Steady state oxide dissolution

In an oversimplified way, it may be stated that acids of the volcanoes have reacted with the bases of the rocks the compositions of the ocean (which is at the fkst end pokit (pH = 8) of the titration of a strong acid with a carbonate) and the atmosphere (which with its 2 = 10 atm atm is nearly ki equdibrium with the ocean) reflect the proton balance of reaction 1. Oxidation and reduction are accompanied by proton release and proton consumption, respectively. In order to maintain charge balance, the production of electrons, e, must eventually be balanced by the production of. The redox potential of the steady-state system is given by the partial pressure of oxygen (0.2 atm). Furthermore, the dissolution of rocks and the precipitation of minerals are accompanied by consumption and release, respectively. 

Figure 6. pH dependence of (a) current density (on log scale) of oxygen ion incorporation into the oxide, at a constant total current density of 0.1 mA/cm2, and (b) the steady-state dissolution (aluminum ion) current density of oxide-covered aluminum at 4 V versus SCE.29... 

The scheme in Fig. 5.5 indicates that the ligand, for example, oxalate, is adsorbed very fast in comparison to the dissolution reaction thus, adsorption equilibrium may be assumed. The surface chelate formed is able to weaken the original Al-oxygen bonds on the surface of the crystal lattice. The detachment of the oxalato-aluminum species is the slow and rate-determining step the initial sites are completely regenerated subsequent to the detachment step provided that the concentrations of the reactants are kept constant, steady state conditions with regard to the oxide surface species are established (Table 5.1). If, furthermore, the system is far from dissolution equilibrium, the back reaction can be neglected, and constant dissolution rates occur. 

However, we have to reflect on one of our model assumptions (Table 5.1). It is certainly not justified to assume a completely uniform oxide surface. The dissolution is favored at a few localized (active) sites where the reactions have lower activation energy. The overall reaction rate is the sum of the rates of the various types of sites. The reactions occurring at differently active sites are parallel reaction steps occurring at different rates (Table 5.1). In parallel reactions the fast reaction is rate determining. We can assume that the ratio (mol fraction, %a) of active sites to total (active plus less active) sites remains constant during the dissolution that is the active sites are continuously regenerated after AI(III) detachment and thus steady state conditions are maintained, i.e., a mean field rate law can generalize the dissolution rate. The reaction constant k in Eq. (5.9) includes %a, which is a function of the particular material used (see remark 4 in Table 5.1). In the activated complex theory the surface complex is the precursor of the activated complex (Fig. 5.4) and is in local equilibrium with it. The detachment corresponds to the desorption of the activated surface complex. 

As was mentioned in the introduction to this chapter "diffusion-controlled dissolution" may occur because a thin layer either in the liquid film surrounding the mineral or on the surface of the solid phase (that is depleted in certain cations) limits transport as a consequence of this, the dissolution reaction becomes incongruent (i.e., the constituents released are characterized by stoichiometric relations different from those of the mineral. The objective of this section is to illustrate briefly, that even if the dissolution reaction of a mineral is initially incongruent, it is often a surface reaction which will eventually control the overall dissolution rate of this mineral. This has been shown by Chou and Wollast (1984). On the basis of these arguments we may conclude that in natural environments, the steady-state surface-controlled dissolution step is the main process controlling the weathering of most oxides and silicates. 

Initial dissolution of Fe oxides can be very rapid and is then followed by a slower steady state process. The initial step often corresponds to less than 1% of the total solid (Cornell et al. 1974 Maurice et al. 1995). Samson and Eggleston (1998) subjected hematite to a pH jump experiment and found that when the pH was lowered to 1, a reservoir of dissolution active sites on the surface was depleted, but then regenerated when the pH was raised to 2. The authors suggested that these active sites, which made up -70% of a monolayer, consisted of an adsorbed nutrient Fe . 

On most corroding metals, the above reactions occur at an oxidized surface and, depending on the peroperties of the surface layer, passivation may occur by which the kinetics of metal dissolution are substantially supressed either by ohmic, ionic, or electronic transport at a surface passivating film or by electrocatalytic hindrance. In passivation phenomena, a steady state with a balance between the formation and dissolution of the surface film takes place. As a result, the ionic flux of metal ions dissolving through the passivating film is highly reduced. 

This assumption is based on three relevant indications. First, this wave results in a limiting-current. This means that steady-state transport phenomena control the rate of this reaction, which is not compatible with a possible oxidation of metallic copper to Cu(I) or Cu(II). If the latter were to be valid, a peak-shaped response should have been obtained because of the limited available amount of metallic copper (initially deposited by reduction of Cu(II) or Cu(I) in the reduction wave). In addition, the second voltammetric oxidation wave in the backward scan direction is actually compatible with such a dissolution reaction. 

Upon contact between the spent nuclear fuel and the groundwater, radiolysis of water will begin. From the point of view of a safety assessment it is relevant to define the worst-case, but still realistic, scenario. Hence, the maximum possible dissolution rate for the UOj fuel matrix (assuming congruent dissolution) must be defined. As shown above, oxidation of U(IV) to U(VI) is required for dissolution to occur. Consequently, the rate of dissolution can never exceed the rate of oxidation and the rate of oxidation can be used to estimate the maximum dissolution rate. It has also been shown that, for longer irradiation times, the only oxidant that must be taken into account is H2O2 and that the surface concentration of H2O2 approaches the steady-state concentration fairly rapidly. The concentration will never exceed the steady-state concentration and therefore we can use the steady-state approach to make a realistic estimate of the maximum dissolution rate. 

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