J. EPSTEIN AND W. A. MOSHER
622
If Q is sufficiently small to neglect Q2, then &/% = k1Clo/k2Czo. Here diffusion is not rate controlling. On the other hand, a predominantly surface reaction corresponding to high olefin concentration should show an effect of relative diffusion coefficients on relative BQl)/ rates in a mixture. Since Q1/QZ = ( A (C EQz),it is evident that Q1/Qz > A / C = klClo/ k2C.20 if E > B, that is, if k2/Dz > kl/D1. Since we have found that kl = 1.6 kz, the results imply that, at9O0K, D1 > 1.6D2if the model is valid. A different set of boundary conditions, in which the surface concentration of olefin is maintained a t zero by the flux of 0 atoms, leads to a solution in which the
+
+
relative rates are equal to D1C10/D2C20 initially. D1 would be required to be greater than Dz by a t least two orders of magnitude under the conditions of the first data point shown in Figure 1 to account for the large difference in rates between propylene and l-butene. This seems unusual, but the results themselves are unusual and appear to require such drastic differences. In summary, the characteristics of the 0 atom-condensed olefin system show that (1) an olefin film behaves like a sink to 0 atoms over very wide olefin concentrations, (2) the relative chemical rates of atom addition to two different olefins can be determined at high dilution, (3) the relative rate data as a function of concentration suggests olefin diffusion effects at high concentration, and finally (4) an isotope effect for the H atom migration required for propionaldehyde formation shows a rather efficient energy transfer from the reaction intermediate to the surrounding matrix.
Magnesium Ion Catalysis of Hydrolysis of Isopropyl Methylphosphonofluoridate. The Charge Effect in Metal Ion Catalysis by J. Epstein Research Laboratories, Edgewood Arsenal, Maryland
81010
and W. A. Mosher Uniwraity of Delaware, Newark, Delaware
19711
(Received July 31, 1967)
At constant pH, hydrolysis of isopropyl methylphosphonofluoridate in water is catalytically accelerated by magnesium ions. The active species is the magnesium-hydroxo complex and is slightly more active than an equivalent concentration of hydroxide ion. The magnesium may provide a very slight acid catalytic effect. The activity of the metalhydroxo complex is explained on a charge-effect concept; i.e., the basicity of the complex to the neutral substrate is greater than would be anticipated from the pK, of its conjugate acid. Metal ions exert their effects in promoting or catalyzing chemical reactions in several ways depending upon, among other factors, the metal ion itself, the substrate, the medium, and specific interactions among the metal, substrate, and medium.’ For the metal ion catalyzed hydrolysis of isopropyl methylphosphonofluoridate (I), two mechanisms, both of which are consistent with the kinetics of the reaction, have been proposed. The first2 pictures the hydrated metal ion (and metal chelates) as polarizing The Journal of Physical Chemistry
the phosphoryl bond, thereby facilitating attack by hydroxide ion in solution. The second3 considers that the reaction is a simple nucleophilic displacement, the active species being the metal-hydroxo ion (formed by (1) M.L. Bender in “Reactions of Coordinated Ligands and Homogeneous Catalysis,” Advances in Chemistry Series, No. 37,American Chemical Society, Washington, D. C., 1963,p 19. (2) T.Wagner-Jauregg, B.E. Hackley, Jr., T. A. Lies, 0. 0. Owens, and R. Proper, J . Am. Chem. SOC.,77,922 (1955). (3) J. Epstein and D. H. Rosenblatt, &id., 80, 3596 (1958).
