Solid homogenous diffusion Solute solution, concentration

When a reaction involves two different phases, that is. when the system is nut homogeneous but heterogeneous, as in reactions lielwccn a solid phase, such us zinc or calcium carbonate, and a liquid phase, such as hydrochloric acid solution, the rate of reaction involves consideration of tl I the area of the surface of contact of the solid with the solution, and 121 the rale of diffusion from the surface of the solid, as well as (31 the concentration of hydrogen ion of the acid solution. 

We have discussed point defects in elements (A) and in nearly stoichiometric compounds having narrow ranges of homogeneity. Let us extend this discussion to the point defect thermodynamics of alloys and nonmetallic solid solutions. This topic is of particular interest in view of the kinetics of transport processes in those solid solutions which predominate in metallurgy and ceramics. Diffusion processes are governed by the concentrations and mobilities of point defects and, although in inhomogeneous crystals the components may not be in equilibrium, point defects are normally very close to local equilibrium. 

A multicomponent HSDM for acid cfye/carbon adsorption has been developed based on the ideal adsorbed solution theory (lAST) and the homogeneous surface diffusion model (H SDM) to predict the concentration versus time decay curves. The lAST with the Redlich-P eterson equation is used to determine the pair of liquid phase concentrations, Q and Qj, from the corresponding pair of solid phase concentrations, q j and q jy at fha surface of the carbon particle in the binary component. 

We have already ascertained that in the diffusion of a gas A into a solid or liquid B, the density of a volume element is practically unchanged, dg/dt = 0, because the mass of the gas absorbed is low in comparison with the mass of the volume element. If substance B was initially homogeneous, g = g x) = const, the density will also be unchanged locally during the diffusion process. We can therefore say a good approximation is that the density is constant, independently of position and time. Furthermore, measurements [2.76] have shown that the diffusion coefficient in dilute liquid solutions at constant temperature may be taken as approximately constant. Equally in diffusion of a gas into a homogeneous, porous solid at constant temperature, the diffusion coefficient is taken to be approximately constant, as the concentration only changes within very narrow limits. In these cases, in which g = const and DAB = D = const can be assumed, (2.328) simplifies to... 

The simplicity of this procedure and the possibility of a simple calculation of the adsorbate concentration are important advantages of this method. Therefore, ground-state diffuse-reflectance absorption spectra of the above-mentioned powdered samples (and also of a blank sample) enable a calculation of the molar extinction coefficients of the probe. These can be compared with the one obtained for transparent samples (homogeneous solutions, films, or solid matrices) by the use of the Beer-Lambert Law. 

The polyclonal or monoclonal antibody maybe exploited in many different analytical methods to compare unknown concentrations of analyte with known standards immunoassay is not a single method but a class thereof [1-3]. Table 1 attempts to demonstrate this, different methods being classified according to the physical process behind the measurement of the analyte, and whether the antibody is employed in a homogenous format (individual molecules freely diffusing in solution) or a heterogenous format (antibody molecules physically or chemically anchored to a solid phase). 

Kitagara ° nsed two commercial granular activated carbons for the adsorption of phenol, p.nitrophenol, and 2,4 dichlorophenol from aqueous solutions, and found that the adsorption data could be explained by the Freundlich isotherm equation. The adsorption at a given concentration decreased with increase in the temperature of adsorption, although the rate of adsorption increased with increase in the adsorption temperature. Scharifov derived a mathematical model for the adsorption of phenols by activated carbons from aqueous solutions and obtained an equation for the static adsorption isotherm, which could help in the calculation of adsorption of phenol at any concentration. Chakravorti and Weber used batch and fixed-bed systems for the removal of phenol from aqueous solutions by activated carbons. The pore-diffusion model and a homogenous solid model were used to explain the results. 

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