J. Phys. Chem. 1984,88, 4185-4191
4185
Epoxide Ring Opening Catalyzed by a Phosphate Aggregate in Concentrated Buffer Solutions' Y. Pocker* and B. P. Ronald2 Department of Chemistry, University of Washington, Seattle, Washington 981 95 (Received: January 18, 1984)
A systematic experimental investigation of kinetic terms associated with the ring opening of propylene oxide in concentrated phosphate buffer has revealed some unusual features. Plots of k, (=kobsd- V,/[epoxide]) vs. [buffer] for a 5 X 5 matrix at ionic strength 4 display marked parabolic character, while conforming to the Setschenow equation. Linear portions when analyzed according to the Bell-Darwent method showed conspicuous failure in acidic buffers. These observations are explicable if both an additional buffer catalytic term and the retarding effects of sodium perchlorate are considered. The origin of the Bell-Darwent failure is revealed when a phosphate system description is applied that includes anion-anion complexes. With data from an additional ionic strength the retarding effect of sodium perchlorate was segregated from the catalytic contributions of HzP04-, HPOd2-, and H4P,Os2-. Using the Bell-Darwent rate coefficients as a starting point, we optimized the three rate coefficients to give the best fit for each concentration of sodium perchlorate. The quality of the fit to experiment is shown by the small average error of -0.03 A 1.63%, whereas fully 96% of the buffer matrix rate data has an error of less than f1.96%. The fit also shows that sodium perchlorate exerts a similar rate-retarding effect on each buffer component. The fact that catalytic capacity by anion-anion complexes appears only in H4P20s2-and that the magnitude of the specific rate coefficient is similar to other buffer components is discussed.
Conceptually, ion association provides a self-consistent theoretical approach for the behavior of electrolytes in media of low dielectric c o n ~ t a n t . ~The enhanced hydrophobicity of such systems proved especially effective for sustaining ion association and furnished a suitable medium for the examination of their molecular structure, dynamics, and s ~ l v a t i o n . ~ - Whether ~ a particular system tends toward associative behavior is determined by a complex interplay of factors including both chemical and physical effects.8-10 Important among these are gross electrolyte concentration, amount of bulk solvent, effective dielectric constant of the medium, H-bonding capacity, and ion p ~ l a r i z a b i l i t y . ~ - ' ~ Ion association is not necessarily limited to media of low dielectric constant, but is found to occur in aqueous media under the proper circumstances.8-" In concentrated aqueous salt solutions the requirement for solvation can reduce the amount of bulk solvent to such low levels that ions necessarily approach one another and form various ionic aggregates. Judicious choice of ion species provides a means of manipulating the delicate energy balance ~~
(1) (a) Part 6 of a continuing study devoted to the examination of the role of epoxides in vicinal diol dehydrations. (b) Part 5: Pocker, Y.; Ronald, B. P.; Ferrin, L. J . Am. Chem. SOC.1980, 102, 7725-32. (c) Part 4: Pocker, Y.; Ronald, B. P.; Ibid. 1980, 102, 5311-6. (d) Part 3: Pocker, Y.; Ronald, B. P.Ibid. 1978, 100, 3122-7. (2) Department of Chemistry, Idaho State University, Pocatello, ID 83209. (3) Bjerrum, N. K.Dan. Vidensk. Selsk. Mat.-Fys. Medd. 1926, 7 , 1-48. (4) Szwarc, M., Ed. "Ions and Ion Pairs in Organic Reactions"; Wiley: New York, 1972 and 1974; Vol. 1 and 2. (5) Gordon, J. "The Organic Chemistry of Electrolyte Solutions"; Wiley: New York, 1975; pp 371-538. (6) Bender, M. L. "Mechanisms of Homogeneous Catalysis from Protons to Proteins"; Wiley: New York, 1971; pp 194-210. (7) Winstein, S.; Appel, B. R.; Baker, R.; Diaz, A. In "Special Publication-Chemical Society"; The Chemical Society: London, 1965; No. 19, pp 109-30. (8) Robinson, R. A.; Stokes, R. H. "Electrolyte Solutions"; Butterworth: London, 1959; Chapter 14. (9) (a) Davies, C. "Ion Assocation"; Butterworth: London, 1961; Chapter 13. (b) Nancollas, G. H. "Interaction in Electrolyte Solutions"; Elsevier: Amsterdam, 1966; Chapters 1 , 3-5. (10) Conway, B. E. "Ionic Hydration in Chemistry and Biophysics"; Elsevier: Amsterdam, 1981; Chapter 19. (1 1) Frost, R. L.; James, D. W.; Appleby, R.; Mayes, R. E. J. Phys. Chem. 1982, 86, 3840-5. (12) Joesten, M. D. J . Chem. Educ. 1982, 59, 362-6. (13) (a) Grunwald, E.; I. T.-P. In "Ions and Ion Pairs and Their Role in Chemical Reactions"; Smid, J., Ed.; Pergmanon Press: Oxford, 1979; pp 53-61. (b) Grunwald, E.; Highsmith, S.; I. T.-P. In "Ions and Ion Pairs in Organic Reactions"; Szwarc, M., Ed.; Wiley: New York, 1974; Vol 2, pp 447-5 19.
