May, 1959
THEMECHANISM OF THE BASE-CATALYZED
HYDRATION OF FUMARATE TO
MALATE ‘185
KINETICS AND MECHANISM OF THE BASE-CATALYZED HYDRATION OF FUMARATE TO MALATE1 BY LUTHERE. ERICKSON AND ROBERT A. ALBERTY Contribution from the Chemistry Department, University of Wisconsin Received October 18. 1068
Thermodynamic and kinetic data are presented for the reversible, NaOH catalyzed hydration of fumarate to D,L-malate in HzO in the temperature range 90-175”. The equilibrium constants are correlated with those obtained for the fumarasecatalyzed hydration of fumarate to L-malate a t room temperature. The reaction follows a reversible first-order rate law in fumarate and malate. Rates are proportional to NaOH concentration at constant ionic strength. Proton magnetic resonance was used to show that the methylene protons of malate exchange with deuterons in D20more rapidly than the over-all reaction occurs. The racemization rate of L-malate catalyzed by NaOH is equal to the rate of dehydration of D,Lmalate, A mechanism is presented which is consistent with these observations.
Introduction The enzyme fumarase catalyzes the reversible hydration of fumarate to L-malate. Extensive studies of this reaction have been The effect of pH on the kinetic constants indicates that acidic groups of the enzyme are involved in the catalytic process.5 With the hope of getting a better understanding of the mechanism of the fumarase reaction] studies are being made of the catalysis of the hydration by strong acidse and bases. For the latter case,’ the reaction may be written H
C ‘’
coz-
COz-
H-LH
+ HzO ~rH - L H
(1)
LO2-
-0zC’ H‘
Experimental Procedure.-Five-ml. samples of the reaction mixture were sealed in ten-ml. alkali resistant glass ampules supplied by Corning Glass Co., and heated to the desired tamperature in an aluminum block thermostat with the temperature controlled to f0.2’. Sodium hydroxide concentrations and temperatures were chosen so that the rates were slow enough so that errors due to the time lag in heating the samples to temperature were insignificant. Sodium chloride was used to control the ionic strength. After being heated, the samples were cooled rapidly and analyzed, with a Beckman DU spectrophotometer, for fumarate. The absorbancy A at wave lengths from 270-300 mp is proportional to the fumarate concentration, and malate does not absorb significantly in this region of the spectrum. It was, however, necessary to use a blank, i.e., a solution of the same NaOH concentration, heated for the same time, with every sample, to correct, for the absorbancy due to substances dissolved from the glass walls. Equilibrium Quotient.-Representing sodium fumarate by F and sodium malate by M, reaction 1 can be written
F
+ HzO
M
(2)
for which the equilibrium constant is given by
K = aFaHeO % = Q AvFaH20
(3)
the equilibrium molar concentration ratio of disodium malate to disodium fumarate, and YM and YF are the corresponding mean ionic activity coefficients. Experimentally, Q is determined from the absorbancies of a fumarate solution before reaction and after i t has reached equilibrium, Le., Q = (A0 - A m ) / A c o . The following considerations show that fumarate and malate are the only substances present in the reaction mixture at significant concentrations a t equilibrium. A synthet,ic “equilibrium” mixture, whose composition was based on the assumption that all the absorbancy is due to fumarate, showed no change in absorbancy when it was heated for several half-lives. If a third component were involved, the fumarate-malate ratio and the absorbancy of this mixture would have changed upon heating unless the absorbancy of the third component were just enough to compensate for the decrease in fumarate concentration. It is unlikely that it would exactly compensate at all wave lengths and temperatures studied. However, samples of 2 M sodium malate in 4 M NaOH, heated for several days (approximately 100 times as long as necessary to reach within 1% of fumarate-malate equilibrium), showed significant yellow coloration. The yellow product was separated from fumaric and malic acids by artition chromatography using a celite column, 0.5 N 6 C l stationary phase and 65% CClaH, 35% butanol as the eluent.* The yellow product could be separated completely from fumaric acid with a 50 cm. column. Since it came off the column before fumaric acid, it is probably less polar than fumaric acid. The yellow compound can be titrated with NaOH; therefore, it contains an acidic group. The infrared. spectrum showed strong absorption in the carboxyl region. Even under the extreme conditions required to produce significant color, the yellow product amounted to only 0.5% by weight of the initial fumarate. Therefore, no further attempt was made to complete the characterieation. Reaction Rate Constants.-The reaction obeys the rate law
- d(F) -- = k’h(F)(OH-) dt
-k’d(M)(OH-)
=
kh(F) - kd(M) (4) where kh is the fist-order rate constant for the hydration reaction; k d , the first-order rate constant for the dehydration reaction. Both kh and kd are proportional to the (OH-) a t constant ionic strength. For this reversible, first-order reaction log [(F)t - W)w1 log (FhI
-
+
-
where a represents activity, Q , the equilibrium quotient, is (1) This research was supported by the National Science Founda-
tion and by the Research Committee of the University of Wisconsin from funds supplied by the Wisconsin Alumni Research Foundation. (2) R.A. Alberty, W. G. Miller and H. F. Fisher, J . An. Chem.Soc., 79,3973 (1957). (3) R. A. Alberty, Advances i n Enzymology,17, 1 (1956). (4) R. A. Alberty and B. M. Koerber, J . A m . Chem. Soc., 79, 6379 (1957) and earlier papers. (5) R. A. Alberty, J . CeZl. C o m p . Phyaiol.,47,245 (1956). (6) L. T. Rozelle and R. A. Alberty, THIEJOURNAL, 61, 1637 (1957). (7) V. Loyde, Ann.,198, 80 (1878).
