OCt. 20, 1Rt32
ALKALINE DEHYDROHALOGENATION O F HALO-FUMARATE AND -MALEATE IONS
able from his own work and the data of previous papers to convert his specific activity t o that in maleate buffer a t @H7 and 25'. He has givena the molecular weight of urease as 480,000 and evidence has been presented15that such a molecule contains four active sites. Thus the expression for ki per active site is found to be k i = 7 X lo9 exp(-8850/RT) sec.-'. This is written as a unimolecular rate constant since the kinetic function of water is not known. The numerical magnitude of the pre-exponential factor is somewhat unusual, being much smaller than the median value for reactions involving small molecules. From the data on the temperature dependence of the Michaelis constants in Table I11 the following expressions are readily obtained
-
In Kg = (-6.5 & 5 ) / R (1600 =k 1500)/RT and In KB = (-0.5 =tJ ) / R - (3100 i: l500)/RT
There has been considerable discussion in the literature concerning the kinetic meaning of the Michaelis constant. On the first glance the invariance of K' to changes in pH and solvent, as (15) J. F Ambrose, G B. Kistiakowsky and .4 G. Kridl, THIS JOIJRNAL, 73, 1232 (1951).
,5025
compared with substantial changes in l'm, suggests that k ; > k; and therefore that K' has the meaning of a thermodynamic equilibrium constant k i / k ; . By the same argument, then, K = k 3 / k l . This is, of course, not impossible but another interpretation appears more likely. The values of Vm here reported are relative to the rates measured under a standard set of conditions. Hence Vm = k i ( E o ) / (ki(Eo))ataudsrd;it involves not only the dependence of k; but also that of (EO) on such variables as pH, temperature, etc. It seems rather arbitrary to assume that the latter dependence is nil. Acidbase ionization equilibria'e may result in a fraction of the catalytic sites being inactive. These equilibria may be the entire cause of the pH dependence of V m , in which case the previous argument as to the nature of K' is invalid and the comments on the temperature dependence of Vm may have to be revised. It is clear that the interpretation of the nature of the Michaelis constant must await the elucidation of the complete mechanism of urea hydrolysis by urease. (16) L Michaelis, Biochem Z
, 35, 182 (1911)
CAMBRIDGE, MASS.
-
[COXTRIBUTION FROM
THE
DEPARTMENT OF CHEMISTRY, UXIVERSITY OF COLORADO]
Mechanisms of Elimination Reactions. VII. The Alkaline Dehydrohalogenation of Chloro- and Bromo-Maleate and Fumarate1 BY STANLEY J. CRISTOLAND ARTHURBEGOON' RECEIVED FEBRUARY 9, 1952 The kinetics of the alkaline dehydrohalogenation in water and in aqueous ethanol of the halofumarate ions and halomaleate ions have been studied. The determinations of the reaction order and of the effect of ionic strength upon rate constant have been interpreted to indicate that the reaction is between the bivalent ion of the salt and hydroxide ion. The extent of the superiority of trans over cis elimination has been measured, and this has been considered in terms of coulombic repulsions and in terms of mechanistic differences between cis and trans elimination.
I n many bimolecular elimination reactions, a stereochemical preference is observed, trans substituents being more readily removed than corresponding cis substituents.3 This paper is a continuation of a program relating to the factors contributing to relative reactivities in cis-trans systems. Two factors have been suggested as being of particular importance, one4 involving cis repulsions and 0ne3,jbeing based upon a postulated concerted one-stage mechanism for the trans process and a multiple-stage mechanism for the cis process. As further tests of the relative importance of these factors, i t seemed worthwhile to study the alkaline dehydrohalogenation of halomaleates (Ij and halofumarates (II). Here, assuming that the attack is by hydroxide ion upon the hydrogen atom of the bivalent ion, i t is seen that electrostatic repulsion will be greater between the negative hydroxide ion and the carboxylate group (which (1) Previous paper in series: S. J. Cristol, N. L. Hause, A. J , Quant, H.W. Miller, K. R . Eilar and J. S. AMeek,TITISJOURNAL, 74, 3333 (1952). (2) Deceased December 15, 1951. (3) Appropriate references have been given earlier (S. J. Cristol, hT. L.Hause and J. S . Meek, Txrs JOURNAL, 75, 674 (1951)). (4) W, Hiickel, W .Tappe and G. Legutke, A n n . , 648, 191 (1940). (5) S. J. Cristol, THIS JOURNAL,69, 838 (1947).
