NOTES ing value of ca. 9.3 kcal/mol for AHm,which happens t o be very close to our experimental figure. I n view of the oversimplified model underlying eq 3 in our case, this coincidence may be somewhat fortuitous. I t is conceivable that a t temperatures higher than 13’ and at slightly lower concentrations, HMT molecules may induce in water a local order reminiscent of that of the clathrate. I n our opinion, speaking of solvent structure around solute particles would thus mean, in the case of HMT, building of a sphere of solvation whose geometry is strongly influenced by the fourfold symmetry of donating +IT groups of the solute. Acknowledgments. This work has been sponsored by the Consiglio Nazionale delle Ricerche, through the “Istituto di Chimica delle Macromolecole” Milan. We wish to thank Dr. lf.Pillin of this institute for the measurements of the integral heat of solution of HMT.
3635 may easily be modified to accommodate other possibilities. Suppose that a measured absorption band with a shape function F ( v ) 5 1 a t a fixed temperature consists of two overlapping components corresponding to two distinct chemical species. The shape of the composite band may be written as
F(v)
Bands According to a Two-Absorber Model
sfl(Y)
+ YfdV)
Al(v1m)
+ Az(vzm)
2
Al(vm)
+ Az(vm)
Department of Chemistry, Brandeis University, Waltham, Massachusetts 02154 (Received April 1, 1971) Publication costs assisted by the National Science Foundation
The optical absorption of alkali metal solutions in liquid ammonia consists of a single broad band under a variety of experimental conditions. l-6 The dependence of the spectrum on composition of the solution is slight.1~2~6~6 This fact has been cited in support of a one-absorber model of the optical spectra of these solut i o n ~ . ’ ~ ~n’evertheless, ~’ the fact that the spectra do depend on composition at all suggests that the observed band may be a composite of broadly overlapping absorbances from two or more distinct absorbers.* To test this possibility we have developed a method of analyzing a composite band into two components whose behavior as a function of solution composition provides a test of the validity of the txo-absorber model. In addition, possible equilibria between the absorbers may be tested under certain circumstances. Although the method of analysis was developed with metal-ammonia solutions in mind, it mag be applied to any case in which two absorption bands overlap. To suit our purpose it has been assumed in the development which follours that the overlap between the components is great enough so that only one maximum in the spectrum occurs at each composition. The analysis
= A(vm)
(2)
it follows that x + y l l
by T. R. Tuttle, Jr.,*Gabriel Rubinstein, and Sidney Golden
(1)
in which fi(v) andfz(v) are the characteristic shape functions for the two components and thus depend only on frequency v, and x and y are coefficients which depend only on composition. Each shape function is normalized so that its maximum value is unity. F ( v ) is thus a function of metal concentration as determined by the magnitudes of the coefficients x: and y. I t is easy to show t h a t s = Al(V1m)/A(Ym) and y = A 2 ( ~ 2 m ) / A ( ~ m )in which Al(vlm) and AZ(vZm) are the absorbances due to species 1 and species 2, respectively, at the positions of the maxima of fi(v) and fi(v), respectively, and A ( v m ) is the total absorbance at the position of the maximum of F( v) Because
.
Analysis of Broadly Overlapping Absorption
=
(3)
The equal sign applies when vim = VZm. When the bands are close together and have comparable widths the sum(3) will be close to unity. To apply eq 1 to separate F ( v ) into components it is necessary to know a t least one of the shape functions fi(Y) or f z ( v ) . Suppose fi(v) has been determined by extrapolation to infinite dilution.6 Then if s is also known yfz(v) and hence f z ( v ) may be determined through an application of eq 1. If there is a region in the spectrum wheref2(v) = 0, then s = F(v)/fl(v) for frequencies in this region. When no such region exists, as is the case for metal-ammonia solutions, x: cannot be determined directly. However, a useful analysis can still be made which under certain circumstances leads to a value of c. Let
F(v)
+ YOfi”(V)
(4) in which 1 2 fz’(v) 2 0 and yo 2 0; Le., za is chosen = ZOfi(Y)
(1) R. C. Douthit and J. L. Dye, J . A m e r . Chem. Soc., 82, 4472 (1960). (2) M. Gold and W. L. Jolly, Inorg. Chem., 1,818 (1962). (3) D. F. Burow and J. J. Lagowski, Advan. Chem. Ser., 50, 125 (1965). (4) R.K.Quinn and J. J. Lagowski, J . Phys. Chem., 72, 1374 (1968). (5) W . H.Koehler and J. J. Lagowski, ibid., 73, 2329 (1969). (6) I. Hurley, T. R. Tuttle, Jr., and S. Golden, “Metal Ammonia Solutions,” Butterworths, London, 1969, p 503. (7) iM.Gold, W. L. Jolly, and K. S. Pitser, J . Amer. Chem. Soc., 41, 3089 (1964). (8) S. Golden, C. Guttman, and T. R. Tuttle, Jr., J. Chem. Phys., 44, 3791 (1966).
