Dissociated electrolytes

The effect of die concentration on the conductivity of an electrolyte in very dilute solution is represented by a simple empirical limiting law introduced by Kohlrausch (1898) and deduced theoretically by Onsager (1927)  

The lAPWS recommended values for the viscosity and dielectric constant of water can be found in lAPWS Releases (lAPWS, 2003 and 1997 respectively). 

Equation (4.11) is a limiting law that in the case of fully dissociated electrolytes is used to obtain A by extrapolation at infinite dilution of the molar conductivity of very dilute solutions. This limiting law assumes that the electrophoretic and relaxational correction terms are separable and it ignores higher orders contributions to conductance due to short-range interactions. 

The strategies for including these higher order contributions in the conductance equation have been analyzed in detail in the literature (Fem dez-Prini, 1973). At the end of the 1970s there were several alternative equations to the original treatment by Fuoss and Onsager (1957) to account for the effect of concentration on electrolyte conductances the Pitts (1953) equation (P), the Fuoss-Hsia (Fuoss and Hsia, 1967) equation (FH) later modified by Femandez-Prini (1969) (FHFP) and valid only for dilute, binary, symmetrical electrolytes, and the Lee and Wheaton (1978) equation (LW) valid for unsymmetrical electrolytes. 

A comparison of the performance of the FHFP and TBBK equations has been carried out recently by Femdndez-Prini and co-workers (Bianchi et al., 2000) at 25 °C. They concluded that, for symmetrical electrolytes in dilute solutions the FHFP equation is superior to the TBBK equation. The TBBK equation is claimed to be precise even at high concentrations however, the deviations from the experimental data are systematic. 

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A special corrverrtion exists concerning the free errergies of ions in aqueous solution. Most themrodyrramic iirfomration about strong (fiilly dissociated) electrolytes in aqueous solutions comes, as has been seen, from measiiremerrts of the eirrf of reversible cells. Sirrce tire ions in very dilute solution (or in the hypothetical... 

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... 

For very weak or slightly ionised electrolyes, the expression a2/( 1 — a) V = K reduces to a2 = KV or a = fKV, since a may be neglected in comparison with unity. Hence for any two weak acids or bases at a given dilution V (in L), we have a1 = y/K1 V and a2 = yjK2V, or ol1/ol2 = Jk1/ /K2. Expressed in words, for any two weak or slightly dissociated electrolytes at equal dilutions, the degrees of dissociation are proportional to the square roots of their ionisation constants. Some values for the dissociation constants at 25 °C for weak acids and bases are collected in Appendix 7. 

An appreciable advance in the theory of electrostatic interaction between ions in solution was made in 1923 by Peter Debye and Erich Hiickel, who introduced the concept of ionic atmosphere to characterize the averaged distribution of the ions. In its initial form the theory was applied to fully dissociated electrolytes hence, it was named the theory of strong electrolytes. 

The above relationship is easy to grasp since A0 represents the contribution of the fully dissociated electrolyte and Ac the contribution of a partially dissociated one. The ratio, therefore, gives the extent of dissociation or ionization. Measurement of Ac permits the evaluation of a if A0 is known. 

If a solute of the general formula AX (A is the chiral ion and X is an achiral ion) dissociates completely into ions once dissolved, then the solubility of the racemic conglomerate, SR, is equal to n%V2-SA (where SA is concentration of A in a solution saturated with AX ). If the solute is of the type AX, then 5 = V2-5a. The subscript n refers to the achiral ion and may be fractional, and so A2X must be represented by AXi/. If dissociation of AX is incomplete, SA lies between n i/2-SA and 2SA. For weakly dissociated electrolytes (such as carboxylic acids), SR is approximately 2SA. 

