Mass transport total metal concentration

On the other hand, bulk concentrations are required for estimation of the respective surface concentrations that are the terms of kinetic equations. To obtain the data for the solution layer adjacent to the electrode surface, mass transport of chemically interacting species should be considered. Quantitative formulation of this problem is based on differential equations representing Pick s second law and supplemented with the respective kinetic terms. It turns out that some linear combinations of these equations make it possible to eliminate kinetic terms. So produced common diffusion equations involve total concentrations of metal, ligand and proton donors (cj j, c, and Cj4, respectively) as functions of time and space coordinates. It follows from the relationships obtained that the total metal concentration varies in the same manner as the concentration of free metal ions in the absence of ligand. Simultaneously, the total ligand concentration remains constant within the whole region of the diffusion layer. This proposition also remains valid for proton donors and acceptors. 

It will be apparent from the previous section that ion-selective electrodes can be made suitable for analysis in the field and that, in circumstances where the overall composition of the medium is not too variable, they may also be used directly to monitor metal ion and/or anions in plant streams, effluents, water supplies and even rivers. In such applications of ion-selective electrodes, however, it is necessary to avoid electrical pick-up and ground loops by correct placement and shielding of the electrodes. There are also many other situations where the capabiUties of electrochemistry and the characteristics of an analysis can be matched to allow the manufacture of on-line or portable devices. The actual measurement may be the potential of an ion-selective electrode, the mass-transport-controlled current at an electrode held at constant potential or even conductivity. This latter measurement, for example, remains the optimum way of estimating the total salt concentration in solution. 

Transient techniques including an EPS voltammetry are often more sensitive than the steady-state measurements. To extend the scale of information on the system, an analysis of EPS voltammetric maxima is desirable. Unfortunately, analytical expressions for EPS voltammograms are not available for circumstances discussed in Chapter 4. Nevertheless, it is of interest to use for this purpose some relationships derived for simple redox systems replacing the concentration of the oxidant by the total concentration of metal. Certain grounds for such operation follow from the regularities of mass transport of labile complexes (Section 3.2). 

Use of low and perhaps unrepresentative analytical values for total Al and difunctional CAA concentrations may be one reason why mass balance calculations and computer model simulations of formation waters produce results that de-emphasize the role of organo-metallic complexes in the subsurface transportation of Al and Si (1.2.72.79). In addition, the thermodynamic constants for organo-metallic complexation by these species are unknown at elevated temperatures, and van t Hoff-type approximations used in many models may not be valid as the temperature extrapolation is too large. Complexation and transportation of Al and Si by polar organic compounds remain the only viable mechanism to explain the widespread Al and Si mobility noted in many clastic hydrocarbon reservoirs (3.35.39). 

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