The Journal of Phgsical Chemistry, Vol. 76, No. dS, 1971
NOTES
3636 such that subtracting xofl(v) from F ( v ) gives no negative values. Although yofio(v) determined in this way is not the true absorption band for the second species the quantity Amyofzo(v)is proportional to its concentration if the two-absorber model is correct as can be seen from what follows. Since yofzo(v) is positive definite and YOfZ0(V)
=
YfZ(Y) -
(20
- X)fl(V)
(5)
it follows that
The equal sign applies only at frequencies for which If vo is one such frequency, then
f z o ( v ) = 0.
f z b o ) - xo - x fl(V0)
(7)
Y
This value is a minimum in the ratio of fz/f~. Therefore the frequency vo is fixed by t'he condition that yofzo(v) 2 0 since a minimum value of fz/fl can only occur at fixed frequency independent of composition. Since vo is independent of composition, it follows that
xo - x
=
(9) Since k is independent of composition, we obtain the result that Amyo a Amy, i e . , the amount of residual absorption extracted is proportional to the concentration of the second species. A value of x may be determined with the aid of =
xo - cy
= 20
Na+.S-
Xa+
+ S-
(11)
t8heequilibrium constant relationship yields
so that in the presence of the excess NaI at a constant concentration in solution [Na+]and yk2should be practically constant, and hence the ratio of the two absorbers, [SI-/[Na+.S-], should also remain constant. Since the relative amounts of residual absorption did not remain constant on changing metal concentration, we concluded that the residual absorption should not be attributed to the ion pair. Aclcnowledgment. This work has been supported in part by a grant from the National Science Foundation.
Intermediates in Nucleophilic Aromatic Substitution. V1.I Kinetic Evidence
of Intramolecular Hydrogen Bonding
cy
(8) in which c is a constant independent of frequency and composition. Combining eq 8 with eq 5 yields
x
tive amounts of residual absorption which depended on metal concentration. For the ion-pairing equilibrium
-
pC o
(10)
by choosing c/k so that the resulting AmxfL(v) and Amyfz(v) satisfy a particular equilibrium relationship. Such a fitting procedure is not generally possible when the equilibrium is sensitive to activity corrections, as is the case for ionic equilibria. A particular value of the present analysis is that certain possible equilibria may be rather easily eliminated from consideration. For example, in the case of sodium solutions in ammonia we were interested to test whether the observed shifts in the optical absorption band could be described in terms of an equilibrium between two species and whether the two species were ions and ion pairs. The analysis of our experimental results yielded residual absorptions, i.e., yofzo(Y), for which fz" (v) was independent of metal concentration. Therefore, the assumption of a two-absorber model is justified. I n addition, spectra of solutions containing an excess but constant concentration of sodium iodide yielded relaThe Journal of Physical Chemistry, Vol. 76,No. IS,1971
in Meisenheimer Complexes
by Claude F. Bernasconi2 M a x Planck Institut f a r Physikalische Chemie, Gbttingen, Germany (Received M a y $1, 1.971) Publication costs assisted by the Petroleum Research Fund
Recently we reported a temperature-jump study on the Meisenheimer complex formation between 1,3,5trinitrobenzene (TNB) and aliphatic amines in 10% dioxane-90% water, which allowed determination of kl, k-1, and K X H in eq 1. The data suggested the presence of an intramolecular hydrogen bond to the o-nitro group in XHa3 Inasmuch as XH and X- are models for the intermediate in nucleophilic aromatic substitution reactions by amines, these findings have considerable bearing on the mechanism of such reactions, in particular with regard to the rate-limiting step. This is because intramolecular H bonding will influence the rates of intermediate conversion into products as well as their reversion to reactants, but in different mays, depending on the specific arninee4 Thus, it seemed highly desirable to obtain more direct evidence for intramolecular hydrogen bonding in these systems. (1) Part V: C. F. Bernasconi and R. G . Bergstrom, J . Org. Chem., 36, 1325 (1971). (2) Address correspondence to the author at the Division of Natural Sciences, University of California, Santa Cruz, Calif. 95060. (3) C. F. Bernasconi, J . Amer. Chem. Soc., 92, 129 (1970). (4) C. F. Bernasconi, in preparation.