where (F)o,(F)t and (F)eqare the fumarate concentrations at time t = 0, t = t and t = a. The rate constants were obtained by plotting -log (At - Aeq) os. t . Linear plots were obtained when either fumarate or malate was used as substrate. The individual first-order rate constants, k h and kd, for the hydration and dehydration reactions were determined by making use of the additional relation Q = kh/kd. Table I summarizes the rate and equilibrium quotient data. Racemization Rate of L-Malate.-In order to compare the first-order rate constants for racemization k, and de(8) W. G. Miller, Ph.D. thesis, University of Wisconsin, 1958.
LUTHER E. ERICKSON AND ROBERT A. ALBERTY
706
Vol. 63
TABLEI RATEAND EQUILIBRIUM DATAFOR REACTION 1 T
od. 175
(I
Substrate concn., M X 108
10 10 10 10 10 10 10 10 10 -9 2 10 10 10 2 2 2 5 2 2.3 2 2= 2
(NaOH) M
Ionic strength
kh X
Q
lo',
8ec-L
0.023
0.060 0.69 3.1 .loo .130 .65 13.7 .loo .330 .70 17.5 .loo .330 .70 21 .loo .530 .74 25 * 100 ,530 .77 29 .loo ,530 27 .78 .300 .530 .78 81 .500 ,530 ... 80 .090 -6.0 -1.65 ... 150 0.108 0.117 0.88 3.4 .loo .130 0.93 3.5 .loo .330 1.00 3.7 .loo .530 1.04 5.2 ,108 ,546 1.03 5.1 ,150 .546 1.06 10.0 .302 .546 1.06 ... .480 .50 1.05 ... 125 0.217 0.224 1.42 1.90 .217 .224 1.42 1.70 .217 .546 1.49 2.8 .217 ,546 1.49 2.8 .536 .546 1.58 7.5 2Q .536 .546 1.49 8.3 110 2000a.b 0.50 6.50 -10 147 Indicates malate used as substrate; all others fumarate. In DpO.
-
q
k d X lo6,
sec. - 1
k h X 106, (OH-)
M
-1
sec. -1
136 137 175 210 250 290 270 270
4.5 21 25 29 36 38 35 103
5 x 106, (0M - 1 sec.-l 197 210 250 290 360 380 360 340
... ...
...
...
...
3.8 3.8 3.7 4.9 5.6 10.3
31 35 37 52 57 67
35 38 37 49 51 69
... ....
...
1.39 1.20 1.9 1.9 4.8 5.6 13.9
9.0 7.7 12.8 12.8 14.0 15.5 294
...