0
0
-0-c
I111
I1I1
H )C=C(;-"-
0
-0-c
I1 I1
,c=c(
H'
I
X
C
A 0 0I1
bears a whole negative charge) than between the hydroxide ion and the negative end of a carbonhalogen dipole. Thus if electrostatic repulsions were the determining factor in trans vs. cis elimination, the formation of sodium acetylenedicarboxylate from sodium halomaleate might be expected to be more rapid than from sodium halofumarate. Michael6 has reported that chlorofumaric and bromofumaric acids lose hydrogen halide more rapidly than the corresponding halomaleic acids upon treatment with excess aqueous alkali. In view of the fact that the argument given above is based upon reaction of the dicarboxylate ion, rather than upon either of the acid salts or the free acid with hydroxide ion, i t seemed desirable to study the reaction more mtensively than did Michael. Accordingly we have determined the (6) A. Michael, J prakl. Chem., 62,289 (1895).
.?OX
STANLEY J. CRISTOI. AND ARTHPR REGOON
order of the reaction and have studied the effect of ionic strength upon the reaction rate, dernonstratiiig that the reaction is indeed one between the hivalent anion and hydroxide ion; in addition we have measured the rates of reaction a t various temperatures in water and in 34.2 wt. yo aqueous ethanol and have calculated the quantities of activation for the four compounds from these data. h consideration of the ionization constants for the 2-halo-2-butenedioic acids' shows that, in the basic media used in the rate experiments, the second ionization of the acid may be regarded as substantially complete. Thus, only if the reaction were between the dicarboxylate ion and hydroxide ion would the reaction be first order in organic halide and first order in hydroxide ion. Thus the determination of reaction order may be used to define the reacting species. The usual test for second-order kinetics made by varying the concentration of each of the reactants separately and noting the constancy of the reaction-rate constant was inapplicable in this study, as i t was found that the reaction involved the bivalent anion and hydroxide ion and was thus subject to primary salt effects. In any given run the ionic strength is invariant, acetylenedicarboxylate ion replacing halobutenedioate ion and halide ion replacing hydroxide ion. In accordance with this, each run was found to obey the second-order rate expression; as in many cases hydroxide was in large excess, obedience to this law proves the first-order relationship with respect to organic halide, The variation of rate constant with ionic strength and the constancy of the rate constant when ionic strength was maintained constant and hydroxide ion or butenedioate concentration was varied are shown in Tables I and 11. Sodium nitrate was used as neutral salt in these experiments. Thus, for bromomaleate ion, the variation of the secondorder rate constant with ionic strength may be
Ynl. 74 TABLE I1
\
ARIATION O F THE S E C O Y D - O R D E R K A T E COUSTANT WITH
IOYIC STREYGTH FOR THE DEHIDRDHALOC.EYATIOU OF THF
1141 OFVMARATE
A\D
HALOVALEATE IONS
1'4
AQTiFOU\
SODXtJM IikDROXIDP:
IO'k, Ion Bromomaleate
Bromofumarate
[Na-
[sa-
TEmp
, [Halide],
OH],
43.12
0.00969 ,00967 ,00967 ,00961 ,00965 ,00965 ,00972 ,00970 ,00963 ,00962 ,00964 .00962
