Energy states in solution

Usually the corresponding redox potential is given on a conventional scale using the normal hydrogen electrode (NHE) or a saturated calomel electrode (SCE) as a reference electrode, as already described in Section 3.2.3. Different scales are given in Chapter 5. Theoretically, however, one can also use the vacuum level as a reference, as is common in solids. 

In the case of a typical redox couple, such as M . aq/M. aq, dissolved e.g. in water, the M. aq ions represent unoccupied electron energy levels and the M. aq ions the 

For simplicity we have assumed that the shapes of the two curves are equal (only one y value in both cases). In consequence the reorganization values arc equal, i.e. Ared = Aox = A. The fluctuation of the solvent molecules leads finally to a broadening of the electronic levels as derived below. 

It should be mentioned here that only one single electronic state of the redox system is considered in this model. Wox and Wrej are then only the probabilities of finding the empty and occupied electronic state, respectively, at the energy . The variation of the electronic state is only due to the interaction of the redox couple with the solvent. 

The gaussian types of functions (Eqs. 6.37 and 6.38) yield the distribution of electronic levels of the redox system. Wred describes the fluctuation and therefore the distribution of the occupied electronic level and the distribution of the empty level. The density of electronic states is proportional to the concentration of the reduced (Cred) and oxidized species (cq ) of the redox system. Accordingly, the total distribution is given by  

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Energy states in solution, 1462 1463 Boltzmann distribution law, 1466 distribution, 1462 1464 ground state, 1464, 1468 number of, 1462 Enthalpy... 

Gao et al. located the saddle point of the two-dimensional free energy surface at Rc-n = 1.96 A and Rc-ci = 2.09 A, and used this point to define the transition state in solution. This way, their most striking finding was that on going from the gas phase... 

Concentrations of aqueous electrolyte solutions are conventionally expressed using the aquamolality scale (L = moles salt per 55.508 mol solvent (l,000g for H20)). Some typical solubilities (298.15K) are listed in Table 5.13. Almost all salts are less soluble in D20 than in H20. For those salts whose solubility increases with temperature, which is the ordinary behaviour, the isotope effects decrease with temperature. Writing the standard state partial molar free energy of pure solid salt as Pxsalt) and its standard state in solution as p, (HorD) we have on comparing the saturated solutions in H20 and D20,... 

In principle, fluorescence spectra from shortlived upper metalloporphyrin states in solution can be shifted in the longwave direction with vibrational energy relaxation at the cost of short-wave excitation (7). However, in our case the energy difference of annihilatTng and direct excitation was slight ( <... 

Similar photovoltaic cells can be made of semiconductor/liquid junctions. For example, the system could consist of an n-type semiconductor and an inert metal counterelectrode, in contact with an electrolyte solution containing a suitable reversible redox couple. At equilibrium, the electrochemical potential of the redox system in solution is aligned with the Fermi level of the semiconductor. Upon light excitation, the generated holes move toward the Si surface and are consumed for the oxidation of the red species. The charge transfer at the Si/electrolyte interface should account for the width of occupied states in the semiconductor and the range of the energy states in the redox system as represented in Fig. 1. 

However, in solutions, there is what is called line broadening, i.c., the characteristic shapes seen in molecular spectra in the gas phase are substantially wider in the range of energies they cover. Thus, the separability by means of spectroscopic measurements of the vibrational and rotational states in solution is greatly reduced. 

Another key feature of redox thermodynamic cycles is that the free energy change in solution is still defined to involve a gas-phase electron, that is, the solvation free energy of the electron is happily not an issue. And, once again, redox potentials in soludon typically assume 1 M standard states for ad species (but not always in this chapter s case study, for instance, all redox potentials were measured and computed for chloride ion concentrations buffered to 0.001 M). So, free energy changes associated with concentration adjustments must also be properly taken into account. 

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