Condition of electroneutrality

This thermodynamic equation defines the equilibrium distribution of all permeating ions between the two phases. For quantitative calculations, the conditions of electroneutrality of the phases must be taken into account in addition to this equation. 

When combining Eqs. (A.l) and (A.4), we obtain a second-order nonlinear differential equation for /o(r) which is mathematically very difficult to solve. Therefore, in DH theory a simplified equation is used The exponential terms of Eq. (A.4) are expanded into series and only the first two terms of each series are retained [exp(y) 1 +y]. When we include the condition of electroneutrality and use the ionic strength we can write this equation as... 

In geothermal waters, the condition of electroneutrality must be fulfilled ... 

Fig. 2.2. Relation between the Na+ and CI concentrations of geothermal waters and of inclusion fluids. The solid line indicates the condition of electroneutrality approximated by the equation = mc -. Solid and open circles mean the chemical analytical data on inclusion fluids and geothermal waters, respectively. S = Salton Sea R = Reykjanes W = Wairakei B = Broadlands O = Otake H = Hveragerdi C = Climax D = Darwin P = Providencia (Shikazono, 1978a).

Although Eq. (25) has no physical meaning and although its simplification is not valid thermodynamically, since the condition of electroneutrality in both phases is not fulfilled if the proton cannot partition, it agrees very well with experimental data, which justifies its use. In fact, computerized fitting procedures correct for this error in commercial two-phase titrators, so that the experimental value of p K can directly be introduced in Eq. (25). 

In the simple case of a diffusible, univalent cation B+ and anion A- and non-diffusible anion X present in phase 2, the condition of electroneutrality gives... 

The six equations in the six unknowns xlt x2,..., x6 are the electroneutrality condition, conservation of mercury and chloride components, plus the three mass action laws corresponding to water dissociation and mercury complexation by Cl- and OH-. The condition of electroneutrality reads... 

The condition of electroneutrality of the interface as a whole says that... 

In addition to these six independent equations, we must take the condition of electroneutrality into consideration ... 

Since in the steady state, it is necessary to maintain a condition of electroneutrality in any macroscopic part of the system, the total charge flux through all cross-sections of the circuit must be the same. In particular, the rate of electron flow in the external circuit is equal to the rate of charge transfer at each electrode/electrolyte interface. 

For a uni-univalent electrolyte in nearly neutral solution (CPS 2 CNS = Cs) and a membrane containing a concentration CF of univalent fixed charged groups, application of the condition of electroneutrality (CP = CF + CN) to Eq. (37) yields... 

Up to this point it has been tacitly assumed that A and B move independently across the reaction product. This can be true for intermetallic compounds, but not for ionic crystals in which there is always a flux coupling due to the condition of electroneutrality. Let us formulate this coupling condition in a general way in the form... 

Let us also consider the pairing reaction B A -t-V A = [B, V] in an ionic crystal AX, where the dopant BA is a heterovalent cation and V A is the compensating cation vacancy. We define the degree of pairing to be NP = A[B>V T/VB. From the mass balance equation A B = AB+AjB Vj and the condition of electroneutrality jVv + A b = NyA, one finds for the case that the undoped AX crystal exhibits Schottky type disorder (which means that = Ks)... 

If local point defect equilibrium prevails and space charge effects can be neglected, one finds from the condition of electroneutrality that... 

If the cations of variable valency (e.g., Fe2+/Fe3 + ) are present in not too low concentrations, the crystals will be semiconductors. In non-equilibrium vermiculites, the internal electric field is then strongly influenced by their electronic conductivity, as explained in Section 4.4.2. If we start with an equilibrium crystal and change either pH, ae, aor a, (where i designates any other component), coupled transport processes are induced. The coupling is enforced firstly by the condition of electroneutrality, secondly by the site conservation requirements in the T-O-T blocks (Fig. 15-3), and thirdly by the available free volume in the (van der Waals) interlayer. It is in this interlayer that the cations and the molecules are the more mobile species. However, local ion exchange between the interlayer and the relatively rigid T-O-T blocks is also possible. 

Rule 2 The second rule is the condition of electroneutrality. It means that in an electrochemical cell, the sum of positive charges must equal the sum of negative charges. Thus, separation of positive and negative charges occurs at every interface, but their sum is always zero. 

The condition of electroneutrality, which must exist in both compartments. 

The negative sign in (6.8) is due to the negative charge of the anion. The condition of electroneutrality in each compartment dictates that, on the side of the membrane without polyelectrolytes, the concentration of the salt is... 

The analogy between self-dissociation of water to H+ and OH- is obvious. Addition of an impurity (or dopant) is analogous to the addition of a weak base or a weak acid to water. The same condition of electroneutrality must apply. 

In an extrinsic semiconductor, containing only one type of dopant, there are equal densities of mobile charges (electrons in the n-type and holes in the jp-type) and ionized dopant atoms (positively charged for the n-type and negatively charged for the jp-type). For simplicity, we restrict this discussion to a jp-type extrinsic semiconductor. The condition of electroneutrality applies only in the absence of an external electric field. 

In the previous chapters the condition of electroneutrality was applied to all systems that contained charged species. In this chapter we study the results when this condition is relaxed. This leads to studies of electrochemical systems, especially those involving galvanic cells. Cells without transference are emphasized, although simple cells with transference are discussed. At the end of the chapter the conditions of equilibrium across membranes in electrochemical systems are outlined. 

The effect of relaxing the condition of electroneutrality in terms of the electrical potential of a charged phase must first be considered. We choose a single-phase system containing 10 10 mol of an ionic species with a charge number of +1. The phase is assumed to be spherical with a radius of 1 cm and surrounded by empty space. Essentially, all of the excess charge will reside on the surface of the sphere. The electrical potential of the sphere is given by... 

Equations (12.127) and (12.128) give the relation between the molalities of the sodium and chloride ions at equilibrium under the appropriate conditions. The molalities, mx and m2, are not equal but are related by the condition of electroneutrality, so... 

Due to the condition of electroneutrality, diffusion flows can be used in Eq. (6.166). The flows relative to the water velocity are... 

Under the condition of electroneutrality, Eq. (10.1) describes the Donnan equilibrium across a membrane, which separates solutions containing nonpermeating ions. With the Donnan equilibrium, differences of pressure and electric potential will appear. If the nonpermeating components are electrically neutral, only the pressure difference occurs. 

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