Detachment, rate-determining step

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. 

Fig. 5.13 displays the dissolution scenario of the gibbsite surface and of the edge surface. The dissolution reaction can be interpreted as a coupled release of Al and Si. The detachment of the Al center is the rate determining step. In a fast subsequent step Si is released from the same surface site. The AI(III) H+ stoichiometry of the precursor group (the group to be detached) is 1 3 at the gibbsite surface and 1 1 at the edge surface. 

Penetration into insects is greatly influenced by the manner in which the compound is presented. Classic studies by Treherne (19) indicated that when the toxicant is supplied to detached insect cuticle in aqueous solution penetration decreased with increasing polarity, explicable on the assumption that partition into and passage through the lipoidal epicuticle is the rate determining step. In contrast several studies (20 - 22) have shown that when the toxicant is dissolved... 

Dissolution of goethite and ferrihydrite at pH 6 by M-EDTA (M = Pb, Zn, Cu, Co, Ni) is slower than that by EDTA alone (Nowack Sigg, 1997). Dissolution was considered to involve the formation of a ternary surface complex which then dissociated releasing M into solution after which Fe was detached from the oxide as Fe-EDTA. For ferrihydrite, the rate of dissolution depended on the nature of M, because the rate determining step was dissociation of M-EDTA. For goethite, on the other hand, this step was fast, hence the rate of dissolution was independent of M. 

Figure 7.8 shows schematically the various steps in the surface reaction-controlled dissolution of hydrous oxides or hydroxides. A number of protons equal to the valency of the Me center is needed to detach an Me(aq) group into the aqueous solution. Stepwise protonation occurs relatively quickly. The slow, rate-determining step is detachment of the Me(aq) group (Stumm, 1986). With a divalent metal oxide, two neighboring surface groups must become protonated. The rate of detachment (step... 

Figure 7,8. Schematic representation of the steps involved in the dissolution of a (hydr)-oxide, illustrating that the rate-determining step is the detachment of a suitably protonated surface group. [From Stumm (1986), with permission.]...

The foregoing equations suggest that either electron transfer (eq 14b) or detachment (eq 14c) is the rate-determining step. The oxidized reactant Ox is often a radical that may undergo further non-rate-determining reactions with the oxidant. Equations 14a and 14b may be coupled. The reaction sequence accounts for the observation (24-27) that the reaction rate, R, is proportional to the density of the surface concentration of the surface species, =FeM,R (mol/m2), provided that the concentration of the oxidized reactant Ox is at steady state or is negligible. The reaction rate is given by... 

Our results do not allow us to decide which of these pH effects is predominant. The experimental observation, however, that in the pH range between 3 and 5 the overall rate constant depends on the concentration of surface protons to the power 1.6 may be an indication that proton catalysis of the detachment of surface Fe(II) is an important factor. In this case, the detachment of surface Fe(II) would be the rate-determining step of the overall process. The experiments presented here serve as an illustrative example, pointing out that reductive dissolution of oxide minerals may be catalyzed by protons, and hence that the rates of proton-catalyzed and of reductive dissolution may not be merely additive. However, more experimental evidence is needed to evaluate the validity of applying the rate expression of the proton-catalyzed dissolution to the overall rate constant of reductive dissolution. 

The surface iron(II) thus formed is detached from the surface of hematite as the rate-determining step (Suter et al., 1988). This pathway is a thermal reductive dissolution of hematite, which leads, however, to an increase of the concentration of dissolved iron(III) while the concentration of dissolved iron(II) remains constant Fe11 acts as a catalyst for the dissolution of iron(III) hydroxides. 

The rate of formation of dissolved iron(II), d[Fe2 + ]diss/df, depends, in addition, on the efficiency of detachment of reduced surface iron ions from the crystal lattice. The detachment step is a key step in the overall dissolution kinetics of slightly soluble minerals, since it is assumed to be the rate-determining step (Stumm and Furrer, 1987). The efficiency of detachment depends primarily on the crystallinity, and thus the stability of the iron(IIJ) hydroxide phase, and also on the coordinative surrounding of the reduced surface metal centers. It has been shown that a combination of a reductant and a ligand that forms stable surface complexes in the dark is especially efficient for the thermal reductive dissolution of hydrous iron(III) oxides (Banwart, et al. 1989). The role of a ligand as an electron donor and as a detacher in the photochemical dissolution of hydrous iron(III) oxides remains to be elucidated. 

Under most of the natural conditions, the rate of dissolution of carbonate minerals is far less than that expected for rate control by diffusion. The chemical reaction at the water-mineral interface is then assumed to be the rate-determining step. This reaction consists in the attachment or interactions of reactants with specific surface sites where the critical crystal bonds are weakened, which, in turn, allows the detachment of anions and cations of the surface into the solution. 

The rate-determining step is detachment of the coordination complex at the surface, and the rate of dissolution is proportional to the degree of ligand binding on the mineral surface or the concentration of ligand in bulk solution to fractional power (p), the slope of the Freundich adsorption isotherm for [HA-] on the mineral surface for a 1 1 metal-to-ligand complex ... 

Limoni and Schmuckler [ref. 37, 38] demonstrated that the anionic complexes of transition metal ions interact strongly with polyacrylamide gels. Based on the kinetic data obtained from breakthrough curves of chioro-complexes of copper, palladium and platinum on Bio-Gel P-2, the rate-determining step in the chromatographic process was found to be the detachment of solute molecules from the functional groups of the gel. 

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. 

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