J. Phys. Chem. 1986, 90, 3686-3690
3686
Discussion The most important observation from this work is that the rate of electron exchange of the Ru(en)?+I2+ couple is more rapid than that of the R u ( N H ~ ) ~ ~couple. + / ~ + This is qualitatively what is predicted by the Marcus theory' but is contrary to the original results reported by Meyer and Taube.6 Their experiments were technically difficult, requiring mixing by conventional means of relatively large volumes of dilute, air-sensitive solutions. We have been unable to reproduce their observations. The present results are consistent, however, with the earlier observations of Elsbernds who used rapid mixing with circular dichroism detection to set a lower limit of lo3 M-' s-l on the rate constant. Our results are also compatible with the more recent observations of Brown and Sutin" who measured the rate of the cross reaction 3. Their rate constant of 2.7 X IO4 M-I s-l at 25 "C
+
R ~ ( e n ) ~ ~Ru(NH3)2+ +
-+
R ~ ( e n ) ~ '+ + R u ( N H ~ ) ~ ~(3) +
and = 0.1 M CF3S03-media when corrected for the free energy change of this reaction gave a mean rate constant for the selfexchange of the ruthenium complexes of 3.2 X lo3 M-' s-l. The present results indicate that the R ~ ( e n ) ~ ~exchange + / ~ + is less than a factor of ten faster than the R u ( N H ~ ) ~ ~ exchange. +/~+ The Brown and Sutin result then would indicate a rate constant for the R u ( N H , ) ~ + / ~exchange + at 0.1 M ionic strength of just grater /~+ of than 1 X lo3 M-I s-l a nd that for the R ~ ( e n ) , ~ +exchange just less than 1 X lo4 M-' s-l , in reasonable agreement with our results. According to the Marcus theory, an increase in the rate of electron exchange for the larger tris(ethy1enediamine) complexes compared with the hexaammine complexes arises from two effects. One is a decreased electrostatic work term due to the larger distance of closest approach for the larger complex. This effect is small, particularly for the solutions of high ionic strength used in these studies. The second, more important, factor is the reduced outer-sphere reorganization energy, AGO*. This contribution to the activation free energy for a general outer-sphere electrontransfer reaction depends on the radii of the complexes, a , and u2, and the distance between the reaction centers, R, according to
AGO* = ((Ae)2/4){'/,u,+ Y2u2- 1/R](l/n2 - l / D ] ( 4 )
For the self-exchange reaction, where a, = a2 = R / 2 (in angstroms), in water at 25.0 "C, this reducesI6 to AGO* = 45.0(Ae)2/R
(5)
The radius of the hexaammine complexes has been estimated" to be 3.3 A, giving AGO*= 6.8 kcal mol-'. The equatorial radius of the tris(ethy1enediamine) complexes can be estimated4-" to be 5.1 A, giving AGO* = 4.4 kcal mol-'. This difference of 2.6 kcal mol-' in the predicted outer-sphere activation free energy corresponds to a rate difference of IO2. A precise value for the difference in rate constants for the hexaammine and tris(ethy1enediamine) electron exchange reactions is difficult to determine, because of the different conditions under which the two reactions have been studied, but it is certaintly less than lo2 and is probably less than 10. There are several possible reasons for this discrepancy between the predictions of the theory and the present results. One is that the tris(ethy1enediamine) complexes do not undergo electron transfer along the larger equatorial radius, perhaps because this pathway is nonadiabatic. A suggestion of this was previously found in our study of the reduction of Co(II1) complexes." A second possibility is that ion-pairing and ionic medium effects differ between the two complexes. Our results clearly show a strong specific effect of chloride ions. It is necessary to examine these reactions at low ionic strengths to ascertain the intrinsic reaction parameters. Another possibility is that the dielectric continuum model upon which the theory is based is not sufficiently sensitive to elucidate these small differences. The hydrogen-bonding properties of the two complexes are obviously different and may produce a significant difference in the surrounding solvent structure. Whatever the reasons for the absolute difference in electron exchange rates between the R ~ ( e n ) ~ ~and + / the ~ + Ru(NH,),~+/~+ couples, the present results remove an anomaly from the literature: the larger tris(ethy1enediamine) complexes do undergo exchange more rapidly than do the hexaammine complexes. A similar difference, also uncertain in absolute magnitude, is now accepted between the rates of electron exchange of C ~ ( e n ) , ~ + and / ~ + Co(NH3)63+/2+.18Furthermore, the differences between the cobalt and ruthenium rates can be understood on the basis of the known differences in their structures arising from their different d-electron configurations. All of these general observations are explicable within the framework of the Marcus theory. Registry No. [ R U ( ~ ~ ) J ( C F , S O101031-50-9; ~)~, [Ru(en)J(CFyS0,)3, 63703-89-9. (16) Sutin, N. Annu. Rev. Nucl. Sci. 1962, 12, 285. (17) Beattie, J. K.; Binstead, R. A.; Broccardo, M. Inorg. Chem. 1978,17, 1822. (18) Geselowitz, D.; Taube, H. Adu. Inorg. Bioinorg. Mech. 1982, I, 391.
