Stoichiometry of redox reactions

The first step In balancing a redox reaction is to divide the unbalanced equation into half-reactions. Identify the participants in each half-reaction by noting that each half-reaction must be balanced. That Is, each element In each half-reaction must be conserved. Consequently, any element that appears as a reactant In a half-reaction must also appear among the products. Hydrogen and oxygen frequently appear in both half-reactions, but other elements usually appear In just one of the half-reactions. Water, hydronium ions, and hydroxide ions often play roles In the overall stoichiometry of redox reactions occurring in aqueous solution. Chemists frequently omit these species in preliminary descriptions of such redox reactions. 

It is generally believed that the oxidation of thiourea and related compounds by aqua-metal ions involves an inner-sphere electron-transfer process, whereas an outer-sphere mechanism is more commonly associated with substitution-inert complexes. The stoichiometry of redox reactions with one-electron oxidizing agents is different for acid and alkaline media. The oxidation of both thiourea and thioacetamide by [Mo(CN)g] in the range 0.02 < [HCIO4] < 0.08 M proceeds in a 1 1 ratio, yielding the disulfide as a product (108) ... 

Techniques responding to the absolute amount of analyte are called total analysis techniques. Historically, most early analytical methods used total analysis techniques, hence they are often referred to as classical techniques. Mass, volume, and charge are the most common signals for total analysis techniques, and the corresponding techniques are gravimetry (Chapter 8), titrimetry (Chapter 9), and coulometry (Chapter 11). With a few exceptions, the signal in a total analysis technique results from one or more chemical reactions involving the analyte. These reactions may involve any combination of precipitation, acid-base, complexation, or redox chemistry. The stoichiometry of each reaction, however, must be known to solve equation 3.1 for the moles of analyte. 

What Do We Need to Know Already This chapter extends the thermodynamic discussion presented in Chapter 7. In particular, it builds on the concept of Gibbs free energy (Section 7.12), its relation to maximum nonexpansion work (Section 7.14), and the dependence of the reaction Gibbs free energy on the reaction quotient (Section 9.3). For a review of redox reactions, see Section K. To prepare for the quantitative treatment of electrolysis, review stoichiometry in Section L. 

We begin this chapter with a discussion of the principles of redox reactions, including redox stoichiometry. Then we introduce the principles of electrochemishy. Practical examples of redox chemistry, including corrosion, batteries, and metallurgy, appear throughout the chapter. 

We have seen how analytical calculations in titrimetric analysis involve stoichiometry (Sections 4.5 and 4.6). We know that a balanced chemical equation is needed for basic stoichiometry. With redox reactions, balancing equations by inspection can be quite challenging, if not impossible. Thus, several special schemes have been derived for balancing redox equations. The ion-electron method for balancing redox equations takes into account the electrons that are transferred, since these must also be balanced. That is, the electrons given up must be equal to the electrons taken on. A review of the ion-electron method of balancing equations will therefore present a simple means of balancing redox equations. 

The photophysical properties (extinction coefficient, shifts in absorption and emission spectra, quantum yield, and lifetime) of a variety of probes are modified by pH changes, complexation by metal ions, or redox reactions. The resulting changes in photophysical parameters can be used to determine concentration of H+ and metal cations with suitably designed fluorophores. Most of these resulting sensors involve an equilibrium between the analyte, A, and the free probe (unprotonated or noncom-plexed by metal ion), Pf. If the stoichiometry of this reaction is 1 1, the reaction may be represented by... 

Spectrophotometry has been a popular means of monitoring redox reactions, with increasing use being made of flow, pulse radiolytic and laser photolytic techniques. The majority of redox reactions, even those with involved stoichiometry, have seeond-order characteristics. There is also an important group of reactions in which first-order intramolecular electron transfer is involved. Less straightforward kinetics may arise with redox reactions that involve metal complex or radical intermediates, or multi-electron transfer, as in the reduction of Cr(VI) to Cr(III). Reactants with different equivalences as in the noncomplementary reaction... 

Titration — A process for quantitative analysis in which measured increments of a - titrant are added to a solution of an - analyte until the reaction between the analyte and titrant is considered as complete at the - end point [i]. The aim of this process is to determine the amount of an analyte in a -> sample. In addition, the determination can involve the measurement of one or several physical and/or chemical properties from which a relationship between the measured parameter/s and the concentration of the analyte is established. It is also feasible to measure the amount of a - titrand that is added to react with a fixed volume of titrant. In both cases, the -> stoichiometry of the reaction must be known. Additionally, there has to be a means such as a -> titration curve or an - indicator to recognize that the -> end point has been reached. The nature of the reaction between the titrant and the analyte is commonly indicated by terms like acid-base, complexometric, redox, precipitation, etc. [ii]. Titrations can be performed by addition of measured volume/mass increments of a solution,... 

While all of these reactions are favored thermodynamically, they are almost always enzymatically catalyzed by bacteria. It has been observed from the study of pore waters in deepsea sediments (e.g., Froelich et al., 1979) and anoxic basins (e.g., Reeburgh, 1980) that there is an ordered sequence of redox reactions in which the most energetically favorable reactions occur first and the active electron acceptors do not overlap significantly. Bacteria are energy opportunists. Using estimates of the stoichiometry of the diagenesis reactions (Table 2) one can sketch the order and shape of reactant profiles actually observed in sediment pore-water chemistry... 

Formal potential may also include some constant or selected components of the medium that participate in the overall redox reaction. Thus pH, and concentrations of complexing reagents, for example, are often included in E° [35] when the O and R molecules are not interconnected by a simple electron transfer. To explicate this point, let us discuss a typical example related to aldehyde oxidation. The stoichiometry of the reaction in Eq. (27) involves an overall transfer of two electrons and one oxygen atom. 

