Completely dissociated electrolytes

Furthermore, about 1920 the idea had become prevalent that many common crystals, such as rock salt, consisted of positive and negative ions in contact. It then became natural to suppose that, when this crystal dissolves in a liquid, the positive and negative ions go into solution separately. Previously it had been thought that, in each case when the crystal of an electrolyte dissolves in a solvent, neutral molecules first go into solution, and then a certain large fraction of the molecules are dissociated into ions. This equilibrium was expressed by means of a dissociation constant. Nowadays it is taken for granted that nearly all the common salts in aqueous solution are completely dissociated into ions. In those rare cases where a solute is not completely dissociated into ions, an equilibrium is sometimes expressed by means of an association constant that is to say, one may take as the starting point a completely dissociated electrolyte, and use this association constant to express the fact that a certain fraction of the ions are not free. This point of view leads directly to an emphasis on the existence of molecular ions in solution. When, for example, a solution contains Pb++ ions and Cl- ions, association would lead directly to the formation of molecular ions, with the equilibrium... 

The binary parameters Tcajm and tm ca then become the only two independent adjustable parameters for a single completely-dissociated electrolyte, single solvent system. 

It can be observed that g is the ratio between the observed osmotic pressure and the osmotic pressure that would be observed for a completely dissociated electrolyte that follows Henry s law [see Equation (15.47)], hence the name, osmotic coefficient. A similar result can be obtained for the boiling point elevation, the freezing point depression, and the vapor pressure lowering. 

So far it has not been possible to measure the chemical potentials of the components in the mesophases. This measurement is possible, however, in solutions which are in equilibrium with the mesophases. If pure water is taken as the standard state, the activity of water in equilibrium with the D and E phases in the system NaC8-decanol-water is more than 0.8 (4). From these activities in micellar solutions, the activity of the fatty acid salt has sometimes been calculated. The salt is incorrectly treated as a completely dissociated electrolyte. The activity of the fatty acid in solutions of short chain carboxylates has also been determined by gas chromatography from these determinations the carboxylate anion activity can be determined (18). Low CMC values for the carboxylate are obtained (15). The same method has shown that the activity of solubilized pentanol in octanoate solutions is still very low when the solution is in equilibrium with phase D (Figure 10) (15). 

C.-C. Chen, H. I. Britt, J. F. Boston, et ah, Local compositions model for excess Gibbs energy of electrolyte systems. Part I Single solvent, single completely dissociated electrolyte systems, AIChE J., 1982, 28, 588-596. 

Although Debye and Hiickel worked out their theory to solve the problem of strong, completely dissociated electrolytes, the results may be applied to weak and transition electrolytes as well, if the actual ionic concentration is substituted in the equation for ionic strength. With strong electrolytes, which are completely dissociated, it is possible to substitute in the term directly the analytical concentration of the substance, but with weak electrolytes their dissociation degree a has to be considered. For example with uni-... 

Generally, strong acids in hydrogen peroxide remain strong. For example, plots of equivalence conductance versus the half-power of concentration yield straight lines which are characteristic of completely dissociated electrolytes. 

Fig. 4.100. Argand diagrams of a completely dissociated electrolyte and its pure solvent. Full circles experimental data from frequency domain measurements on aqueous potassium chloride solutions at 25 °C. Curve 1 Argand diagram of pure water. Curve 2 Argand diagram, ff = f(E ), of an 0.8 Waqueous KCI solution, Curve 3 Argand diagram, e"=f(e )r obtained from curve 2. (Reprinted from P. Turq, J. Barthel, and M. Chemla, in Transport, Relaxation and Kinetic Processes in Electrolyte Solutions, Springer-Verlag, Berlin, 1992, p. 78).

The free ions and ion pairs play a distinct role in the dielectric properties of electrolyte solutions. Due to the saturation of the dipole orientation near free ions, the dielectric constant of the system decreases with the increase of free ion concentration. Ion pairs possess the dipole moments and produce an additional contribution to the dielectric properties. Due to the new polarization effect, the dielectric constant of the entire system increases with the increase of the ion pair concentration. It is generally accepted to distinguish the solvent dielectric constant, es, and the solution dielectric constant, e [3], The dielectric constant of the solvent describes the polarization effect of the solvent molecules in the presence of ions es decreases with the increase of ion concentration. The dielectric constant of the solution also includes the polarization effect from the ion pairs that can increase or decrease with the increase of ion concentration. Due to this, e > es, and only for a completely dissociated electrolyte, (a = 1) e = es. 

The evidence just given, which is typical of that obtained from all recent measurements, shows that the Onsager equation is valid for very dilute aqueous solutions of strong electrolytes. This fact is important as it lends additional and strong support to the correctness and utility of the interionic attraction theory. As has already been emphasized Onsager s equation is a limiting equation and deviations from it, even for completely dissociated electrolytes, are to be expected as the concentration is increased. 

Before going on to define single ion activities and activity coefficients, let s pause to reflect on the similarity between the case considered here (a completely dissociated electrolyte in water), and the olivine solid solution case considered in Chapter 12 ( 12.7). The physical systems are completely different, but the thermodynamic problem is almost identical, the only significant difference being that in the olivine case the concentrations were measured by mole fractions and ideality consisted in conforming to Raoult s Law, while here concentrations are measured in molality and ideality is represented by Henry s Law. Apart from that, the problem in both cases consists in choosing a solute component that is appropriate to the situation. 

