Z-valent ions

The ionic strength (/) of the medium whose pH is to be measured affects the and hence the pH. The Debye-Httckel equation deHnes the activity coefficient y of a Z-valent ion by [62]... 

In the classical nucleation theory the ions flux jfl, to the critical nucleus is set equal to the ratio //z+e where ic = k astv aAJilkT) coincides with the cathodic current in the Butler-Volmer equation [2.30] and z+e is the amount of electricity carried out by a single z+-valent ion. As shown in [2.31] the... 

Now the Einstein relation (4.172) will be used to connect the transport processes of diffusion and conduction. The starting point is the basic equation relating the equivalent conductivity of a z z-valent electrolyte to the conventional mobilities of the ions, i.e., to the drift velocities under a potential gradient of 1 V cm, ... 

Consider that a solution of az z-valent electrolyte (ofconcentration c moles dm" ) is instantaneously brought into contact with water at the plane x = 0 (Fig. 4.75). A concentration gradient exists both for the positive ions and for the negative ions. They therefore start diffusing into the water. 

In these expressions, the square brackets represent the molar concentrations of the species indicated, and y is the activity coefficient of a Z valent species. In order to calculate the free ionic concentrations in these expressions, it is necessary to take into account ion-pair and complex formation. The equilibria in pure calcium phosphate solutions are -... 

The ionic conductivity is achieved by a nonrandom, direct movement of ions, which results in the transport of matter and a flow of charge [4], The rate of the transport density is called the flux. It is the number of moles of a certain species crossing a unit area of a reference plane in 1 s. The migration or conduction is a flow of charge produced by an electric field between the electrodes [3]. Cations move to the cathode and anions to the anode. In a simple z z-valent electrolyte the current density, or the flux of charge, is proportional to the concentration of ions (c = c+ = c also z = = z ), their conventional mobility... 

In addition, the polymer layer is assumed to be characterized by a constant volume concentration of fixed charges (A per unit volume) of valence Z, and it is permeable to the ionic species in the solution. This contains a z-valent symmetrical electrolyte with concentration n (number of each kind of ions per unit volume). Hence, the electric potential at the solid surface, r = fl, is the Donnan potential, fDON> given by [14-16] ... 

Electrochemistry uses chemical potentials of the type given by Eqs. (91a)-(91c) for single ions. The link to thermodynamics is established by the help of mean mole fractions and mean activity coefficients f . For a binary electrolyte as the solute, Y2 = AjI (z+, valent cation Z, valent anion), for example, Na2S04 (where z+ = +2, z = — 1, = 2, i = 1), the chemical potential/X2(p, T)... 

Debye Length/nm, Radius of Ion Cloud, and Thickness of Diffuse Double Layer for Various Concentrations of Some z,z Valent Electrolytes... 

Gold complexes, with a few exceptions, are either 2-coordinated with the two ligand molecules bonded to the central Au+ ion in linear configuration or 4-coordinated with the ligand molecules bonded to the central Au + ion in a square-planar configuration. Complex stability in aqueous solution is assessed by determining the equilibrium stability constant of the complex formation reaction. The formation of an n-coordinated complex of a z-valent metal cation with a ligand species... 

Now consider a polarizable interface that consists of a metal electrode in contact with a solution of a l l-valent electrolyte (i.e., Z+ = 1 and z = -1). It will be remembered that in order to apply electrocapillaiy thermodynamics to a polarizable interface Mj/S, the interface has to be assembled in a cell along with a nonpolarizable interface. Suppose that the nonpolarizable interface is one at which negative ions interchange charge with the metal surface, i.e., Zj = — 1. Hence, Eq. (6.99) for the polarizable interface becomes... 

Remember that the equations for the Bjerrum theory as presented here are correct only for electrolytes yielding ions of the same valence z-, i.e., only for symmetrical 1 1- or 2 2-valent electrolytes. 

Still more interesting conclusions may be drawn from eq. (49), as to the effect of the valency of the ions upon the flocculating concentrations. Eq. (49) contains v both explicitly and in the quantity y, implicitly. If, however, the double layer potential is sufficiently large, so that even for univalent fons (p = 1) the factor y approaches 1, the value of y will, a fortiori, be = 1. for larger valencies, and therefore practically independent of v. (For z = 8, y = (e — l)/(e -I- 1) = 0.9 and y == 0.864). In that case the concentration c is simply proportional to v. Hence, under the conditions presumed in this chapter (involving in particular the assumption that the diffuse layer theory of Gouy and Chapman may be applied), eq. (49) leads to the very important result that we must expect the quantities of 1—1 valent, 2—2 valent and 3—3 valent electrolyte, needed to flocculate a lyophobic sol or suspension, to be in a ratio... 

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