0.0262 ,0262 ,0262 ,0264 ,0263 .0263 ,0718 ,0718 ,0719 ,0719 ,0719 .0719
0.00965
0.0263 ,0263 ,0262 ,0719
0.0250 .0502
c
45.12
M
Chloromaleate
71.02
,0456 ,0455 .0910 ,0908 .1363
0.055 ,055 ,080 ,080 ,105
,105 ,101 ,147 ,146 ,192 .1!32 .237
,0719
.0455
.0717 .0718
.0908 .I363
0.00987 .00996 ,00980 ,00978 .00999
0.0714 ,0712 ,0716 ,0716 ,0712
0.0453 ,0909 .1363 ,2000
0.101 .146 ,192 .237 .301
0.00993 .0099 1
0.0713 ,0713 ,0714 ,0714 ,0716
,00962 ,00961 ,00974 .00970 71.02
C1.0232 ,0251 ,0302 ,0300
Ionic strength
0.055 ,080 .lo5 .lo1 .146 .192 ,237
,00967 ,00971
Chlorofumarate
.If
NOsl, if
,00988 ,00987 .00973
0,0454
.0464 ,0909 ,1366
0.101 ,147 .147 ,192 ,238
I/ sec / mole 0.663 ,627 ,746 .709 .810 ,822 .781 .962 ,902 1.0:; 1.03 LO!>
12.3 14 8 17.1 16.9 19.2 21.6 24 1 9.08 10.5 12 2 12 7 14.6
0 900 1.08 1.oti 1.13 1.23
noted from Table I, experiments 1, 2, 3 and 5 , and the fact that this was an ionic strength effect and not the effect of a reaction of higher order in hydroxide ion may be noted by a comparison of experiments 3 and 4 , 5 and 6, and 7 and 8, where the substitution of nitrate ion for hydroxide ion did not affect the second-order rate constant. Analogous comparisons are available in Tables I and I1 for the other compounds. Thus the reactions were ~ . \ H L EI shown to be first order in hydroxide ion. VARIATION OF THE SECOSD-ORDER RATE COXSTANT WITH Further evidence that the ions involved in the Ioxrc STRENGTH FOR I HE DEHYDROI-IALUCENATION OF rate-determining step are the bivalent anion and the RROMOPUMARATE, BROMOMALEATE, CHLOROFUMARATE AND univalent hydroxide ion may be obtained by applyCFILOROMALEATE I O V S I N 54.2 \VT. 7 0 AQLTEOCS %HANOLIC ing the Bronsted e q u a t i ~ n , which ~ * ~ relates rate SODIVM HYDROXIDE constant and ionic strength. In this method log10'k. [Na[NaI./ arithms of the specific reaction-rate constants are mpt. T e m p . , [Halidel, O H ] . N O I ~ , Ionic sec.1 no. Ion M M Jf strength mole plotted against corresponding values of a function 4.73 1 Bromo6 1 . 4 0 0.00976 0 0717 0 112 of the ionic strength, and approximate values of the 5 00 2 maleate .Of321 ,01455 117 product of the charges on the reacting species are ,1173 . 163 6 . 4 0 obtained 3 ,00976 from the slope of the lines obtained. 4 6.59 .163 0716 0.0456 ,00983 From data of Table 11, values for the product of 5 .00996 7.35 ,214 1626 6 7.41 ,00973 ,0718 ,0908 ,213 the charges of $1.9 f 0.2 for bromofumarate and ,00974 39.77 ,2522 0 803 ,312 $1.7 f 0.2 for bromomaleate were obtained, as ,0097 1 8 ,1618 ,0910 ,313 0.810 compared with the theoretical value of $2.0. 9 Bromo45.12 ,00974 1167 ,162 2 6 . 3 Similar treatments of the data for the chloro 10 fumarate 0713 ,162 2 7 . 6 .0094 1 ,0453 1 1 Chloro80.14 ,0723 .112 2.48 ,00969 systems give values of +l.S and 1.3 as values for 12 maleate 2.37 ,01460 ,0625 .118 the product for chlorofumarate and chloromaleate, 13 ,00991 ,1616 .212 3.91 respectively. 14 ,0909 .214 3.85 ,00977 ,0722 O C .
i
+
15 Chloro72.95 16 fumarate 17 18
,00983 ,00977 00979 ,00977
.1165
0708
,0456
.162 ,162
,1620 0712
,0908
,212 ,212
17.7 17.5 21.8 22.2
(7) N. W. Ashton and J. R . Partington. Trant. Faraday Soc., SO, S98 (19341.
