General Redox Reaction

The general half-reaction written as a reduction reaction in conformity with the Stockholm or lUPAC (International Union of Pure and Applied Chemistry) convention, with electrons on the left, is 

TABLE 11.1 Oxidation states of some important elements as they occur in natural waters and mineral systems 

Element Symbol Number of protons (atomic number) Oxidation states 

Note Values in parentheses are found in mineral systems only. 

There is a logical reason for writing the Eh reaction as given above so that all the terms are positive, and the oxidized species always appears in the numerator on the right. This conforms to the rationale that, as the concentrations of oxidized species increase, the system becomes more oxidizing, that is, the Eh increases. 

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Many redox reactions are more complicated than that given by Eq. (2-9). For a general redox reaction, with components X- and their coefficients n, written as... 

It is of interest to consider the calculation of the equilibrium constant of the general redox reaction, viz. ... 

The results obtained under standard conditions can be used to predict thermodynamic behavior at other concentrations and temperatures. To derive the necessary equations, consider the general redox reaction. 

The free energy change for the general redox reaction occurring in solution... 

PRINCIPLES OF ELECTRON TRANSFER CATALYSIS The general redox reaction... 

Redox potential is the measure of the oxidation-reduction state of a soil, and is determined by redox reactions involving the transfer of electrons from one chemical species to another. A generalized redox reaction can be written as... 

Generally, redox reactions used in titrimetry are sufficiently complete that the equilibrium concentration of one of the species (in this case fCe J) is minuscule with respect to the other species present in the solution. Thus, the foregoing two equations can be simplified to... 

Equation (3.8) is known as the Nernst equation for a metal electrode. Similar considerations can be used to derive the Nernst equations for other electrochemical reactions. For the general redox reaction... 

We have seen how to use standard reduction potentials to calculate for cells. Real cells are usually not constructed at standard state conditions. In fact, it is almost impossible to make measurements at standard conditions because it is not reasonable to adjust concentrations and ionic strengths to give unit activity for solutes. We need to relate standard potentials to those measured for real cells. It has been found experimentally that certain variables affect the measured cell potential. These variables include the temperature, concentrations of the species in solution, and the number of electrons transferred. The relationship between these variables and the measured cell emf can be derived from simple thermodynamics (see any introductory general chemistry text). The relationship between the potential of an electrochemical cell and the concentration of reactants and products in a general redox reaction... 

We have observed that voltaic cells use spontaneous redox reactions to produce a positive cell potential. We can use this fact together with half-cell potentials to decide whether a given redox reaction is spontaneous. In doing so, it is useful to make Equation 20.8 more general so that we can see how it pertains to general redox reactions, not just... 

In fact, the earliest application of kinetic methods was to determine trace levels of substances exerting catalytic activity in oxidation-reduction reactions involving multiple electron transfers (1885-trace level V on its catalysis of the oxidation of aniline). For example, the reduced form of many triphenylmethane dyes is colorless , and loses two electrons on oxidation to the dye. The rate of reaction with such oxidants as 104 is relatively slow, but can be catalyzed by trace levels of transition metal ions which involve single electron transfer in their own redox steps. Thus, trace levels of manganese can be determined by the proportionality of the rate of oxidation of leuco-malachite green by iodate at less than micromolar concentrations. Similarly, trace levels of Cu ", < 10 M, can be determined from the catalytic effect on the atmospheric oxidation of ascorbic acid. Such systems can be written as a generalized redox reaction... 

A general chemical equation for a pH-dependent redox couple is given in Equation (1) (note generalized redox reactions in this section are written as reductions to follow the convention that... 

Pourbaix (or ErpH) diagrams are frequently used in the context of metal CMP to categorize the reactant/product surface species expected for a given slurry composition. The thermodynamic foundation of this approach follows from the Nemst equation for general redox reactions in the aqueous environment, where the components of water (H" /OH ) join the redox species to support the faradaic steps. Such a reaction has the form x(Ox) + y(H ) + ne = w(Rd) + w(H20), where Ox and Rd denote the oxidized and reduced species of the active redox couple (such as the oxidized and pure forms of a metal), respectively x, y, n, u, and w denote the mole numbers of the participating species. The Nemst equation for this reaction can be written as... 

The following discussion will pertain to general redox reactions, not just reactions in voltaic cells. Thus, we will make Equation 20.8 more general by writing it as... 

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