3190
NOTES Calculations based on conductance measurements by Paul and coworkersQindicate the solvation number of the lithium ion for lithium chloride in D M F to be 3.24, in rough agreement with this work. The dielectric constant of D M F is not exceptionally largelo (D = 36.7) and ion pair format!ion cannot be excluded, indeed Prue and Sherrington" have calculated from conductivity measurements an ion pair formation constant of 35, while Criss and Held12 calculated a value of 2 X lo3 from calorimetric measurements. Butler and Synnott13 have measured the electrode potential for the cell Tl(s)lTlCl(s)[ Li+CI-(DhIF)ILi(s). From this work, they have calculated a free energy of formation of solvated lithium ionsfrom lithium chloride to be in -9.6 kcal/mol. These authors indicate that Lif in DMF may be one of the most strongly solvated cations known.
185 184 175 u)174
T
(L
173 172 171
1
Acknowledgments. We wish to thank the Beach State College foundation for financial aid. 1
2
3
4
5
mole ratio (DMF / L i I )
6
7
8
Figure 4. Curves for the chemical shifts of the methyl protons as a function of mole ratio DMF-LiI in dioxane.
DMF shift in the absence of salt. Such "two component" systems are found in the work described in ref 4 and 8. I n this work the chemical shift increases rapidly after the stoichiometric ratio is reached. Obviously the methyl protons are experiencing an environment very different from the salt free environment of the D M F solution. We attribute this to the excess lithium ions competing successfully for DMF ligands already complexed to other lithium ions to form nonspecific lower solvates. I n order to assure ourselves of the validity of this result the work was repeated using lithium iodide (see Figure 4). Essentially the same results were obtained, the break being at 4.3: 1. The solvation of the lithium ion in D X F is apparently independent of the anion. The resonance of the dioxane protons was also found to vary slightly with the concentration of lithium perchlorate. At small mole ratios of DMF-LiC104, the dioxane protons underwent a shift of 2 Hz, however for larger ratios it remained constant. This may be due to the fact that dioxane competes favorably with DblF for solvation of lithium ions, particularly when the D M F is present in low concentrations. In all of this work, care was taken t o ensure anhydrous conditions. Chemicals were dried by standard techniques and solutions made up on a drybox. The nmr spectra were recorded on a JEOLCO J N M C60H instrument, using TMS as an internal standard. The frequencies were measured by the side band technique, and displayed on a Hewlett-Packard scalar. Reproducibility of measurements was to within 0.2 Hz. In order to overcome solubility problems all spectra were run a t 30". The Journal of Physical Chemistry, Vol. 75, Mo. $0,1971
Long
(8) M. K. Wong, W. J. McKinney, and A.I. Popov, J . Phys. Chem., 75, 56 (1971). (9) R. C. Paul, J. P. Singla, and S. P. Marula, ibid., 73, 741 (1969). (10) G. R. Leader and J. F. Gormley, J . Amer. Chem. Soc., 73, 5731 (1951). (11) J. E. Prue and P. J. Sherrington, Trans. Faraday Soc., 57, 1795 (1961). (12) R . P. Held and '2. M. Criss, J . Phys. Chem., 69, 2487 (1965). (13) J . N. Butler and J. C. Synnott, J . Amer. Chem. Soc., 92, 2602 (1970).
Proton Exchange and Nitrogen Inversion of
a-PhenylethylbenzylmethylamineUsing Nuclear Magnetic Resonance Spectroscopy
by Donald E. Leyden* a,nd W. R. Morgan Department of Chemistry, University of Georgia, Athens, Georgia 30601 (Received March 11, 1971) Publication costs borne completely by The Journal of Physical Chemistry
The use of nuclear magnetic resonance spectroscopy in the study of fast reactions in solution is well documented.*-5 Recent studies1t3 indicate that the rate equation for proton exchange of tertiary amines in aqueous acid can be expressed as (1) E. Grunwald and E. K. Ralph, 111, J . Amer. Chem. Soc., 89, 4405 (1967). (2) E. Grunwald, R. L. Lipnick, and E. K. Ralph, 111, ibid., 91, 4333 (1969). (3) D. E. Leyden and W. R. Morgan, J . Phys. Chem., 73, 2924 (1969). (4) W. R. Morgan and D. E. Leyden, J . Amer. Chem. Soe., 92,4527 (1970). (5) W. R. Morgan, Ph.D. Dissertation, University of Georgia, 1970.
