepancies exist between these values and those reported in Table I of ref 8. Additional potentiometric titrations indicate that the present values are more accurate.
--
off the benzene-water azeotrope. The second isopropyl group was introduced by repeating the above procedure. The reaction mixture was worked up in the usual manner and distilled through a 24-in. spinningband column to give dimethylisopropyl malonate, bp 63-68’ (3 mm), which could be further alkylated as described above and 7.0 g (13y0 yield) of 95% pure dimethyl diisopropyl malonate, bp 75-80’ (3 mm). The infrared and particularly the nmr spectra were used to assign the structure of the dialkylated product. Since the methods reported for the hydrolysis of the ester to the diacid give poor yields,lo*‘lthe procedure of Chang and Wood1* mas rased. To 400 ml of a 1 N solution of pctassiuin tertiary butoxide in dimethyl sulfoxide mas added 5.0 g of dimethyldiisopropyl malonale, and the mixture was heated a t 100’ for 48 hr. The mixture was worked up as reported and gave after recrystallization from acetone and petroleum ether 2 g (50% yield) of the pure acid, mp 199’ dec (lit. 198’ dec). T h t isopropylmalonic acid was prepared by base hydrolysis of the dimethylisopropyl malonate obtained as described above.‘ All acids were recrystallized several times from the appropriate solvents, gave the reported physical properties, and had a purity of better than 99% according to titrations. Potentiometric Titra!iorzs. The ionization constants were determined as reported previouslys~ except that carbonate-free NaOH (NaOD) prepared by allowing metallic sodiuni in toluene to react with WzO (DZO) in a separatory funnel was used as the standard base rather than KOH prepared by an ion-exchange method. The base solutions were standardized against potassium biiodate, E(H(IO3)2,using B potentiometric end point. The Radiometer pH apparatus was standardized against solutions prepared from NBS buffer substancesla
-
such that the pH meter read correctly within 8.01 pH unit a t both pH 4.008 and 9.180. The standardization of the pH meter in DzO was by the methods reported in the 1 i t e r a t ~ r e . l ~ The ~ ~ acid ~ dissociation constants given in Table I are actually “mixed constants”’6 A/= where is approxidefined by K = mately17the hydrogen ion activity, U H +, Temperature-Jump Method. Our temperature-jump technique was the same as previously d e ~ c r i b e d . ~ ? ~ An IBM 7044 computer was used in calculating t,he individual rate constants.
Results and Discussion Normally, pKD - pKH tends to increase as pKH increases.’* For many dicarboxylic acids where the monoanion contains an intramolecular hydrogen bond, pKID - pKIH is unexpectedly large and pKzD- pKzE‘ is abnormally small. 19*20 However, for exceptionally strong internal hydrogen bonding in the HA- ion as in di-t-butylsuccinic acid, “normal” pKD - pKH values (10) F. C. B. Marshall, J. Chem. SOC.,2754 (1930);2336 (1931). (11) J. C. Shivers, B. E. Hudson, and C. R. Houser, J. Am. Chem. Soc., 66, 309 (1944). (12) F.C. Chang and N. F. Wood, Tetrahedron Letters, 2969 (1964). (13) R. G.Bates, J. Rea. Natl. Bur. Std., A66, 179 (1962). (14) P.K.Glasoe and F. A. Long, J . Phys. Chem., 64, 188 (1960). (15) R. Gary, R. G. Bates, and R. A. Robirson, ibid., 68, 3806 (1964). (16)A.Albert and E. P. Serjeant, “Ionization Constants of Acids and Bases,” Methuen and Co., London, 1962,p 57. (17) R. G. Bates, “Determination of pH-Theory and Practice,” John Wiley and Sons, Inc., New York, N. Y.,1964, pp 75-77, 91. (18) R. P. Bell, “The Proton in Chemistry,” Cornell University Press, Ithaca, N. Y.,1959, Chapter 11. (19) G. Dahlgren and F. A. Long, J. Am. Chem. Sac., 82, 1303 (1960). (20) A. 0. McDougall and F. A. Long, J . Phys. Chem., 66, 429 (1962).
