202
NOTES
The experimental data of X I and Xz have been comI pared with the values given by eq 6-8. The best
Figure 6. Comparison of experimental monomer and dimer fractions with the values computed through eq 6, 7, and 8 for q1 = 5.5 and q 2 = 0.26.
amount of aggregates higher than dimers is negligible: = 0.355 a t 517 mp. Using these data and eq 11 the distribution of the different species was computed through the equation
agreement has been obtained for the following values of the q constants: q1 = 5.5 and q 2 = 0.26. The graph of Figure 6 shows that the agreement between experimental and statistical data is very good for the X I and reasonably good for the X z values. A low value of qz indicates a particular stability of dimers with respect to higher order aggregates; the fraction of dimer molecules is in fact much higher than that expected in the absence of second-neighbor interactions (q, = 1) (see Figure 5). The agreement of the experimental results with the statistical model seems to us of some interest because generally statistical treatments do not apply easily to the binding of small molecules because of the too many factors implied in the phenomenon. The good agreement obtained in our case, even with the limitation of several simplifying assumptions, by using only two binding parameters should be a good point in favor of the actual possibilities for a statistical treatment of the binding of dyes to polymers.
E,
A617 = 0.214Xi
+ O.355Xz +
0.180(1 - XI - X,)
(12)
Acknowledgment. The authors wish to thank Miss Paola Bianconi for her help during the experimental work.
NOTES
Rates of Mercapto Proton Exchange of Mercaptoacetic Acid in Acetic Acid'
by Jerry F. Whidby and Donald E. Leyden2 Department of Chemistry, University of Georgia, Athens, Georgia 90601 (Received March $0, 1969)
Recently there has been a great interest in the utilization of high-resolution and pulse nuclear magnetic resonance for the study of protolysis kinetics. For the great part this work has concentrated upon the exchange of amines and carboxylic acids in a variety of solv e n t ~ . * - ~An interesting and important acidic functional group which has received less study is the mercapto g r o ~ p . ~The , ~ importance of this functional group in compounds of chemical and biological interest The Journal of Physical Chemistry
led us to investigate the nature of the protolysis kinetics of a representative compound. Because of its own importance and the similarity between some other important compounds, mercaptoacetic acid was chosen. Other mercapto compounds which have been studied include 2-mercaptoethanol in aqueous solutionE and (1) This investigation was supported by Public Health Service Research Grant GM-13935 from the National Institutes of Health. (2) Author to whom inquires should be addressed. (3) W. F. Reynolds and T. Schaefer, Can. J . Chem., 42,2641 (1964). (4) M . Cocivera, J . Amer. Chem. SOC.,88, 672, 677 (1966). (5) M . S. Puar and E. Grunwald, ibid., 89,4403 (1967). (6) E. Grunwald and E. K. Ralph, 111, ibid., 89,4405 (1967). (7) E. Grunwald and M. S. Puar, ibid., 89, 6842 (1967). (8) M. M. Kreevoy, D. S. Sappenfield, and W. Schwabacher, J . Phys. Chem., 69, 2287 (1965). (9) I. P. Gragerov, V. K. Pogorrelyi, and A. I. Brodskii, Dokl. Akad. Nauk SSSR, 178,880 (1968).
NOTES thiophenol-methanol proton exchange in carbon tetrac h l ~ r i d e . ~The mercapto proton exchange of 2-mercaptoethanol was reported to be base catalyzed but not acid catalyzed up to 11 M perchloric acid. This is contrary to the well known exchange behavior of alcoholic protons which undergo fast exchange in both acidic and basic media.1° The proposed rate expression for 2-mercaptoethanol was given as
where lcl is a pseudo-first-order rate constant and k g is a second-order rate constant of a reaction catalyzed by a base B. Rate constants for proton exchange at room temperature of kl =32 sec-l and ~ o A . , = 2 X lo3 1. mol-l sec-' for the acetate ion catalyzed exchange were reported. Both acid and base catalysis of the mercapto proton exchange have been observed in liquid 2-mercaptoethanol. l1 However, quantitative data are not available. The proton exchange between thiophenol and methanol in CC1, was found to be catalyzed by HC1 or sodium methoxide. The second-order rate constants at 27" are kg = (1.4 f 0.3) X 1041.mol-1sec-1forthebasecatalyzed exchange and k~ = (2.8 f 0.5) X lo21. mol-' sec -l for the acid-catalyzed reaction. Corresponding activation energies are 7.5 i 0.5 and 11.0 f: 0.5 kcal/ mol, respectively. In the absence of a catalyst the exchange is too slow to be measured by nmr.