MAGNESIUM IONCATALYSIS OF HYDROLYSIS OF ISOPROPYL METHYLPHOSPHONOFLUORIDATE ionization of the hydrated metal ion). I n the latter mechanism, it is postulated that the high rate of reaction between I and the metal-hydroxo species is due to a concerted1 and simultaneous push-pull upon the substrate, the metal portion acting as an electrophile and attacking either of the electronegative elements (0 or F), while the hydroxo portion attacks the electrophilic phosphorus atom. Martel14 considers that a distinction between catalytic species in the hydrolysis of I is meaningless, since he feels that both species, through a series of interdependent equilibria, arrive at the same reactive intermediate, and the rate-determining step follows the formation of this intermediate. Nevertheless, the concepts of the role of metal ions as catalysts are quite different in thie two mechanisms, and the differences could be important when applied to other systems. I n the second mechanism, the metal-hydroxo complex can serve as a carrier of hydroxide ion in neutral solution, with the metal serving as a Lewis acid. If the substrate is subject to acid catalysis, then the metalhydroxo complex can serve as a bifunctional catalyst; if the substrate is subject only to base catalysis, the metal-hydroxo complex would serve as a base catalyst, the activity of the complex being due to the hydroxyl group alone. Thus, in the last mentioned case, if a 0.001 M solution of a hydrated metal ion were completely ionized at the pH of an experiment to its metalhydroxo complex, and other factors, such as successive ionizations of the hydrated species, polymerizations, etc.,6 were kept to a minimum, the reactivity of this solution could. be equivalent to that of a solution 0.001 M in hydroxide ion. Since many hydrated metal ions have ionization constants equal to or greater than one may effectively have, at near neutral pH, a relatively high concentration of hydroxide ions. The practical consequence of this hypothesis is that it should be possible to carry out base-catalyzed reactions under acid or neutral conditions. Support for the hydroxo-metal complex as the active intermediate comes from an extrapolation of the findings in studies of the reactivities of cation-bearing anions with I in aqueous solution in which it was shown that cation-bearing anions of phenols, catechols, pyrogallols, and hydrated aldehydes have higher reactivities than would be anticipated from their proton Thus, for example, the anion of m-trimethylammoniophenol, whose conjugate acid has a pKa = 8.12, is more than three times as active in displacing fluoride ion from I as would be anticipated of a phenolate of the same proton basicity, but possessing no cationic group; the monoanion of the diprotonated 3,6-bis(dimeth~ylaminomethyl)catechol is 38 and the monoanion of the 3,4,6-tris (dimethylaminomethyl) catechol, 75 times as reactive as their noncation-bearing but same proton-basicity analogs. The effect of‘thecationic substituent, called the charge
623
effect,is explained on the basis that the pK, of the conjugate acid is not a true measure of the basicity of the anion to a neutral substrate and that a cation-bearing nucleophile will be much more basic to a neutral substrate than to the positively charged proton, because the repulsion factors, operative in the ionization equilibrium of the acid, are either absent or less important in the reaction between the nucleophile and the neutral substrate. For a nucleophile to exhibit a charge effect, there must be a contribution to the ionization of its conjugate acid by an electrostatic repulsion of the proton by the cationic group. Qualitatively, the difference between the pK, of water and the pKa of a hydrated metal ion can be predicted on electrostatic grounds,5 and, while the electrostatic effect cannot account for the quantitative ionization data of hydrated metal ions, it appears that a dominant factor in the extent of ionization is due to a repulsion of the proton by the charged metal ion. It follows, then, that the activity of the metal-hydroxo complex should approach that of hydroxide ion in its reactivity to a neutral substrate (provided that there is no contribution to the rate from the metal ion). Compound I, however, is subject to acid c a t a l y ~ i s ,and ~ one would expect to find a contribution to the rate by the metal ion in the complex, the magnitude of the contribution being proportional to its effectiveness as an acidic catalyst. As a first approximation, then, in the reaction of a series of hydroxo-metal complexes with I, the bimolecular rate constants should decrease as the acid catalytic properties of the ion decreases. In this paper, we report on the hydrolysis rate of I in water in the presence of magnesium ion, a very weak Lewis acid.
