Equilibrium potential, rate attainment

When cathodic polarization is a result of negative total current densities 7., the potential becomes more negative and the corrosion rate lower. Finally, at the equilibrium potential it becomes zero. In neutral water equilibrium potentials are undefined or not attainable. Instead, protective potentials are quoted at which the corrosion rate is negligibly low. This is the case when = 1 flA cm (w = lOjUm a ) which is described by the following criteria for cathodic protection ... 

The liquid junction potential always acts in such a way that the motion of ions that move rapidly is retarded, while the motion of the slower ions is accelerated. Accordingly, equilibrium is soon attained (within a few milliseconds of the two solutions being joined via a membrane), thus allowing a constant value of Ej to be recorded. The absolute magnitude of Ej will depend on the concentrations (again, strictly the activities) of the constituent ions in the two half cells, on the charges of each ion and on the relative rates of movement across the membrane. 

Regarding the first point, as shown below, if the current drawn in the measurement is kept small compared with the exchange current (Sections 14-2 and 14-4) that passes in both directions at equilibrium, the shift in potential (polarization) can be made small enough to be negligible. (Topically exchange currents are of the order of 10 A/cm for favorable systems and 10 ° A/cm or lower for imfavorable ones.) With modern instrumentation the current drain can be made so low that this condition need not be the limiting factor. When the exchange current is small, however, the rate of attainment of the equilibrium potential may be low. 

The extreme left and right hand ends of the V-shape are horizontal as the system becomes diffusion-controlled, so that rate of electron transfer at the electrode no longer affects the current. However, as the system approaches Ee, the equilibrium potential for that particular electrochemical system, there is a sloping region where a linear approximation may be made before attaining values close to E, where... 

When a metal is in contact with a solution containing its own ions, it attains a state of dynamic equilibrium where the rate of dissolution of metals from the surface is equal to the rate of deposition from solution. If the reaction is to proceed in one direction or another, the equilibrium must be displaced in an anodic sense to promote the dissolution reaction (oxidation, see Equations 10.2 and 10.3) and in a negative sense to promote the deposition reaction (reduction). The extent to which the potential of an electrode is displaced from its equilibrium value is termed the polarisation of the electrode. In the corrosion situation the difference between the equilibrium potential for metal dissolution and for the cathodic reaction on the same metal provides the driving force for the dissolution of the metal. 

This is seen to be significantly higher than the rates attained for non-electrolytes. The comparison is, of course, not valid the derivation assumes that only the concentration difference in (CrOJ) provides the driving force. Instead, the work of Wallace [11], Smith [12] and Melsheimer et al. [13], indicates that the driving force is the Donnan potential, which drives the system toward the equilibrium ... 

On a noble metal, equilibrium of the HER (reversible H /H2 electrode) may be attained provided that the partial H2 pressure in solution is high enough because the kinetics are fast from thermodynamic arguments, the HER occurs with a net rate if the potential is cathodic with respect to the equilibrium potential at the given H2 pressure and pH. Conversely, if the overpotential is anodic, the reverse reaction, i.e., the H2 oxidation reaction (HOR), prevails, involving H2 dissociation into adsorbed H followed by H electrodesorption [27]. 

The obvious method of reducing corrosion in fused salts is to choose a system in which either the metal can come to equilibrium with the melt, or else truly protective passivity can be attained. In most cases in industry neither of these alternatives is used. In fact, fused salt baths are usually operated in air atmosphere, and the problem is the prevention of excessive corrosion. This can be done in two ways, (a) by reducing rates of ingress of oxidising species (mainly O2 and H2O) from the atmosphere, and rates of their diffusion in the melts, and (b) by keeping the oxidising power (redox potential) of the melt low by making periodic additions to the bath. 

Supercritical fluid extraction can be performed in a static system with the attainment of a steady-state equilibrium or in a continuous leaching mode (dynamic mode) for which equilibrium is unlikely to be obtained (257,260). In most instances the dynamic approach has been preferred, although the selection of the method probably depends just as much on the properties of the matrix as those of the analyte. The potential for saturation of a component with limited solubility in a static solvent pool may hinder complete recovery of the analyte. In a dynamic system, the analyte is continuously exposed to a fresh stream of solvent, increasing the rate of extraction from the matrix. In a static systea... 

