James P. Birk and Stephen Ci. Kozub
1186 Inorganic Chenzistry, Vol. 17, No. 5 , 1978 (a) F. T. T. Ng and P. M. Henry, J . Anz. Chem. Soc., 98, 3606 (1976); (b) E. Pelizzetti, E. Mentasti, and C. Baiocchi. J . Pliys. Chem., 80, 2979 (1976); (c) E. Mentasti and E. Pelizzetti, In?. J . Chem. Kinet., 9, 215 (1977). P. Hurwitz and K.Kustin, Trans. Faraday Soc., 62, 427 (1966). R. Stasiw and R. G. U'ilkins, Inorg. Chem., 8, 156 (1969). These x's should give some information on AG** values of the reacting couples. A value of 2.3 X I O 5 L mol-' s-' is quoted for IrC1,2-/3- at 25 "C, p = 0.10 M;l6 because a value of wII= 1.20 can be calculated with eq 9 (r = 4.3 A), a value AG** = 6.5 kcal mol-' can be estimated or, better, a range 6.0-7.0 can be suggested.19 This value leads to AG** = 6 . s 7 . 0 kcal mo1-l for H2Qt./H2Q exchange, that is, the rate constant of 7 X 105-4 X I O 6 L mol-' s-' for the selfexchange rates. Since these values seem low with respect to other exchange rates between radicals and parent molecules,14 it must be noted that the x's for benzenediol oxidation were derived by setting the deprotonation constant of semiquinone of parent quinol (H,Q+. HQ. + Ht)equal to I O mol L:'.5b If the effective value is higher, then AGOl; is higher, and consequentlj the X's which fit the data are lower. For example, by setting this deprotonation constant at 100 mol L-', the A's are decreased by about 4 kcal mol-]; then AG** (HzQt./H2Q) = 4.0-5.0 kcal mol-'; that is, self-exchange rate constants are 2 X 107-1 X IO8 L mol-[ s-'. E. Pelizzetti, E. Mentasti, and E. Pramauro, J . Chem. Soc., Perkin Trans., 2, in press. For Fe"'L3/Fe"L3, AG** = 1.O-2.0 kcal mol-' derives from comparison with X determined from the reaction of benzenediols with IrCIz-. A value of 3 X lo8 L mol-' S K I (that is, AG* = 3.4 kcal for the self-exchange between Fe(~hen),~'and Fe(phen)32t has been reported. I. Ruff and M. Zimonyi, Elecrrochim. Acta, 18, 515 (1973). A value AG** = 3.5-4.5 kcal mol-' can be assigned to IrBr *-I3self-exchange. The rate of reaction between IrCI6*- and IrBr63- i", 1.2 X IO7 L mol-' s-', at 20 'C and p = 0.10 M.I6 If w12 = 1.20 and LE'' = 0.075 V X of ca. 20 is derived; then. if the difference between AG** for IrC162-/3-and IrBr62-!3- is 2.5 kcal mol-',20 AG** for IrC162-/3-should be ca. 6.25 and for IrBr,2-/S- ca. 3.75. E. Pelizzetti, E. Mentasti, and E. Pramauro, Inorg. Chem., in press. The rate for M O ( C N ) ~ ~ -exchange /~is reported as 3 X lo4 L mol-' s-' in absence of electrolytes;26wll = 5.3 ( r = 4.8 A) and then AG** = 3.6 kcal mol-'. From comparison with IrC162--benzenediol reaction, a value 3.5-4.5 is obtained. R . J. Campion, unpublished observations, quoted in ref 27. R. J. Campion, N . Purdie, and N . Sutin, Inorg. Chem., 3, 1091 (1964). Extrapolation to zero ionic strength (at 20.7 "C) gave a value 19.2 L mol-' s-' for Fe(CN)a-/24- exchange rate (extrapolation using Bronsted-Bjerrum equation should give a lower value); that is, AG* = 13.0 kcal Since wI1 = 5.6 ( r = 4.5 A), AG** = 7.4.30 A value of AG** = 8.0-9.0 kcdl mol-' can be assigned to the Fe(CK)a-:4- couple, by comparison with the IrCI6*--benzenediol reaction. R. J. Campion, C.F. Deck. P. King. and A . C.Wahl, Inorg. Chenz., 6, 672 (1967). It can be noted that the suggested ranges of AG** for self-exchange reactions can be tentatively used for calculating the reaction rates of cross-electron exchanges that have been experimentally evaluated. If an "averaging" empirical method is utilized for estimating work term^,^'
