Redox reactions, equilibration

The species dissolved in a fluid may be in partial equilibrium, as well. Many redox reactions equilibrate slowly in natural waters (e.g., Lindberg and Runnells, 1984). The oxidation of methane... 

Equilibrium considerations other than those of binding are those of oxidation/reduction potentials to which we drew attention in Section 1.14 considering the elements in the sea. Inside cells certain oxidation/reductions also equilibrate rapidly, especially those of transition metal ions with thiols and -S-S- bonds, while most non-metal oxidation/reduction changes between C/H/N/O compounds are slow and kinetically controlled (see Chapter 2). In the case of fast redox reactions oxidation/reduction potentials are fixed constants. 

Even when forward reactions proceed rapidly at laboratory conditions, as is observed with Se(IV) and Cr(VI) reduction, evidence exists that chemical and isotopic equilibrium are not approached rapidly. Altman and King (1961) studied the kinetics of equilibration between Cr(III) and Cr(Vt) at pH = 2.0 to 2.5 and 94.8°C. Radioactive Cr was used to determine exchange rates, and Cr concentrations were greater than 1 mmol/L. Time scales for equilibration were found to be days to weeks. The mechanism of the reaction was inferred to involve unstable, ephemeral Cr(V) and Cr(IV) intermediates. Altman and King (1961) stated that the slowness of the equilibration was expected because the overall Cr(VI)-Cr(III) transformation involves transfer of three electrons and a change in cooordination (tetrahedral to octahedral). Se redox reactions also involve multiple electron transfers and changes in coordination. 

The difference between the two reactions of Scheme 2.9 may also be considered in terms of the complete electron transfer in both cases. If the a-nitrostilbene anion-radical and metallocomplex cation-radical are formed as short-lived intermediates, then the dimerization of the former becomes doubtful. The dimerization under electrochemical conditions may be a result of increased concentration of reactive anion-radicals near the electrode. This concentration is simply much higher in the electrochemical reaction because all of the stuff is being formed at the electrode, and therefore, there is more dimerization. Such a difference between electrode and chemical reactions should be kept in mind. In special experiments, only 2% of the anion-radical of a-nitrostilbene were prepared after interruption of controlled-potential electrolysis at a platinum gauze electrode. The kept potential was just past the cathodic peak. The electrolysis was performed in the well-stirred solution of trani -a-nitrostilbene in AN. Both processes developed in this case, namely, trans-to-cis conversion and dimerization (Kraiya et al. 2004). The partial electrolysis of a-nitrostilbene resulted in redox-catalyzed equilibration of the neutral isomers. 

The treatment of excited species as new chemical entities, and hence, the use of thermodynamics in dealing with their redox reactions is justified because in the condensed phase, the electronic relaxation times are usually several orders of magnitude longer than the time for thermal equilibration in all other degrees of freedom of a polyatomic molecule49, 50). 

Oxidations of carbon-heteroatom species often results in the destruction of a stereogenic center, as in the oxidation of a secondary alcohol to a ketone. In some instances, this reaction can be coupled with another to provide a chiral product (see Chapter 21). One example is the enzymatic acetylation of one enantiomer of a secondary alcohol, where a redox reaction with a transition metal catalyst equilibrates the unreactive isomer of the alcohol (Scheme 9.1).10 12 The redox reaction can also be performed by an enzyme.13... 

ESR spectroscopy has been used to study a number of other redox reactions of phytochemical interest. It has been demonstrated that reduction of Cr(VI) to Cr(V) and Cr(III) can be brought about in the cortex of garlic (Allium sativum) roots (Micera and Dessi, 1988). Plant roots equilibrated with 250 ppm Cr(VI) as dichromate showed spectra attributed to Cr(V) species (g0 = 1.970) even after short incubation times. From the hyperfine splitting it was concluded that the Cr(V) was coordinated primarily to oxygens. With longer contact time, a second signal attributed to Cr(III)... 