Kinetic Studies of Outer-Sphere Redox Reactions of p-Pyrazinedecaamminedlruthenium(II,II), - ( I I , I I I ) , and - ( I I I , I I I ) Urs Furholz and Albert Haim* Department of Chemistry, State University of New York, Stony Brook, New York I I794 (Received: December 9, 1985; In Final Form: February 28, 1986)
Rate constants for outer-sphere cross-reactions of the couples R u ~ ( N H ~ ) ~ ~(pz ~ z=~ pyrazine), +/~+ RU~(NH~),~~Z~+/~+, R U R ~ ( N H ~ ) ~ , , ~ ZR~U+(/ N ~ +H, ~ ) ~ ~ Zand ~ +R~U~( N + ,H ~ ) ~ P Z C H ~(pzCH3 ~ + / ~ += methylpyrazinium) with the couples Ru(NH3)5py3+/2+ (py = pyridine), R u ( N H J ~ ( ~ ~ ~ ) (bpy ~ + / '=+2,2'-bipyridine), and C~(bpy),'+/~+ have been measured at 25 OC and ionic strength 0.10 M (trifluoromethanesulfonate). The rate constants for the R U ( N H ~ ) ~ ~ ~and ~ +Ru/'+ (NH3)4bpy3+/Z+ reactions were treated according to the electrostatically corrected, adiabatic Marcus equation and yielded the following estimates of the rate constants for self-exchange reactions (in the same order as above): 15, 6.7 X lo3, 9.0, 1.4 X lo4,and 39 M-' s-I. The trends are discussed on the basis of inner-sphere and outer-sphere reorganization energies. couple appear to be mildly nonadiabatic. The cross-reactions of the C~(bpy),~+/'+
Following the initial report' on the title compounds, hereafter formulated as R U ~ ( N H ~ ) ~ ~ ~ Zthere ~ + /has ~ +been / ~ +a ,publication 0022-3654/86/2090-3686$01,50/0
explosion on the subject of discrete, mixed valence compounds.2 Most, if not all, of the work emphasis synthetic,2 s t r ~ c t u r a l , ~ 0 1986 American Chemical Society
Outer-Sphere Redox Reactions
The Journal of Physical Chemistry, Vol. 90, No. 16, 1986 3687
thermodynamic: and spectroscopic5aspects of such compounds. TABLE I: Second-Order Rate Constants for Reactions of Ru(I1) and It was noted p r e v i ~ u s l ythat ~ * ~the dynamic solution behavior of Ru(II1) Complexes at 0.10 M Ionic Strength (CF3S03H)and 25 OC" mixed valence compounds, in particular redox work, has been oxidant reductant k , M-I sW1 neglected. In order to remedy this unsatisfactory situation, we R u ~ ( N H ~ ) ~ ~ ~ Ru(NH&py2+ z ~ ' (1.2 f 0.2) X lo7 have started a program to investigate the kinetics of redox reactions Ru~(NH~)IOPZ~' Ru(NH3)4bpy2' (1.9 f 0.2) X lo6 of mixed valence compounds. We reported previously6 studies Ru2(NH3)lopz6+ Co( bpy) 32+ (1.1 i 0.2) x 105 with (NC)SFepzRu(NH3)