Volume 70. Number 11 hTovember 1966
M. MILES,E. EYRINO, W. EPSTEIN,AND M. ANDERSON
3492
Table I1 : Arithmetic Mean Values of the Rate Constants kas' and Ic23' at 25" Determined by the Temperaturdump Method in Water and in DzO with the Ionic Strength Adjusted to 0.10 F Using KCl (Data Were Obtained Using o-Cresol Red Indicator Except as Noted) 6ar",O
Malonic acid
Isopropyl Methyl (l-methylbutyl) Diethyl Ethylisoamyl Ethylphenyl Ethyl isopropyl Diisopropyl
i,,","
id=,* M-X
88C-I
8ec -1
107 M-' 8ec-1
50 12
30 10
340 128
107 ~
-
1
107
5' 2.5 -3 1.4 0.55'
2.7 2.0 2.0 1 0.4
Crr'D,~
nd
107 M - 1 eec-1
43 15.5
5 12
-260 87.2
5.5 3.20 1.96 1.07 1.35
20 12 4 7
SC
23.5' 17.5 16.7 5.04 4.58'
11.5 9.44 8.47 3.24' 3.05'
9
;k?a"/ 8C
nd
kidD
4 4
1.5
176 12.7 3.78 2.75 3.36 0.61 0.68
11 11 6 10 6
2.0
1.9 2.0 1.6 1.5
Mean rat.e constant in water. * Mean rate constant in DzO. Standard deviation calculated from the range. Number of indeCombined pendent determinations. ' Combined average for experiments using phenol red and experiments using o-cresol red. average of experiments using phenolphthalein and experiments using 0-cresol red.
'
of -0.5 have been observed.21 We have observed experimentally (see Table I) that pK2D - pKzHvalues for a series of substituted malonic acids are 0.5 or less. In Table 11, we have rate constants kZ3' for reaction 1, which in our experiments was coupled to an acidbase indicator equilibrium.22 The values of k23' can be calculated from
form of the acid-base indicator, which was o-cresol red in virtually all the experiment,s reported here. Values of h a , the rate constant for the reaction HIn-
+ OH- +In+ + HzO
(6)
are known.23 Values for k331,the rate constant for the reaction
HA-
+ In-2 -+
A-2
+ HIn-
(7) given in Table I1 can be determined near pH 7 using the relation k23F2
-
kzsF2
+
ha2
- kta'R3
k33IF3
- 7i-l
>
(2)
where r1is the experimental relaxation time and
Fl=HA+OH p2= HIn
Kw + -= Ri + HA ~1K2
Kw = + OH + - +w n Y~KHI~ R2
(8) (3)
As we have shown previously,22 a high precision in kaa' is not essential for a calculation of good values of
(4)
k23'.
K2
Also, K2 = 10-PHX/HA, KHIn = 10-PHs/HIn, Kw = aHaoH, y1 is the activity coefficient of the hydroxide ion, and y2 is the activity coefficient of the hydrogen ion calculated with the Debye-Huckel limiting law. The bars over the chemical species denote equilibrium concentrations. HIn represents the protonated The Journal of Physiud Chemistry
In every case except that of isopropylmalonic acid, an F test indicates that the averages 523" and K23ID, for a given acid may be legitimately compared. Student's 1 test then confirms the relation i 2 3 I H > 523ID, for each acid at the 95% confidence level. Thus reaction 1 is definitely slower in DzO than in water for this (21) P.K.Glasoe and L. Eberson, J . Phys. Chem. 68, 1560 (1964). (22) J. L. Haslam, E. M. Eyring, W. W. Epstein, R. P. Jensen, and C . W. Jaget, J. A m . Chem. Soc., 87, 4247 (1966);for a schematic of the interdependent equilibria, see eq 3. (23) M. Eigen, W. Kruse, G. Maass, and L. DeMaeyer, "Progress in Reaction Kinetics," Vol. 2, G. Porter, Ed., Pergamon Press Lt.d., Oxford, England, 1964,Chapter 6.