Later, Guillamont, et al. [6,7] considered some aspects of the environmental solution chemistry of tracers (complexation, redox reactions) and of solving the specia-tion problems using partition methods. They paid most attention to the concentrations at which the mutual encounters of the tracer entities are somewhat probable. These conditions affect stoichiometry of the reactions and the kinetic laws of the interactions. Below this limit, if two different chemical forms of the tracer were... 

Construct a coulometric titration curve of 100.0 mL of a 1 M H2SO4 solution containing Fe(ll) titrated with Ce(lV) generated from 0.075 M Ce(lll). The titration is monitored by potentiometry. The initial amount of Fe(II) present is 0.05182 mmol. A constant current of 20.0 mA is used. Find the time corresponding to the equivalence point. Then, for about 10 values of time before the equivalence point, use the stoichiometry of the reaction to calculate the amount of Fe produced and the amount of Fe + remaining. Use the Nemst equation to find the system potential. Find the equivalence point potential in the usual manner for a redox titration. For about 10 times after the equivalence point, calculate the amount of Ce " produced from the electrolysis and the amount of Ce + remaining. Plot the curve of system potential versus electrolysis time. 

If our intent is to write an overall redox reaction, this procedure is followed first to obtain each half-reaction. The stoichiometry of one reaction is then adjusted so that the electrons are cancelled out by subtraction (cf. Appelo and Postma 1993). 

In this chapter we will examine oxidation-reduction stoichiometry, equilibria, and the graphical representation of simple and complex equilibria, and the rate of oxidation-reduction reactions. The applications of redox reactions to natural waters will be presented in the context of a discussion of iron chemistry the subject of corrosion will provide a vehicle for a discussion of the application of electrochemical processes a presentation of chlorine chemistry will include a discussion of the kinetics of redox reactions and the reactions of chlorine with organic matter finally, the application of redox reactions to various measurement methods will be discussed using electrochemical instruments as examples. 

Oxidation of aliphatic aldehydes by benzyltrimethylammonium chlorobromate to the corresponding carboxylic acid proceeds via the transfer of a hydride ion from the aldehyde hydrate to the oxidant. The oxidation of aUyl alcohol with potassium bromate in the presence of osmium(Vin) catalyst in aqueous acidic medium is first order in bromate, Os(Vni) and substrate, but inverse fractional order in H+ the stoichiometry of the reaction is 2 3 (oxidantsubstrate). The active species of oxidant and catalyst in the reaction were understood to be BrOs and H2OSO5, respectively, which form a complex. Autocatalysis by Br, one of the products, was observed, and attributed to complex formation between Br and osmium(VIII). First-order kinetics each in BrOs, Ru(VI), and substrate were observed for the ruthenium(VI)-catalyzed oxidation of cyclopentanol by alkaline KBrOs containing Hg(OAc)2. A zero-order dependence on HO concentration was observed and a suitable mechanism was postulated. The oxidation reaction of aniUne blue (AB+) with bromate at low pH exhibits interesting non-linear phenomena. The depletion of AB+ in the presence of excess of bromate and acid occurs at a distinctly slow rate, followed by a very rapid reaction. A 12-step reaction mechanism, consistent with the reaction dynamics, has been proposed. The novel cyclohexane-l,4-dione-bromate-acid system has been shown to exhibit a rapid oscillatory redox reaction superimposed on a slower... 

Comparative studies have been made in the oxidation of N2H4 and NH2OH by Co(III) complexes. The reactions of [Co(edta)(OH2)] with the substrates in acid media are considered to proceed via an inner-sphere mechanism with a proton bridge between the cobalt(III) species and (a filled orbital on) the nitrogen of the reductant. The rates are greater than for [Co(ox)3] or [Co(acac)3] despite the fact that all three species have similar redox potentials. Reactions with cationic cobalt(III) species appear to be much slower. The stoichiometry of the reaction between NH2OH and V(V) in HCIO4 media is dependent on the reaction conditions.In the presence of excess reductant, however, the reaction is first order with respect to [VO ] and the dependence on hydroxylamine concentration... 

Consider the cyclic voltammetry trace of electrically activated iridium oxide (the so called AIROF) which features reversible reactions (Fig. 3.3). The scan rate is very slow, so the dynamic behavior of the Helmholtz capacitance has a negligible effect on the measured trace. The positive peaks A and B correspond to two distinct oxidation reactions at the surface of the electrode, pertaining to different electrode potentials. The negative peaks C and D correspond to reduction reactions. C matches A and D matches B, as they have similar shape. The reduction potential peak (for example at C, Epc) does not happen at a negative electrode-electrolyte voltage drop, but at a positive one even near to the potential where oxidation potential peak (at A, Epa) is located. If the surface redox reactions are fast and the reaction rate is limited by the diffusion of the reactants in the solution, the difference between the oxidation and reduction peaks is only 59 mV/n for a reaction where n electrons are transferred in the stoichiometry of the reaction. This state is called electrochemical reversibility, which means that the thermodynamic equilibrium in the redox reaction at the surface is established fast at every applied electrode potential. Note that this concept is not the same as the chemical reversibility explained before. A system can be electrochemically irreversible but chemically reversible. As seen in Fig. 3.3, iridium oxide is already electrochemically irreversible even at the very slow potential ramp of 50 mV/s, as the , 4 — is already larger than 59 mV. 

For any redox reaction, the number of moles of electrons transferred depends on the stoichiometry of the reaction. For example, if copper is placed in a solution of silver nitrate, the following overall reaction implies two half-reactions, the reduction and oxidation... 

---