J. Phys. Chem. 1985,89, 3101-3102 a H-region f0.3 units around the pK,. Over this interval
(7) The factor in eq 7 increases to 1.925 if one considers a region * O S units around the pK,. As is seen in Figure 2 of the text, the titration curves have a sharp bend a t H- 1 unit lower than the pKa (where$the slope is 33% of that at the maximum) and a reasonably linear region that extends for about 1 unit in H- and is centered at the pK,. The difference ab- a, can therefore be determined quite well by multiplying the observed slope of the linear region by 1.80 (1.93if a H- range of 1 unit is used). Once this difference is determined the pK, is readily obtained as the basicity at which a(&) = a, I/z(ab- a,). The linear region should, of course, be followed by a region of curvature of sign opposite to that at low H-.Where this characteristic is observable, determination of the pK, follows directly from the midpoint in the titration curve. In practice one can usually evaluate the hyperfine differences to better than 10% from consideration of the slope. An uncertainty of this magnitude is reflected as an error of 0.10 in the pKa. For the radicals studied here all except radical IX show a sufficiently linear region in the H-dependence of a(&)
+
3101
to be able to evaluate the pK, in this manner. In all cases eq 6 gives a lower limit td ab- a, and, therefore, a lower limit to the PKa. The approach described here is quite general and can, of course, be used in conjunction with any other physical parameter which represents the weighted average of the two forms of a simple equilibrium. Registry NO. I, 11084-15-4; 11, 96575-26-7;111, 56092-92-3;IV, 11084-23-4;V, 11084-24-5;VI, 52934-45-9;VII, 56092-93-4;VIII, 52934-48-2;IX, 56092-94-5;X, 52934-46-0;XI, 52934-47-1;XII, 52934-55-1;XIII, 52934-56-2;XIV, 52934-58-4;C&, 71-43-2;5NOz-1,3-(COzH)2C6H3, 618-88-2; PhC02H, 65-85-0; terephthalic acid, 100-21-0; phthalic acid, 88-99-3;isophthalic acid; 121-91-5; trimesic acid, 554-95-0;pyromellitic acid, 89-05-4;benzene pentacarboxylic acid, 1585-40-6.
Supplementary Material Available: The g factors and hyperfine data of the acidic and basic forms of the radicals discussed here are given in Table SI. Numerical results from the individual experiments are given in Tables SII-SIX. Figures SI and SI1 illustrate the basicity dependence observed for radicals VI, VII, and VI11 (1 1 pages). Ordering information is given on any current masthead page.
Ionic Dissociation of Hydroxycyclohexadienyl Radical: Effect on 13C Hyperfine Splittings Michael Lefcourt,+ Keith P. Madden, and Robert H. Schuler* Radiation Laboratory' and Department of Chemistry, University of Notre Dame, Notre Dame, Indiana 46556 (Received: January 7, 1985)
The 13Chyperfine constants of 1,2,4,5-tetracarboxyhydroxycyclohexadienyI radical are shown to be substantially unaffected by ionization of the hydroxyl grqup. This result, which contrasts with the large decrease noted in a(H6), implies that the relatively low values for a(&) observed in hydroxycyclohexadienyl radicals and their anions result not from distortion of the radical at the C6 site but rather from perturbation of the wave function at H6 by the OH or 0-group.
Hydroxyl proton dissociation in hydroxycyclohexadienylradicals results in relatively large changes in the hyperfine splitting of the proton at the hydroxyl site ((26) but has little effect on the distribution of unpaired spin density in the r system of the radical.' It is of interest, therefore, to examine effects of ionization on the 13Csplittings with particular emphasis on possible effects ori the carbon atom at the hydroxyl position. We have been able to record 13Clines of the 1,2,4,5-tetracarboxyhydroxycyclohexadienyl radical at natural abundance levels up to 5 M K O H where the radical population is -33% in the ionized form. It is found that there is no substantial effect on the 13Csplittings, including that of the c 6 carbon atom. We briefly report our observations here.