6.4 5.5 8.7 8.7 9.0 10.5 27.8
hydration k d , of L-malate, catalyzed by NaOH, both the absorbancy and optical rot,ation of L-malate solutions were measured as a function of time of heating. To increase sensitivity, a citrate, L-malate complex of molybdate was used to increase the small specific rotation of L-malate. Solutions for optical activity measurements were conveniently prepared by accurately pipetting into a flask 5.0 ml. of the L-malate solution to be analyzed, 5.0 ml. of 1 M trisodium citrate solution, 1.0 ml. of glacial acetic acid and 9.0 ml. of 29% (by weight) reagent quality ammonium molybdate solution.9 The specific rotation [ ~ t ] ~ ~ofb n L-malate in this solution is about +1,400, over 500 times that of L-malate alone. Solutions 10 m M in L-malate gave optical rotations of +0.85 f 0.02 at 25' using a 20 cm. cell and sodium lamp. The first-order rate constants for racemization at two temperatures are listed in Table 11, along with kd obtained from the same sam les. The data show that the rates of racemization and o f dehydration of L-malate, catalyzed by NaOH, are equal.
TABLE I1 FIRST-ORDER RATE CONSTANTS FOR RACEMIZATION IC, AND DEHYDRATION k d , of L-MALATE, CATALYZED BY NaOH T, OC.
150 175
(NaOH) M
Ionic strength
0.30
0.530 ,530
.10
kd
X lo',
sec. - 1
9.7 3.5
Proton Magnetic Resonance Studies.-Ten-ml.
kr X Ip", sec. -
10.0 3.3 samples
of 2.0 M sodium malate, 0.5 N in NaOH, were prepared and
+CPS
Fig. 1.-High resolution proton magnetic resonance spectra of 2 M disodium malate heated in 0.05 M NaOD, DzO at 90' showing exchange of CH2 protons: (a) unheated; (b) 1.2 hr.; (c) 5.0 hr.; (d) 18.9, hr.
then frozen and sublimed to dryness under vacuum. The OH proton of the malate and the protons in the medium were exchanged out by adding 2-3 ml. portions of DzO and subliming to dryness three times. The solution then was reconstituted with DzO. The NaOD concentration was checked by neutralizing 1.0 ml. of the solution with excess standard HC1 and back titrating with standard NaOH. The solutions were placed in 0.5 mm. 0.d. Pyrex tubes and heated for the desired time in an aluminum block thermostat. The spectra were observed at 40 megacycles using (9) H. A. Krebs and L. V. Eggleston, Biochem. J . , 81, 334 (1943).
707
THEMECHANISM OF THE BASE-CATALYZED HYDRATION OF FUMARATE TO MALATE
May, 1959
a Varian V-4300 n.m.r. spectrometer equipped with superstabilizer. The com lete analysis of the proton magnetic resonance spectra of $sodium malate in DIO,lO using the methods described in recent publications,"*'a makes it possible for the chemical shift, a i , of particular protons and the spin-spin coupling constant, Aij, between proton pairs to be calculated. From a knowledge of the chemical shifts of the three protons and of the three coupling constants for pairs of protons, the spectra of various partially deuterated malates can be predicted. Table I11 lists the resonance frequencies (relative to HzO in a capillary) a t 40 Mc. for the protons in dipotassium malate and three partially deuterated dipotassium malates.13 TABLE I11 PROTON MAGNPTICRESONANCE FREQUENCIES (RELATIVE TO WATER)AT 40 Mc. FOR DIPOTASSIUM MALATEAND PARTIALLY DEUTERATED MALATES IX DzO Compound Structure
Symbol
+.I
Frequencies of resonance (C.p.8.) Methine Methylene
Na2M
a
7 . 0 , 1 1 . 8 , 15.4, 19.6
NaznbM NazDDM NazDbDaM
b c d
11.9, 14.9 8.8, 18.2 13.4
62.9,67.5,77.8, 78.9, 81.5, 86.6, 93.6, 101.0 74.6, 77.0 81.5, 90.9
cos 0
COS C
b
COS
d
As shown in Fig. 1, when solutions of 2 AI' sodium malate in DZO, containing 0.5 N NaOD, were heated to about loo", the resonance lines associated with the methylene protons disappeared. In addition, while the spectrum in the methine region changed from a quadruplet to a singlet, its intensity remained virtually constant. This showed clearly that methylene protons were being replaced by deuterons from the medium. The spectrum of NazD,M in both methylene and methine regions is evident in spectra (b) and (c). The Na&M lines are not resolved from those of NazM and NazDbD,M. Lack of resolution is partly a result of quadrupole broadening and the unresolved spin-spin splitting due to the deuterium. After prolonged heating, virtually all the methylene protons are exchanged and the spectrum of Na2DbD,M predominates. If one assumes, as a first approximation, that the exchange of CHZ protons in DzO-NaOD is random and not affected by a deuterium on the same carbon, that the concentration of protons in the medium is negligible, and that there is no incorporation of deuterium through dehydration to fumarate and subsequent addition of DzO, the rate of ex(10) R. A. Alberty a n d P. Bender, J . Am. Chem. SOC.,80, 542 (1958). (11) H. J. Bernstein, J. A. Pople a n d W. B. Schneider, Canadian J . Cham., 8 5 , 65 (1957). ( 1 2 ) H. S. Gutowsky, C. H. Holm, A. Saika a n d G. A. Williams, J . Am. Chem. Soc., 79, 4596 (1957).