NOTES
3191 the rate constant for nitrogen inversion of tert-benzylamines is of the order of 108-109sec-l a t room temperature.
where the rate parameters are as given in previous examples. 1 3 v 5 The parameter k2 represents the secondorder rate constant for the transfer from the protonated amine to the unprotonated amine through a solvent bridge. A more recent study indicates that the mechanism for nitrogen inversion involves the kinetically controlled formation of a nonhydrated species RsN which is capable of i n v e r ~ i o n . ~This ~ ~ can be expressed as R,NH+** *HOH
+ HOH
ka
k--8
RaN. * *HOH
+ HsO+
(2)
R3N” where RJY” indicates an inverted species of R3N. In some cases, inversion may be further promoted through a mechanism involving two amine molecules in a concerted proton exchange involving a “well aligned, hydrogen-bonded hydrate” species as represented by the second term in eq 1. Using a steady-state approximation on the concentration of R3N in eq 2, an expression for the rate of inversion of the nitrogen atom as a function of hydrogen ion concentration may be represented by eq 3. The
+
quantity f is k i / ( k i k - ~ ) . ~The second term in eq 3 is introduced as a generality as a mechanism second order in amine has been observed for similar compound~.~ Of particular interest here are the values k~ and le, which are the rate constants for the rupture of the R3N. .HOH hydrogen bond leading to exchange and the rate constant for uninhibited nitrogen inversion, respectively. The relationship between k H and the ability of the water molecule hydrogen bonded to the amine nitrogen to participate in hydrogen bonding to the benzene a-electron cloud has been di~cussed.~The value of k~ found here is in agreement with previous predictions. in different solvent sysStudies by Grunwald, et tems also indicate that the strength of dispersion force interactions between the water molecule and the amine substituents is a definite factor in the rate of rupture of the R2N. .HOH bond. Previous studies on a series of substituted a-phenylethylbenzylmethylamines indicated that the rate constants of inversion, k,, for these compounds are in the range 104-10e sec-’.’ However this study and previous i n v e ~ t i g a t i o n s ~indicate ,~J that
Experimental Section Spectra were obtained on a Hitachi-Perkin-Elmer R-20 nmr spectrometer operated under slow passage conditions. Data were obtained a t 50” to eliminate a slight viscosity dependence upon the line width at the higher concentrations used. Temperature regulation was obtained to within ?=lo using a variable temperature probe available with the instrument. Solutions from which the experimental data were obtained were prepared using standard dilution techniques. Amine concentrations ranged from 1.0 to 0.25 M , while excess acid, HC1, was present in concentrations from 0.01 to 4.0 M . Specific rates were obtained by use of equations given for first-order interaction. 3 ~ 6 T values were adjusted to yield a minimum standard deviation between computed and experimental spectra. T , values were assumed to be controlled by the inhomogeneity of the magnetic field and were found to be approximately 0.3 sec from measurement of N-CH, proton line widths under conditions where no exchange broadening occurs. The spectral changes associated with the increased rates of proton exchange and nitrogen inversion have been discussed in some detail5t6and will not be presented here. However, it should be mentioned that an asymmetric carbon center adjacent to an asymmetric nitrogen allows the observation of the two diastereomers under conditions of slow nitrogen inversion. Integration of the two signals shows that one diastereomer is more favorable (1.3:l) than the other. However, the rate of exchange and inversion measured from the methyl resonance of the two isomers is the same. a-Phenylet hylbens ylmet hylamine (I) was obtained by refluxing acetophenone and bensylamine in benzene forming a Schiff base.g Reaction was deemed complete when the calculated amount of water was collected in a Dean-Stark tube. Reaction time for 0.5 mol of reactants was approximately 8 hr. The Schiff base was reduced to the secondary amine and then converted into the desired tertiary amine by methylation with methyl iodide in ethanol. Identification was obtained from nmr and infrared spectra. The acid dissociation constant, Ka, for the amine salt ( 6 ) R . B. Martin has drawn to our attention that the f term in the denominator of eq 3 was missing from our eq 10 in ref 4. Fortunately, this did not affect any conclusions in the earlier work as the f terms cancel in the low acidity region and the product kHf is negligible in the denominator in the high acidity region. (7) A. Ehrenberg, B. G. Malmstron, and T. Vanngard, Ed., “Magnetic Resonance in Biological Systems,” Pergamon Press, New Y o r k ,
