Electroneutrality, condition

The electroneutrality condition can be expressed in temis of the integral of the charge density by recognizing the obvious fact that the total charge around an ion is equal in magnitude and opposite in sign to the charge on the central ion. This leads to the zeroth moment condition... 

This is called the DHLL+52 approximation. On carrying out the integrations over q y(r) and q iryll and using the electroneutrality condition, this can be rewritten as [63]... 

For a synnnetrical system in which the reference species are identical (e.g. hard spheres of the same size), the integral can be taken outside the summation, which then adds up to zero due to the electroneutrality condition, to yield... 

Equation (3.7) describes the equality of the chemical potentials of the mobile ions on both sides of the gel boundary expressed through the Donnan ratio KD and the ion charges z, Eq. (3.8) concerns the dissociation equilibrium of ionizable (carboxyl) groups of the network a is the degree of dissociation, eg is the concentration of the hydrogen ions in the gel Eq. (3.9) represents the gel electroneutrality condition. 

The degree of dissodation,a, was calculated from the electroneutrality condition... 

The Gibbs energy of an electroneutral system is independent of the electrostatic potential. In fact, when substituting into Eq. (3.7) the electrochemical potentials of the ions contained in the system and allowing for the electroneutrality condition, we can readily see that the sum of aU terms jZjF f is zero. The same is true for any electroneutral subsystem consisting of the two sorts of ion and (particularly when these are produced by dissociation of a molecule of the original compound k into x+ cations and x anions), for which... 

Diffusion in Binary Electrolytes at Nonzero Currents Consider a reaction in which one of the ions of the binary solution is involved. For the sake of definition, we shall assume that its cation is reduced to metal at the cathode. The cation concentration at the surface will decrease when current flows. Because of the electroneutrality condition, the concentration of anions should also decrease under these conditions (i.e., the total electrolyte concentration c. should decrease). 

The above dependence, which has been known for a long time, can be directly derived from Eq. (3) and the electroneutrality conditions of Eq. (14) which for that case are in the form ... 

Using the equation, very strong concentration effects in small systems have been calculated. For instance, if the macroaqueous phase contains 1 M NaCl and 1 /rM NaTPB, the concentration of this electrolyte in the micro-organic phase at partition equilibrium is 1390/rM [14] This approach is valid if the phases in small systems are thick enough (> 1 /rm), in comparison to the Debye screening length, to fulfill the electroneutrality conditions. 

When the extraction of the hydrophilic counteranion from the aqueous solution into the membrane bulk is negligible (cation permselectivity preserved), the concentration of the complex cation in the membrane bulk Cb, is equal to that of the fixed anionic sites, X, in the membrane matrix, due to the electroneutrality condition within the membrane bulk ... 

The sample solution contains a fixed concentration of supporting electrolyte E" L and a varying concentration of primary salt M X . The ionophore I is confined in the membrane. Only the primary cation can be complexed with the ionophore I (given stoichiometry 1 1 stability constant The complex MI and the anionic site are the lipophilic species that are present only in the membrane phase. In this system, the electroneutrality condition at the membrane bulk leads to... 

The electroneutrality condition decreases the number of independent variables in the system by one these variables correspond to components whose concentration can be varied independently. In general, however, a number of further conditions must be maintained (e.g. stoichiometry and the dissociation equilibrium condition). In addition, because of the electroneutrality condition, the contributions of the anion and cation to a number of solution properties of the electrolyte cannot be separated (e.g. electrical conductivity, diffusion coefficient and decrease in vapour pressure) without assumptions about individual particles. Consequently, mean values have been defined for a number of cases. 

Because of the electroneutrality condition, the individual ion activities and activity coefficients cannot be measured without additional extrather-modynamic assumptions (Section 1.3). Thus, mean quantities are defined for dissolved electrolytes, for all concentration scales. E.g., for a solution of a single strong binary electrolyte as... 

Here S Nft = 0 because of the electroneutrality condition.) Equation (1.3.10) is substituted into Eq. (1.3.6) and the Laplace operator is expressed in polar coordinates (for the spherically symmetric problem) ... 

