Thermodynamics of Reduction

Reduction is an inevitable step in the preparation of metallic catalysts. It is often also a critical step, because if it is not performed correctly the catalyst may sinter or may not reach its optimum state of reduction. The reduction of a metal oxide MO by H2 is described by the equation 

Thermodynamics predicts under which conditions a catalyst can be reduced As with every reaction, the reduction will proceed when the change in Gibbs free energy, AG, has a negative value. Equation (2-2) shows how AG depends on pressures and temperature  

AG° is the same under standard conditions (see e.g. [3]) n is the stoichiometric coefficient of reaction (2-1)  

If the reaction, in which the metallic fraction serves as a catalyst, produces water as a byproduct, it may well be that the catalyst converts back to an oxide. One should always be aware that in fundamental catalytic studies, where reactions are usually carried out under differential conditions (i.e., low conversions) the catalyst may be more reduced than is the case under industrial conditions. An example is the behavior of iron in the Fischer-Tropsch reaction, where the industrial iron catalyst at work contains substantial fractions of Fe304, while fundamental studies report that iron is entirely carbidic and in the zero-valent state when the reaction is run at low conversions [6]. 

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A simple-minded picture suggests that the CC K bonds in aUcynes and alkenes ought to be similar. Are they Consider the thermodynamics of reduction of phenylacetylene to first give styrene and then phenylethane. (The energy for H2 is given at right.)... 

Figure 6.5.12 shows the thermodynamics of reduction of iron oxides by CO (and also by H2, although this is not so relevant for the blast furnace). For example, at 900 °C, only traces of CO (in a mixture with CO2) are needed to reduce Fe203 to Fe304. The reduction of Fe304 to FeO is thermodynamically also favored as long as the CO content is above 15%. The final step of wuestite (FeO) reduction to iron is the crucial step, as we now need more than about 70% CO (and this reaction is also slow compared to reduction of hematite and magnetite). 

The thermodynamics of electrochemical reactions can be understood by considering the standard electrode potential, the potential of a reaction under standard conditions of temperature and pressure where all reactants and products are at unit activity. Table 1 Hsts a variety of standard electrode potentials. The standard potential is expressed relative to the standard hydrogen reference electrode potential in units of volts. A given reaction tends to proceed in the anodic direction, ie, toward the oxidation reaction, if the potential of the reaction is positive with respect to the standard potential. Conversely, a movement of the potential in the negative direction away from the standard potential encourages a cathodic or reduction reaction. 

Next consider the energetics of reduction. Calculate AH for the first step in the reduction process using free reagents (BHT and AlHT). Energies for formaldehyde, and for the two intermediate adducts are provided at left. Which reduction is thermodynamically more favorable Are these results consistent with the predictions made using atomic charges ... 

These considerations have been based entirely on thermodynamics and take no account of the overpotential, which is dependent on the rate of the process and the nature of the surface at which the reaction occurs. For this reason, the rate of reduction of HjO or HjO is usually low, and remains so to potentials from 0-5 to 1-OV below that given in equation 12.1. Even so, the instability of water is an insuperable obstacle to electrodepositing... 

The thermodynamics of interchange and reduction reactions are of particular interest, since knowledge of the feasibility areas of these reactions is of great assistance in determining the best conditions of processing for any given system. 

Let us consider the general trends of the reactivity of C-C, C-S, and C-Q (Q = Cl, Br, I) bonds towards oxidative addition and reductive elimination (Scheme 7-25). In many cases, either C-C bond-forming reductive elimination from a metal center (a) or the oxidative addition of a C-Q bond to a low-valent metal center is a thermodynamically favorable process (c). On the other hand, the thermodynamics of the C-S bond oxidative addition and reductive elimination (b) lies in between these two cases. In other words, one could more easily control the reaction course by the modulation of metal, ligand, and reactant Further progress for better understanding of S-X bond activation will be achieved by thorough stoichiometric investigations and computational studies. 

Cross-coupling to form carbon heteroatom bonds occurs by oxidative addition of an organic halide, generation of an aryl- or vinylpalladium amido, alkoxo, tholato, phosphido, silyl, stannyl, germyl, or boryl complex, and reductive elimination (Scheme 2). The relative rates and thermodynamics of the individual steps and the precise structure of the intermediates depend on the substrate and catalyst. A full discussion of the mechanism for each type of substrate and each catalyst is beyond the scope of this review. However, a series of reviews and primary literature has begun to provide information on the overall catalytic process.18,19,22,23,77,186... 

Fig. 4. Catalytic activities of metals (as potentials measured at 10-4 A.cm-2) for anodic oxidation of different reductants. Er thermodynamic oxidation-reduction potentials of reductants. H2 reversible hydrogen electrode potential in solution used to study oxidation of each reductant. Adapted from ref. 38.

As mentioned previously, siderophores must selectively bind iron tightly in order to solubilize the metal ion and prevent hydrolysis, as well as effectively compete with other chelators in the system. The following discussion will address in more detail the effect of siderophore structure on the thermodynamics of iron binding, as well as different methods for measuring and comparing iron-siderophore complex stability. The redox potentials of the ferri-siderophore complexes will also be addressed, as ferri-siderophore reduction may be important in the iron uptake process in biological systems. 

The so-called midpoint potential, Em, of protein-bound [Fe-S] clusters controls both the kinetics and thermodynamics of their reactions. Em may depend on the protein chain s polarity in the vicinity of the metal-sulfur cluster and also upon the bulk solvent accessibility at the site. It is known that nucleotide binding to nitrogenase s Fe-protein, for instance, results in a lowering of the redox potential of its [4Fe-4S] cluster by over 100 mV. This is thought to be essential for electron transfer to MoFe-protein for substrate reduction.11 3... 

In the case of the Bergman cyclization and the C1-C5 cyclization of enediynes, both the activation barrier for cyclization as well as the thermodynamics of the reaction became more favorable upon one-electron reduction compared to the thermal counterparts. The cyclization barrier drops by up to 12kcal/mol (in the C1-C5 cyclization) and the process becomes exothermic (as opposed to the endothermic cyclizations of the neutral counterparts) as illustrated in Fig. 19 and Fig. 20. 

FIGURE 2.34. a Reductive cyclic voltammetry of an aromatic hydrocarbon (e.g., anthracene) in an aprotic solvent (e.g., DMF) upon successive additions of a weak acid (e.g., phenol), b Thermodynamics of the combined addition of two electrons and two protons. 

Although thermodynamically favorable, reductive dissolution of Fe(III)(hydr)oxides by some metastable ligands (even those, such as oxalate, that can form surface complexes) does not occur in the absence of light. The photochemical pathway is depicted in Fig. 9.3e. In the presence of light, surface complex formation is followed by electron transfer via an excited state (indicated by ) either of the iron oxide bulk phase or of the surface complex. (Light-induced reactions will be discussed in Chapter 10.)... 

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