0022-3654/84/2088-4185$01.50/0
existing between ionic hydration and association. A particularly interesting instance of this may occur when H-bond donor and acceptor sites are present in one or both ions, as for example is the case in certain oxyanions. Although H bonding is a well-known factor in promoting ion association, a unique example of binding of this type is apparently displayed by simple phosphate ~ a l t s . l ~ - ~ ~ The properties of their more concentrated solutions, it was suggested, could be satisfactorily explained if anion-anion complexes were present t h e r e i ~ ' ~Interionic -~~ electrostatic repulsion, according to the proposal could, in favorable cases, be overcome by the attractive force of H bonding. Thus, several types of complexes have been proposed and more recently confirmed by electro~ h e m i c a 1 , ' ~ J ~colligative,16 J~J~ and spectroscopic1g-22observations. In this study we report the kinetic participation of a phosphate anion-anion complex in the ring opening of an epoxide. The experimental conditions employed high concentrations of the inert salt both to maintain constant ionic strength and to suppress the spontaneous reaction. Thus, the bulk water concentration was reduced to such low levels that phosphate anion-anion complex formation could compete effectively with anion hydration.23 Since only a moderate portion of the total phosphate is bound in the form of complexes, their catalytic contribution and that from the simple buffer species could be observed simultaneously. As anticipated, the Setschenow inhibitory effect of sodium perchlorate upon buffer catalysis is e ~ i d e n t . ~ A ~ -combination ~~ of buffer complexation and inhibition of catalysis accounts for the dramatic upward curvature of the rate data reminiscent of the incursion of third-order velocity terms. The results reported herein dissect the combined effect of salt and buffer terms upon the velocity and provide a distinct basis for the identification and separation of three buffer contributions. The novel catalytic term for a phosphate anion-anion complex is of interest both for its mechanistic and for its biochemical implications. (14) Childs, C. W. J . Phys. Chem. 1969, 73, 2956-60. (15) Ivakin, A. A,; Voronova, E. M. Rum. J . Inorg. Chem. (Eng!. Transl.) 1973. 18. -, - ,465-8. -- (16) Wood, R. H.; Platford, R. F. J . Solufion Chem. 1975, 4, 977-82. (17) Ferroni, G.Electrochim. Acta 1976, 21, 283-6. (18) Pitzer, K. S.; Silvester, L. F. J . Solution Chem. 1976, 5 , 269-78. (19) Madsen, L.; Slutsky, L. J.; White, R. D.; Harkness, J. J . Solufion Chem. 1980, 10, 715-22. (20) Glonek, T. J . Am. Chem. SOC.1976, 98, 7090-2. (21) Preston, C. M.; Adams, W. A. J . Phys. Chem. 1979, 83, 814-21. (22) Adams, W. A.; Preston, C. M. J . Chem. Phys. 1979, 70, 2074-80. (23) Lee, W. K.; Prohofsky, E. W. J . Chem. Phys. 1981, 75, 3040-50. (24) Marburg, S.; Jencks, W. P. J . Am. Chem. Soc. 1962, 84, 232-9. (25) Hogg, J. L.; Jencks, W. P. J . Am. Chem. SOC.1976, 98, 5643-5. (26) Hand, E. S.; Jencks, W. P. J . Am. Chem. SOC.1975, 97, 6221-30. ~
0 1984 American Chemical Society
4186
The Journal of Physical Chemistry, Vol. 88, No. 18, 1984