Experimental Section Mercaptoacetic acid (Eastman grade, Distillation Products Industries) was distilled under vacuum before use. The methyl ester of mercaptoacetic acid was obtained by fractional distillation of a mixture of mercaptoacetic acid and methanol. Glacial acetic acid (J. T. Baker, AR) was further purified by the addition of acetic anhydride followed by fractional crystallization.12 The solvent was stored in a sealed container prior to use. The acetate salts used were all reagent grade anhydrous materials and were used without further purification. The nmr spectra were recorded using a HitachiPerkin-Elmer R-20 high resolution spectrometer equipped with a variable-temperature probe. The spectrometer settings varied but were checked to ascertain that saturation was not encountered. All temperatures reported with the nmr data were calibrated and are accurate to f 1". A low-temperature limit of 30" was used because viscosity broadening became significant below this temperature. All data are at 40" unless stated otherwise. Limitations upon the precision of activation energy data were determined by the inaccuracies given for temperature calibration and the narrow temperature range of approximately thirty degrees. This range was established by viscosity broadening at the low temperature side and coalescence on the high-temperature limit.
203 Viscosity broadening can be distinguished from kinetic broadening quite easily before the spectrum has coalesced. An increase in temperature will sharpen the multiplet broadened as a result of viscosity but will normally lead to increased kinetic broadening as a result of the relationship between rate and temperature. The precision of the activation data is given with the results as the standard deviation of the data. The natural line width of the sample was determined several times during each run. These line widths were approximately 0.5 Hz and assumed to be determined by magnetic field homogeneity. The 13Cside band of the acetic acid methyl resonance was found to be a convenient monitor of the field homogeneity and was used for that purpose. Variation of the concentration of mercaptoacetic acid had no effect on the line width.
Results and Discussion The nmr spectrum of mercaptoacetic acid in glacial acetic acid is simple. There is a t riplet at T 7.77(SH), a doublet a t T 6.69(CH2), and the merged spectrum of the solvent and sample carboxyl protons at lower field. The mercapto proton is hidden by the methyl proton resonance of the solvent unless &-acetic acid is used. I n principle, either the SH or methylene proton resonance may be used for the exchange study. The spin-spin coupling between these protons will collapse as the exchange rate is increased. The shape of the methylene proton signal is therefore determined by the rate of exchange. Because the coupling constant (7.88 cps) is much smaller than the chemical shift difference between the SH and solvent carboxyl proton resonance, the coupling will collapse at a slower exchange rate than the coalescence of the SH and solvent peaks. I n practice it is advantageous to use the methylene doublet to determine the exchange rate to avoid interference of the solvent methyl resonance or the alternative use of &-acetic acid. Therefore, the observed phenomenon of direct interest is a broadening and eventual coalesence of the methylene proton resonance. The rate of exchange is computed from individual spectra using a computer program prepared utilizing the general approach as given by Arn01d.l~ Several relative intensities at various points in the methylene resonance spectrum are used as data and the program computes the rate of exchange by minimizing the differences between the relative intensities of the experimental and simulated spectra. As in most applications, it is necessary to assume that the spectral parameters of the compound are not dependent upon (10) (a) E. Grunwald, C. F. Jumper, and S. Meiboom, J. Amer. Chem. SOC., 84, 4664 (1962); (b) Z. LUZ,D. Gill, and S. Meiboom, J . Chem. Phys.r 309 1540 (1959)* (11)Footnote l4 in ref 8' (12) G. W. Ceska and E. Grunwald, J . Amer. Chem. SOC.,89, 1371 (1967). (13) J. T.Arnold, Phys. Rev., 102,136 (1956). Volume 74,Number 1
January 8, 1970
204
NOTES
20
20
10
0
0 0
4
2
6
8
[M(Ach] x 105
Figure 1. Rate of mercapto proton exchange of mercaptoacetic acid us. salt concentration: x, potassium acetate; 0, sodium acetate; A, barium acetate.