N.Y.,1966,p 94. (8) C. H. Bushweller and J. W. O’Neal, J . Amer. Chem. Soc., 92, 2159 (1970). (9) 6 . I. Kegam and S. Yamada, Chem. Pharm. Bull., 14, 1389 (1966). The Journal of Physical Chemistry, Val. 76, N o . 80,1971
3192
NOTES
was obtained at 50" in a mixed solvent system using a differential potentiometric method. lo The solvent system water-tert-butyl alcohol was used due to the insolubility of I in water. Apparent pKa values were obtained for a series of solutions of varying volume per cent tert-butyl alcohol and extrapolated to 0%. This value was found to be 7.45 and was used in the treatment of the rate data.
Results and Discussion A plot of 1 / us. ~ l / a H + for N-H proton exchange for I is linear with no amine concentration dependence. The linearity permits the assumptions k~ > k2Ka[BH+]/[H+]. These assumptions yield eq 4 which describes the rate of exchange in terms of
k~ and the acid dissociation constant K,. This allows only the evaluation of the parameter k~ which was found to be 1.3 X lo9 sec-I. Values of k, and k-, cannot be determined separately from the data. Comparison of the value of k~ with those previously obtained can be made only if the value of k~ for I is corrected to 25". An activation energy for exchange was not determined for this compound, but an estimate may be made on the limits of activation energies using the range of values previously determined for similar compound~.~ Assuming that the value of the activation energy falls between 8 and 16 kcal/mol, one may calculate a range of k~ a t 25" of 1.4 X lo8 to 4.2 X los sec-I. Space-filling models indicate that there is much steric hindrance to rotation about the nitrogen atom and the substituent phenylethyl-carbon bond. This reduction in the movement of the substituent groups would allow the interaction between the R&. . .HOH water molecule and the a-electron cloud of either benzene ring to be favorable. Therefore, a k~ value of the order of that for dibenzylmethylamine would be expected for I. The results given above may be compared with a value of 2.8 X lo* sec-' for dibenzylmeth~lamine.~ Interpretation of the results for inversion was complicated by a chemical shift change between the K-CH, protons in the tn-o diasteromers as a function of the concentration of amine. The same effect was observed for the methylene protons in dibenzylmethylamine. These variations in chemical shift may lead t o false kinetic results unless corrections are made. However, unlike dibenzylmethylamine the chemical shift between the methylene protons of the benzyl group in I did not appear t o be concentration dependent. This would indicate that the factor producing change was localized about the nitrogen atom. Grunwald suggested that in the high salt concentrations being used the possibility of a "well aligned, hydrogen-bonded hydrate, B -HzO* HB+" exists." If such a species were favorable, this The Journal of Phgsical Chemistry, Val. 76, N o , BO, 1971
PH Figure 1. Log 1 / vs. ~ p H for the inversion of a-phenylethylbenzylmethylamine: A, data obtained from N-methyl protons; 0, data obt,ained from phenylethyl protons.
may account for the abnormal chemical shift changes observed. Previous investigators have observed internal chemical shift changes with variation in the dielectric constant of the solvent.12s13 Whatever the cause, it does not appear to affect all compounds or all groups in a given compound equally. Thus careful evaluation of the spectral parameters must be made in studies of this type. Figure 1 shows a plot of log 1,'. us. pH for inversion of the nitrogen atom in I. Figure 1 includes data from analysis of the spectra arising from both the N-CH3 and phenylethyl protons. There was no amine dependence observed, thus eliminating the secondorder term of eq 3. From the linearity of Figure 1 it is also assumed that kHf
