Electron free energy change

When the e.m.f. of a cell is measured by balancing it against an external voltage, so that no current flows, the maximum e.m.f. is obtained since the cell is at equilibrium. The maximum work obtainable from the cell is then nFE J, where n is the number of electrons transferred, F is the Faraday unit and E is the maximum cell e.m.f. We saw in Chapter 3 that the maximum amount of work obtainable from a reaction is given by the free energy change, i.e. - AG. Hence... 

M Tachiya. Relation between the electron-transfer rate and the free energy change of reaction. J Phys Chem 93 7050-7052, 1989. 

A schematic diagram of the free energy changes in an electron exchange reaction, showing the intersection of two parabolas. The lighter curve represents n,c the darker one, eng, ncg. 

The reactivities of potassium and silver with water represent extremes in the spontaneity of electron-transfer reactions. The redox reaction between two other metals illustrates less drastic differences in reactivity. Figure 19-5 shows the reaction that occurs between zinc metal and an aqueous solution of copper(II) sulfate zinc slowly dissolves, and copper metal precipitates. This spontaneous reaction has a negative standard free energy change, as does the reaction of potassium with water ... 

Warshel is to utilize a formula identical to (11.22) in this chapter to compute the free energy change. They employed an empirical valence bond (EVB, below) approach to approximately model electronic effects, and the calculations included the full experimental structure of carbonic anhydrase. An H/D isotope effect of 3.9 1.0 was obtained in the calculation, which compared favorably with the experimental value of 3.8. This benchmark calculation gives optimism that quantum effects on free energies can be realistically modeled for complex biochemical systems. 

The gas-phase lifetime of N20- is 10-3 s in alkaline solutions, it is still >10-8 s. Under suitable conditions, N20- may react with solutes, including N20. The hydrated electron reacts very quickly with NO (see Table 6.6). The rate is about three times that of diffusion control, suggesting some faster process such as tunneling. NO has an electron affinity in the gas phase enhanced upon solvation. The free energy change of the reaction NO + eh (NO-)aq is estimated to be --50 Kcal/mole. Both N02- and N03- react with eh at a nearly diffusion-controlled rate. The intermediate product in the first reaction, N02-, generates NO and... 

With M as Be, Mg, Ca, Sr, or Ba, the reaction has a positive free energy change due to the overcompensating effect of ion hydration energy relative to electron affinity. Therefore, these ions do not react with eh. ... 

FIGURE 10.5 Standard free energy change, in various liquid hydrocarbons, versus temperature upon electron trapping from the quasi-free state according to the quasi-ballistic model. Reproduced from Mozumder, (1996), with the permission of Am. Chem. Soc. ... 

In our description of the Marcus theory of electron-transfer reactions we have found it helpful to plot the free energy change in the three dimensional picture shown in Fig. 10 (Albery, 1975c, 1980). This picture emphasizes that... 

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