Binary electrolytes

Binary Electrolyte Mixtures When electrolytes are added to a solvent, they dissociate to a certain degree. It would appear that the solution contains at least three components solvent, anions, and cations, if the solution is to remain neutral in charge at each point (assuming the absence of any applied electric potential field), the anions and cations diffuse effectively as a single component, as for molecular diffusion. The diffusion or the anionic and cationic species in the solvent can thus be treated as a binary mixture. 

In the deduction of the Law of Mass Action it was assumed that the effective concentrations or active masses of the components could be expressed by the stoichiometric concentrations. According to thermodynamics, this is not strictly true. The rigorous equilibrium equation for, say, a binary electrolyte ... 

For sparingly soluble salts (i.e. those of which the solubility is less than 0.01 mol per L) it is an experimental fact that the mass action product of the concentrations of the ions is a constant at constant temperature. This product Ks is termed the solubility product . For a binary electrolyte ... 

If the solute dissociates with increasing dilution, the equation (7) requires modification thus, van Laar (1893) deduced for a binary electrolyte ... 

We shall assume that the solutions are so dilute that the electrolyte can be regarded as completely ionised. Then, for a binary electrolyte, for the amount considered ... 

If F l, corresponding to a small external electrolyte concentration Cs compared with the concentration ic jz- of gegen ions belonging to the polymer, and if we further restrict ourselves to the case of a binary electrolyte for which z = z- = z and consequently v+ — v = l and v = 2j then the appropriate series expansion of Eq. (B-6) is... 

Binary electrolyte solutions contain just one solute in addition to the solvent (i.e., two independent components in all). Multicomponent solutions contain several original solutes and the corresponding number of ions. Sometimes in multicomponent solutions the behavior of just one of the components is of interest in this case the term base electrolyte is used for the set of remaining solution components. Often, a base electrolyte is acmaUy added to the solutions to raise their conductivity. 

For the conductivity of a binary electrolyte solution with the degree of dissociation a, we have, according to Fq. (1.12),... 

In binary electrolyte solntions with an initial concentration q and ionic concentrations c =ax q [cf- Efi- (1-2)] the ionic activities can be written as... 

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). 

We see that in binary electrolytes, the flux of the reacting cation increases by a factor of 1 + (x /x+) relative to the pure diffusion current that would be observed (at a given concentration gradient) in the presence of an excess of foreign electrolyte. We shall call... 

Because of dissociation and the resulting increase in the total number of particles in solution, the parameters of the colUgative properties assume higher values. These values are proportional to the total concentration, c, of particles (ions and undissociated molecules) in the solution, which for a binary electrolyte is given by [1 + a(X(, - l)]q. The isotonic coefficient i is the ratio of and the concentration c, that would be observed in the absence of dissociation ... 

It follows (when taking into account that = x z = Zj) that the molar conductivity of binary electrolyte solutions is given by... 

The simplest system is represented by the nonpolarized interface, which is formed in the presence of a single binary electrolyte RX completely dissociating into ions R+ and in each phase,... 

Apart from the two classifications described above, electrolytes may also be classified according to the number and valence of the ions produced. Thus, sodium chloride and copper sulfate may both be termed binary electrolytes since one molecule of each of these chemical substances is capable of producing two ions. In the case of sodium chloride, both the ions produced are univalent so that this substance may also be called a uni-univalent electrolyte. Copper sulfate, however, yields two bivalent ions and so may be called a bibivalent electrolyte. The valences of the ions are quoted in the positive-negative sequence. Calcium chloride and potassium sulfate are both ternary electrolytes since one molecule of each yields three ions the former is bi-univalent, whilst the latter is uni-bivalent. 

The foregoing text highlights the fact that at the interface between electrolytic solutions of different concentrations (or between two different electrolytes at the same concentration) there originates a liquid junction potential (also known as diffusion potential). The reason for this potential lies in the fact that the rates of diffusion of ions are a function of their type and of their concentration. For example, in the case of a junction between two concentrations of a binary electrolyte (e.g., NaOH, HC1), the two different types of ion diffuse at different rates from the stronger to the weaker solution. Hence, there arises an excess of ions of one type, and a deficit of ions of the other type on opposite sides of the liquid junction. The resultant uneven distribution of electric charges constitutes a potential difference between the two solutions, and this acts in such a way as to retard the faster ion and to accelerate the slower. In this way an equilibrium is soon reached, and a steady potential difference is set up across the boundary between the solutions. Once the steady potential difference is attained, no further net charge transfer occurs across the liquid junction and the different types of ion diffuse at the same rate. 

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... 

The first value is valid for basic SI units, the second is more practical I in moles per cubic decimetre, LD in nanometres.) The radii of the ionic atmosphere for various solution concentrations of a single binary electrolyte (for which / = — z+z vc) are listed in Table 1.2. 

In the binary-electrolyte experiments carried out at large, constant cell potentials, the cell current is ohmically limited. If the conductivity of the solution is proportional to the concentration of electrolyte, the current density at a given overpotential is then proportional to Cb. Under this regime, the concentration cancels out of Eq. (2.3), and the velocity is proportional to the applied potential. For this special case, the velocity can be expressed in terms of the anion drift velocity [27, 28]. For a binary solution, this is equivalent to replacing (1 — t+) by t and i by the ohmically limited current density. 

Fleury and coworkers showed that cellular electrokineitc flow occurs under some conditions at the tips of the branches in the binary-electrolyte thin-layer experiments [37, 38], They constructed a model based on point charges at the growth tips to account for the shape of the induced convection cells. The streamlines of these cells form arcs between adjacent branches. By comparing deposits formed under an electrokineitc regime with deposits formed under a free-convection regime, Barkey et al. 

In the concentrated environment of electroplating baths, the diffusiophoretic force is the only force that can counteract the attractive London-van der Waals force. An appreciable diffusiophoretic force is, however, only present in binary electrolytes. In practice, particles are codeposited from supported electrolytes. In supported electrolytes, the diffusiophoretic force is absent, and Valdes model predict that under... 

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 ... 

As is clear from its derivation, Eq. (299) is quite general it is valid whatever the charges, the masses, and the concentrations of the various species in the system. We shall thus specify the case of a binary electrolyte f we consider a system with Na... 

Cruz, Jose-Luis and H. Renon, "A New Thermodynamic Representation of Binary Electrolyte Solutions Nonideality in the Whole Range of Concentrations," AIChE J., 1978, 24, 817. 

CRUZ (7) equation for gE of binary electrolyte solution which incorporates a DEBYE - HUCKEL term, a BORN - DEBYE - MAC. AULAY contribution for electric work, and NRTL equation, can be used to represent the vapor-liquid equilibria of volatile electrolyte in the whole range of concentration. 

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