Experimental Section Chemicals. Propylene oxide (Aldrich) was purified by fractional distillation; the central fraction, boiling range 35-36 O C , was redistilled twice and stored at -5 OC until required for study. Both 'H and l3CN M R spectroscopy failed to show the presence of impurities. The UV spectrum in water showed only end absorption. Salts were analytical-grade material and were dried at 1OC-110 O C for 24 h. Sodium perchlorate (Fischer Scientific) was dried under vacuum torr) a t 130 O C for 24 h prior to use. An insignificant further weight reduction (0.1%) resulted with an additional 12-h drying period. Solutions were prepared according to accepted analytical procedures. Stock solutions of the buffer (R = 4.0, 2.0, 1.0,0.50, and 0.25; R = [basic form]/[acidic form]) were systematically added to premeasured amounts of sodium perchlorate to make the 5 X 5 buffer matrix at ionic strength 4.0. All solutions were homogeneous, transparent, and colorless. Measurements. Readings of pH were made on a Beckman Model 101900 research pH meter fitted with an Orion Model 90-02 double-junction reference electrode and a Beckman Model C glass electrode. The outer cavity of the reference electrode was filled with a saturated solution of analytical-grade sodium nitrate solution adjusted with dilute N a O H solution to pH 7.0. Both sample and reference solutions were thermostated to 35 OC in a specially designed multiple sample holder. Temperature constancy was maintained to within 35.0 f 0.5 O C throughout any p H measurement. Reference readings were made both before and after each sample to correct for meter drift since slow response necessitated a t least 5 min per reading. Samples were read in duplicate and measurements were discarded unless deviations fell within less than fO.O1 of a pH unit. Stock buffer solutions prepared for kinetic measurements, when diluted to 1% of their original strength, agreed to within 0.007 f 0.017 pH units of expected values. Kinetic measurements were made with a Varian Model T-60 nuclear magnetic resonance spectrometer, by using the technique described earlier; see Figure 1, a and b. The resolution was maintained between 1.0 and 1.5 H z and the phase adjustment, integral balance, and base line were optimized for each signal. A cluster of between five and eight integrals were recorded for each kinetic point (see Figure l a ) with a 20-25s delay prior to each trace to ensure complete relaxation of the spin system. The combined display optimization and integral recording process rarely exceeded 400 s with the midpoint of this period marking the kinetic time. A typical run consisted of between 9 and 20 separate kinetic points with elapsed time periods spaced such that the reaction could be followed for at least 50% and up to 94% of completion (see Figure lb). No attempt was made to follow all runs to the same percentage reaction as the half-lifetimes span approximately 2 orders of magnitude, from 6.5 to 422 h. All runs were performed in duplicate. Sample temperatures were maintained at 35.0 f 0.5 "C during the entire course of the kinetic experiments. Thermostating was accomplished during N M R measurements by the probe and in between measurements by immersion in a Forma-Temp Jr. Model 2095 water bath and circulator. Each integral trace was measured for total height and for the height of the component signal of interest. This generated between 6000 and 7000 data entries which were reduced to kinetic points by statistical methods. Rate coefficients were determined by least-squares analysis of In (area, - area,) vs. time data and were checked graphically for both accuracy and linearity. Linearity was observed for the extent of time that any given run was followed.