Experimental Section ESR spectra were recorded at the steady-state radical concentration present during continuous 2.8-MeV electron irradiation of NzO-saturated aqueous solutions of 1O-* M pyromellitic acid (Aldrich). The pH was adjusted with KOH (Baker). Solutions were saturated with N 2 0 to convert e,, to additional hydroxyl radicals to improve the ESR signal intensity. At pH C14,where the 13C spectra were relatively intense, they were recorded as previously described.'Vz At higher base concentrations, the 13C +University of Waterloo, Waterloo, Ontario, N2L 3G1, Canada. *Theresearch described herein was supported by the Ofice of Basic Energy Sciences of the Department of Energy. This is Document No. NDRL-2666 from the Notre Dame Radiation Laboratory.
lines became very weak and spectra were recorded digitally and a number of traces averaged to improve the signal-to-noise ratio. The hyperfine constants were taken as twice the difference between the 13Csatellite and the main peak and, in general, can be considered to be accurate to f0.02 G.
Results and Discussion The 1,2,4,5-tetracarboxyhydroxycyclohexadienyl radical was prepared by .OH or 0.-addition to the tetraanion of pyromellitic acid (benzene- 1,2,4,5-tetracarboxylate), as previously documented.'S2 In the region above pH 13 the OH proton, because of rapid exchange with water, is not manifested and the main ESR spectrum consists of four equally intense lines produced by two nonequivalent protons with hyperfine constants of 29.77 and 12.24 G centered at a g factor of 2.002 56. Satellites are observed on each side of these main lines corresponding to each of the six singly labeled radicals present at the 1% natural abundance level of 13C. The high-field group recorded at pH 13.3 during the present study is illustrated in Figure 1. Assignments are as previously given.2 This partial spectrum is similar to that previously reported except that the two lines having the largest coupling constants appear slightly less intense than their counterparts. The present spectra were recorded under somewhat higher resolution conditions than previously and the differences in intensity can be accounted for (1) Taniguchi, H.; Schuler, R. H. J . Phys. Chem., in press. (2) Eiben, K.; Schuler, R. H. J . Chem. Phys. 1975, 62, 3093.
0022-3654/85/2089-3101$01.50/00 1985 American Chemical Society
3102
The Journal of Physical Chemistry, Vol. 89, No. 14, 1985
Lefcourt et al.
TABLE I: I3C Hyperfine Coupling Parameters for Hydroxycyclohexadienyl Radical Formed from Pyromellitic Acid" (OH-lb H-C r"' ~"C0,(2,4)~ a1'C0,(1,5) a"C(6) a1'C(2,4) d3C(1,5) 0.2 0.32 0.5 1.o 1.58 2.5 4.0 4.5 5.0
13.3 13.5 13.7 14.0 14.3 14.5 14.8 14.9 15.0
0.01 0.02 0.03 0.05 0.10 0.15 0.25 0.28 0.33
1.34 1.35 1.34 1.36 1.35 1.37 1.41
5.06 5.08 5.06 5.07 5.05 5.06 5.06 5.07
9.39 9.39 9.40 9.41 9.37 9.41 9.40 9.51 9.41
12.00 12.01 12.03 12.00 11.99 12.00
13.31 13.34 13.35 13.31 13.32 13.37
a"C(3) 18.00 18.05 18.07 18.03 18.11 18.02
"For measurements above H- = 14, digital signal averaging methods were employed, with up to I O recordings averaged. bMolar. ' H - basicity scale (vide infra). dFraction of radicals in ionized form. CHyperfinecoupling in Gauss. 1
"
. .
