Communicationsto the Editor
XI0
1771
lized form of the exchanged zeolites. In the partially exchanged LiX, however, the splittings of both species were larger than those of NaX when pretreated at 600'. Therefore it is suggested that the Li+ in the 10% LiX is sited in the more exposed position than that in LiX, possibly due to the interaction with Na+ to give the larger splittings. The result that the observed splittings in 10% LiX treated a t 350' was the same as NaX may imply the preferential adsorption of ClOz on Na+ sites due to the difficulty in eliminating the adsorbed water on the Li+ site.
b
References and Notes (1)J. A. Rabo, C. L. Angell, P. H. Kasai, and V. Schomaker. Discuss. Faraday Soc., 41, 328 (1966). (2)J. T. Richardson, J. Catal., 9, 182 (1967). (3)J. W. Ward, J. Catal., 10, 34(1968). (4) J. W. Ward, J. CataL, 14, 365 (1969). (5) c. L. Gardner, J. Chef??.Phys.. 48, 2991 (1967);C. L. Gardner, E. J. Casey, and C. W. M. Grant, J. Phys. Cbem.,74, 3273 (1970). (6)J. A. R. Coope, C. L. Gardner, C. A. McDowell, and A. I. Pelman, Mol. Phys., 21, 1043 (1971). (7) T. Cole, Roc. Nat. Acad. Sci. U. S., 46, 506 (1960). (8) L. H. Ahrens, Nature(Londort),174, 644 (1954). (9)M. H. Brooker and M. A. Bredig, J. Cbem. Phys., 58, 5319 (1973). (IO) A. I. Pelman, W.D. Thesis, The University of British Columbia, 1971.
K. Shimokoshl' H. Sugihara 1. Yasumori
Department of Chemistry Tokyo institute of Technology Meguro-ku, Tokyo, Japan 152
Figure 1. Esr spectra of C102 adsobred on the alkali-cation-exchanged X-type zeolites; (a) NaX, (b) NaX after treatment in NaN03 aqueous solution; arid (c) KX.
Received February 20, 1974
Equilibrium Studies by Electron Spin Resonance. VIII. The Use of Time Averaged Coupling Constants to Determine Free Ion-Ion Pair Equilibrium Constants Publication costs assisted by the University of Puerto Rico
Sir: Esr spectroscopy has proven itself to be the most useful tool for probing the nature of ion pairing in solution and has been used by several workers to investigate the actual equilibrium constants controlling the dissociation of ion pair 9, to form the free ion a.l 0.5
1
1
1.0
1.5
e/(G,s?ff) Figure 2. The hyperfine splittings of C102 on the alkali-cation-exchanged zeolites as a function of the polarization power ( e / f i s f f of ) the cations with the samples pretreated at 200' (O), 350' (0),and 600' (0)(10% LiX).
the radicals are almost free from the effect of the cationic fields because of the water adsorbed not only on cations, but on the other sites in the zeolites. This effect may interpret the least and nearby equivalent hyperfine splittings as is listed in the second column of the table. Tn the LiX the splitting was smaller than those in the other zeolites, even when the sample was evacuated at 600'. This probably means, as Pelmanlo has suggested in his esr study of (2102 on LiX, that the accessible distance of the radical to Li+ is different from those in the other cations, because decreased size of the cation decreases the extent of exposure of the cation to the cavities in the stabi-
p
= c y
+
M'
(1)
The number of systems for which this equilibrium constant for ion pair dissociation is known, however, is still quite small. This is due to the fact that it has been necessary to observe the free ion ( a )and the ion pair ( p ) simultaneously. That is, the esr signal for the two species must be observed together.2 Further, simultaneous observation of a and fl is rarely encountered, since in most cases there is a rapid interchange between the free ion and ion pair that is fast on the esr time scale.3 This results in an esr spectrum that is a weighted average between that for a and that for fl. Here we wish to report the first use of weighted average equations in terms of esr coupling constants for the determination of an equilibrium constant for ion pair dissociation to form free ion and the conditions under which these equations can be used. It has been previously observed that anion radicals in hexamethylphosphoramide (HMPA) are virtually fully disThe Journal of Physical Chemistry, Vol. 78, No. 17. 7974
1772
Communications to the Editor ions). The free ion can be in equilibrium with either of the two possible ion pairs (structures I and 11) or with both of them as shown in eq 5. 0-
-.-A-
I
S
9 1I
Figure 1. Plot of I/(,@
concentration.
