J . Phys. Chem. 1986, 90, 1193-1 198
-
AE and for large AE DBG> D ( A E ) ; the crossover point is AE 1700 cm-' for methyl isocyanide and increases with molecular complexity. Expression A3 is a better approximation to the true density ratio for all values of AE. Thus the approximation for the constancy of a(E) which underestimates D ( M ) is compensated by the over estimate in using only the linear term for the expansion of In (1 x). The approximations used for D ( A E ) will determine the value Table IV is a summary of calcuof (AE),,, (eq A I ) and yEXP; lational results for representative systems, step sizes, and temshows the peratures. As expected from the form of FE,yTEXP
+
1193
largest deviation from yEXP(exact). The inadequacy of (A2) for D ( U ) is shown by comparing yAzEXP and yA3EXP;for increasing step size and/or molecular complexity the difference between these quantities increases. The difference between the integral apand the summations used in eq A1 proximation by BG (yeGEXP) (yA3EXP)is negligible and for practical purposes can be ignored. The goodness of the BG approximations as illustrated in Figure 3 depends on molecular complexity, step size, and temperature in a complex manner; in general the BG approximation becomes inadequate for small values of E,/. For a given E,/ the difference increases with molecular complexity.
Kinetics of One-Electron Transfer Reactions Involving CIO, and NO,? Robert E. Huie* and P. Neta Chemical Kinetics Division, Center f o r Chemical Physics, National Bureau of Standards, Gaithersburg, Maryland 20899 (Received: August 22, 1985)
Rate constants for the one-electron oxidation of CIOz- and NO2- by several organic and inorganic free radicals have been measured along with rate constants for several reactions of CIO,, NO2, and BrO,. The kinetics of the reactions of CIO, and NO2 are consistent with simple electron-transfer theory, except for the reaction of NO2 with S03z-,which appears to be oxygen atom transfer. Equilibrium constants have been determined for the reactions of CIO, with aniline at pH 6.9 and N,N-dimethylaniline at pH 9.6. This leads to one-electron redox potentials of 1.03 and 0.87 V for these aromatic amines, respectively, at the corresponding pH.
Chlorine dioxide and nitrogen dioxide are simple inorganic free radicals that, upon one-electron reduction, form the stable anions chlorite and nitrite. These radicals are stable in the gas phase and their spectra have been well studied. Therefore, geometric parameters are known for both the radicals and the anions. ClOZ is also stable in aqueous solution and so the redox potential for the CIOz/CIO< couple has been measured directly ( E o = 0.936 V).l NOz undergoes disproportionation in aqueous solution,2but the potential for the N O 2 / N 0 F couple has been estimated to be 1.03 V.3 Far less is known about bromine dioxide or, for that matter, about the bromite ion, but the potential for the BrOz/ BrOz- couple has been estimated as 1.33 V.4 The reactions of CIO, with organic compounds in aqueous solutions recently have been re~iewed.~These reactions have been of interest primarily due to the use of CIOz in bleaching wood pulp and disinfecting water. The most extensive rate measurements have been on the reactions of CIOz with aliphatic amines6 The initial step was found to involve typically one-electron transfer or hydrogen abstraction. The rate constants were found to correlate well with the Hammett u values, which in turn correlate with the polarographic peak potentials. There has been a considerable amount of work on the products of CIO, oxidation, particularly of phenolic compound^.^ In addition, several groups have reported rate constants for phenolic compounds at pH < 8.8-'0 Kinetic results also have been reported for some furans, sulfides, 0 3 , and For the phenols, sulfides, and aliphatic amines, the rate constants increase with pH and with decreasing one-electron redox potential. Rate constants for the reactions of CIOz with OjrNOz-, and substituted furans are slow and show no pH dependence. Electron spin resonance recently has been applied to the study of the formation and reactions of C102.11,1zAromatic amines were observed to produce the corresponding cation radical. Saturated organic compounds and unsaturated compounds containing C=C, C=S, C=N, or C=C bonds were unreactive. Due to the instability of N O z in aqueous solutions, there have been fewer studies of the aqueous reactions of N O 2 with organic 'Dedicated to Professor Leon Dorfman on the occasion of his retirement.
and inorganic substances. Nitrogen dioxide, however, is a very important air pollutant which can lead directly to morphological damage to the lung. Therefore, there have been efforts to establish its reactivity toward organic compounds by bubbling NO2 through aqueous solution^.^^^'^ Of considerable importance is the observation that N O z reacts with primary and secondary amines to produce N-nitro~amines'~ and with tyrosine to make tyrosine dimers and nitrotyrosine.I6 Further, due to the possible importance of the aqueous NOZ-SO2reaction in flue gas scrubbers and in acidification of precipitation, this reaction also has been investigated in a similar rnanner.l7-I9 (1) Troitskaya, N. V.; Mishchenko, K. P.; Flis, I. E. Russ. J . Phys. Chem. 1959, 33, 71.
