water measurcd by five stepwise micrometer readings is so large in relation to the others that only a negligible error of 0.04% in a can be introduced here. The tcmperature differential between the water bath and room temperature could account for a maximum change in a of 0.5%. In practice, however, the maximum error is 0.05% of a,experienced only a t the very low temperature determinations. Assuming maximal additive errors, this gives a *0.26y0uncertainty in the determinations.
Acknowledgments. The author wishes to cxprrss his thanks to Dr. 1'. F. Scholander for his intcrest arid ericouragement during the course of this work. Thc author is indrbted to Edvard Hemmirigsen for the mass spectrometer measurements and to Paul Yeager for the fine glass work on the absorption chamber. Thanks are due to Dr. Scholandrr, llr. D. L. Fox, Dr. T. Enns, and George Pickwell for their stimulating discussions and critical reading of the manuscript.
The Kinetics of Some Oxidation-Reduction Reactions Involving Manganese(II1)*
by H. Diebler2and N. Sutin Chemistry Department. Brookhaven h'ational Laboratory, Upton, New York
(Rcccived Auguat 27,lM.9)
The kinetics of several oxidation-reduction reactions jnvolving manganese(II1) have been studied spectrophotometrically by the use of a flow technique. The free energies of activation for the oxidation of various substituted tris( 1,lO-phenanthroline) complexes of iron(I1) by manganese(II1) in perchloric acid and in pyrophosphoric-sulfuric acid media were found to be linearly related to the standard free energy changes of the reactions. The application of the Marcus theory to the reactions of manganese(II1) with iron(I1) and with various substituted iron(I1)-phenanthroline complexes and to the reaction of cobalt(II1) with manganese(I1) in perchloric acid leads to an estimate of about F-' see. -1 for the rate constant of the manganese(I1)-manganese(II1) electron exchange reaction a t 25.0'. Attempts to determine the rate constant for this exchange by a radioactive tracer method were unsuccessful.
Whereas numerous studies of the kinetics of oxidation- reduction reactions have hecn reported in recent years, very few have dealt with the reactions of manganese(II1) in perchloric acids3 The paucity of data on such reactions is probably due to the belief that free manganic ions cannot exist in significant concentra?;evertheless, perchloric tions i n aqueous s ~ l u t i o n . ~ acid solutions of manganesc(II1) have been used in a few oxidation-reduction studies. For example, Adamso115 has studied the electron exchange reaction between nianganese(I1) and niariganese(II1) in perchloric acid The .Journal of Physical Chemistry
while Ogard and Taube6 have used perchloric acid solutions of manganese(IIT), prepared by the reaction (1) (2)
(3)
(4) (6)
Research performed under the auspices of the U. S. Atomic Energy Commission. Chemistry Department, Stanford University, Stanford, California. For recent reviews of electron transfer reactions, see, for example: (a) H. Taube, Aduan. Inorg. Chem. Radiochem., 1, 1 (1959); (b) d. Halpern, Quart. Reo. (London), 15, 207 (1961); (c) N. Sutin, Ann. Rev. Nucl. Sci.. 12, 285 (1962). W. A. Waters, Quart. Rev. (London), 12, 296 (1958). A. W. Adamson, J . Phys. C h m . , 55, 293 (1951).
1’75
KINETICSOF OXIDATTON-REDUCTION REACTIONS OF MANGANESE(III)
of rnanganese(I1) with cerium(1V) or cobalt(III), to study the effect of manganese(IJ.1) on the dissociation of CrC12+. The kinetics of the oxidation of mercury(1) by manganese(II1) in perchloric acid has been studied by Rosseinsky The stability of manganese(II1) can be increased by complexing it with various ligands. Fluoride, sulfate, and pyrophosphate have been used for this purpose. Indeed, solutions of manganic sulfate and manganic pyrophosphate are stable enough to be used as oxidizing agents in volmmetric analysis.*-ll The oxidation (of numerous organic compounds by manganic pyrophosphate has been studied by Waters and his collaborators.* Polissar12 has studied the kinetics of the electron exchange between manganese(I1) and the oxalate complexes of manganese(III), while Taube13has studied the kinetics of the oxidation of oxalate ions by manganese(111) in hydrochloric acid. We have studied the kinetics of the iron(I1)-manganese(II1) and manganese(I1)-cobalt(II1) reactions in perchloric acid as well as the oxidation of various substituted phenanthroline complexes of iron(I1) by manganese(II1) in perchloric acid and by manganeee(111) pyrophosphate in a pyrophosphoric acid-sulfuric acid medium. Attempts to study the manganese(11)-manganese(II1) electron exchange reaction in perchloric acid were unsuccessful, probably because exchange between the two oxidation states was inducled by the separation procedure. The results are discussed in the light of the Marcus theory of electron-transfer rea~ti0ns.l~In terms of this theory k12, the rate constant for an electron-transfer reaction, should be related to kl and kz, the electron exchange rates of the two reactants, and K12, the equilibrium constant for the electron-transfer reaction, by the expression
.’