To test the validity of the extended Pitzer equation, correlations of vapor-liquid equilibrium data were carried out for three systems. Since the extended Pitzer equation reduces to the Pitzer equation for aqueous strong electrolyte systems, and is consistent with the Setschenow equation for molecular non-electrolytes in aqueous electrolyte systems, the main interest here is aqueous systems with weak electrolytes or partially dissociated electrolytes. The three systems considered are the hydrochloric acid aqueous solution at 298.15°K and concentrations up to 18 molal the NH3-CO2 aqueous solution at 293.15°K and the K2CO3-CO2 aqueous solution of the Hot Carbonate Process. In each case, the chemical equilibrium between all species has been taken into account directly as liquid phase constraints. Significant parameters in the model for each system were identified by a preliminary order of magnitude analysis and adjusted in the vapor-liquid equilibrium data correlation. Detailed discusions and values of physical constants, such as Henry s constants and chemical equilibrium constants, are given in Chen et al. (11). 

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

Systems with weak electrolytes, or partially dissociated electrolytes, can be studied if chemical equilibrium among ionic species and molecular species is considered. Multi-... 

Here Tq is — C2 and is a prefactor proportional to which is determined by the transport coefficient (in this case at the given reference temperature. The constant B has the dimensions of energy but is not related to any simple activation process (Ratner, 1987). Eqn (6.6) holds for many transport properties and, by making the assumption of a fully dissociated electrolyte, it can be related to the diffusion coefficient through the Stokes-Einstein equation giving the form to which the conductivity, <7, in polymer electrolytes is often fitted,... 

Conductivity measurements are often the first to be carried out on an electrolyte however, they provide information only on the total transport of charge. Even in a fully dissociated electrolyte, such measurements do not differentiate between the current carried by the cations and the anions. Transport or transference measurements attempt to probe more deeply into the movement of species in electrolytes. 

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. 

Because Na(Hg) slowly reacts with water, the Na(Hg) electrode in cell (1) is preferably a flow type, in which the electrode surface is continuously renewed. Ethylamine is used in cell (2) because it does not react with Na and Na(Hg) but dissolves and dissociates electrolyte Nal. The composition of the electrolyte solution in cell (2) does not influence its emf. Instead of measuring the emfs of cells (1) and (2), we can measure the emf (-3.113 V) of the double cell (4). The advantage of the double cell is that the emf is not influenced by the concentration of Na(Hg) ... 

Kohlrausch s law can be assumed to apply at concentrations up to about HF4 kmol/mJ. For a fully dissociated electrolyte at these concentrations, from equations 6.72 and 6.73 ... 

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). 

Combined with densities, molecular weights, and transference numbers (fractions of the current carried by the various ionic constituents), the conductivity yields the relative velocities of the ionic constituents under the influence of an electric field. The mobilities (velocity per unit electric field, cm2 s-1 V-1) depend on the size and charge of the ion, the ionic concentration, temperature, and solvent medium. In dilute aqueous solutions of dissociated electrolytes, ionic mobilities decrease slightly as the concentration increases. The equivalent conductance extrapolated to zero electrolyte concentration may be expressed as the sum of independent equivalent conductances of the constituent ions... 

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. 

When ammonium hydroxide dissociates electrolytically it yields the ion NHV". The group of atoms NH4, which is often spoken of as the ammonium radical, resembles in many respects the atom of sodium or potassium. Like these, it can form a monovalent positive ion, or it can form compounds with acid radicals, for example, NH4CI, (NID2SO4 but unlike sodium and potassium, it cannot exist in the uncombined state. 

Assuming that the charge distribution is due only to the ions of a dissociated electrolyte of concentration cE, which obeys Boltzmannian distributions ... 

The value of the fraction representing the ratio of the conductances of two differently concentrated but fully dissociated solutions can be calculated from Onsager s equation (see III-14) which enables us to determine the effect of electrostatic forces of attraction in strong, i. e. fully dissociated electrolytes. In the case of weak electrolytes, however, it is necessary to substitute ct in Onsager s equation by the real concentration of ions, i. e. by equivalent conductance of a hypothetical, fully dissociated solution is considered. In this way we obtain the following equation ... 

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).

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