(13) The proton resonance lines of disodium malate appear a t slightly higher frequencies, relative to HzO in a capillary, than the corresponding lines in the dipotassium malate spectrum.
P
strength dependence of log Q for reaction 1.
Fig, 2.-Ionic
*I
/
I.000
a
I
-0.5001
p'
I
I
I
2.50 +X
3.00
I
I
3.50
103
Fig. 3.-Temperature dependence of Q for reaction 1 a t 0.10 ionic strength: 0 , experimental points, fumarase catalysis; 0,experimental points, NaOH catalysis. Line given by log Q = 9.932 363/T 4.127 log .'2 change of a methylene proton can be calculated. The exchange reaction then can be written k, ka NazM + (NazDbM Na2D,M) -+ Na2DbDaM (0)
+
+
-
LUTHERE. ERICKSON AND ROBERT A. ALBERTY
708
+
For this system the concentration of Na2DbM Na2D,M reaches a maximum at tmax = 0.693/k4. The area under the peak (90.0 c.P.s.) which appears in methylene region of the n.m.r. spectrum of the heated samples (c) is a measure of the Na2D,M concentration. Comparison of spectra from a series of samples heated for different times makes it possible to calculate tmsx and kr to within &lo%. Alternatively, the total area under the methylene proton peaks is a measure of the concentration of Na2M 1/2(Na2DbM NaaD,M). This area reaches half its original value at 1.70 half-lives, according t o mechanism (6). Designating this time as t s , k p = 0.693 X 1.70/t,. The values of kr a t 90 and 110" determined by these approaches are 4.7 X lo-' sec.-l and 27 X 10-6 sec.-l, respectively.
+
+
Results and Discussion Ionic Strength Dependence of Q.-The following considerations indicate that a linear dependence of log Q on ionic strength is expected at ionic strengths below 0.5. From (3) log
Q
=
log K
+ log - log Vhi + log 2/F
UHzO
(7)
A term linear in ionic strength often is added to the Debye-Hiickel limiting law in order to represent the activity coefficient data of an electrolyte over a wider concentration range. With this modification, the mean ionic activity coefficient of a salt, y*, is given by where A and B are constants for a particular solvent and temperature, a and C are constants characteristic of the solute, x+ and z- are the ionic charges, and p is the ionic strength. If a is assumed to be the same for fumarate and malate, the logarithm of their activity coefficient ratio is given by (CF - C M ) ~and , (7) becomes log
Q
E
log K
+ (CF - CM)P + log
UHzO
(9)
In the region where the activity of H2O does not change significantly with electrolyte concentration, a plot of log Q us. p should be linear with slope (CF CM). For NaOH14 and NaC1'6 solutions from zero to 0.6 ionic strength the activity of H2O decreases from 1.00 to 0.98. Therefore, the log U H ~ Oterm in (9) contributes only about 0.01 to log Q at p = 0.60 and would hardly be detectable in these measurements. A plot of log Q us. p is shown in Fig. 2. The best straight lines drawn through the experimental points at 125, 150 and 175" all have a slope of 0.13 0.02. Though no data are available on the activity coefficients of sodium fumarate or malate, C values at 25" for sodium formate (0.148) and sodium acetate (0.252)16indicate that 0.13 is a reasonable value for CF - CM. The value of Q obtained by extrapolation to zero concentration is taken as K. A comparison can be made of the ionic strength dependence of Q observed in these experiments and that obtained by Bock and Alberty for the fumarase-catalyzed reaction.'' They obtained values of Q from 0.5 to 0.1 ionic strength which yield a slope of 0.12 for the log Q us. p plot, indicating that (14) G. C. Akerlof and G. Kegeles, J . Am. Chem. SOC.,61, 620
(1940). (15) R. R. Robinson, Trona. Proc. Rov. Soc. N e w Zeal., 7 6 , 203 (1946).