Experimental Section The methods and apparatus used in studying the magnesium ion catalyzed hydrolysis of I were identical with that used for the study of other metal-catalyzed reactions described in ref 3. In brief, solutions of I and the magnesium salt were mixed in a water-jacketed reaction vessel to give the required concentration of each and the pH was adjusted with base from a microburet. The amount of base required to keep the pH constant during the course of the reaction (hydrolysis (4) A. E.Martell in “Reactions of Coordinated Ligands and Homogeneous Catalysis,” Advances in Chemistry Series, No. 37,American Chemical Society, Washington, D. C., 1963,p 161. (5) J. P. Hunt, “Metal Ions in Aqueous Solution,” W. A. Benjamin, Inc., New York, N. Y.,1963,pp 45-55. (6) J. Epstein, R. E. Plapinger, H. 0. Michel, J. R. Cable, R. A. Stephani, R. J. Hester, C. Billington, Jr., and G. R. List, J. A m . Chem. Soc., 8 6 , 3075 (1964). (7) J. Epstein, H. 0. Michel, D. H. Rosenblatt, R. E. Plapinger, R. A. Stephani, and E. Cook, ibid., 86, 4959 (1964). (8) J. Epstein, P. L. Cannon, Jr., H. 0. Michel, B. E. Hackley, Jr., and W. A.Mosher, ibid., 89,2937 (1967). (9) J. Epstein, Public Health Rept. (U.S.), 71, 955 (1956).
Volume 76, Number 6 February 1968
J. EPSTEIN AND W. A. MOSHER
624 liberates 1 mole each of isopropylmethylphosphonic acid and hydrofluoric acid) was recorded against time. I n several experiments, the concentration of I was determined colorimetrically. Excellent and almost identical first-order plots were obtained when the logarithms of the concentrations of I remaining after various time intervals, determined either colorimetrically or calculated from the volume of sodium hydroxide solution required to maintain a constant pH, were plotted us. time. The catalytic nature of this reaction was established through the facts that: (a) first-order kinetics were observed under conditions where approximately equal concentrations of reactants were used and (b) the rate of decomposition of additional I, after the reaction using equal concentrations of metal ion and I showed no remaining I, was, within the limits of experimental error, identical with that found initially. The bimolecular rate constant for the reaction between I and the metal-hydroxo complex was calculated from the equation k2 =
(kobsd
Table I: D a t a on t’he Effect of Mgz+ on the Hydrolysis Rate of I at 25’ ka X 10-8, 1. mole-1
min-1
8.5
3.83 7.66 11.49 9.0
0
9.5
7.66 0 7.66
Results Table I contains a summary of the data. An average value for the bimolecular rate constant is 2.6 X loa1. mole-’ min-l. Table I1 gives the bimolecular rate constants for the reactions of CuOH+, MnOH+, and MgOH+ with I in aqueous solution at 25”. The pKa values listed are for the ionization of the conjugate acid of the hydroxo-metal species, i.e.
For reference, the bimolecular rate constant for the reaction between I and OH- is 2 X lo3 1. mole-’ min-’. [The average bimolecular rate constant for the reaction between I and OH-, calculated from the data in Table I (zero concentration of Mg2+),is 2.3 X lo3 1. mole-’ min-l, rather than the value of 2 X lo3 given here. The valueof 2 X lo3 1. mole-‘ min-’ is an average of many determinations over a pH range 7-12 and is considered to be a more accurate value.] Consistent with the hypothesis, based upon chargeeffect principles, the data show that : (a) the bimolecular rate constants of the hydroxo-metal complexes are approximately that of the bimolecular rate constant of I with hydroxide ion and (b) they decrease in the expected order Cu > Mn > Mg. The Journal of Physical Chemistry
94 33.2 22.2 13.0 26.6 8.25 11.2 2.0
7.38 20.89 31.30 51.40 26.1
...
...
13,5l 23,92 44.02
2.80 2.48 3.04
84.00
57.9
1.90
284.6
2.94
...
...
...
