Enthalpy redox couple

In Table 1 are summarized representative examples of self-exchange rate constant data for a variety of different types of redox couples based on metal complexes, organometallic compounds, organics and clusters. Where available the results of temperature dependence studies are also cited. For convenience, data obtained from temperature dependence studies are presented as enthalpies and entropies of activation as calculated from the reaction rate theory expression in equation (14). 

A consideration of these relationships reveals8 that because E° is a thermodynamic parameter and represents an energy difference between two oxidation states and in many cases the spectroscopic or other parameter refers to only one half of the couple, then some special conditions must exist in order for these relationships to work. The special conditions under which these relationships work are that (a) steric effects are either unimportant or approximately the same in both halves of the redox couple and (b) changes in E° and the spectroscopic or other parameters arise mainly through electronic effects. The existence of many examples of these relationships for series of closely related complexes is perhaps not too unexpected as it is likely that, for such a series, the solvational contribution to the enthalpy change, and the total entropy change, for the redox reaction will remain constant, thus giving rise to the above necessary conditions. 

To summarise E° values for redox couples of the type M(s)/M"+(aq) can largely be rationalised in terms of the atomisation enthalpies, ionisation energies and hydration enthalpies. The entropy terms can be neglected in most cases. 

The potential of the Bk(III)—Bk(0) couple has been investigated, using radiopolarography (229,230) and theoretical calculations (231), as well as by correlation with enthalpy of formation data (132, 133). Estimates of the potentials of berkelium redox couples have also been made from correlation plots of electron-transfer and f-d absorption band energies versus redox potential and by theoretical calculations (215, 221, 232, 233). 

Recently, Grochala and Peters have shown that the thermal decomposition temperature of many binary hydrides could be correlated with the standard redox potential for the metal cation/metal redox couple and with the standard enthalpy of decomposition [18, 83[. They also showed that, for multinary hydrides, the decomposition temperature could be tuned by a careful choice of the stoichiometric ratio and of the Lewis acid/base character of the constituent elements. 

Similar analyses for other metals can be carried out. For example, Cu and Zn are adjacent rf-block metals, and it is interesting to investigate factors that contribute to the difference between E° values for the Cu +/Cu and Zn +/Zn redox couples, and thus reveal how a balance of thermodynamic factors governs the spontaneous reaction that occurs in the Daniell cell (reaction 7.8). Table 7.3 lists relevant thermodynamic data it is apparent that the crucial factor in making E°q i+ significantly more positive than ii°zn2+/zn is the greater enthalpy of atomization of Cu Na (aq)-I-e Na(s)... 

The metallic end member SrCr03 is a high-pressure phase. At ambient pressure, the system Lai xSrxCr03 is a small-polaron conductor in the range 0 < X < 0.5 with a motional enthalpy AH , 0.1 eV for the Cr(IV) holes in the Cr(IV)/Cr(III) redox couple with a shallow trapping of the holes at the Sr " ions [108-112]. 

Let s recall that the handling of the free enthalpies of redox reactions permits us to calculate unknown standard potentials (see Sect. 2.11 in Chap. 2). This point is also important for the calculation of cell potentials, namely, for the calculation of the electrical charges brought by the electrodes (see below) not all redox couples appear in Tables 13.1-13.3. The standard potentials of the other couples may be calculated by using the additivity of the free enthalpies of the physical or chemical equivalent processes or with the help of Latimer-Luther s rule (see Chap. 2). 

Again students are expected to realise that this does not represent a stand-alone chemical process, and electrons are not found free under usual conditions, and so this process would need to be coupled with one that provides a place for the electron to go. Students may meet this process as part of a simple redox process (say with the reduction of a less reactive metal), or as one component of the analysis of a more complex process using Hess s law to find an enthalpy change by aggregating the enthalpy terms of an indirect route. 

The only thermodynamic condition then required for this reaction to be driven from left to right is that the standard molar free enthalpy of the reaction be negative, that is, the following inequality must hold E pq < E ac, where E ac represents the standard redox potential of the A/C couple. 

Finally, let us point out that the absolute standard electrode potential value of the couple H+w/H2(g) is actually about 4.5 V. This value cannot be verified since we cannot measure an absolute potential. It was obtained by using thermodynamic cycles, taking into account some thermodynamic data such as the proton hydration enthalpy and entropy. These last ones have been approached by considering the quadrupole model of water (see Chap. 1). It is quite evident that the value of 4.5 V differs considerably from the conventional one (0.00 V). However, it does not change the redox phenomena provision since only the standard electrode potential differences are taken into account. 

The standard potentials of the new couples are calculated from those of the initial couples according to the general principles already given (see Chap. 2). The halfredox reactions in which a precipitation reaction or a complexation reaction occurs can always be decomposed into a pure redox equilibrium and into another one that can be a reaction of precipitation or of complexation. For the calculations, we must add the corresponding standard free enthalpies. Thus,... 

Reduction potentials for the actinide elements are shown in Fig. 14.6. These show formal potentials, defined as the measured potentials relative to the hydrogen ion/hydrogen couple taken as zero volts. The redox potentials are corrected to unit concentration of the reactants, but are not corrected for activity. The measured potentials were determined by electrochemical cells, equilibria, and enthalpy of reaction measurements. The potentials for add solution were... 

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