(16) E. A. Guggenheim, Phil. Moo., [7J22, 322 (1936). (17) R. Bock and R. A. Alberty, J . Am. Chem. Soc., 7 6 , 1720
(1853).
Vol. 63
the ionic strength dependence of Q is essentially independent of temperature from 25 to 175". Therefore, a plot of log Q us. 1/T yields AHofor any series of determinations at constant ionic strength less than about 0.5. Thermodynamic Functions.-From studies of the temperature dependence of Q for the reaction catalyzed by fumarase at p = 0.10 and pH 7.3, between 5 and 40°, Bock and Alberty obtained AHo = -3960 f 100 ~al./mole.'~Since these data were obtained a t pH 7.3, where divalent fumarate and malate are the only significant species, the Q values can be compared directly with those obtained in this research. Figure 3 is a plot of log Q us. 1/T including representative experimental points for the fumarase reaction. When the experimental values of Q for the enzymatic and non-enzymatic reactions are compared, the Q of the enzymatic reaction must be doubled since it is defined as (L-M)/(F) rather than [(L-M) (D-M)]/(F). Over a limited temperature range, each set of data yields a straight line, but the slopes differ considerably. The data were fitted by the method of least squares, assuming ACop = C,,,, is constant over the temperature range 5175" and Q = 14.2 at 5 " . This yields ACop= -8.2 cal. mole-' deg.-' and the expression log Q = 9.932 + 363/T - 4.127 log T (10) which is plotted in Fig. 3. No data are available on the heat capacities of aqueous fumarate and malate solutions. However, since for these dilute = solutions CP,,, = 18 cal. mole-' deg.-', COpF = 10 cal. mole-' deg-l, which is reasonable.18 The values of K e y ,AHo,AFO and ASo for the reac- , tion are recorded in Table IV. The entropy decrease is probably to be expected in going from fumarate plus water to malate. These results can be compared with the data for the corresponding acid-catalyzed reaction. For acid-catalyzed hydration of undissociated fumaric acid to malic acid, Rozelle and Albertye obtained ASo = -16 cal. mole-1 deg.-l and AHo, = -4900 cal. mole-1 in the temperature range 125-200'. The AH0 for the acid- and base-catalyzed reactions are not independent but are related through the enthalpies of ionization of fumaric and malic acids.17 Recent determinations of AHM, and AHM~, the enthalpies of ionization of malic acid,lg obtained from ionization constant measurements from 5 to 50°, allow us to calculate the enthalpy change for the acid catalyzed reaction from
+
cPM cop,
copM
AHoa = AHob
+ (AHF, + AHFJ -
+AHd
(A.HM~
.
(11)
where AHo, and represent the enthalpy changes for the acid- and base-catalyzed reactions, AHF~and AHpz, the enthalpies of ionization of fumark acid.20 At 25O, AHo, calculated from equation 11 is -5900 cal. mole-' deg.-'. From the difference in AHo, at 160 and 25', ACop for the acid(18) H. s. Harned and B. B. Owen, "The Physical Chemistry of Electrolytic Solutions," Reinhold Publ. Corp., New York, N. Y., 1950, p. 246. (19) M. Eden and R. G. Bates, Chicago A.C.S. Meeting, September, 1958. (20) E. J. Cohn and J. T. E d s d l , "Proteins, Amino Acids and Peptides," Reinhold Publ. Corp., New York,N. Y., 1943,P. 82.
'
THEMECHANISM O F THE BhSE-CATALYZED HYDRATION O F FUMARATE TO MALATE 709
May, 1959
catalyzed reaction is +7 f 3 cal. mole-' deg.-'. The fact that ACO, for the acid-catalyzed reaction is +7 while ACO, for the base-catalyzed reaction is -8 probably reflects the increased rotational freedom of the undissociated malic acid as compared to the divalent malate anion. Kinetic Data.-Both k h and k d , obtained at NaOH concentrations between 0.10 and 0.53 M and constant ionic strength, are nearly directly proportional to NaOH concentration. This is shown by the near constancy of !&/(OH-) and kd/ (OH-) at a given ionic strength and temperature. The activation energies for both forward and reverse reactions were evaluated by plotting log k/(OH-) us. 1/T at constant ionic strength. Linear plots were obtained a t p = 0.54 with data at 125, 150 and 175'. At the lower ionic strengths, data a t only 125 and 175' were available for the plot. Values of the Arrhenius activation energy E were obtained from these plots; AH* = E - RT and AS*, 'calculated from absolute rate theory, are listed in Table V. Values of AH* and AS* for the corresponding HC1 catalyzed reaction are included for comparison. TABLEI V THERMODYNAMIC DATAFOR REACTION 1 ASO,
AH0
K
kcal: mole-'
kcal.' mole-!
cal. deg. -1 mole-'
8.4 1.34 0.89 0.65
-1.26 -0.23 $0.10 f0.39
-4.1 -4.9 -5. I -5.3
-9.5 - 12 -12 -11
AFO
T, OC.
