Summary and interpretation

The dynamics of spin equilibria in solution are rapid. The slowest rates are those for coordination-spin equilibria, in which bonds are made and broken even these occur in a few microseconds. The fastest are the AS = 1 transitions of octahedral cobalt(II) complexes, in which the population of the e a antibonding orbital changes by only one electron these appear to occur in less than a nanosecond. For intramolecular interconversions without a coordination number change, the rates decrease as the coordination sphere reorganization increases. Thus the AS = 2 transitions of octahedral iron(II) and iron(III) are slower than the AS = 1 transitions of cobalt(II), and the planar-tetrahedral equilibria of nickel(II) are slower again, with lifetimes of about a microsecond. 

The spin equilibria of octahedral iron(II) complexes are the best studied examples in both the solid state and in solution. Both the low-spin lA and the high-spin 5T states are regular octahedra, so the 

These relaxation times correspond to rates which are about 106 slower than the thermal vibrational frequency of 6 x 1012 sec 1 (kBT/h) obtained from transition state theory. The question arises how much, if any, of this free energy of activation barrier is due to the spin-forbidden nature of the AS = 2 transition. This question is equivalent to evaluating the transmission coefficient, k, that is, to assess quantitatively whether the process is adiabatic or nonadiabatic. 

It is not possible to evaluate k directly, for it appears with the entropy of activation in the temperature-independent part of the rate constant. An estimate of k requires an extrathermodynamic assumption. In two cases of iron(II) spin equilibria examined by ultrasonic relaxation the temperature dependence of the rates was precisely determined. If the assumption is made that all of the entropy of activation is due to a small value of k, minimum values of 10-3 and 10-4 are obtained. Because there is an increase in entropy in the transition from the low-spin to the high-spin states, this assumption is equivalent to assuming that the transition state resembles the high-spin state. There is now evidence that this is not the case. Volumes of activation indicate that the transition state lies about midway between the two spin states. This is a more chemically reasonable and likely situation than the limiting assumption used to evaluate k. In this case the observed entropy of activation includes some chemical contributions which arise from increased solvation and decreased vibrational partition functions as the high-spin state is compressed to the transition state. Consequently, the minimum value of k is increased and is unlikely to be less than about 10 2. 

If the above analysis is correct, spin equilibria with AS = 1 will relax significantly more rapidly than those with AS = 2, for two reasons. One is that the transmission coefficient k will be close to unity, because 

Let us summarize the results obtained. The theory is restricted to nonadiabatic electron-transfer reactions. If only classical modes are reorganized during the transition, the rate constant for the oxidation is  

If in addition one inner-sphere mode of frequency oj, with Tuo 3 kT, is reorganized, the total rate constant can be written as a sum over partial rates  

Both the total rate kox and the partial rates are shown in Fig. 19.3 as a function of the energy change Ae e/ — e. As might be expected, the transitions to excited inner-sphere modes become important only 

The density of oxidized states is obtained by changing the signs of the electronic energy e and the overpotential r/  

These expressions can be inserted into Eqs. (6.22) and (6.23) to obtain the concomitant current densities. The factor A in this equation must be replaced by the explicit expression jwj /h, so that  

---

Toxicological Profiles are a unique compilation of toxicological information on a given hazardous substance. Each profile reflects a comprehensive and extensive evaluation, summary, and interpretation of available toxicologic and epidemiologic information on a substance. Health care providers treating patients potentially exposed to hazardous substances will find the following information helpful for fast answers to often-asked questions. 

A) The examination, summary, and interpretation of available toxicologic information and epidemiologic evaluations on a hazardous substance to ascertain the levels of significant human exposure for the substance and the associated acute, subacute, and chronic health effects ... 

Fan specifically excluded the role of i ct when he made the identification, and his major arguments were based on the summary and interpretation of the previously published data on lithium diffusion coefficients in both the cathode and anode and the fact that the surface area of the cathode is normally only a fraction of the anode. Without data from direct measurement, the above speculation seems to be premature hence, further experimental confirmation is needed. 

---