The foregoing text highlights the fact that at the interface between electrolytic solutions of different concentrations (or between two different electrolytes at the same concentration) there originates a liquid junction potential (also known as diffusion potential). The reason for this potential lies in the fact that the rates of diffusion of ions are a function of their type and of their concentration. For example, in the case of a junction between two concentrations of a binary electrolyte (e.g., NaOH, HC1), the two different types of ion diffuse at different rates from the stronger to the weaker solution. Hence, there arises an excess of ions of one type, and a deficit of ions of the other type on opposite sides of the liquid junction. The resultant uneven distribution of electric charges constitutes a potential difference between the two solutions, and this acts in such a way as to retard the faster ion and to accelerate the slower. In this way an equilibrium is soon reached, and a steady potential difference is set up across the boundary between the solutions. Once the steady potential difference is attained, no further net charge transfer occurs across the liquid junction and the different types of ion diffuse at the same rate. 

Although from the thermodynamic point of view one can speak only about the reversibility of a process (cf. Section 3.1.4), in electrochemistry the term reversible electrode has come to stay. By this term we understand an electrode at which the equilibrium of a given reversible process is established with a rate satisfying the requirements of a given application. If equilibrium is established slowly between the metal and the solution, or is not established at all in the given time period, the electrode will in practice not attain a defined potential and cannot be used to measure individual thermodynamic quantities such as the reaction affinity, ion activity in solution, etc. A special case that is encountered most often is that of electrodes exhibiting a mixed potential, where the measured potential depends on the kinetics of several electrode reactions (see Section 5.8.4). 

Biologically mediated redox reactions tend to occur as a series of sequential subreactions, each of which is catalyzed by a specific enzyme and is potentially reversible. But despite favorable thermodynamics, kinetic constraints can slow down or prevent attainment of equilibrium. Since the subreactions generally proceed at unequal rates, the net effect is to make the overall redox reaction function as a imidirectional process that does not reach equilibrium. Since no net energy is produced imder conditions of equilibrium, organisms at equilibrium are by definition dead. Thus, redox disequilibrium is an opportunity to obtain energy as a reaction proceeds toward, but ideally for the sake of the organism does not reach, equilibrium. 

It may not always be clear from the conditions for electrochemical generation which species is the effective EGB. In some cases a possible complication is fast disproportionation of radical-anion to dianion (Scheme 12). This can mean that for electrogeneration at, say, the first reduction potential E Jl) it is possible for either the radical-anion or the dianion to act as base, depending on the relative rates of protonation by acid HA (k and kp, the value of the disproportionation constant (Kj), and the rate at which equilibrium between radical-anion and dianion is attained. In principle, of course, it is also possible that electrogeneration at E p2) could lead to a situation where radical-anion was the effective base as a consequence of rapid reproportionation causing it to be present in high concentration, thus offsetting its probably much lower kinetic basicity. These points are discussed in more detail on p. 157. 

An interesting experiment is to allow oxidative phosphorylation to proceed until the mitochondria reach state 4 and to measure the phosphorylation state ratio Rp, which equals the value of [ATP] / [ADP][PJ that is attained. This mass action ratio, which has also been called the "phosphorylation ratio" or "phosphorylation potential" (see Chapter 6 and Eq. 6-29), often reaches values greater than 104-105 M 1 in the cytosol.164 An extrapolated value for a zero rate of ATP hydrolysis of log Rf) = 6.9 was estimated. This corresponds (Eq. 6-29) to an increase in group transfer potential (AG of hydrolysis of ATP) of 39 kj/mol. It follows that the overall value of AG for oxidation of NADH in the coupled electron transport chain is less negative than is AG. If synthesis of three molecules of ATP is coupled to electron transport, the system should reach an equilibrium when Rp = 106 4 at 25°C, the difference in AG and AG being 3RT In Rp = 3 x 5.708 x 6.4 = 110 kj mol-1. This value of Rp is, within experimental error, the same as the maximum value observed.165 There apparently is an almost true equilibrium among NADH, 02 and the adenylate system if the P/O ratio is 3. 

This stems directly from the fact that the electron transfer kinetics for the forward and reverse processes are so facile that equilibrium is attained at each potential applied in the time-scale of the particular experiment. Thus an electron transfer may be termed electrochemically reversible at a scan rate of 50 mV s but irreversible at 1000 Vs" The term is therefore a practical rather than absolute one and is dependent upon the time-scale of the electrochemical measurement. 

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