1042
Communications to the Editor
Equilibrium Studies by Electron Spin Resonance. XI. The Use of g Values for the Determination of Ion Pair Dissociation Constants
TABLE I: ESR Parameters for the System 2,6-Di-tert- butylbenzoquinone-HMPA-K with Added KI K+concn, M
Publication costs assisted by the University of Puerto Rico
p*a+M+
+ (011
(2)
Combining this expression with that for the thermodynamic equilibrium constant, Ke, = (a)(K+)/(p),where (K+) represents the concentration of added KI, leads to the following expression.
l/Ag = K,,/Ag'(K+)
0.051 0.061 0.080 0.150 0.328
0 3.18 3.52 3.95 5.29 6.94
1
(1)
Since the first accurate measurements of g values for organic anion radicals in solution, several workers have noticed changes in g values with Recently it has been reported that the g value dependence upon temperature is at least partially due to ion ~ a i r i n g The . ~ ion pair and free ion of durosemiquinone in dimethoxyethane have been accurately determined for a series of counterions, and for all cases the g value is larger for the free ion than it is for the ion paira4 The reduction of 2,6-di-tert-butylbenzoquinone in hexamethylphosphoramide (HMPA) by potassium metal results in the formation of the free anion radical? which is characterized by the coupling constants given in Table I and a g valuelo of 2.004814 f 0.000008. Successive additions of potassium iodidell to this solution result in a gradual decrease in the observed g value, Figure 1. This decrease is due to the formation of the ion pair, which exists in rapid equilibrium with the free ion, eq 1. The observation of a time-averaged g value is due to the fact that the time between ion association and dissociation events is small on the ESR time scale.3 If the opposite were true the two radicals (ion pair and free ion) would be observed simultaneo~sly.~~~~ The difference in the observed g value with a given quantity of KI added to the solution and that for the free ion (&) is a weighted average, and it varies from zero (for a solution that contains only free ion) to the difference in g value for the free ion and ion pair (Ag') = Ag'(PM(4
2.346 2.260 2.245 2.223 2.182 2.122
0
Sir: To date equilibrium constants controlling the dissociation of ion pairs have been determined by the use of three different ESR techniques. These techniques include the use of (1)coupling constants,lg2 (2) line widths (relaxation time^),^ and (3) line intensities (spin concentration^).^^^ Here we wish to report the use of the remaining ESR parameter (g values) for the determination of equilibrium constants for the dissociation of an ion pair (p) into a free anion radical ( a )and a solvated cation
1 0 5 ~ ~
AH, G
+ l/Ag'
(3) Since the two jump model expressed in eq 1 (ion pair to free ion) has been shown to be correct for this system,2 a plot of l/Ag vs. l / ( K f ) should be linear and have a slope of Keq/Agf and an intercept of l/Ag'. Treated in this manner our data did yield a straight line, Figure 1. Table I shows a representative set of ESR parameters for various concentration of potassium ion. At 28' the equilibrium constant determined from Figure 1 is 0.076 f 0.009. The equilibrium constant for this reaction has been recently determined by the use of time-averaged ESR coupling constants,2J2 and it was found to be The Journal of Physical Chemistry, Vol. 79, No. 10. 1975
I 2
I
I
6
10
I 1/(X*)
14
I 18
Figure 1. Plot of lov4/& vs. the reciprocal of the added KI for the system 2,6-di-fert-butylbenzoquinone-HMPA-K. The g values used to make this graph were determined using the g value for the free ion as a standard.