(31) (32) (33) (34)
the following values are obtained: IrCI,'--Fe(CN)t-, 6.2 X IOs L mol-' S K I (with X = 30 kcal mol-'; experimental 3.8 X lo5 L mol-' s-');'' IrC162--Mo(CN)8", 6.2 X 10, L mol-' s-' (A = 21 kcal mol-'; experimental 1.9 X lo6 L mol-' M O ( C N ) ~ ~ - - F ~ ( C X8.3 ) ~X~ IO4 - , L mol-' SKI ( X = 25 kcal mol-'; experimental 3.0 X lo4 L mol-' S-I).~'The calculated values are slightly higher than the experimental ones, but there is not a relevant discrepancy. It has been recently reported by Haim and Satin3' that neglect of the work terms results in discrepancies of 2-3 orders of magnitude. and, although the observed agreements are probably fortuitous, the relevant importance of the electrostatic contributions in such electron-transfer reactions can be noted. A. Haim and Y . Sutin, Inorg. Chem., 15, 476 (1976). See references quoted in ref 1. R. A. Richman, R. L. Sorensen, K. 0 . Watkins, and G. Davies, Inorg. Chem., 16, 1570 (1977). Z . Amjad, J. C. Brodovitch, and A. McAuley, Can. J . Chem., 55,3581 11 977)/ ' ,--
(35) E. Pelizzetti, E. Mentasti, and E. Pramauro, J . Chem. Sac.. Dalton Trans., 61 (1978). (36) G . Davies, Coord. Chem. Rec., 14, 287 (1974); Inorg. Chin?. Acta, 14, 1-13 (1975). (37) E. Pelizzetti and E. Mentasti, J . Chem. Soc., Dalton Trans., 2222 (1976). (38) E. Pelizzetti, E. Mentasti, and G. Giraudi. Inorg. Chim.Acta, 15, LI (1975). (39) (a) E. Mentasti, E. Pelizzetti, and C. Baiocchi, J . Chem. Soc., Dalton Trans., 132 (1977); (b) E. Pelizzetti and E. Mentasti, Z . Phys. Chem. (Frankfurt a m Main), 105. 21 (1977). (40) A. L V Chester, J . Org. Chem., 35. 1797 (1970). (41) P. G. Rasmussen and C. H. Brubaker, Inorg. Chem., 3, 977 (1964). (42) S. Petrucci, "Ionic Interactions", Vol. 11, Academic Press, New York, Y.Y., 1971. Chapter 7; P. Debye. Trans. Electrochem. Soc., 82, 265 ( 1942) (43) Z; the frequency factor, can be estimated by means of an equation suggested bv Marcus.' The importance of this parameter has been recently (44) K. Suga and S. Aoyagui, Bull. Chem. Soc. Jpn., 46, 755 (1973). (45) M. E. Peover, Electrochim. Acta, 13, 1083 (1968). (46) p for ascorbic acid was obtained from "Handbook of Chemistry and Physics", 53rd ed, Chemical Rubber Publishing Co., Cleveland, Ohio, 1972. (47) B. M. Gordon, L. L. Williams, and N. Sutin, J . A m . Chem. Sot., 83, 2061 (1961). (48) I. Poulsen and C. S. Garner, J . A m . Chenr. Soc., 84, 2032 (1962). (49) P. Hurwitz and K. Kustin, Inorg. Chenz., 3, 823 (1964). (50) M. H. Ford-Smith and J. H . Rawsthorne, J . Chem. Soc. A, 160 (1969). (51) A. A. Schilt, J . A m . Chem. Soc., 82, 3000 (1960). (52) A. A. Schilt, "Analytical Application of 1,lO-Phenanthroline and Related Compounds", Pergamon Press, London, 1969. (53) R. Cecil, .I.S. Littler, and G. Easton, J . Chem. Sac. B, 626 (1970). (54) E. Mentasti and E. Pelizzetti, Transition Met. Chem., 1, 281 (1976). (55) E. Mentasti, and E. Pramauro, and E. Pelizzetti, Ann. Chim. ( R o m e ) , 66. 575 (1976). (56) U. S. hlehrotra, M. C. Agrawal, and S. P. Mushran, J . Phys. Chem., 73, 1996 (1969).