where log J = (log Kl2)2/4 log
(IClk2/22)
and Z is the collision frequency between two uncharged molecules in solution ( ~ 1 0 1.’ mole-’ ~ sec.-l). Equation l is applicable to outer-sphere electron-transfer reactions when the various work terms approximately cancel or are negligible. Since the completion of this work, a brief report has appeared on the kinetics of the iron(I1)-manganese(II1) reaction in perchloric acid.15 The rate constant for this reaction, determined by a polarographic technique, is in good agreement with the value we have determined spectrophotoinetricaIly.
Experimental Chemicals. Manganese(I1) and cobalt(I1) perchlorates were prepared by dissolving manganese (Fisher Scientific Co.) and cobalt (A. D. Mackay Inc.) in perchloric acid (Baker Analyzed Reagent). Iron(I1) perchlorate was obtained from the G. Frederick Smith Chemical Co. Solutions of manganese(II1) and cobalt(111) in perchloric acid were prepared by electrooxidation of the lower oxidation states a t platinum anodes. The manganese(I1) solution was electrolyzed a t room temperature a t a current density of about 2 ma. while the cobalt(I1) solution was electrolyzed a t 0’ a t a current density of about 50 ma. cm.-2, Since the tendency of manganese(II1) to disproportionate to manganese(I1) and manganese(1V) (with the eventual precipitation of l!tn02)is suppressed by high manganese(11) and perchloric acid concentrations, the solutions used in the electrolyses contained up to 0.1 F manganese (11) and from 1 to 6 F perchloric acid. In most of the studies the manganese(I1) concentration was 5 X 1 P 2 F . At lower manganese(I1) concentrations, particularly at lower acidities and higher current densities, the solutions turned pink during the early stages of the electrolysis. Spectrophotometric measurements established that this pink color was due to the formation of permanganate; at higher manganese (11)concentrations and acidities the reaction of manganese(I1) with permanganate is rapid enough to prevent the formation of an appreciable permanganate concentration during the electrolysis. The concentrations of manganese(II1) and cobalt(111) were determined by adding an excess of standardized iron(I1) solution to aliquots of the electrolyzed solutions and titrating the excess iron(I1) with ceriwm(IV). The phenanthroline complex of iron(I1) was used as the indicator in the estimation of manganese(111) and cobalt(II1) in perchloric acid and its 5,6-dimethyl phenanthroline complex in the estimation of manganese(II1) in pyrophosphoric-sulfuric acid. Manganese(II1) pyrophosphate was prepared by electrooxidation of a solution of manganous sulfate (6) A. E. Ogard and H. Taube, J . Phys. Chem., 62, 357 (1958). (7) D. R. Rosseinsky, J . Chem. Soc., 1181 (1963). (8) A. R. J. P. Ubbelohde, ibid., 1605 (1935). (9) J . I. Watters and I. M. Kolthoff, J . Am. Chem. Soc., 70, 2466 (1948). (10) R. Belcher and T. S. West, Anal. Chim. Acta, 6, 322 (195%). (11) W.C. Purdy and D. N. Hume, Anal. Chem., 27, 257 (1955). (12) M.J. Polissar, J . Am. Chem. SOC.,58, 1372 (1936). (13) H. Tauba, ibid., 70, 1216 (1948). (14) R. A. Marcus, J . Phys. Chem., 67,853 (1963). (15) M. J. Nicol and D. R. Rosseinsky, Chem. Ind. (London), 1166 (1963).