In view of the definition of the mean activity coefficient and of the electroneutrality condition, v+z+ = -v z, the limiting law also has the form... 

A great many electrolytes have only limited solubility, which can be very low. If a solid electrolyte is added to a pure solvent in an amount greater than corresponds to its solubility, a heterogeneous system is formed in which equilibrium is established between the electrolyte ions in solution and in the solid phase. At constant temperature, this equilibrium can be described by the thermodynamic condition for equality of the chemical potentials of ions in the liquid and solid phases (under these conditions, cations and anions enter and leave the solid phase simultaneously, fulfilling the electroneutrality condition). In the liquid phase, the chemical potential of the ion is a function of its activity, while it is constant in the solid phase. If the formula unit of the electrolyte considered consists of v+ cations and v anions, then... 

This part will be concerned with the properties of electrolytes (liquid or solid) under ordinary laboratory conditions (i.e. in the absence of strong external electric fields). The electroneutrality condition (Eq. 1.1.1) holds with sufficient accuracy for current flow under these conditions ... 

It is characteristic for the actual diffusion in electrolyte solutions that the individual species are not transported independently. The diffusion of the faster ions forms an electric field that accelerates the diffusion of the slower ions, so that the electroneutrality condition is practically maintained in solution. Diffusion in a two-component solution is relatively simple (i.e. diffusion of a binary salt—see Section 2.5.4). In contrast, diffusion in a three-component electrolyte solution is quite complicated and requires the use of equations such as (2.1.2), taking into account that the flux of one electrically charged component affects the others. 

For simplicity, the effect of the activity coefficients is neglected it should be recalled that the membrane is not completely impermeable for anions so that neither c p nor c q is equal to zero.) These relationships and the electroneutrality condition in the membrane... 

While ionophore-free membranes based on classical ion exchangers are still in use for the determination of lipophilic ions, such sensors often suffer from insufficient selectivity, as it is governed solely by the lipophilicity pattern of ions, also known for anions as the Hofmeister sequence. This pattern for cations is Cs+ > Ag+ >K+ > NH > Na+ > Li+ > Ca2+ > Mg2+ and for anions CIOT > SCN- > I > Sal- > N03- > Br > N02- > Cl- > OAc- HC03- > SO - > HPO4. While the ion exchanger fixes the concentration of hydrophilic analyte ions in the membrane on the basis of the electroneutrality condition within the membrane, the second key membrane component is the ionophore that selectively binds to the analyte ions. The selectivity of... 

The electroneutrality condition can be expressed by the condition of charge balance among the species in solution, according to... 

According to the mass balance Equation 3.28, the expression in parentheses is Mi. Further, the charge Z, on a species component is the same as the charge z, on the corresponding basis species, since components and species share the same stoichiometry. Substituting, the electroneutrality condition becomes,... 

The electroneutrality condition is almost always used to set the bulk concentration of the species in abundant concentration for which the greatest analytic uncertainty exists. In practice, this component is generally Cl- because most commercial labs, unless instructed otherwise, report a chloride concentration calculated... 

On the basis of crystallochemistry consideration and taking into account electron microscopy observations of the surface of crystals upon which some polymer was formed,99 Arlman and Cossee13 concluded that the active sites are located on crystal surfaces different from the basal (001) ones. In particular, these authors considered in detail active sites located on crystal surfaces parallel in the direction a — b of the unit cell defined as in Ref. 98. Figure 1.13 illustrates that, if we cut a TiCl3 layer parallel to the direction defined above, which corresponds to the line connecting two bridged Ti atoms, electroneutrality conditions impose that each Ti atom at the surface of the cut be bonded... 

In pure ceria, taking the electroneutrality condition into consideration and using the reasonable approximation ... 

In contrast with the equilibrium case, this equation still depends upon the charges of a and ft in a complicated manner. Although methods exist to treat the general case,8 we shall limit ourselves here to the case of a binary electrolyte, composed of species a and (a / ). The electroneutrality condition thus reads ... 

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