A CROSS RELATION IN VOLUMES OF ACTIVATION FOR ELECTRON-TRANSFER REACTIONS

For the reduction of aqueous Fe(H2O)6(3+) by Co([9]aneS3)2(2+), over a wide range (0.02-0.8 mol kg-1) of ionic strength I, the rate constant k12 varies according to ln(k12/k12(0)) = 2AZ1Z2I1/2/(1 + BaI1/2), where A and B are the Debye-Huckel parameters and k12(0) = 369 +/- 7 with a = 798 +/- 10 pm for CF3SO3- media at 25-degrees-C. The pressure dependence of the electrode potential difference DELTAE gives the volume of reaction DELTAV12(0) = -17.1 +/- 0.4 cm3 mol-1 at I = 0.26 mol kg-1. The volume of activation DELTAV12double-dagger (-15.9 +/- 0.3 and -13.7 +/- 0.4 cm3 mol-1 for 0.1 mol kg-1 CF3SO3- and ClO4-media, respectively) agrees well with that calculated from a volume cross relation DELTAV12double-dagger = 1/2(DELTAV11double-dagger + DELTAV22double-dagger + DELTAV12(0)) + C, derived from the Marcus cross relation for k,2 (J. Phys. Chem. 1968, 72, 891), where DELTAV11double-dagger and DELTAV22double-dagger are for the Fe(H2O)6(3+/2+) and Co([9]aneS3)2(3+/2+) self-exchange reactions and the small contribution C incorporates the pressure dependence of Marcus' f. For the reduction of aqueous Fe(H2O)6(3+) by Co(sepulchrate)2+ at 1.8-degrees-C, for which DELTAE is large (1.03 V), k12 is 130-fold slower, and DELTAV12double-dagger (-5.0 cm3 mol-1) is 4-5 cm3 mol-1 more positive, than predicted by the cross relations. These results suggest the usefulness of the volume cross relation as a mechanistic criterion, at least for reactions with moderate DELTAE; in particular, they militate against nonadiabaticity as the cause of the perceived slowness of cross reactions involving the Fe(H2O) 6(3+/2+) couple. Conversely, the volume cross relation affords a means of obtaining experimentally inaccessible volumes of activation for adiabatic outersphere redox processes in water.