'
Results Two limbs of the pH-log rate profile were examined to establish and k, a t ionic strength 4. In the acidic limb, values for kHJO+ reaction rates catalyzed by dilute perchloric acid were measured was found by over a range of two pH units. The value of kHJO+ extrapolation of the linear kobsdvs. p H plot and was checked by least-squares analysis (see Table I). The very slow (tip= 422
Pocker and Ronald TABLE I: Limb Components at Ionic Strength 4
rate coeff
ratio'
kw,o+,bM-' s-'
0.38 4.56 f 0.26 4.43 f 0.12 1 .o
1OYk,,c s-' 107k,: s-1 108kHz0,eM-' s-'
2.7 0.40 0.39 0.43/
'Ratio of the value of the limb component determined at ionic strength 4 divided by the value at ionic strength 2. bIntercept of a plot of log kobsdvs. pH in the acidic region of the pH rate profile. CDeterminedby direct measurement at pH 7.9. dDetermined from the common intercept of a plot of k , vs. [buffer] where k, is the rate coefficient containing only the buffer and spontaneous terms at constant ionic strength. 'Derived from the water concentration, 45 M at ionic strength 4 and the measured value of k,. f A t ionic strength 2 the water concentration was 50 M and k, was 1.13 X SKI. TABLE II: Measurements of Buffer pH
R" 4.0 2.0 1 .o
0.5 0.25
ionic strength 4'sd
ionic strength 0.04c
6.968 6.560 6.092 5.556 5.026
7.620 7.326 7.019 6.752 6.415
"Buffer ratio as mixed, R = [basic form]/[acidic form]. bStock buffer solutions of ionic strength 4.0 at 35 OC. These were kinetic run solutions after complete reaction. CStockbuffer solutions diluted 100fold to ionic strength 0.04 at 35 OC. These pHs agree on the average to within f 0.007 pH unit with the values calculated or found in the literature. See: Bates, R. G . "Determination of pH: Theory and Practice"; Wiley: New York, 1964; Chapter 4. dThe shift of pH to the acidic region in these concentrated buffers is attributed to the formation of anion-anion complexes. The acid dissociation constant is larger for certain of these complexes than for the uncomplexed species. 1 4 J 5 , I7
h) spontaneous rate was determined well within the pH-independent region, namely, pH 7.9. This value of k, was confirmed by analysis of buffer rate data shown in Table I. The kobsdrate coefficients determined for a family of buffer solutions (fixed [basic form]/[acidic form]) contain two terms: k,, due to a specific acid contribution, and k,, the principal component. The velocity constant k,, containing the sum of spontaneous and buffer terms, is readily separated from kobsd through subtraction of the acid term. Thus, k, = kobsd- V,/ [epoxide] where V, is the velocity contribution from acid. Values of k, when plotted against the sodium dihydrogen phosphate concentration in the buffer displayed marked parabolic character (Figure 2a). The curves extrapolate to a common intercept, corresponding to k,, and confirm the value measured independently (Figure 2b). Analysis of this dilute buffer region by Bell-Darwent yields a nonlinear plot (Figure 2c). It is noteworthy that the deviation from linearity is pronounced in the region where the concentration of the buffer acid is dominant (R = [basic form]/ [acidic form]; 0.25-1). Specific buffer rate coefficients extracted in this manner not only fail to reproduce the observed reaction velocity in the acidic regions but also fail over the entire buffer matrix. Further, attempts to fit the rate data by the use of quadratic terms also fail. The p H measurements of the stock buffer solutions show a marked shift to lower values as compared to samples of the dilute buffer (Table 11). The agreement between the pH of dilute buffer and both literature and calculated values supports the conclusion that near ideal behavior prevails at ionic strength 0.04. In contrast, at ionic strength 4 the p H shifts of all the buffers in the matrix used in kinetic studies indicate a significant departure from ideal behavior. This could be due simply to an ionic strength effect or as we surmise to a combination of ionic strength effects and association. (27) Bell, R. P.; Darwent, B. deB. Trans. Faraday SOC.1950, 46, 34-41. Bell, R. P.; Clunie, J. C. Proc. R . SOC.London, Ser. A 1952, 212, 33-7. Bell, R. P.: Evans, P. G. Ibid. 1966, 291, 297-323.
The Journal of Physical Chemistry, Vol. 88, No. 18, 1984 4187
Epoxide Ring Opening
t 0
x 10-4 m i n 2
1
3
I I
2
1
t
3
4
x 10-3 m i n
Figure 1. (a) Representative samples of kinetic data taken during a typical kinetic run. These integral traces are of the methyl region resonances. The downfield inflection points are the signals of interest and correspond to the methyl resonance signals of propylene oxide. The upfield inflection points are due to the methyl resonances in propylene glycol and propylene glycol 1- and 2-phosphate. Each cluster of integrals represents a kinetic point, with those shown here plotted as oversized symbols for clarity in the first line of Figure lb. (b) A plot of In (area, - area,) vs. elapsed time for sample runs from phosphate buffer, R = 1, where R = [basic form]/[acidic form], at ionic strength 4 and 35 O C . The area, is the height from the base of the integral to the inflection point. The area, is due to the glycol methyl signal base at the epoxide chemical shift. The time axis for the upper three lines is located at the top of the figure while that for the lower two is located on the bottom; both are in minutes for convenience of plotting. The very top line plotted as 0 is from the most dilute buffer and has a rate coefficient and correlation coefficient of (1.04 0.01)X lo4 s-' and 0.999. respectively. The points plotted as 0,0,and A correspond to the numerical values for the integrals shown in Figure la. The succeeding lines arise from increasing concentrations of the buffer and have rate coefficients and correlation coefficients, respectively, as follows: (0)(1.75f 0.03)X lod s-*, 0.999;(A) (3.69f 0.04) X lo4 s-', 0.999;(0)lower time axis, (7.09f 0.13)X lod s-', 0.998;(A)lower time axis, (1.74f 0.07)X IO-'s-', 0.997.
