Diffusion potential, elimination

Practically all liquid cells with reversible interfacial equilibria examined can be considered as liquid galvanic cells of the Nernst, Haber, or intermediate type [3]. Usually, a dashed vertical bar ( ) is used to represent the junction between liquids. A double dashed vertical bar ( ) represents a liquid junction in which the diffusion potential has been assumed to be eliminated. 

Another promising alternative to the rather restrictive MBLL model is the layer model using diffusion equation. Diffuse optical imaging provides a better model for photon migration where approximation of path length is possible. This would provide a much improved focal change information and potentially eliminate crosstalk noise. 

It will be noted that liquid junction diffusion potentials can be eliminated almost completely by ensuring that the bulk of the current is carried by cations and anions possessing equal mobilities, e.g. KCl or NHiNOg. Thus by inserting a saturated solution of B.s,o. 16... 

Poorly Conducting Samples. Samples with low ion concentrations (less than a few mM) will result in poor conductivity of the sample solution. Low conductivity not only causes a slow response time from the electrode but also creates a diffusion potential between the reference electrolyte and the measuring solution which results in an inaccurate pH reading. Using circular ground junctions that create optimal contact between the reference electrolyte and measuring solution can eliminate the problem. Adding conductive-free ions such as a few drops of... 

Determine the shear stresses acting on the three types of boundary segments present. When diffusion is extremely rapid, all differences in the diffusion potential will be eliminated, and all three normal stresses at the three different types of boundary segments will be uniform along each segment and equal to one another. Therefore,... 

Values of/x = Ac/A may be calculated from Kohlrausch s measurements of electrical conductivity of hydrochloric acid solutions. /h and fci can be evaluated from the potentiometric measurements on hydrochloric acid solutions performed by Scatchaed. These data are very reliable since the concentration chain was so arranged as to eliminate diffusion potentials. In this way, ScATCHARD determined the mean activity coefficient V/h/ci instead of the individual ion activities. If we assume that in a potassium chloride solution/ = /ci— which is plausible when we recall that both ions have the same structure—and that fci is the same in hydrochloric acid solutions and potassium chloride solutions of the same concentration, then we can calculate/h and fci in hydrochloric acid solutions. Naturally these values are not strictly correct since the effect of the potassium ions on the activity of the chloride ions probably is different from that of the hydrogen ions at the same ionic strength. In the succeeding table are given values of /x, /h, and fci calculated by the above method. 

The patentees suggest that the CO2 should be used as a reaction solvent, as the high diffusivity of CO2 will enable it to penetrate the pores of the solid support, and volatile reagents can be removed from the system by venting the CO2. The use of CO2 would potentially eliminate the need for repetitive washings with chlorinated solvents. The... 

The use of reference electrodes frequently poses the problem of an additional potential drop between the electrolytes of the electrode under study and of the reference one. For liquid electrolytes, this drop arises at the solution/solution interface (liquid junction). The symbol conventionally denotes an interface of two solutions with a diffusion potential drop in between if this drop is eliminated (see later), then the... 

In practice, in place of model calculations and corresponding corrections, the elimination of the diffusion potential is conventionally applied. This is achieved by introducing the so-called salt bridges filled with concentrated solutions of salts, which contain anions and cations of close transport numbers. A widely known example is saturated KCl (4.2 M) in aqueous solutions, potassium and ammonium nitrates are also suitable. However, the requirement of equal transport numbers is less important as compared with that of high concentration of electrolyte solution, which fills the bridge [33, 34]. A suitable version of the salt bridge can be chosen for any type of cells, when taking into account the kind of studies and the features of chosen electrodes. 

The universal definition of the standard potential of a redox couple Red/Ox is as follows the standard potential is the value of emf of an electrochemical cell, in which diffusion potential and thermo-emf are eliminated. This cell consists of an electrode, on which the Red/Ox equilibria establish under standard conditions, and a SHE. 

For unknown activities the measurement of the standard electrode potential is more complicated. The standard electrode potential is defined at /ra = 1 mol kg with the hypothetical activity coefficient of y = 1 (ideal diluted solution). First principal experimental determinations of standard potentials may only be made by extrapolation to this hypothetical value. For measurements, selected cell arrangements are used with complete elimination of the diffusion potential and with diluted electrolytes. For the correction of the activity the Debye-Hiickel approximation (Eq. (1.15)) may be used, for example, for the Hamed cell Ag/AgCl, HCl (m+)/Pt(H2). A concentration corrected potential value is plotted versus the square root of the molaUty. The extrapolation to 7ra+ = 0 gives the standard potential of the Ag/AgCl electrode (Figure 3.5). Using this electrode as reference electrode other standard potentials can be determined. 

This is the usual Planck-Henderson expression for the diffusion potential. In the present situation it is containing the contribution of the protons and only. Eliminating AVfrom Eqs. (1) and (4) we have... 

Because of the condition of electroneutrality, the local concentrations and must be equal to each other at all times, even during the equilibration reaction. Therefore, yV is always equal to. By using this condition, we can eliminate the diffusion potential (j) from the flux equations. Furthermore, the laws of ideal dilute solutions may be used in the present case. Setting rji = fXi 4- ZiF and pi = /i H- i T In Cf, we obtain the following equation for the flux ... 

If the ionic mobilities (or the component diffusion coefficients) are known, then it is possible to calculate the diffusion profile, as well as the displacement of inert markers, if we assume that local thermodynamic equilibrium is maintained and that the markers are firmly bound to the anion lattice. In order to calculate the chemical diffusion coefficient, we start once again with the flux equations of section 5.2 and eliminate the diffusion potential using the condition of electroneutrality. For an ideal solid solution we obtain the equation [13] ... 

Calculations involving diffusion processes in inhomogeneous multicomponent ionic systems have been recently performed by Kirkaldy [30] and Cooper [38]. They worked with the same assumptions that have been made in this section in which quasi-binary systems have been discussed constant molar volume of the solid solution, and independent fluxes of ions, which are coupled only by the electrical diffusion potential. The latter can be eliminated by the condition zJi 0 which means that local electroneutrality prevails. With these assumptions, and with a knowledge of the thermodynamics of the multicomponent system (which is a knowledge of the activity of the electroneutral components as a function of composition), the individual ionic fluxes can be calculated explicitly with the help of the ionic mobilities and the activity coefficients of the components. 

The constant Ic can be calculated from the flux equations (5-13), with the condition of electroneutrality being used to eliminate the diffusion potential < >. The calculation is performed just as in the derivation of the rational rate constant for spinel formation in section 6.2.1. According to eq. (6-22), Tc kv, where n is the increase in volume of the product layer following the passage of one ionic equivalent, k is the rational tarnishing rate constant as introduced by Wagner [12]. It is equal to the flux in equivalents per unit area per unit time for a unit product layer thickness. By the method outlined above, k may be calculated as ... 

Equations (20.1.2-2) and (20.2.1-7) relate the diffusion potential to mass-transport within the electrolyte and to transference numbers, respectively. If both the transference numbers are equal to one-half in the latter equation, then the diffnsion potentials in solution arising from contact of solutions with differing concentrations will be eliminated. The limiting values of the ionic diffusion coefficient are related to their mobility by the Einstein law, equation (20.2.1-10), which provides justification for the argument that balancing the mobilities of the electrolyte s constituent ions wiU nullify any diffusion potential. This approach to eliminating diffusion potentials clearly suffers from the severe restriction that... 

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