(2) Schwartz, S. E.; White, W. H. In Trace Atmospheric Constituents, Schwartz, S. E., Ed.; Wiley: New York, 1983; Chapter 1. (3) Wilmarth, W. K.; Stanbury, D. M.; Byrd, J. E.; Po, H . N.; Chua, C. P. Coord. Chem. Rev. 1983, 51, 155. (4) Field, R. J.; Koros, E.; Noyes, R. M. J . Am. Chem. Sac. 1972, 94, 8649. ( 5 ) Rav-Acha, Ch. Water Res. 1984, 18, 1329. (6) Rosenblatt, D. H.; Hayes, A. J.; Harrison, B. L.; Streaty, R. A,; Moore, K. A. J . Org. Chem. 1963, 28, 2790. Rosenblatt, D. H.; Hull, L. A,; DeLuca, D. C.; Davis, G. T.; Weglein, R. C.; Williams, H . K. R. J. A m . Chem. SOC. 1967, 89, 1156. Hull, L. A.; Davis, G . T.; Rosenblatt, D. H.; Williams, H. K. R.; Weglein, R. C. J. Am. Chem. SOC.1967, 89, 1163. Hull, L. A,; Davis, G. T.; Rosenblatt, D. H.; Mann, C. K. J . Phys. Chem. 1969, 73, 2142. Hull, L. A,; Grordano, W. P.; Rosenblatt, D. H.; Davis, G . T.; Mann, C. K.; Milliken, S. B. J. Phys. Chem. 1969, 73, 2147. Hull, L. A,; Davis, G. T.; Roenblatt, D. H. J . A m . Chem. SOC.1969, 91, 6247. (7) Lindgren, B. 0.; Ericsson, B. Acta Chem. Scand. 1969, 23, 3451. (8) HoignE, J.; Bader, H. Vom Wasser 1982, 59, 253. (9) Grimley, E.; Gordon, G. J . Inorg. Nucl. Chem. 1973, 35, 2383. (10) Wajon, J. E.; Rosenblatt, D. H.; Burrows, E. P. Enuiron. Sci. Technol. 1982, 16, 396. (11) Ozawa, T.; Kwan, T. Chem. Pharm. Bull. 1983, 31, 2864. (12) Ozawa, T.; Kwan, T. Chem. Pharm. Bull. 1984, 32, 1589. (13) Nash, T. J . Chem. SOC.A 1970, 3023. (14) Kobayashi, H.; Takezawa, N.; Niki, T. Enuiron. Sci. Technol. 1977, 11, 190. (15) Challis, B. C.; Kyrtopooulos, S. A. J. Chem. SOC.,Chem. Commun. 1976, 877. (16) Priitz, W. A. Z . Naturforsch. C 1984, 39, 725. (17) Nash, T. Atmos. Enuiron. 1979, 13, 1149.
This article not subject to U S . Copyright. Published 1986 by the American Chemical Society
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The Journal of Physical Chemistry, Vol. 90, No. 6, 1986
Huie and Neta
TABLE I: Rate Constants for the Oxidation of Sulfite, Chlorite, and Nitrite Ions by Several Species k," M-' s-l oxidant
so,25.5 x
1096
2.6 X IO8 9.5 x 108 (9.3) I x 107 2 x 108 (7)e 9.9 x 10*(11)e I x 107 ( I I . I ) ~ 3.2 x 105' 5.6 x 104'
c10,-
NO,-
5.7 x 1 0 9 ~ 2.0 x 107 (6.7)
1 x 10'0d 2 x 107 (6.7) 2.2 X l o 6 (6.6) 2 X IO6 (9.2) 4 x losg
f 3.6 X l o 7 (9.2) 3.1 X l o 7 (11.7) 9) 2.2 x 107 (6.9) 3.2 x 107 (5.7) 4.4 X l o 6 (9.6) < I X l o 4 (6.6-7.3) 1.86 x 104k 1.06 x 104k
< I O 5 (7-12)
h 2 81 9.8,
"Determined in this work unless otherwise noted. Number is parentheses is the pH. bReference 36. 'Reference 29. dReference 26. 'Reference 37. 'Reaction between SCN- and (210,- dedeted reactants. ZReference 38. h T h e reverse reaction, NO, DMA, was measured, see Table 11. t Reference 39. 'Reference 3. Reference 2 i .
+
Reactions involving the C102/Ci02- and N 0 2 / N 0 2 - redox The irradiation of aqueous solutions at pH 3-1 3 produces the couples are also of interest in extending the theory of electronhydroxyl radical and the hydrated electron in similar concentransfer reactions. These couples have similar redox potentials trations, along with a small (