61.9 346.5
Table 11: pK, Values and Bimolecular Rate Constants for Reaction of Metal Ions and I a t 25’“
x 10-3, 1. mole-1 min-1
kz
- ~H)(K, 4- [Ha+I)/Kaco
where k2 is the bimolecular rate constant in units of 1. mole-’ min-l, k o b s d is the observed first-order rate in min-’, k H is the spontaneous hydrolysis rate at the pH of the experiment, K , (the acid dissociationlo constant of the hydrated magnesium ion) is 3.98 X 10-l2, and Co is the concentration of magnesium added.
0
Metal ion
PKB.
cut + MnZ+ Mgz +
10. 6c 11.4“
8
+
12b 6.6‘ 2.6
*
Value taken from a %f(HzO), e (HO)M(HZO),,I H+. ref 3. Calculated from data in ref 3. pK, from ref 10.
‘
The order Cu > Mn > Mg is an order of stabilities found in many systems’l involving coordination of the metal with various ligands and may be interpreted as an order of strength of covalent bonding of these metals. Schwarzenbach12gives the values for the logarithms of the formation constants of the EDTA complexes of Cu2+, Mn2+, and Mg2+ as 18.80, 13.79, and 8.69, respectively. The stabilities of their hydroxides (negative logarithms of their solubility products) l 3 are : 19.66, 12.8, and 11.0. A relative quantitative measure of the strength of covalent bonding of these metal ions to the oxygen atom can be estimated from the above values. The shift in cm-l of the P=O adsorption of uncoordinated triphenyl phosphate when complexed with the chlorides of cupric copper14 and manganese(I1) l6 (10) “Stability Constants. Part 11: Inorganic Ligands,” Special Publication No. 7, The Chemical Society, London, 1958. (11) E.g., no single exception was found to this order in the binding with thirteen amino acids and one polypeptide: J. P. Greenstein and M. Winitz, “Chemistry of the Amino Acids,” Vol. I, John Wiley and Sons, Inc., New York, N. Y., 1961; see also H.Irving and R. J. P. Williams, J . Chem. SOC.,3192 (1953). (12) G. Schwarzenbach, “Complexometric Titrations,” Interscience Publishers, Inc., New York, N. Y., 1957,p 8. (13) E. J. King, “Qualitative Analysis and Electrolytic Solutions,” Harcourt, Brace, and World, Inc., New York, N. Y., 1959,Appendix
D. (14) D. M. L. Goodgame and F. A. Cotton, J. Chem. SOC.,2298 (1961). (15) D.M.L. Goodgame and F. A. Cotton, ibid., 3735 (1961).
MAGNESIUM IONCATALYSIS OF HYDROLYSIS OF ISOPROPYL METHYLPHOSPNONOFLUORIDATE
-
'036
625
points to a value of the bimolecular rate constant of 2000 1. mole-' min-l (constant for the reaction between I and OH-) indicates that such a reactant should produce a shift in the adsorption frequency of the uncoordinated P=O of ca. 13 cm-'. The change occurring due to H bonding with the P=O group in triphenyl phosphate by methanolI6 was found to be 13.6 cm-l. This suggests that one of the roles played by water in nucleophilic displacement reactions of phosphorus esters is to hydrogen bond to the phosphoryl oxygen. A plausible picture of the transition state in the reaction between hydrated hydroxide ion and I is
9 12 15 18 21 Log of Formation Constants
L
I
I
I
I
I
IO
20
30
40
50
60
A V ,crn-l
Figure 1. 0, plot of log of bimolecular rate constants us. log of formation constants; X, plot of log of bimolecular rate constants us. Av of P=O absorption.
(no similar data were available for magnesium) is also in accord with the above statements. It is of interest that ti plot (Figure 1) of the bimolecular rate constants in Table I1 vs. either the logarithm of Schwarzenbach's formation constants or the shift in phosphoryl oxygen stretching frequencies is linear. Of perhaps greater significance is the fact that extrapolation of the
I
H By analogy, and lending support to the postulation that the hydroxo-metal complex is the reactive species, the transition state of the reaction between I and the hydrated metal ion may be depicted as
(16) J. Goldenson, Appl. Spectry., 18, 156 (1964).
Volume 76, Number 2 February 1968