DEUTERIUM OXIDESOLVENT ISOTOPE EFFECTS
3493
- _ -diffusion - _ _ _ _controlled_ _ - - - - --a-a-O- - - - - - _ _ ___
and the bonding of the proton in the transition state is essentially the same as in the HA- monoanion.’ Methyl(1-methylbutyl) malonic acid seems to be of an intermediate reaction type. Willi2’ is one of several workers who have used absolute rate theory to predict trends and limiting values for the DzO kinetic isotope effect. The statistical analysis of our experimental k23’ values (see Table 11) indicates, however, that the range in values of k23“/ kz3D, possible for a given malonic acid at the 95% confidence limit level, is too great to distinguish trends reliably for this homologous series from our data. Thus, a lengthy statistical mechanical interpretation of our data taking Willi’s approach is unwarranted. However, we can safely predict from the data of Table 11, as well as from similar data for cis-cyclopropane-1,2-dicarboxylic acids and polysubstituted succinic acids,2zthat the solvent DzO kinetic isotope effect &“/W23’D will not exceed 2.5 for those dicarboxylic acids having values of KI/Kz >> 4. This is an interesting result since temperature-jump studies of N,N-disubstituted anthranilic acids have yielded28 values of kZ3’H/k23’D as large as 3.4, and the forward and reverse reaction solvent DzO isotope effects for an isomerization of ribonuclease, also thought to involve the transfer of a proton between a nitrogen and an oxygen atom, have been reportedz9to be 4.3 and 6.4. Thus, it may prove possible with temperature-jump kinetic data of high accuracy to characterize the reacting moieties in enzyme reactions involving proton transfer by comparing solvent DzO kinetic isotope effects with those measured for simpler 0-H. N-H.. .O, N . .H-0, N-H.. .N, and S-H.. .O systems.
lsopropylmalonic acid Methyl (I-methylbutyl) malonic acid 0 Diethyl, Ethylphenyl, Ethylisoamyl Ethyl Isopropyl ond Diisopro yimolonic acid in Order o r increasing pK2
0
A
A ‘m I , ”
z4
\
-Slope = a a 0 . 5
6
7
8
9
PK;
A-*
+
+
kd“ Br@nstedplot for the reaction HAOH- ---f HzO of substituted malonic acids in water a t 25”.
Figure 1.
series of malonic acids. The conclusion that follows from this result is that a proton transfer is rate determining in reaction l. As Bell has remarkedlZ4the Brgnsted relationz6 k A = G A K Awas ~ devised for catalyzed reactions but should also apply to the rates of rapid acid-base reactions determined by relaxation techniques. Eigen has explored this subject in considerable detail.’ A Brgnsted plot for our data obtained in water is shown in Figure 1. A very similar plot can be made of our DzO data. For the substituted malonic acids with significant intramolecular hydrogen bonding, a linear log kz3’ os. pKzH is observed which gives a value of a G 0.5. I t was similarly found that the Brgnsted exponent p S 0.5 when the reverse reaction is considered. These values for a and /3 indicate*‘j that in the transition state the proton is about equally bonded to the A-2 dianion and the OH- ion in the case of acids having an intramolecularly hydrogen-bonded monoanion. Formation of the activated complex in the forward reaction requires, at the least, a weakening of the internal hydrogen bond and the establishment of a bridge between the reacting proton and the hydration sphere whereby tJhe positive charge may be rapidly transferred through the solvent structure. For isopropylmalonic acid monoanion where intramolecular hydrogen bonding is largely absent, bridging with the solvent is initially present in the monoanion and a diffusion-controlled reaction mechanism is apparently involved. For such reactions a = 0 and p = 1
-
.
G
O
,
Acknowledgment. The authors wish to acknowledge very helpful discussions with Dr. John L. Haslam and Dr. George W. Latimer regarding the interpretation of the kinetic data. (24) R. P. Bell, “The Proton in Chemistry,” Cornell University Press, Ithaca, N. Y., 1959, p 156. (25) J. N. BrGnsted and K . Pedersen, 2. Physik. Chem., 108, 185 (1923). (26) J. F. Bunnett, “Technique of Organic Chemistry,” Vol. VIII, Part I, 2nd ed, 5. L. Friess, E. 9.Lewis, and A. Weissberger, Ed., Interscience Publishers, Inc., New York, N . Y., 1961, pp 230-240. (27) A. V. Willi, “Saurekatlytische Reaktionen der Organkchen Chemie,” Verlag Vieweg, Braunschweig, Germany, 1965, pp 91-101. (28) J. L. Haslam and E. M. Eyring, in preparation. (29) T . C. French and G. G. Hammes, J. A m . Chem. SOC.,87, 4669 (1965).
Volume 70,Number 11 November 1966