0.094 f 0.01 at 28'. The equilibrium constant measured here for eq 1 by the use of g values is within experimental error with that previously reported. Since the first attempt to study ion pair-free ion equilibria in 1960 by Atherton and Weissman,13 this work represents the first report of the use of g values for the determination of equilibrium constants for ion pair free ion equilibria. The use of g values for the determination of equilibrium constants, however, is not unprecedented. Solvent exchange equilibria have been previously studied by means of ESR g ~ a 1 u e s . l ~ Since there are many systems in which the ESR coupling constants are insensitive to ion pairing phenomena and g values are a sensitive function of ion pairing, the use of time-averaged g values should be very useful in the investigation of ion pair equilibria in these systems. Further, since g values can now be measured to high precision, accurate equilibrium constants can now be obtained. Acknowledgments. We are grateful to Research Corporation and the National Institutes of Health for support of this work. The NIH support was from Grant No. RR-8102 of the Division of Research Resources. References and Notes (1) (a) N. Hirota, J. Phys. Chem., 71, 127 (1967); (b) A. M. Hermann, A. Rernbaurn, and W. R. Carper, ibid., 71, 2661 (1967). (2) G. R. Stevenson and A. E. Alegria, J. Phys. Chem., 78, 1771 (1974). (3)G. R. Stevenson and R. Concepcion, J. Am. Chem. Soc., 96, 4696 (1974). (4) R. D.Allendoerfer and R. J. Papez, J. Phys. Chem., 76, 1012 (1972). (5) (a) G. R. Stevenson and L. Echegoyen, J. Phys. Chem., 76, 2339 (1973); (b) G. R. Stevenson and A. E. Alegria, ibid., 76, 3100 (1973). (6) B. G. Segal, M. Kaplan. and G. K. Fraenkel, J. Chem. Phys., 43, 4191 (1965). (7) R. D. Allendoerfer, J. Chem. Phys., 5 5 , 3615 (1971). (8) (a) J. Kelrn and K. Mobius, Angew, Chem.. lntl. Edit. Engl., 9, 73 (1970); (b) M. T. Jones, "Advances in Magnetic Resonance", Vol. VII, J. S.
1043
Communications to the Editor Waugh, Ed., Academic Press, New York, N.Y., 1973. (9) M. T. Jones, T. C. Kuechler, and S.Mertz, J. Magn. Resonance, I O , 149 (1973). (IO) (a) The g values were measured on a Varian E-9 ESR spectrometer using the dual cavity technique.lob (b) J. E. Wertz and J. R. Bolton, "Electron Spin Resonance: Elementary Theory and Practical Applications", Mcgraw-Hill, New York. N.Y., 1972, p 464. (c) The p-benzosemlquinone-tert-butyl alcohol system was used as a g value ~tandard.~.' (1 1) (a) It has been previously observed that salts of this type are dissociated in HMPA: see P. Bruno, M. D. Monica, and E. Righetti, J. fhys. Chem., 77, 1258 (1973). (b) The ion association constant for KI was found to be about 4 in HMPA. (12) G. R. Stevenson and A. E. Alegrk, unpubllshed results. (13) N. M. Atherton and S. I. Weissman, J. Am. Chem. Soc., 83, 1330 (1961). (14) T. Yonezawa, T. Kawamura, M. Ushlo, and Y. Nakao, Bull, Chem. SOC. Jpn., 43, 1022 (1970).
Gerald R. Stevenson,' Antonio E. Alegrla
Department of Chemistry University of Puerto Rico Rio fiedras, fuerto Rico 0093 1
Received November 1 1 , 1974
TABLE I: Experimental Trimethylsilane: Methylethylsilane Ratios for the Singlet Methylene ('AI) -Dimethylsilane Reaction Singlet methylene precursor
Temp, "C CF,:DMS
TMS:MESa
CHzNz-3660 24 2.30 i 0.13 2.24 i 0.03 0 CHzNz4358b 24 CHzNz4358 2.34 i 0.01 CH2Nz4358 A 90 2.40 * 0.08 24 CHzNz4358b 5.4 2.30 24 CHzNz4358A 17.0 2.28 0 CHzCO-3340 b 2.17 i 0.08 24 CH2CO-3340 2.25 * 0.02 100 2.16 i 0.12 CH2CO-4340 A a For experiments where no error is given only one measurement was made.