25 125 150 175
The mechanism provides for the fact that bhe hydration reaction is first order in fumarate, the dehydration, first order in malate, and that both kh and kd are proportional to (OH-). I n addition this mechanism provides for exchange of methylene hydrogens through the intermediate and does not permit racemization of L-malate except via fumarate. Rate Constants for Mechanism 12.-If it is assumed that the intermediate is in a steady state, the relation between the four rate constants in this mechanism and the rate constants k h and k d , obtained spectrophotometrically, is given by k h = klh/(kZ k.3); k d = k2k4/(h f k.3) (13) where k~ = L''(OH-), k3 = k'a(HzO), and kq = k'd(OH-). -, Some idea of the relative magnitudes of kl, kz, k3 and k4 can be obtained from a comparison of the rate of exchange of methylene protons and k h and &i determined under the same conditions. Neglecting incorporation of deuterium into the methylene position of malate via dehydration to fumarate and subsequent addition of DzO, the first-order rate constant for exchange calculated from n.m.r. studies is just k4 in mechanism 12. With a sample of 2 M NazM, 0.5 N NaOD in DzO a t llOo, kq = 27 X sec. -l. Spectrophotometric analysis of the set.-' and same samples yielded k h = 15 X k d = 1.5 x 10-5SeC.-'. From (13) k ~ / k z= k4/kd 1 g 19. Therefore, kl = kh(1 kz/k3) kh. The magnitude of k3 can be estimated by considering the first step in the dehydration of malate. The equilibrium constant for this step is given by
+
+
K ks/kr = (M)(OH-)/(I) = KwJKs (14) TABLEV where K , is the acid dissociation constant of the ENTHALPIES AND ENTROPIES OF ACTIVATION FOR REACTION 1 methylene proton in malate. Pearson and Dillon Ash-,
ASd-,
koal. mole-1
AHd-,
Catalyst
Ionic strength
kcal. mole-'
cal. deg.-l mole-'
cal. deg.-l mole-'
NaOH NaOH NaOH 1 N HC1
0.54 -33 .I3 1.0
19 22 19 22
24 27 24 27
-34 -28 -35 -26
-22 -17 -23 -10
AHh-,
Mechanism of the Reaction.-The results of these three types of experiments suggest the mechanism shown below H OH-
+
e
- 0 k H' Fumarate, F
COz-
H
COz-
\c/
"1:
7
\ / -C I C
/A'\
-Oca O H H Intermediate, I
(12)
suggest a value of Ka = 10-24 for the methyl protons of acetate ion.21 Their estimate is based on the rate of OD- catalyzed exchange of methyl protons of acetatez2 and the assumption that the ratio of rates of removal of protons by HzO and OH- is the same as in acetone, as determined from bromination rate studies. The rate of exchange of methyl protons by acetate ion is within a power of 10 of the rate of exchange of methylene protons of malate at loo', and both reactions have a activation energy of about 22 kcal. mole-'. Since K W z 3 at 110' is 3 X K,/Ka = k3/k4 = 3 X 10". Hence k3 = 3 X loll X 27 X set.-' E los set.-' and kz = k3/19 g 5 X lo6 sec.-' at 110'. Thus, both kz and k3 are much greater than either k~ or k4. Acknowledgment.-The authors are indebted to Prof. P. Bender for assistance with the proton magnetic resonance experiments. (21) R. G. Pearson and R. L. Dillon, J. A m . Chem. Soc., 7 6 , 2439 (1953). (22) K. F. Bonhoefier, X. H. Greib and 0. Reizt, J. Chem. Phya., 1, 664
-C
I
D,L-malate, M
(1939).
(23) H. 8. Harned and B. B. Owen, (1953).
J. A m . Chem. Soc., 7 6 , 493