the conditions which are varied in order to vary the rate of exchange. A plot of the rate of mercapto proton exchange us. the concentration of potassium, sodium, and barium acetate gave linear plots as shown in Figure 1. These results indicate that the species which catalyzes the proton exchange is the ion pair of the added salt rather than the acetate ion. If the acetate ion were the catalytic agent, consideration of the ion pair dissociation equilibrium shows that the rate of exchange would be proportional to the square root of the added salt concentration. The fact that the exchange rate is dependent upon the cation is further evidence that the ion pair is involved in the reaction. The pKd values for the ionpair dissociation of potassium, sodium, and barium acetates in acetic acid have been given as 6.1,6.56, and 6.48, respectively. l4 Thereforelif the reaction werecatalyzedby acetateion, at a given concentration of the three salts the decreasing order of rates would be potassium, barium, and sodium. This is not the case. A plot of the exchange rate vs. the concentration of mercaptoacetic acid showed no dependence upon the concentration of the acid. A study of the exchange of the methyl ester of mercaptoacetic acid was performed. Figure 2 shows a plot of the rate of mercapto proton exchange for the methj;I ester of mercaptoacetic acid vs. the concentration of added potassium, sodium, and barium acetate. Like the acid, there was no dependence of the exchange rate upon the concentration of the ester. Because there is no dependence of the exchange rate of the mercapto protons upon the acid or ester concentration, any mechanism involving the transfer of the protons between these molecules is not an important contributor to the observed rate. It would be expected that the extraction of a mercapto proton by acetate ion is a more effective process than extraction by the ion The Journal of Physical Chemistry
0
I
2
3
4
[MiAcInlx 10'
Figure 2. Rate of mercapto proton exchange of mercaptoacetic acid methyl ester os. salt concentration: X, pqtassium acetate; 0, sodium acetate; A, barium acetate.
pair. However, the ion-pair concentration in all experiments reported here is approximately one hundred times the concentration of acetate ion. Therefore, an exchange reaction catalyzed by the latter would be required to be better than ten times faster than that of the ion-pair catalyzed reaction to be detected. Evidently, this is not the case. Therefore, a reasonable proposed mechanism is the transfer of the thiol proton to the acetate ion of an ion pair acetate. This newly formed solvent molecule could then diffuse into the bulk solvent to permit the reprotonation of the thiolate ion by the solvent. This cycle would accomplish the observed proton exchange at the sulfhydryl site. The observation that barium acetate is the most effective catalyst of the three investigated is at least partially explained by the fact that there are two acetate groups in the ion pair to accept the thiol proton. The exchange of the mercapto acetic acid is measurably faster than that of the ester. This observation indicates that the carboxyl group may lead to an intramolecular exchange route of some significance. Although the carboxyl protons are undergoing rapid exchange with the solvent, these reactions occur by a route which involves the exchange of protons with solvent molecules hydrogen bonded to the carboxyl sitesb However, base catalysis is an important reaction which is generally too fast to measure by nmr. Under base catalysis, for example, by acetate ions or an ion pair, a low concentration of carboxylate ions is formed which will be protonated at a very rapid rate. An intramolecular transfer of protons from the mercapto site to the carboxylate ion may occur. This provides an exchange route for the acid which is not available to the ester. (14) 0.W. Kolling and J. L.Lambert, Inorg. Chew., 3 , 202 (19641
NOTES
205
The rate expressions for the mercapto proton exchange may be written as 1 / ~ = (kl
+ kz)[iLIOAc]
In solvents of low dielectric constant, the base may be an ion-pair species.