Volume 68, Number 1
JalzUaTy, 1964
(Baker Analyzed Reagent) in sulfuric acid (Baker and Adamson) containing a large excess of sodium pyrophosphate (Jlatheson Coleman and Bell). The iron(1I)-phenanthrolirie complexes were prepared as described previouslyI6 and standardized spectrophotometrically using published extinction coefficients.l7 I s Sodium perchlorate was prepared from sodium carbonate (Baker Analyzed Reagent) and perchloric acid. Dibutyl phosphate (Fisher Chemical Co.) was separated from its mixture with the monobutyl compounds by continuous extraction with water. Procedure. The spectra of the electrolyzed solutions were measured on a Beckman DU spectrophotometer. The formal potentials were measured with a Heckrnan p H meter by inserting a platinum electrode into the electrolyzed solutions and using a saturated calomel half-cell as reference electrode. I t took several hours for the potentials to reach their equilibrium values. The experiments on the marigariese(I1)-nianganesc(111) exchange reaction mere carried out by adding carrier-free Mns4 (as manganese(I1)) to a solution coritaining both oxidation states. The slim of tlie conceiitratioris of the two oxidation states was varied from 2 X to 1 X lo-* Iimethyl-l~ 10-phenanthroline
B-Methyl-l,l0-phenanthroline 1,lO-l'henanthroline 5-Phenyl-l , 10-phenanthroline
x
0.85
2.3
0.88 0.96"
1.4 x 103 4.3 x 102
1 .OO 1 .06 1.l0 1.12
3.9
103
x 102 1 . 4 X 102
7 . 2 X 10' 6 . 8 x 10'
' The formal oxidation potentials of the complexes are in 0.1 P
* See ref. I7 and 18. The Eo of this complex is reported to be 0.93 v. in ref. 17: we have determined the value reported above. The forinal potentials of other phcnanthroline complexes we have measured agreed well with the published values. H&K),.
sulfuric acid, are changed in a systematic manner by the high concentration of pyrophosphate prcserit in these studies. I n addition, the rate constants show a large pH-dependence, suggesting that a t least two manganese(II1) pyrophosphate species are involved in the reactions. The measured rate constants are over-all rate constant,s and it may well be that the rate constants for the individual steps will give better agreement with eq. 1. Conditions under which the application of eq. 1 to over-all rate constants is appropriate have been described by Marcus.14 Comparison oJ Observed and Calculated Rate Constants. The geometric mean of the estimated rat,(?con(26) M. €1. Ford-Smith arid N . Sutin, J . Am. Chem. Soc., 83, 1830 (1961).
Volume 68,Number 1 January, 1964
180
H. DIEBLERAND N. SUTIN
stants for the manganese(I1)-manganesc(II1) exchange reaction in 3 F perchloric acid a t 25.0' is 3 X F-I set.-'. The substitution of this value together with the appropriate exchange rate constants and equilibrium constants into eq. 1 leads to the calculated rate constants presented in Table 111. The agreement between the observed and calculated rate constants is encouraging in view of the large differences in the natures of the reactions. It may be noted that, as required for the application of eq. 1, the various work terms either cancel or have been corrected f ~ r . ~ ~ ~ ~ ~
The rate constants were calculated from eq. 1 on the assumption that the manganese( 11)-manganese( 111) exchange rate is 3 X lo-' P-' sec.-l in 3 P HClO, a t 25.0".
has been made recently.I6 The agreement was found to be satisfactory. The one notable exception is the iron(I1)-cobalt(II1) reaction which proceeds by a factor of about lo5 more slowly than predicted by eq. 1. In view of the various successful prcdictions of eq. 1 and the satisfactory agreement of the values in Table 111, it is possible that the mechanism of the iron(I1)-cobalt(111) reaction is more complex than that of the other reactions considered. Clearly, further studies of cross reactions involving the cobalt(I1)-cobalt(II1) system and using eq. 1 are in order. A direct determination of the rate constant for the manganese(I1)-manganese(111) exchange reaction would also be of considerable value. I t is of interest that the rate constant for the manganese(I1)-manganese(II1) reaction estimated above is much smaller than the observed rate constants for the iron(I1)-iron(II1) and cobalt(II)-cobalt(III) exchange reactions. The relative values of the rate constants for these reactions are consistent with calculations of the amount of energy required to reorganize the inner coordination shells of the various reactants prior to the electron transfer. 3c
A more extensive comparison of the values of some observed rate constants with those predicted by eq. 1
Acknowledgment. It is a pleasure to acknowledge helpful discussions with Drs. R. W. Dodson, R. A. Marcus, and J. K. Rowley.
Table 111: Comparison of Observed and Calculated Rate Constants in 3 F HC104 a t 25.0" (obsd.). F - 1 see. -1
kii
Reartioo
+ +
Fe(I1) Mn(II1) Mn(I1) Co(II1) Fe(phen)aa+ Mn(II1)
+
I 46 1 00 1 55
x x x
104 10% 10,
k12 (oalcd.),' F-1 see.
3 3 I
x x x
-1
104 10' 104