Measurement of Reaction Rates.-The rates were determined in carbon dioxide-free water and in 54.2 weight yo aqueous ethanol. In the work at 30 to 40°, a water-bath (8) E . S. Amis, "Kinetics of Chemical Change in Solution," The Macmillan Co., Inc., New York, N. Y., 1949, p. 72. (9) G . J. Doyle and N. Davidson, THIS JOURNAL, 71, 3491 (1949).
Oct. 20, 1952
-ALKALINE
DEHYDROHALOGENATION O F HALO-FUMARSTE
maintained at constant temperature to within * 0 . 0 2 O was used, the solutions were made up a t the reaction temperature, and the reactions conducted in volumetric flasks. In the experiments at 50 to 90°, an oil-bath maintained a t constant temperature f0.04' was employed, and the reactions were run in sealed soft-glass test-tubes. The solutions were prepared a t room temperature, aliquots were placed in test-tubes which were then sealed and placed in the ther-
AND
-MALEATE IONS
5027
mostated bath. In these runs, the rate constants were corrected for the expansion of solvent.10 The extent of reaction was followed by titration for halide ion by the Volhard procedure. Details of the procedures employed for the measurements and for the calculations of rate constants were substantially as described previously. 11,12 The results obtained are given in Tables I , 11, 111 and IV. The data in Table I11 were obtained a t an ionic strength of 0.11 molal and those in Table IV a t a n ionic strength of 0.10 molal.13
TABLE I11 TABLE11 DATAASD SECOND-ORDER REACTION-RATE CONSTANTS FOR DATAA N D SECOND-ORDER REACTION RATECONSTANTS FOR THE DEHYDROHALOGENATION OF BROMOMALEATE, BROMOTHE DEHYDROHALOGESATION OF BROMOMALEATE, BROMOAND CHLOROFUMARATE IONS FUMARATE, CHLOROMALEATE FUMARATE, CHLOROMALEATE AND CHLOROFUMARATE IONS I N 54.2 WT. 70AQUEOUS ETHANOLIC SODIUMHYDROXIDE IS AQUEOUSSODIUM HYDROXIDE AT A N IONICSTRENGTH OF AT AN IONIC STRENGTH OF 0.11 0.10 Rate Rate constant,
constant Temp.,
Ion
Bromomaleate
O C .
39. 77 49.90
53.59 61.40
73.31
Bromofumarate
Chromomaleate
Chlorofumarate
45.12
[H%del,
0,00991 ,00982 ,00968 ,00970 ,00954 .00976 ,00977 .01455 .01457 ,00973 .00983 ,00970 .00981 .00971 .00970
34.84
,00968 .00973
23.36
.00985 ,00974
69.49
.00983 .00980
72.49
.00985 .00981
73.31
,01060 ,00956 .01043
80.14
.00969 .00971
88,32
,00977 ,00961
61.53
,00973 ,00985
72.95
.00970 ,00984
81.05
,00985 ,00974
[PiaOH], A4
0.0708 ,0716 ,0720 ,0719 Av. ,0725
.Oil7 ,0721 ,0621 ,0626 Av. ,0721 ,0719 Av. ,0714 ,0712 ,0714
,0714 Av. .Oil4 .0713 Av. ,0711 ,0713 Av. ,0720 .0721 Av. ,0717 ,0717 Av. ,0703 ,0724 ,0707 Av. ,0723 .0723 Av. ,0718 ,0721 Av. .0713 ,0711 Av. .0713 ,0711 Av. ,0710 ,0713 Av.
lO'k,
I./sec./mole
0.407 1.25 1.27 1.30 1.27 2.13 4.73 5 06 5.00 4.97 4.94 17.4 17.2 17.3 18.7 18.0 18.7 19.0 18.6 6.49 6.41 6.45 1.67 1.65 1.66 0.830 0.813 0.822 1.11 1.10 1.11 1.21 1.14 1.08 1.14 2.48 2.47 2.48 5.82 5.98 5.90 3.84 3.90 3.87 14.0 13.8 13.9 31.4 31.3 31.4
Ion
Broniornaledte
Temp., OC.