Conductance equations for completely dissociated electrolytes are obtained in the form... 

Formic acid melts at 8.40°C and has a cryoscopic constant Ac = 1.932 K kg mol". These results of J. Lange were obtained by a Beckmann cooling-curve technique in which a differential apparatus gave values of freezing point depression for which a precision of 0.0001 K was reported. Formic acid has a dielectric constant of 58.5 at 16°C and results for potassium chloride, potassium picrate and tetramethylam-monium chloride were fitted to an extended Debye-Hiickel equation for completely dissociated electrolytes. Tetramethylammonium chloride showed the smallest deviation from the limiting law and this was ascribed to the affinity of the organic cation for the solvent. 

Let us consider first a solution containing a completely dissociated electrolyte of molarity c (mol 1 or mol dm ) made up of cations and anions X, The transference number t of either ion is then defined as the number of faradays of electricity carried by the ion concerned across a reference plane, fixed with respect to the solvent, when one fara-day of electricity passes across the plane. Since the number of faradays transported by any ionic species i depends directly upon the magnitude of its algebraic charge number Zi, its molarity Cj, and its mobility (i.e. its velocity in unit electric field), it follows that ... 

For reasons given later the discussion in this section will be written in terms of symmetrical and completely dissociated electrolytes. In the event of ion association the transference number is not affected directly since always equals and these cancel out in eqn. 5.8.3. There remains the indirect effect, in that the concentration c in the interionic terms must be replaced by the ionic concentration cue. The variation of the transference number with concentration is then even smaller than is... 

A thermodynamic model developed by Barba, Brandani and di Giacomo (1982) described the solubility of calcium sulphate in saline water. A system of equations based on Debye Hiickel and other models was used to describe isothermal activity coefficients of partially or completely dissociated electrolytes. Using binary parameters, good agreement was claimed between experimental and predicted values of calcium sulphate solubility in sea water and brackish brines including those with a magnesium content. 

When an external electric field is imposed on an electrolyte solution by electrodes dipped into the solution, the electric current produced is proportional to the potential difference between the electrodes. The proportionality coefficient is the resistance of the solution, and its reciprocal, the conductivity, is readily measured accurately with an alternating potential at a rate of 1 kHz in a virtually open circuit (zero current), in order to avoid electrolysis at the electrodes. The conductivity depends on the concentration of the ions, the carriers of the current, and can be determined per unit concentration as the molar conductivity Ae. At finite concentrations ion-ion interactions cause the conductivities of electrolytes to decrease, not only if ion pairs are formed (see Sect. 2.6.2) but also due to indirect causes. The molar conductivity Ae can be extrapolated to infinite dilution to yield Ae" by an appropriate theoretical expression. The modern theory, e.g., that of Fernandez-Prini (1969), takes into account the electrophoretic and ionic atmosphere relaxation effects. The molar conductivity of a completely dissociated electrolyte is ... 

In practical applications, it is advantageous not to set up the chemical potential for the dissociated ions but for the entire electrolyte component itself Taking a completely dissociated electrolyte, each molecule consisting of Vc cations and Va anions, the chemical potential of the entire electrolyte can be written as... 

The application of Eq. (3) or Eq. (4) to electrolyte solutions would require a solution made up of completely dissociated electrolytes. This restriction can be overcome by the introduction of sources that do not produce spatial inhomogeneities in the solution. A simple but important example of such sources is the chemical reactions of ion-pair formation and decomposition, which produce particle densities per unit of time cr at rate constants A i and k2. 

The progress in equilibrium correlation functions has also been used to extend the validity range of relations of irreversible thermodynamics to higher concentrations. An example is the Nernst-Hartley equation, Eq. (24), for completely dissociated electrolytes to yield the relationship... 

For a completely dissociated electrolyte, the appropriate equivalent conductivity expression, A = follows... 

Completely dissociated electrolytes under ambient conditions has long been a major topic in solution chemistry, so the seeond option is traditionally used. That is, for the mole fraction of an aqueous solution of a strong eleetrolyte such as NaCl or KCl, Equation (7.1) is modified to... 

These assumptions were displayed pictorially for a solution of one solvent with one completely dissociated electrolyte as ... 

From C-C Chen H. I. Britt J.F. Boston and L.B. Evans, "Local Composition Model for Excess Gibbs Energy of Electrolyte Systems Part I Single Solvent, Single Completely Dissociated Electrolyte Systems", AIChE J., v. 28, 4, p. 592 (1982)... 

Although there is ample evidence of its existence, the NaSO ion is generally ignored when calculating activity coefficients in solutions containing sodium and sulfate ions. Sodium sulfate is treated as a completely dissociating electrolyte. As early as 1930. Righellato and Davies (S34) stated that, even in dilute solutions, most uni-bivalent salts are incompletely dissociated. Based on conductance measurements at 18 C, they presented dissociation constants for a number of intermediate ions. For the salt MzX the dissociations were defined ... 

Rather surprisingly, another century was to pass before a general transference formula was published (15.16) that applied to simple and complex electrolytes alike. It depended upon the recognition that transference experiments measured the net transport, not of ions, but of ion-constituents. Only in solutions of completely dissociated electrolytes are the two terms synonymous. The ion-constituent concept was assiduously fostered in Duncan MacInnes classic textbook "The Principles of Electrochemistry" (J2) and elaborated by Harry Svensson (J[8) but its consequences had not been fully realised. Thus for a solution containing ions 1, 2,... 

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