*
4188 The Journal of Physical Chemistry, Vol. 88, No. 18, 1984
3.c
Pocker and Ronald
I’1j
> 1
C NaHzPC, 1
2
3
4
R
1
F““ i
/
LA
The parabolic character of the k, vs. [buffer] plots, the pH shifts, and the failure of the Bell-Darwent method are all significant. As Jencks has shown, the parabolic character may arise in part from the sodium perchlorate2’ and can account for the fact that the catalytic coefficients which satisfy one particular buffer concentration fail at another. However, the failure of the Bell-Darwent treatment when the acidic form of the buffer is dominant requires special considerations. First, sodium perchlorate could exert a differential salt effect upon the buffer species, or, second, an additional catalytic term becomes manifest in this region. The latter is an appealing conclusion since concentrated phosphate solutions display anomalous properties that are ascribed to the formation of anion-anion complexes.“’-18 Such complexes could be the origin of an additional catalytic term and thus explain the failure of the Bell-Darwent treatment. The analysis that follows accounts for both the Bell-Darwent behavior and the retarding effect of sodium perchlorate. A self-consistent description of the phosphate system composition has been presented by Ferroni.]’ It is attractive both for its completeness encompassing the acidic as well as the basic region and for its ease of application (Table 111). The consequences of its adaptation are that the parabolic character of k, vs. [buffer] remains but the Bell-Darwent analysis now provides a much closer fit (see Figure 2d). This is explicable since the formation of various anion-anion complexes necessarily alters all buffer ratios from their original stoichiometric values. The systematic deviation still
TABLE I11 Species and Percentage Composition of Concentrated Phosphate Buffer at Ionic Strength 4“ comDosition. 75 Rb H2P04- HPOZ- H4P203- H3P,0g3- HZP2024 8.2 58.8 1.o 25.8 6.2 2 14.0 47.0 2.0 33.0 4.0 1 25.0 29.0 6.0 38.0 2.0 16.7 12.3 32.5 1.o 0.5 37.4 17.9 21.9 0.5 0.25 49.8 10.0 “The numerals refer to the percentage of the total phosphate found in the form described. Concentrations of each species were derived from these data and the total phosphate content as determined from weights of dry phosphate salts. Note that for species containing two phosphorus atoms the percentage total phosphate is exactly twice the concentration. This table is taken from the data of Ferroni.I7 bThe buffer ratio as mixed, R = [basic form]/[acidic form]. apparent for acidic buffers can now be accounted for by catalytic contributions from the anion-anion complexes. On the basis of both concentration and equilibrium behavior, the most probable source for this contribution is the phosphate anion-anion complex H4PzOg2-. The retarding effect of sodium perchlorate upon the simple catalytic components kHzp0,-and kHm,z- was deduced with the aid of data from ionic strength 2. Linear extrapolation provided initial values for these parameters as a function of sodium per-
The Journal of Physical Chemistry, Vol. 88, No. 18, 1984 4189
Epoxide Ring Opening 100
a: 80
-
60
-
40
-
a Y a x
R 100
100
I
I
80
60
a Y
H 40
I
C
\
R
I
20
0
R
60
a
Y
w 40
20
0
R
Figure 3. (a) Plots of the % k, vs. R as mixed at ionic strength 4 at constant [NaCIO,] showing the contribution of each catalytic term. The velocity constant, k,, is a sum of components k , = k,
+ ~ H ~ ~ o ~ - [ H ~+Pk~po~Z-[HP04~-] OQ] + k~g@~2-[H4P208~-]
The inserts in each part display the error in the fit of k , to k?lcd. The region bounded by the dashed lines represents an error value of *1.96%. The error is defined as 100(k,c"led- kp)/k,. The symbols 0, 0 , A,and identify the spontaneous, dihydrogen phosphate, monohydrogen phosphate, and H4P20sZ-contributions, respectively, to k,. Parts a-e are for [NaC104] of 0.0, 1.O, 2.0, 3.0, and 3.6 M, respectively. chlorate concentration. These were optimized to fit the alkaline are buffer region where catalytic contributions due to H4P20H2negligible. Further iteration was necessary to achieve the best fit with the three combined catalytic terms. The quality of this
fit to experiment is seen in Figure 3a-e, where each catalytic contribution is shown as a percentage of the experimental value of k,. Noteworthy is the very low average error in this fit, -0.03 f 1.63% with fully 96% of the calculated results fitting the ex-
4190 The Journal of Physical Chemistry, Vol. 88, No. 18, 1984
I
2 ,
i?