Chloromaleate
Chlorofumarate
'I
45.12
0,00972 ,00977
59 48
,00970 ,00973
71.02
,00974 ,00967
23.38
,00979 ,00978
34.03
,00968 ,00965
45.12
,00962 .00981
71.02
,00986 ,00993
80.49
,00977 ,00981
90 63
.0099 1 .0099 1
59.48
,00985 .00995
71.02
,00977 ,00983 ,00987 .00994
80.49
.00984 ,00991
t
Bromofumarate
[NaOH],
10dk,
M l./sec./mole 0.0717 0.781 ,0716 . tail Av. ,768 .0718 3 90 ,0717 3.72 Av. 3 81 ,0717 12 2 ,0718 12.8 Av. 1 2 . 5 ,0716 1.95 ,0716 2.00 -4v. 1.98 ,0718 5.86 .Oil9 5.77 Av. 5.82 .0719 16.9 ,0715 16.8 Av. 16.9 ,0714 0.930 ,0713 .goo Av. .915 ,0716 2.47 2.46 ,0715 Av. 2.47 ,0713 6.79 ,0713 6.97 Av. 6.88 ,0714 2.97 ,0713 2.89 Av. 2.93 ,0716 9.24 ,0715 8.85 ,0714 9.08 ,0713 9.24 Av. 9.10 ,0715 20.4 ,0713 20.5 Av. 2 0 . 5
---
Activation energies were obtained from plots of log k us. 1 / T and entropies of activation were determined from these values and values of k read off these curves a t 70.00°.* These values are given in Table V. We estimate the experimental uncertainties in E.,t a t about 0.7 kcal./mole and in AS$a t about 3 entropy units. (10) N. S. Osborne, E. C. McKelvy and H. U'. Bearce, Bull. Bur. Sfonderds, 9,327 (1913). (11) S.J. Cristol, THISJOURNAL,67, 1494 (1946). (12) S. J. Cristol and N. L. Hause, i b i d . , 71, 2193 (1952). (13) The experiments were conducted a t approximately identical molarities in each solvent, but the ionic strength8 differ in the t w o solvents due to differencu in densities of the wlventr.
'l'AtlLE
\'
ACTIVATION ENERGIES A N D ESTROPIES O F AcrrvArIos FOR T H E DEHYDROHALOGBKATIOS OF T H E HALOFUMARATE AND EIALOMALEATE IOSS IVITH S O D I C M HYDROXIDE AT 70" ASfW
1Wk;ia 1 'kec 'mole
I o I1
A.
E,,, kcal ,'mole
cal /mole (leg
Solveiit: rvater; ioiiic strength, O.lfi
Chlorofurnarate Chloromaleate Bromofumarate Ilromonialeatc
S 15 0 809 1 I,?
I 1 :i
"1.1 2.5.; 17.5 23 .i ,
~- I *'3 - 19
-
reflection of these ionic bond strengths.17 On the other hand, it was assumed that the cis process was multiple stage; the first and presumably ratedetermining step involved the removal of a proton arid the formation of a carbanion; the energy of the transition state was thus a reflection only of the carbon-hydrogen ionic bond strength. The difference between the heat of reaction of the rate-determining step of the trans process and that of the cis process is thus equivalent to the process, carbanion to olefin (or acetylene) plus halide ion, viz. .3RC-=CRS
fj
---+R C z C R + S -
(11
The data of Remick18were used for values of the carbon-chlorine and carbon-bromine ionic bond strengths; no value was available for the ionic 2,j :i -- 1 Chlorofurnarate 9 . !4fj bond strength involved in the ionization of the 26.2 - 3 Chloromaleate 0,832 third bond in a triple bond. This was estimated as "4 20.8 - 8 Nromofumarate 250 kcal./niole by using the method of Remick and 12,s 24.2 - 4 Hromomaleate values of 123 kcal./mole for the bond strength of a carbon-carbon triple bond,IY 100 kcal.,'mole for Discussion of Results.-As noted in Table V the that of a double bondIgand the values for ionization second-order rate constants for the halofumarate energy and electron affinity used by Remick for systems (TI) in both water and aqueous ethanol a t saturated atoms. Using these values, i t was esti70" are ten to seventeen times greater than those mated that reaction (1) would be exothermic by for the corresponding halomaleate systems (1). 