5
4
fect of excess CHZ(lA1) vibrational energy and temperature on Si-H and C-H relative insertion reactivities. Singlet methylene insertion was studied by photolyzing ketene or diazomethane with added oxygen. Oxygen is an effective scavenger for the CHz(3B1) radicals.'P2 Ketene, diAbsence of an Energy Dependence for azomethane, and dimethylsilane were prepared by convenCHP('AI) Reaction with the C-H and Si-H Bonds tional technique^.^^^^^ The diazomethane 4358-8, photolyses were performed using a Hanovia 673 A medium-pressure of Dimethylsilane mercury arc lamp with Corning colored glass filters, No. Publication costs assisted by the Petroleum Research Fund 5850 and 3389. For the rest of the photolyses a 200-W Osram high-pressure mercury arc lamp was used. Corning Sir: The insertion of singlet methylene radicals into Si-H colored glass filter No. 5840 was used to isolate the 3130-, bonds is one of the fastest CHZ(lA1) reactions.' For various 3340-, and 3660-8, lines for the ketene photolyses and Corsubstituted alkylsilanes CH&A1) radicals formed by diazoning colored glass filters No. 5860 and 7380 were used for methane photolyses a t 3660 and 4358 8, insert 7-9 times 3660-A photolyses of diazomethane. The reaction mixtures faster into Si-H bonds than C-H bonds.1,2 Though various were photolyzed in Pyrex vessels. A normal mixture conhypotheses have been suggested, the origin of this reactivisisted of dimethylsilane-ketene or diazomethane-oxygen in ty difference has not been identified.2 a ratio of 10:l:l. Total pressures were always greater than In this work we have investigated the effect of excess 50 Torr so the trimethylsilane and dimethylsilane, eq 1and methylene vibrational energy and temperature on the rela2, were collisionally stabilized.l0 Tetrafluoromethane was tive reactivity of CHZ('A1) radicals with dimethylsilane added to some mixtures as a moderator. Trimethylsilane (TMS) and methylethylsilane (MES) were measured by 'CHZ + CH3SiHzCH3 (CH&SiH [TMS] (1) glpc. The experimental results are listed in Table I. Though C2H5SiHzCHs (MES] (2) the filter used in the ketene photolyses transmitted the 3130-, 3340-, and 3660-A mercury lines, most of the photolFor many bimolecular reactions, excess vibrational energy ysis occurred at 3340 A. The combination of the filter and has a significant effect on reaction cross sections and the Pyrex vessel removed most of the 3130-A line and as a reresulting product distribution^.^ In addition, if there is an sult of the small extinction coefficient" and photodissociaArrhenius activation energy difference for singlet methylene insertion into Si-H and C-H bonds, it should be detion quantum yields12 for CH&O at 3660 8, only a small fraction of the singlet methylenes were formed by 3660-8, tectable by relative rate measurements a t different temperphotolyses. However, even if the 3660- and 3130-8, lines atures. There is a continuing controversy concerning the elecwere not completely removed, it would have only a minor tronic energy difference between CHd'A1) and CHZ(~BI), effect on our experiments since the average energies of sinwhich is the ground ~ t a t e . The ~ - ~major point of dispute inglet methylenes formed a t 3660 and 3130 8, are only -1 volves the interpretation of different chemical activation kcal/mol lower and higher, respectively, than those formed rate r n e a ~ u r e m e n t s .It ~ *has ~ been suggested that these difby 3340-A p h o t ~ l y s e s . ~ J ~ ferences could be reconciled if there was a threshold for The key in comparing the results using diazomethane singlet methylene insertion reaction^.^ Some discrepancies and ketene is the difference in the vibrational energy conmay also arise if there are different excitation functions for tent of the singlet methylenes. The average vibrational enCHz(lA1) reactions with various types of bonds, so that ergy of the singlet methylenes formed by diazomethane some molecules select the more energetic methylenes while photolysis a t 3660 8, is -13 kcal/mol higher than that of others react with thermalized methylene radicals. Since those formed by CH2CO photolysis at 3340 Ae7J4By photoSi-H bonds are more highly reactive than C-H bonds, lyzing CH2N2 a t 4358 8, and using CF4 as a moderator to these suggestions can be partially tested by studying the efdeactivate vibrationally the singlet methylene radicals,
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The Journal of fhyslcal Chemlstry, Vol. 79, No. 10, 1975