Pocker and Ronald TABLE IV: Properties and Structure of Phosphate Anion-Anion ComDlexesm Complex
Ka Md
structuree
References
and notes
n2P20g4-
f
1 VI
0 X Y
'0
1
2
3
l
4
CNaCl0,I Figure 4. Plot of specific :'BLZ coefficients vs. the [NaC104] in the buffer system. The symbols C . and identify the specific rate coefficients for dihydrogen phosphate, monohydrogen phosphate, and H4PzOsZ-,respectively. The curvature shown here is characteristic of the effect of sodium perchlorate and represents Setschenow behavior, log k = K,. [NaClOJ, with the respective Setschenow coefficients -0.1 1, -0.18 and I
II(a) 10.10.17.18
-0.15.
perimental values to within an errror of less than =t1.96%28 (Figures 3a-e inserts). The inhibitory effect of sodium perchlorate concentration upon all of the buffer catalytic components is characterized by the Setschenow equation (Figure 4).
Discussion The differential behavior displayed by kHaO+ and k, with increasing ionic strength is consistent with the mechanisms of propylene oxide ring opening proposed for these reactions' (Table I): Increasing the amount of sodium perchlorate not only lowers the total water concentration but produces a further reduction through the solvation requirements of the cation.29 The increased value of kHpO+reflects the particular sensitivity of hydronium ion activity to the presence of salt and to a reduced effective water concentration; both circumstances characterize experimental conditions far removed from ideality. In contrast, the spontaneous ring-opening reaction of propylene oxide is dependent upon the nucleophilicity of water as well as its H-bonding.capacity. The solvent isotope effect supports the conclusion that several molecules of water participate in this ring-opening process.' Thus, water in one portion of the solvent sheath, through H bonding, activates the propylene oxide oxygen and renders it more susceptible to rear side attack by a molecule from another portion. The decreases in both k, and kHZOarise from a reduced water concentration associated with the presence of salt and from an ion-induced disruption of the catalytically effective array of solvent molecules in the sheath surrounding the epoxide. The reduced water concentration has a particular impact upon the phosphate buffer system. In addition to its role as general solvent, water is necessary for the specific solvation of both sodium and phosphate ions.19 The ionic strength employed in this study falls within the region where these individual ion solvation requirements cannot be entirely fulfilled. Ionic association therefore accompanies this diminished solvating capacity. Because of both its polyprotic character and the magnitude of its acid dissociation constant, phosphate ion association may adopt the form leading to the production of anion-anion complexes of the general formula HG,P2Os"-. Exact structural detail pertaining to these complexes is sparse; however, there is agreement that hydrogen bonding is the force that holds the anions together in the c o m p l e ~ . ~ ~ JAcid *-~~ dissociation constants, probable structures, and related computed (28) The percent error in the fit is defined as 100(k,cstcd- k p ) / k p (29) Although there is debate as to whether sodium ion requires our or six water molecules of hydration, such solvation nevertheless is necessary.I0 Perchlorate ion, on the other hand, apparently has very low solvation re-
quirements which are at best exceedingly weak."
