Dilution component

Blanc provided a simple limiting case for dilute component i diffusing in a stagnant medium (i.e., N 0), and the result, Eq. (5-205), is known as Blanc s law. The restriction basically means that the compositions of aU the components, besides component i, are relatively large and uniform. 

Solubility equilibria are described quantitatively by the equilibrium constant for solid dissolution, Ksp (the solubility product). Formally, this equilibrium constant should be written as the activity of the products divided by that of the reactants, including the solid. However, since the activity of any pure solid is defined as 1.0, the solid is commonly left out of the equilibrium constant expression. The activity of the solid is important in natural systems where the solids are frequently not pure, but are mixtures. In such a case, the activity of a solid component that forms part of an "ideal" solid solution is defined as its mole fraction in the solid phase. Empirically, it appears that most solid solutions are far from ideal, with the dilute component having an activity considerably greater than its mole fraction. Nevertheless, the point remains that not all solid components found in an aquatic system have unit activity, and thus their solubility will be less than that defined by the solubility constant in its conventional form. 

A wide variety of in situ techniques are available for the study of anodic hhns. These include reflectance, eUipsometry, X-ray reflectivity, and SXRD. X-ray reflectivity can be used to study thick surface layers up to 1000 A. The reflectance technique has been used to study oxide growth on metals, and it yields information on oxide thickness, roughness, and stoichiometry. It the only technique that can give information on buried metal-oxide interfaces. It is also possible to get information on duplex or multiple-layer oxide hhns or oxide hhns consisting of layers with different porosity. Films with thicknesses of anywhere from 10 to 1000 A can be studied. XAS can be used to study the chemistry of dilute components such as Cr in passive oxide hhns. 

Soft X-ray XAS is a useful method for studying surface films and the chemical environment of dilute components in alloys, oxides, and corrosion films. 

The peak symmetry, resolution, and detector response are directly dependent on the concentration of the sample. As the concentration of a sample increases, the retention time, separation, and peak symmetry generally decrease. These phenomena are due to isotherm nonlinearity. The detector response may also be nonlinear above or below certain concentrations. In some cases, small amounts of a dilute component are irreversibly adsorbed to the column, leading to reduced recovery. Above some concentration, the response of any detector will cease to be linear. The UV-VIS is one of the most linear detectors, generally exhibiting at least three decades of linearity, while RI, electrochemical, and fluorimetric detectors have a markedly narrower range of linearity. 

A timely chapter on the theory and applications of electrochemical gas separation processes is presented by Jack Winnick. These alternatives for the removal of dilute components from gas streams in pure form are characterized by high selectivity, simplicity, and favorable economics. 

In dealing with dilute solutions it is convenient to speak of the component present in the largest amount as the solvent, while the diluted component is called the solute. 

Gas chromatography is a method of separation wherein gaseous or vaporised components are distributed between a moving gas phase and a fixed liquid phase or solid adsorbent. By a continuous succession of adsorption or elution steps, occurring at a specific rate for each component, separation can be achieved. The components can be detected by one of various methods as they emerge successively from the chromatographic column. From the detector signal, proportional to the instantaneous concentration of the dilute component in the gas stream, information about the number, nature and amounts of the components present is obtained. 

In general, the rule of thumb is to add the diluting component to the abrasive component. There are, however, exceptions to this rule of thumb, so experience and the recommendations of the slurry manufacturer should be considered. In the case of silica-abrasive oxide-polishing slurries, this means slurry first, water second. Even when practiced in this manner, slurry diluted at the user site will typically have more agglomerates than slurry diluted to use-concentration by the slurry manufacturer. The primary reason... 

Identification of metal particles dispersed in pictorial or decorative layers in works of art is often difficult for microscopy techniques because of (i) their presence as highly diluted components and concentrated in microparticles that, in turn, are included in binding media and attached to priming and protective layers (ii) the coexistence of metals with priming, ground or pigmenting layers in the samples and (iii) the presence of products resulting from the alteration of metals. 

Parts per million (or ppm) in solution usually refers to a dilute component of a solution as a portion of the whole in terms of mass. A solute present in one part per million would amount to one gram in one million grams of solution. This is also one mg of solute in one kg of solution. 

Fast and satisfactory mass transfer calculations are necessary since we may have to repeat such calculations many times for a rate-based distillation column model or two-phase flow with mass transfer between the phases in the design and simulation process. The generalized matrix method may be used for multicomponent mass transfer calculations. The generalized matrix method utilizes the Maxwell-Stefan model with the linearized film model for diffusion flux, assuming a constant diffusion coefficient matrix and total concentration in the diffusion region. In an isotropic medium, Fick s law may describe the multicomponent molecular mass transfer at a specified temperature and pressure, assuming independent diffusion of the species in a fluid mixture. Such independent diffusion, however, is only an approximation in the following cases (i) diffusion of a dilute component in a solvent, (ii) diffusion of various components with identical diffusion properties, and (iii) diffusion in a binary mixture. 

The waiting time depends on the nature of the surroundings. If the diffusing species is a dilute component in linear chains which occupy Ng steps, the constraint release contribution (with Eqs. 2, 9 and 86) is... 

So, each dilute component interacts only with the solvent. 

A similar model often used by reaction engineers is derived for the limiting case in which all the convective fluxes can be neglected. Consider a dilute component s that diffuses into a homogeneous mixture, then J 0 for r 7 s. To describe this molecular transport the Maxwell-Stefan equations given by the last line in (2.298) are adopted. With the given restrictions, the model reduces to ... 

It should be noted that gives the standard chemical potential for the ideally dilute solute in a hypothetical system in which the mole fraction of B is unity. This is obviously a fictitious state which is impossible in reality but whose properties are obtained by extrapolating the Henry s law line to Xb = 1 (see fig. 1.12). When Henry s law is not obeyed, an activity coefficient 73 introduced so that the product Yb h b is equal to the vapor pressure Pb- The activity of the dilute component Ub is defined to be 73 3- Thus, the general expression for the concentration dependence of pb becomes... 

For dilute binary mixtures, use the fluid properties of the concentrated component. This is reasonable since the concentration of the dilute component will have a negligible effect on the physical properties of the fluid. For concentrated solution, you will need to use averaging rules for that property. 

Low-pressure gas states can be conveniently represented by /, for / = p, for an ideal gas. It follows for a real gas at a low or moderate pressure that / p . The fugacity of a dilute component in a liquid is equal to the fugacity of the component at a small partial pressure in a gas mixture at equilibrium with the liquid, again f p . Since the partial pressure of a gas is a well-behaved mathematical quantity, the fugacity is also well behaved at small partial pressures in a gas or at a small concentration in liquids. In contrast, for a dilute component, as its p -> 0 in an ideal-gas mixture, by Equation (4.301). It follows that p, —> -°o for a dilute component in a real gas or in a liquid. The limit of is ill-behaved and is avoided with the replacement of p by 1), which simply approaches zero. 

Gas-phase devices treating dilute components must deal with high concentration overpotentials and subsequent low current densities. Technical solutions to this problem have been found in the case of liquid treatment, as outlined earlier similar solutions may be found for gases. Electrocatalysts for selective oxidation of gaseous components are only now receiving some attention (54). Thus, there appears to be fertile ground for explorative research in these areas. 

A more complex line of approach is that involving the use of two-component liquid systems, the dilute component of which is surface active. Thus Fowkes and Harkins [14] measured the contact angles of aqueous solutions of n-butyl alcohol at various solid-air interfaces. The film pressure at the solution-solid interface was then given by ... 

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