10 kcal.,'mole and 19 kcal.,'mole for the chloro These results are in agreement with the semi- and brorno systems, respectively. If, following Polanyi,Ii it is assumed that there (quantitative results of Michael6 I t is to be further noted that the activation energies for the fumarates is a relationship between reaction heat and activaare lower than for the halomaleates. Calculations tion energy in analogous reactions, the decrease in of the effect of electrostatic repulsions*J indicate activation energy being one-fourth to one-half the higher repulsions (and thus higher activation increase in heat of reaction, a prediction results that energiesj for the halofuniarates than for the halo- chlorofumarate will react with an activation energy maleates. As these calculations lead to predictions 2.5 to 5.0 kcal./mole less than chloromaleate and opposite to experimental results, we interpret the bromofumarate 5 to 10 kcal./mole lower than experimental results as indicating that the effect bromomaleate. These predictions are in excellent of electrostatic repulsion upon the energy of activa- agreement with the observed differences (see Table tion for elimination reactions is not of major iin- Y j in water, values of 4.3 and 6.0 kcal./mole being portance (at least in solvents of suficiently high observed.20 This represents the second case8 in which this test has been applied and the results dielectric constaritj. The rate constants in aqueous ethanol are greater have been analogous. I t thus appears that these than those in water, in opposition to predictions results furnish additional evidence regarding the from simple electrostatic theory.Is The higher rate proposed mechanistic differences between cis and constants are the result of opposed effects in the trans elimination. quantities of activation. The higher activation Materials Used.-Chlorofumaric acid was prepared by energies observed are in accord with the simple the method of Pedkin.23 I t melted a t 190-191' (Perkin electrostatk theory, but the greater effects oi reported 191-192 and Michael6 190-191'). Bromofuacid was prepared by the method of blichael.6 I t changing solvent upon the entropies of activation inaric melted a t 183-1 84", whereas Michael reported 185-186'. are superimposed upon these to give the larger rate We were unable to reproduce this melting point, although constants. The inconsistency of rate constant and recrystallizatioIi from many solvents was tried. Bromoactivation energy in mixtures of ethanol and water maleic acid, prepared according to Michael,6 melted a t 128130" (recrystallized from nitromethane). Michael rehas been commented upon previously.16 ported a melting point of 136-138', but we were unable to The superiority of the trans process has also been (17) R. A . Ogg and h i . Polanyi. T r a i i s . F a r a d a y Soc.. 31, 1376 attributed3 to a difference in mechanism between it (1935); %I G.Evans and hi. Polanyi, ibid., 34, 11 (1938); E . T. Butand the cis process. I t was assumed that the ler and 11 Polanyi, ibid., 39, I 9 (1943); 11. Polanyi. Eiiiicnuour, 8 , trans process involved a one-stage concerted mech- 3 ( l 9 4 9 l . (18) A. E Remick, "Electronic Interpretations of Organic Chemisanism in which the proton was removed by base, the multiple bond was formed and the halide ion try," John X'iley and Sons, Inc., New York, N. Y.,1943, p. 219. (19) I,. Pauling, "Nature of the Chemical Bond," Second Edition lost; the energy of the transition state was thus a Cornel1 University Press, Ithaca, N.Y., 1940, p. 131. Solveiit: 54.2 w t . (,o aqueous ethaiiol; ioiiic btrciigth
U.
0.11
,
~
(14 j 'These calculations were made substantially as described previously for another casea giving estimates of the differences in coulombic energies involved in the approach of an hydroxide ion t o within the transition-state distance of the hydrogen atom being removed, a s affected by the c i s - or trmzs-halogen atom and the c i s - or Irans-carboxy l a t e group on the beta carbon atom. ( 1 5 ) ii. I). Hughes a n d C E: Ingold, 7rii)ri f ' u d , i . v .Sur., 37,11.57 ( I !).4
,
I), 11;)
5. J
Cristol
allrl
\V. f