Contribution from the Department of Chemistry, Arizona S t a t e University. Tempe. Arizona 8528 I , and the Department of Chemistry and Laboratory for Research on the Structure of Matter, University of Pennsylvania, Philadelphia, Pennsylvania 191 74
Mechanism of the Reduction of Bromate Ion by Cyano( bipyridyl)iron(II) Complexesla J A M E S P. BIRE;*lb and S T E P H E N G. K O Z U B I C
Receiued July 6. 1977 T h e kinetics of the B r 0 3 - oxidation of F e ( b ~ y ) ( c N ) ~ Fe(bpy),(CN),. ~-, and F e ( b ~ y ) , ~have + been determined in acidic perchlorate solutions at 25.0 O C and 0.50 M ionic strength. Each reaction is autocatalytic, the first two complexes following the same mechanism a s the Fc(CN):rcaction, with the rate law -d[Fe(II)]/dt = 6(c d[Ht]2)[Fe(II)][Br03-] M-' s-' d = 0.227 6k3[Br-][Br03-][H']2 where k3 = 2.86 W3s-', and c = (6.2 1.1) X 0.018 W3 s-I for Fe(bpy)(CN)42-, and c = (2.95 0.44) X lo-* M-' sK1, d = 0.755 0.047 M-3 s-' for ke(bpy)*(CN),. A different rate law and mechanism were found for the autocatalytic Fe(bpy),,' reaction, with the slope (-b) of Guggenheim plots being given by -b = g[BrO,][Ht] h[BrO3J2[H'I2, where g = 12.8 5 0.3 M-, s-l and h = 964 f 56 W4s-l. Rate correlations based on Marcus theory suggest that all these reactions proceed by outer-sphere mechanisms.
*
*
+
*
*
+
+
Introduction One of the predictions of the Marcus theory for oxidation-reduction is that the relative rates of oxidation of a series of reducing agents by two different oxidants should be independent of the identity of the reducing agent if both sets of reactions are outer sphere. Comparison of the rates of the Cr(V1) oxidations4of Fe(CNj:-, Fe(bpy)(CN):- (bpy = 2,2'-bipyridylj, Fe(bpy)z(CN)z, and Fe(bpy),2f with the 0020-1669/78/1317-1186$01.00/0
rates of the corresponding outer-sphere oxidations by Ce(IVj5 suggested that the first three Fe(I1) complexes reacted by an inner-sphere mechanism while the last system was outer sphere. These conclusions were supported by examination of the corresponding V(Vj oxidation^.^,' nhere the predictions of the relative rate comparisons were confirmed by observation of binuclear successor complexes with the cyanide-containing Fe(I1) complexes. These rate comparisons thus appear to be CZ 1978 A m e r i c a n C h e m i c a l Society
Inorganic Chemistry, Vol. 17, No. 5, 1978 1187
Reduction of Bromate by Cyano(bipyridyl)iron(II) viable criteria for distinguishing between inner-sphere and outer-sphere mechanisms and have been successful in confirming the outer-sphere nature of the V(V) oxidation of 1~c1~3-.* A comparison of rate laws, variation of central atom charge or oxidation state, variation of central atom size, and hydrogen isotope effects for substitution and oxidation-reduction reactions of many oxyanions9 suggests that substitution occurs prior to or coincident with the electron-transfer step in the redox processes. Since this mechanistic description so closely resembles that of the inner-sphere process commonly applied to transition-metal redox reactions, we decided to develop the appropriate rate comparisons to determine whether the oxyanion redox reactions can indeed properly be classified as inner sphere. Bromate ion was chosen as the oxidizing agent to be reacted with the same series of Fe(I1) complexes, because Br03- reacts more rapidly than C103-, while it is not complicated by the formation of significant amounts of a protonated species, as is IO3-, and because these systems are also of interest to the study of oscillating reactions involving bromine species. We have previously reported the results of a study of the reaction between Fe(CN)64- and Br03-.10 The Br03- oxidation of Fe(CN)64- followed partially autocatalytic kinetics: -d[Fe(CN)64-]/dt = 6kl [Fe(CN),4-] [Br03-] + 6k3[Br-1 [Br03-l[H'12 (1) with k l = 0.0125 0.193[HfI2 M-' s-l and k3 = 2.86 M-3 s-l a t 25.0 "C and 0.50 M ionic strength. This rate law was interpreted in terms of the coupled reactions:
+
Fe(I1)
+ BrO;
4Fe(II)
k,
+ '/,Br, + 3H,O
--SFe(II1)
(2)
2HC 4H+
fast
Fe(I1) Br-
+ */2Br2
+ BrO; + 2H'--
Fe(II1)
+ Br'
(3)
3Br, t 3H,O
(4 )
k, 4Br4H'
Reaction 2 initiates the process and reactions 3 and 4 become increasingly important as the reaction proceeds. We report here on the bromate oxidation of the remaining three iron(I1) complexes in the series, all of which reactions involve autocatalysis. Experimental Section T h e preparation and analysis of solutions of LiC104,4 HC104,4 NaBr03,'' K 2 F e ( b ~ ~ ) ( C N ) 4F, ~7 ( ~ P Y ) ~ ( CFNe () b~p, ~~) ~ ( C l O ~and )~,' the analogous Fe(II1) complexes7 Rere previously described. The kinetics of the Fe(I1) reductions of B r 0 3 - were determined under pseudo-first-order conditions with [BrO