I
1G Figure 1. Second-derivative ESR spectrum of the hydroxycyclohexadienyl radical from pyromellitic acid in 0.2 M KOH. Dashed line is high-field main line of spectrum, recorded at normal gain; solid lines are "C satellites, recorded at gain X 100. Assignments are noted near satellite peaks.
by slight differences in line width which have very pronounced effects on the amplitudes in the second derivative mode of presentation. At low modulation the area under the absorption in these examples will be proportional to the third power of the line width. From the observed intensities we estimate that the widths of the lines observed for C3are -20% and for C, and C5 10% greater than the other lines in the spectrum. At high basicities these line widths increase even more and lines of the Cl, Cs, and C3 carbon atoms are not observable above 5 M KOH. The additional width demonstrates rather conclusively that the previous assignments of the 15-G hyperfine constant to the carbon atoms at the C, and C5positions and the 18-G value to that at C3 are correct. These atoms are at positions of high-spin density and are expected to have anisotropic dipolar couplings which lead to line broadening as a result of incomplete averaging by tumbling of this relatively large radical. The dipolar contributions for the carboxyl carbon atoms and for the ring carbon atoms at C2,C, and c6 should be small so that the corresponding ESR lines remain narrow even at low tumbling frequencies. Although the signals in the very basic solutions were weak, initial observations showed that there was no substantial effect on the I3Ccoupling constants up to a basicity (H-; see ref 1) of 14.5 where the radical is 15% ionized (see Table I). Detailed measurements were made on the 9.4-G c6 hyperfine constant up to 5 M KOH (H- = 15.0) using digital signal averaging methods. At the highest basicity the measurement required about a 4-h accumulation of data over a 0.5-G region to allow an accurate measurement of the line position. Measurements at higher basicity were precluded by rapid decrease of signal intensity. Data presented in Figure 2 show that there is no observable effect on a(I3C6)up to the point where the radical is -33% ionized. We conclude that the I3C hyperfine constaqt is not affected in any substantial way by ionization of the OH group although a(H6) decreases to 28.67 G from the 29.77 G observed at lower pH. Dissociation of the OH proton has only a trivially small effect on the unpaired spin distribution in the r system of these radicals' so that the hyperfine constants of the carboxyl carbon atoms are not expected to change on ionization. This lack of effect is also manifested in the constancy of the splittings of the carbon atoms
-
-
I
1 13
I 14
I 15
I 16
I 17
H- b a s i c i t y s c a l e
Figure 2. Plot of H 6 proton hyperfine coupling (0) and C6 carbon- 13 hyperfine coupling ( 0 ) as a function of solution basicity for the hydroxycyclohexadienyl radical from pyromellitic acid. The pK, of this radical is 15.3 (see ref 1).
at Cl through Cs.One might expect a(I3C6)to reflect the large change manifested in a(H6) (Figure 2) but this carbon hyperfine splitting is unexpectedly constant. The present results show that, as described theoretically? a(I3C6)is determined very directly by the spin populations at Cl and C5 and as a result is relatively insensitive to dissociation of the OH proton. Previous results show that a(H6) of the cyclohexadienyl radicals is extremely sensitive to the local environment at c6, varying from 47.76 G in the unsubstituted radical to 21.06 G in the basic form of the 1,3,5-tricarboxyhydroxycyclohexadienylradical. These large values arise from constructive overlap of r orbital spin populations at C1and C53with a pseudo x orbital formed by combination of the atomic orbitals contributed by the c6 substituents. It was previously thought that the relatively low a(H6) value of 34.5 G in hydroxycyclohexadienyl* resulted from distortion of the radical geometry at (26. The observed constancy of a(C6) on dissociation of the hydroxyl proton shows that there cannot be significant change in the geometry at C6 We conclude, therefore, that the spin is not transmitted to H6 through the C6carbon atom, but rather results from direct overlap of the cyclohexadienyl x system with the H6 atoms via the pseudo x orbital. This very interesting point has yet to receive adequate theoretical treatment.
Acknowledgment. The authors thank Professor R. W. Fessenden for suggestions and stimulating discussions. Registry No. 1,2,4,5-TetracarboxyhydroxycyclohexadienyIradical, 52934-56-2; 1,2,4,5-tetracarboxyhydroxycyclohexadienyI anion, 9657527-8; pyromellitic tetraanion, 3308-42-7. (3) Whiffen, D. H. Mol. Phys. 1963,6, 223. (4) Karplus, M.; Fraenkel, G. K J . Chem. Phys. 1961, 35, 1312