I
I
13
17
(X'l
- A) vs. the reciprocal of the potassium ion
sociated,l E4ut the addition of alkali metal salts to these anion radical solutions in HMPA often results in the formation of ion airs.^,^ The reduction of 2,6-di-tert-butylbenzoquinone in " V I A by potassjum metal results in the formation of the free anion radical, which exhibits an esr signal consisting of a triplet due to two equivalent protons with a coupling constant of 2.346 f 0.005 G.Succesive additions of potassium iodide to this solution result in a gradual decrease in this coupling constant, This decrease is due to the formation of the ion pair, which exists in rapid equilibrium with the free ion, eq 1. Since the observed coupling constant for the time averaged species ( A )smoothly decreases with the addition of the potassium ion,6 this coupling constant must be a weighted average between the coupling constant for the free ion (Ao) and that for the ion pair (A'). This weighted average can be expressed by = { ( a ) A o+ (P)Af}/{(@) +
(P)}
(2)
Combining this ex,pression with that for the thermodynamic equilibrium constant, K,, = (a)(K+)/(@),where (K+) represents the concentration of added potassium iodide,7 leads to the following expression.
l/(x - A')
= Keq/(K+)(A' - Ao)
+
l/(A' - A') (3)
If the two jump model expressed in eq 1 (ion pair to free ion) is correct, a plot of 1/(A - Ao) us. l/(K+) should be linear and have a slope of Keq/(Af- Ao) and an intercept of l/(Af - ,4O). Treated in this manner our data did yield a straighLt line (Figure 1).A t 23" this plot yields an intercept and slope of 3.45 and 0.36, respectively. This leads to a value of 2.06 for A' (the coupling constant for the ion pair) and a value of 0.105 f 0.01 for Keq. 13eranleauRhas recently pointed out that equilibrium constants for' weak complexes determined with the use of weighted average t?quations are most reliable when they are based upon spectral data that extend as much as possible into the region where the saturation factor (s) is between 0.2 and 0.8. For the esr experiment described here
s == @ ) / { ( a )-I- ( p ) } =
(K - A O ) / ( A '
- AO)
(4)
Calculated in this manner our saturation factor varied from 0.34 to 0.85. We must note here that the data treated as described above should yield linear plots only if there is no formation of triple ions (ion pairs consisting of one anion and two catThe Journal of Physical Chemistry, Vol. 78, No. 17. 1974
I I1 The existance of both ion pairs would not necessarily give curvature to the plot of l/(A - Ao) us. l/(K+) since the two structures could be in rapid equilibrium and only the time average between them observed. The position of this equilibrium and hence the fraction of ion pair of each structure would not be expected to be a function of the concentration of K+. However, if either the interconversion between structures I and I1 is slow on the esr time scale or the triple ion is formed, curvature of this plot would be expected. The fact that neither of these two possibilities occurred for the potassium system is probably due to the fact that the potassium cation is sterically hindered from entering on the side of the ring in which the carbonyl group in sandwiched by the two tert-butyl groups. A smaller cation, however, might not be so hindered. Addition of sodium iodide to the free anion radical of 2,6-di-tert-butylbenzoquinonein HMPA also results in a decrease in the observed coupling constant, but a plot of 1/(A - Ao) us. l/(Na+) is not linear. Further, an asymmetry is observed in the esr line widths. That is, the line widths increase with decreasing magnetic field. This spectrum is obviously due to the formation of two different ion pairs with slightly different coupling constants and g values. If the radical with the smaller coupling constant also possesses the smaller g value then the difference in the positions of the lines due to the two ion pairs will decrease with magnetic field. A similar effect was observed for the nitrosamine anion radicals in ethereal solventsg and for the benzoquinone anion radical in a saturated solution of KI in HMPA.2 The two ions observed for the sodium reduction are probably best represented by structures I and 11. The formation of 11 is not as sterically hindered in the case of the sodium ion pairs as it is in the case of the potassium ion pairs due to the smaller size of the sodium cation. From this we would predict that the addition of lithium iodide to the free ion in HMPA would also result in the observation of an asymmetric esr spectrum. Experimentally this is the case. The work presented here indicates that time averaged esr coupling constants can be used to determine ion pair dissociation constants, but care must be taken to be sure that the system can be represented by a single ion pair and free ion, or if more than one ion pair exists that they are rapidly interconverted and the equilibrium between the two is not a function of the counterion concentration.
Acknowledgment. The authors are grateful to Research Corporation and the National Institute of Health for support of this work. The NIH support was from Grant No. RR8102 from the Minority Schools Biomedical Support Program of the Division of Research Resources. References and Notes (1)R. D. Allendoerfer and R. J. Papez, J. Pbys. Chem., 76, 1012 (1972). (2)G.R. Stevenson and A. E. Alegria, J. Pbys. Chem., 77,3100 (1973).