7K -
25
k,%-
Ill(b)
"Numerals are to references. bThe number of interionic H bonds is not known. Some authors suggest that triple, double, and single H bonds may occur; 14,20-22 others prefer a single H bond.Is CNoattempt has been made to account for cationic association effects although such are conceivable for highly charged forms. dData obtained at 25 O C and ionic strength 3, ref 11 and 13. eThe ion complex dimensions shown here are those computed from standard bond angles and bond lengths found for simple phosphate ions in: Corbridge, D. E. C. "Phosphorus: Studies in Inorganic Chemistry"; 2, 2nd ed.; Elsevier: Amsterdam, 1980; Chapter 3. /This complex dissociates into PO>and HPOt- upon further loss of a proton. structural dimensions are presented in Table IV. The catalysis of propylene oxide ring opening by simple buffer species has been shown to occur by two processes. One involves hydration with both proton donation and abstraction steps while the other occurs by direct nucleophilic reaction. Catalysis by phosphate anion-anion complex 111, by analogy, could be expected to utilize these same paths but to different degrees. Regardless of how the structure of complex I11 is formulated at least one proton remains free to participate in a catalytic step. This proton could activate the epoxide oxygen by H bonding as shown in
The Journal of Physical Chemistry, Vol. 88, No. 18, 1984 4191
Epoxide Ring Opening Scheme I. Mode of Catalysis by Complex HIa n --H
r
a Parentheses depict the solvent shell. Dots depict H-bonding. Dashes depict partially broken bonds in the transition state.
Scheme I. This is analogous to the mode of action followed by dihydrogen phosphate ion. An almost 10-fold larger acidity constant for complex I11 as compared to dihydrogen phosphate ion supports this view. Although complex I is expected to possess substantial nucleophilic character, it does not result here in a detectable level of catalysis. If the capacity to H bond to the substrate represents an important requirement for the expression of catalytic activity in propylene oxide ring-opening processes, then it is immediately explicable why there is an absence of catalysis by complex I (Table IV) . The most abundant complex, complex I1 is interesting because expression of catalytic activity could depend upon whether form IIa or IIb is present. Although form IIb is anticipated to possess substantial nucleophilic character, this certainly should be less than that associated with complex I. Form IIa, however, has a proton available for H bonding and should be catalytically active. Careful inspection of Table I11 reveals, however, that the concentration of complex 11, regardless of whether it exists as form IIa or IIb, undergoes only a small change across the entire buffer ratio range. This small concentration change does not provide a sound basis for either the unequivocal identification of or sep-
aration of a potential catalytic contribution from complex 11. .Thus, a low background of catalytic activity could arise from this modest albeit constant concentration term and escape detection. We therefore have cast our interpretation in the simplest form consistent with the data, which provides that any catalytic activity due to anion-anion complexes resides solely with complex 111. The partitioning of kbuffer (our k , - k,) into three components utilizes the alkaline buffers, where the concentration of complex and kHPO4z-. I11 is negligible to define initial values for kHZPo4When the remaining buffer ratios are fitted by including a catalytic contribution from complex 111, all three catalytic coefficients are found to differ yet follow the same trend and have similar magnitudes (Figure 4). This parallel behavior of the catalytic coefficients for H2P04-and complex I11 may simply reflect a similarity in catalytic mechanism. The fact that complex I11 is a somewhat better catalyst than H2PO4- is fully consistent with its greater acid dissociation constant and the B r ~ n s t e drelationship. The nonlinear catalytic effects observed in propylene oxide ring opening in concentrated phosphate buffer has led to an appealing model explaining their origin. The implication of these results is that high-order kinetic terms can arise out of the catalytic potential of species produced by anion-anion association. Such association and its accompanying potential can be seen now as an essential feature characteristic of phosphate systems. This kinetic analysis of the manifold contributions to upward curvature in phosphate buffer-rate relationships imparts some appreciation for the catalytic potential of phosphate anion-anion complexes in a wide range of systems. The significance of such complexes has not escaped our attention, for conceivably some of them may play an important and heretofore overlooked role in metabolic, regulatory, and genetic transformations involving the ubiquitous phosphate moiety.
Acknowledgment. Acknowledgment is made to the donors of the Petroleum Research Fund, administered by the American Chemical Society, for support of this research. We also gratefully acknowledge additional support of this work by grants from the National Science Foundation and the National Institutes of Health of the US.Public Health Service. We thank Dr. Anna Pocker for expert assistance in the preparation of this manuscript and especially for incisive contributions and helpful comments. Mr. Donald B. Moore provided technical assistance with the computer and guided execution of the figures for which we are grateful. Registry No. H2P04-, 14066-20-7; HPO>-, 14066- 19-4; propylene oxide, 75-56-9.