Acknowledgment. The authors thank J. F. Garst for helpful discussions.
for the acid and 1 / ~ = ~~[MOAC]
Solvated Radius of Ions in Nonaqueous Solvents
for the ester where ICl and k3 represent the second-order rate constants for the direct exchange of the proton from the mercapto site in the acid and ester, respectively. If k1 and kg are assumed to be equal, k2 which represents the transfer of a proton from the mercapto site to the carboxylate ion is obtained from the difference between the observed exchange rates for the acid and ester. Values of the second-order rate constants are given in Table I.
by Mario Della Monica and Lucio Senatore Istituto Chimico dell' Uniwersita' di Bari, Bari, Italy (Received May 1, 1060)
If in the conduction processes of electrolyte solutions the ions are regarded as spheres moving in a continuous medium, then the radius of an ion is given by the relationship
Table I: Rate Const,ant for Mercapto Proton Exchange" Salt
K (CzHaOz) Na(CzH302) Ba(CzH3Oz)z
(kl = ks) 1. mol-1
x
10-8
8130-1
0.68 st 0 . 1 0.71 0.1 2 . 1 32 0 . 1
kz x 10-8 1. mol-1
am-1
2.1 f0.1 1 . 3 f 0.1 1.4 f 0.1
a Mercaptoacetic acid solutions were 0.72 M and the mercaptoacetic acid methyl ester solutions were 0.46 M .
The values for k2 are in the expected order if the transfer of the proton from the mercapto group involves the dissociation of the ion pair formed between the carboxylate group of mercaptoacetic acid and the cation present. However, the direct exchange rate of the mercapto proton, kl, is mostly influenced by the number of acetate ions available in the ion pair. Because there are two such groups in the barium salt, the exchange in the presence of barium acetate is the most rapid. The thiol proton exchange was investigated as a function of temperature in acetic acid. The activation parameters obtained were E, = 12.4 f 0.9 kcal/mol; log A = 8.5 i= 0.6and E, = 11.4 f 1.0 kcal/mol; log A = 9.4 f 0.7 for mercaptoacetic acid and the methyl ester respectively. The activation parameters in trifluoroacetic acid were obtained for mercaptoacetic acid and found to be Ea = 14.9 i 0.9 kcal/mol; log A = 10.8 h 0.6. An exchange of approximately 2 sec-l was measured at 40" in this solvent with no added salts. The results of this investigation support the previous conclusions8tQthat base-catalyzed exchange of mercapto protons is significantly faster than acid catalyzed exchange. In special cases such as the one presented here, the base may be part of the molecule under study.
where Xoi is the limiting equivalent conductance of the ion, 1x1 is its absolute charge, and 7 is the viscosity of pure solvent. The rs values obtained from eq 1 in aqueous and nonaqueous solvents are always too small. I n order t o obtain the correct radius of ions in nonaqueous solvents we have reported, for the tetraalkylammonium ions, a plot of the crystallographic radius (re)against the Stokes radius (yS), using Nightingale's suggestion for aqueous solutions.' In each solvent the rs values of the tetraalkylammonium ions, except the methyl, are a linear function of rc. This fact suggests the hypothesis that the tetramethylammonium ion is partly solvated in solution.'S2 A further support to the idea of a partial solvation of the MedNf ion in all the solvents considered is given by the results of Figure 1 and Table I. From this figure it appears that while Xo+q products of Et4N+, Pr4N+, and Bu4N+ ions increase linearly increasing 7) the Xo+7 product of Me4N+isnot a definite function of the medium viscosity. (We are currently engaged in this problem and we will give more definite conclusions in a further note.) Returning t o the main problem with which we are concerned, a calibration curve has been prepared by plotting the Stokes radius against the crystallographic radius for all the tetraalkylammonium ions except the tetramethylammonium ion in all the solvents considered. Figure 2 shows the results in methanol; in the same figure, the Stokes radius values are also shown plotted against the crystallographic radii for a number of cations and anions. The Stokes radius of the anions and the cations of a given charge type is a linear function of the crystallographic radius. (This is also true in the other solvents considered.) (1) E. R. Nightingale, Jr., J . Phys. Chem., 63,1381 (1959). (2) E. G. Taylor and C. A. Kraus, J . Amer. Chem. Soc., 69, 1731 (1947).
Volume 74, Number 1
JanUaTy 8 , 1070
