Concentrated solution diffusion

If the two electrode systems that compose a cell involve electrolytic solutions of different composition, there will be a potential difference across the boundary between the two solutions. This potential difference is called the liquid junction potential, or the diffusion potential. To illustrate how such a potential difference arises, consider two silver-silver chloride electrodes, one in contact with a concentrated HCl solution, activity = the other in contact with a dilute HCl solution, activity = Fig. 17.7(a). If the boundary between the two solutions is open, the and Cl ions in the more concentrated solution diffuse into the more dilute solution. The ion diffuses much more rapidly than does the Cl ion (Fig. 17.7b). As the ion begins to outdistance the Cl ion, an electrical double layer develops at the interface between the two solutions (Fig. 17.7c). The potential difference across the double layer produces an electrical field that slows the faster moving ion and speeds the slower moving ion. A steady state is established in which the two ions migrate at the same speed the ion that moved faster initially leads the march. 

Figure I. Schematic of pressure solution. Initially, two hemispheres are in contact. Ai compaction proceeds, the mineral at grain contacts dissolves due to high stress concentration. Solutes diffuse from the interface into the pore space. Finally, precipitation occurs as a result of oversaturation of solutes in the pore fluid. Grain geometries are no longer spherical.

Gases from the concentrated solutions diffuse from their watch glasses (shallow dishes) and react to give a smoke of ammonium chloride. 

The diffusion coefficient is related to the rate at which molecules migrate down a concentration gradient (it is treated in detail in Section 8.5) and can be measured by observing the rate at which a concentration boundary moves or the rate at which a more concentrated solution diffuses into a less concentrated one. The diffusion coefficient can also be measured by using laser light-scattering methods (Section 11.3). It follows that we can find the molar mass by combining measurements of sedimentation and diffusion rates (to obtain S and D, respectively). 

One contribution to band broadening in which solutes diffuse from areas of high concentration to areas of low concentration. 

Solution—Diffusion Model. In the solution—diffusion model, it is assumed that (/) the RO membrane has a homogeneous, nonporous surface layer (2) both the solute and solvent dissolve in this layer and then each diffuses across it (J) solute and solvent diffusion is uncoupled and each is the result of the particular material s chemical potential gradient across the membrane and (4) the gradients are the result of concentration and pressure differences across the membrane (26,30). The driving force for water transport is primarily a result of the net transmembrane pressure difference and can be represented by equation 5 ... 

The error due to diffusion potentials is small with similar electrolyte solutions (cj = C2) and with ions of equal mobility (/ Iq) as in Eq. (3-4). This is the basis for the common use of electrolytic conductors (salt bridge) with saturated solutions of KCl or NH4NO3. The /-values in Table 2-2 are only applicable for dilute solutions. For concentrated solutions, Eq. (2-14) has to be used. 

Equations (4) and (5) predict that the optimum linear velocity should be linearly related to the diffusivity of the solute in the mobile phase, whereas the minimum value of the HETP should be constant and independent of the solute diffusivity. This, of course, will only be true for solutes eluted at the same (k ). It is seen, from Table 1, that (by appropriate adjustment of the concentration of ethyl acetate) the values of both (k ) and (k e) have been kept approximately constant for all the mobile phase... 

Consider a lean phase, j, which is in intimate contact with a rich phase, i, in a closed vessel in order to transfer a certain solute. The solute diffuses from the rich phase to the lean phase. Meanwhile, a fraction of the diffused solute back-transfers to the rich phase. Initially, die rate of rich-to-lean solute transfer surpasses that of lean to rich leading to a net transfer of the solute from the rich phase to the lean phase. However, as the concentration of the solute in the rich phase increases. 

In many process design applications like polymerization and plasticization, specific knowledge of the thermodynamics of polymer systems can be very useful. For example, non-ideal solution behavior strongly governs the diffusion phenomena observed for polymer melts and concentrated solutions. Hence, accurate modeling of... 

Mechanistically, in approximately neutral solutions, solid state diffusion is dominant. At higher or lower pH values, iron becomes increasingly soluble and the corrosion rate increases with the kinetics approaching linearity, ultimately being limited by the rate of diffusion of iron species through the pores in the oxide layer. In more concentrated solutions, e.g. pH values of less than 3 or greater than 12 (relative to 25°C) the oxide becomes detached from the metal and therefore unprotective . It may be noted that similar Arrhenius factors have been found at 75 C to those given by extrapolation of Potter and Mann s data from 300°C. 

There are a number of differences between interstitial and substitutional solid solutions, one of the most important of which is the mechanism by which diffusion occurs. In substitutional solid solutions diffusion occurs by the vacancy mechanism already discussed. Since the vacancy concentration and the frequency of vacancy jumps are very low at ambient temperatures, diffusion in substitutional solid solutions is usually negligible at room temperature and only becomes appreciable at temperatures above about 0.5T where is the melting point of the solvent metal (K). In interstitial solid solutions, however, diffusion of the solute atoms occurs by jumps between adjacent interstitial positions. This is a much lower energy process which does not involve vacancies and it therefore occurs at much lower temperatures. Thus hydrogen is mobile in steel at room temperature, while carbon diffuses quite rapidly in steel at temperatures above about 370 K. 

Equation 10.96 does not apply to either electrolytes or to concentrated solutions. Reid, PRAUSNITZ and Sherwood"7 discuss diffusion in electrolytes. Little information is available on diffusivides in concentrated solutions although it appears that, for ideal mixtures, the product /xD is a linear function of the molar concentration. 

The effect, which arises in cases where the interfacial tension is strongly dependent on the concentration of diffusing solute, will generally be dependent on the direction (sense) in which mass transfer is taking place. 

A solute diffuses from a liquid surface at which its molar concentration is C, into a liquid with which it reads. The mass transfer rate is given by Fick s law and the reaction is first order with respect to the solute, fn a steady-state process the diffusion rate falls at a depth L to one half the value at the interface. Obtain an expression for the concentration C of solute at a depth z from the surface in terms of the molecular diffusivity D and the reaction rate constant k. What is the molar flux at the surface ... 

The beauty of the reptation model is that it is able to make predictions about molecular flow both in solution and at fracture by assuming that the molecules undergo the same kind of motions in each case. For both self-diffusion in concentrated solutions and at fracture, the force to overcome in pulling the polymer molecule through the tube is assumed to be frictional. 

The mobility ratio equal to the diffusion ratio in this equation would naturally follow from application of the Nemst-Einstein equation, Eq. (88), to transport gels. Since the Nemst-Einstein equation is valid for low-concentration solutes in unbounded solution, one would expect that this equation may hold for dilute gels however, it is necessary to establish the validity of this equation using a more fundamental approach [215,219]. (See a later discussion.) Morris used a linear expression to fit the experimental data for mobility [251]... 

Historically, the absorption of lipid-soluble nutrients has been considered to be carrier-independent, with solutes diffusing into enterocytes down concentration gradients. This is true for some lipid-soluble components of plants (e.g. the hydroxytyrosol in olive oil Manna et al., 2000). However, transporters have been reported for several lipid-soluble nutrients. For example, absorption of cholesterol is partly dependent on a carrier-mediated process that is inhibited by tea polyphenols (Dawson and Rudel, 1999) and other phytochemicals (Park et al., 2002). A portion of the decreased absorption caused by tea polyphenols may be due to precipitation of the cholesterol associated with micelles (Ikeda et al., 1992). Alternatively, plant stanols and other phytochemicals may compete with cholesterol for transporter sites (Plat and Mensink, 2002). It is likely that transporters for other lipid-soluble nutrients are also affected by phytochemicals, although this has not been adequately investigated. 

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