The solution phase of an electrochemical cell does not contain free electrons, but it does generally contain a redox couple which can equilibrate with the free electrons in the electrode. This allows us to extend the concept of the Fermi level to the solution. Consider the redox couple 0,R in contact with an electrode el at which the redox reaction 0 H- nt R occurs. When the system is at equilibrium, the work of transferring an electron across the electrode/solution interface to transform (l/n)0 to (l/n)R is zero, i.e. 

First, we consider cyclic voltammetry and focus on the non-turnover experiment in which there is no substrate in solution. As the potential is scanned, electrons transfer back and forth between the electrode and the redox-active site(s), producing a current peak in each direction. These two peaks constitute the signal . Provided the scan rate is slow enough to equilibrate all the processes required in the redox reaction, the signal obtained will be as predicted by the Nemst equation that holds for a reversible electron-transfer process. The current peaks will be compact and... 

The slower relaxation reflects re-equilibration between the forms of reduced azurin and favour A r. This step is spectrally silent but is reported through the coupled redox reaction which is displaced towards ferricytochrome C55, as Ar is converted to A r. 

Keggin-type phosphomolybdates (POM s) were tested as catalysts for the selective oxidation of isobutane to methacrylic acid. Doping the POM with antimony improves the catalytic performance especially at isobutane-lean conditions, since a redox reaction between Sb " " and Mo leads to the development of a reduced POM which is stable even in an oxidizing environment, and which is more selective to methacrylic acid. Another important factor to control the reactivity is the pH of precipitation of the POM. When the preparation of the catalyst is carried out via the formation of a lacunary precursor, the time necessary to reach steady catalytic performance ( equilibration time ) is considerably less than that for POM s prepared conventionally at strongly acid pH. An hypothesis about the nature of the active sites is formulated. 

The suffixes o and r refer to the oxidised and reduced protein respectively. Thus, the electron transfer reaction between the redox proteins is coupled to a transition between two forms of reduced azurin, only one of which participates directly in the redox reaction. As the mechanism involves two independent equiUbria, two relaxation processes are observed following an increase in temperature. Fig. 6 shows a typical progress curve monitored at a wavelength characteristic of reduced cytochrome Cjj]. This transient is comprised of a rapid increase in absorbance followed by a slower decrease. The rapid relaxation reflects the initial re-equilibration of the second-order redox reaction, an increase in temperature favouring ferrocytochrome... 

For the following reaction schemes, describe how the voltammetric response for the redox reactions will vary as a function of pH over the full aqueous pH range (0-14). Assume that the rate of electron transfer is fast, such that the electrode kinetics are fully reversible, and that the protonation/deprotonation steps are so fast as to be equilibrated throughout. Note that the chemical steps have been written as deprotonations so that the equilibrium constants are readily related to the pKa of the species. 

The equilibration of redox reactions can be done in several steps. Let s consider the oxidation reaction of iodide ions by dichromate ions. It must be written as... 

Redox-induced difference spectra were obtained by first equilibrating the sample at the initial potential for several minutes and then recording the IR (128 interferograms) and visible/near IR (VIS/NIR) spectra of the initial state. The potential was then switched to the final state and the time dependence of the current was recorded. After the current had effectively decayed to zero (generally 3-5 minutes), the IR and VIS/NIR spectra of the final state were recorded. Generally, several cycles of these redox reactions were averaged. 

The above considerations also apply to situations in which a donor and an acceptor are both reversibly adsorbed on a common surface. For example, it has been known for over a century that molecules adsorb and desorb reversibly on electrodes, producing a complex nonhomogeneous layer near the electrode surface with a substantially different composition relative to the bulk solution with which it is in contact. Electrochemists refer to this space as an electrode surface region, or a double layer, if the contacting solution is an aqueous electrolyte. Chemical reactions take place with ease in this region as the electrode potential is scanned through the oxidation or reduction potential of the reactant. After the redox reaction has taken place, equilibration takes place with the neighboring bulk solution. 

PHREEQE can calculate pH, redox potential, concentration of elements, molalities and activities of aqueous species, and mineral or gas mass transfer as a function of reaction progress. The program is capable of simulating reactions due to mixing, titrating, net irreversible reaction, temperature changes, and mineral- or gas- phase equilibration. 

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