Homogeneous redox equilibria

Fig. 17 Double potential step chronoamperometric results at 23°C for the reduction of lucigenin (B +) in DMF containing BU4NBF4 (0.1 M). The circles are experimental values, and the lines show the results of digital simulation for the EEC mechanism (a) including, and (b) without the homogeneous redox equilibrium (eqn 51). Potential-step times varied between 1 and 100 ms. (Ahlberg, et al., 1981)...

Another example of a redox electrode with a homogeneous redox equilibrium is the so-called quinhydrone electrode for pH measurements reported by Biilmann in 1921 [1], Quinhydrone is a charge transfer complex consisting of quinone and hydroquinone in a 1 1 ratio. If this compound is placed into an aqueous solution, the chemical equilibrium appears as follows [2] ... 

Here Ox and Red represent the oxidized and reduced form of the substance respectively, a and b are stoichiometric numbers, while n is the number of electrons exchanged. If the numbers of moles on the two sides of the equilibrium are equal (that is a = b) we have a homogeneous redox system like those (i) to (v), in other cases as (vi) and (vii) it is called inhomogeneous. In the simplest cases a = b = 1, when the system can be written as... 

The electric potential difference in equilibrium can be calculated analogously to how homogeneous redox systems are calculated, but the equation... 

W For example, in an aqueous solution containing fully dissociated potassium iodide, Kl, and dissolved diiodine, I2, the redox equilibrium of the couples 2l f and Ij"/ " is rapidly observed in the homogeneous phase ... 

Both potentiometric (equilibrium) and amperometric (dynamic) modes of operation, however, require facile electron transfer between the biomolecule and the surface of an electrode. For most large, electroactive biomolecules such direct heterogeneous electron transfer is extremely slow and even for the measurement of equilibrium potentials, which requires only very small currents, a suitable mediator must be added to the solution. Clearly, provision for charge transfer mediation is essential for the successful construction of sensors of both types. The selection of an appropriate mediator is usually based on the fulfillment of certain criteria. Its heterogeneous and homogeneous redox reactions must take place rapidly at a well-defined potential in the medium of interest and involve the transfer of a definite number of electrons to and from stable redox species. In addition the mediator should be adequately soluble, usually in aqueous media at pH 7, and should not inhibit the reaction of the biomolecule with its substrate. Very few substances meet all these demands. 

In contrast to NaZSM-5 zeolite, introduction of CoZSM-5 or HZSM-5 zeolite in the reaction system shifts the "light-off" temperature and modifies the chemistry now not only NO but Nj is formed. Hence, some intermediate species required for Nj formation must be stabilized on the catalyst surface. The "light-off"temperature shifts observed with CoZSM-5 and HZSM-5 catalysts may result from the enhanced redox capacity provided by these catalysts or from the NOj/NO equilibrium achieved more readily than with NaZSM-5. Moreover, equilibrium is approached at a somewhat lower temperature over CoZSM-5 than HZSM-5, and much lower than with the empty reactor (see Fig. 1 of Ref. lOl.The decomposition reaction of NOj into NO -t- occurs readily on these catalysts and the "light-off" temperature of both combustion and SCR is lower in comparison with that of the homogeneous reaction. 

As discussed already in Chapter 7, redox reactions constitute a second class of geochemical reactions that in many cases proceed too slowly in the natural environment to attain equilibrium. The kinetics of redox reactions, both homogeneous and those catalyzed on a mineral surface are considered in detail in the next chapter, Chapter 17, and the role microbial life plays in catalyzing redox reactions is discussed in Chapter 18. 

Hence, equilibrium constants of homogeneous electron-transfer reactions between (A) and B are evidently connected with a difference in reduction potentials of A and B. This connection reflects a dehnite physical phenomenon. Namely, if two redox systems are in the same solution, they react with each other until a unitary electric potential is reached. For the transfer of only one electron at room temperature, the equation log K = 2.3 [ i/2(A) - 1/2(6)] 0.059 can be employed. 

In the real world, the simple redox couple may be perturbed by finite ET rates, by adsorption of O and/or R on the electrode surface, and by homogeneous (i.e., in solution) chemical kinetics involving O and/or R. Various combinations of heterogeneous ET steps (E) with homogeneous chemical steps (C) are encountered. It should be clear that if one or more species in equilibrium in solution are electroactive, electrochemistry can be used to perturb the equilibrium and study the solution chemistry. 

In situ STM of metalloproteins with localized low-lying redox levels can be expected to follow ET patterns similar to metalloprotein ET in homogeneous solution and at electrochemical surfaces. The redox level is thus strongly coupled to the protein and solvent environment. A key notion is that the vacant local level (oxidized form) at equilibrium with the environmental nuclear motion is located well above the Fermi levels of both the substrate and tip, whereas, the occupied level (reduced form) at equilibrium is located well below the Fermi levels. Another central notion is that the local redox level at the transition metal centre is still much lower than environmental protein or solvent electronic levels. The redox level therefore constitutes a pronounced indentation in the tunnel barrier. This alone would strongly enhance tunnelling. Configurational fluctuations in the environment can, secondly take the redox level to such low values that temporary physical population occurs. This requires nuclear activation but can still be favourable due to the much shorter electron tunnel distances... 

In general, homogeneous catalysts based on HPANs consist of complex equilibrium mixtures of polyanions of different compositions with products of the deg-radative dissociation of the heteropolyanion. All these species can function as the active form or as ligands of a transition metal complex [16]. The HPAN + Pd(II) and HPAN + Rh(I) systems are also used in carbonylation, hydroformylation, and hydrogenation reactions [17]. Other redox systems based on HPANs are also known. Their second component is Tl(III)/Tl(I) [18], Pt(IV)/Pt(II) [19], Ru(IV)/ Ru(II), or Ir(IV)/Ir(III) [20]. 

Part of almost all homogeneous kinetic calculations will be some method to decouple the reactive species, which are often redox species. In kinetic calculations, the species are obviously not at equilibrium with each other, at least at the start of the calculation they approach equilibrium during the calculation. But speciation programs such as phreeqc and react assume all species to be at equilibrium unless told otherwise. In this case we want CH4 to not react with other species, partly to see what it is doing during the reaction, and partly because in nature it is extremely unreactive. We also want acetate to be decoupled because it is metastable and will not even exist in the solution at equilibrium. At the time of writing, this is not necessary in phreeqc, because the... 

---