Dilute electrolyte solutions

So far, very dilute solutions have been considered such that the interaction between ions is only coulombic. When other (unreactive) ions are nearby, the direct interaction between ionic reactants is partially screened and was first developed by Debye and Hiickel [91]. They showed that the potential energy, eqn. (39), is modified and becomes 

Normally, the validity of the Debye—Hiickel theory extends little further than kR 1. At room temperature, this requires ionic concentrations 0.1 mol dm-3 for univalent ions in water, 0.03moldm-3 for univalent ions in ethanol or 0.01 mol dm-3 for univalent ion in ethers. In these cases, ions may be regarded as point particles and the strong repulsive core potential ignored. Furthermore, the time taken for non-reactive ions to diffuse far enough to establish an ionic-atmosphere around an ion, which was suddenly formed in solution containing only univalent ions, is 

Bearing in mind these limitations on the Debye—Hiickel model of electrolytes, the influence of ionic concentration on the rate coefficient for reaction of ions was solved numerically by Logan [54, 93] who evaluated the integral of eqn. (56) with the potential of eqn. (55). He compared these numerical values with the predictions of the Bronsted— Bjerrum correction to the rate of a reaction occurring between ions surrounded by equilibrated ionic atmospheres, where the reaction of encounter pairs is rate-limiting 

For reactions between ions of like charge, the term in xrc (1 + kR) 1 should be multiplied by a number 0.6—0.9, whereas for unlike charges, this number is 0.3—0.6 depending on R. Certainly, eqn. (58) is not the appropriate correction term. In eqn. (57), the ionic relaxation time for univalent ions is Tjon = 1/(477[rc Dn), where n is the electrolyte concentration. This is also the characteristic time for reaction (pseudo first-order decay time) of a univalent species reacting with one or other ion of the 

Equation (56) tends to the Debye—Smoluchowski rate coefficient [eqn. 

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Here, x denotes film thickness and x is that corresponding to F . An equation similar to Eq. X-42 is given by Zorin et al. [188]. Also, film pressure may be estimated from potential changes [189]. Equation X-43 has been used to calculate contact angles in dilute electrolyte solutions on quartz results are in accord with DLVO theory (see Section VI-4B) [190]. Finally, the x term may be especially important in the case of liquid-liquid-solid systems [191]. 

Martynov G A and Salem R R 1983 Electrical Double Layer at a Metal-Dilute Electrolyte Solution Inteiface (Berlin Springer)... 

Used for dilute electrolytic solutions. Not applicable to reactions that are catalyzed by mercury. 

The idea in these papers67,223,224 was to identify the potential of the capacitance minimum in dilute electrolyte solutions with the actual value of Ea=o (i.e., <7ge0m( min) = Ofor the whole surface) and to obtain the value of R as the inverse slope of the Parsons-Zobel plot at min.72 Extrapolation of Cwom vs- to Cgg0m = 0 provides the inner-layer capacitance in the / C geom, and not C ea as assumed in several papers.67,68,223,224 In the absence of ion-specific adsorption and for ideally smooth surfaces, these plots are expected to be linear with unit slope. However, data for Hg and single-crystal face electrodes have shown that the test is somewhat more complicated.63,74,219,247-249 More specifically,247,248 PZ plots for Hg/... 

According to a theoretical analysis,262,267 the CDL model is valid for pc electrodes with very small grains (y < 5 to 10 nm) with a moderate difference of Eas0 for the different faces (A ff=0 = 0.1 to 0.15 V) and for dilute electrolyte solutions (c < 0.01 M) near the point of total zero charge. For the other cases, the IDL model should be valid. 

Solid Bi2S3 does not appear in the expression for K,p, because it is a pure solid and its activity is 1 (Section 9.2). A solubility product is used in the same way as any other equilibrium constant. However, because ion-ion interactions in even dilute electrolyte solutions can complicate its interpretation, a solubility product is generally meaningful only for sparingly soluble salts. Another complication that arises when dealing with nearly insoluble compounds is that dissociation of the ions is rarely complete, and a saturated solution of Pbl2, for instance, contains substantial... 

Measurement of the differential capacitance C = d /dE of the electrode/solution interface as a function of the electrode potential E results in a curve representing the influence of E on the value of C. The curves show an absolute minimum at E indicating a maximum in the effective thickness of the double layer as assumed in the simple model of a condenser [39Fru]. C is related to the electrocapillary curve and the surface tension according to C = d y/dE. Certain conditions have to be met in order to allow the measured capacity of the electrochemical double to be identified with the differential capacity (see [69Per]). In dilute electrolyte solutions this is generally the case. 

Finally, it must be recalled that the transport properties of any material are strongly dependent on the molecular or ionic interactions, and that the dynamics of each entity are narrowly correlated with the neighboring particles. This is the main reason why the theoretical treatment of these processes often shows similarities with models used for thermodynamic properties. The most classical example is the treatment of dilute electrolyte solutions by the Debye-Hiickel equation for thermodynamics and by the Debye-Onsager equation for conductivity. 

In contrast to nonelectrolyte solutions, in the case of electrolyte solutions the col-ligative properties depart appreciably from the values following from the equations above, even in highly dilute electrolyte solutions that otherwise by all means can be regarded as ideal (anomalous colligative properties). 

Figure 7.4 shows such functions for binary solutions of a number of strong electrolytes and for the purposes of comparison, for solutions of certain nonelectrolytes (/ ). We can see that in electrolyte solutions the values of the activity coefficients vary within much wider limits than in solutions of nonelectrolytes. In dilute electrolyte solutions the values of/+ always decrease with increasing concentration. For... 

In 1922, Johannes Nicolaus Br0nsted estabhshed an empirical relation for the activity coefficients in dilute electrolyte solutions ... 

A more general theory of solutions would require detailed notions of solution structure and of all types of interactions between the particles (ions and solvent molecules) in the solution. Numerous experimental and theoretical studies have been carried out, and some progress has been made, but a sufficiently universal theory that could describe all properties in not very dilute electrolyte solutions has not yet been developed. 

Electrokinetic processes only develop in dilute electrolyte solutions. The second phase can be conducting or nonconducting. Processes involving insulators are of great importance, since they provide the only way of studying the structure and electrical properties of the surface layer of these materials when they are in contact with the solution. Hence, electrokinetic processes can also be discussed as one of the aspects of insulator electrochemistry. 

It also follows from what was said that a zeta potential will be displayed only in dilute electrolyte solutions. This potential is very small in concentrated solutions where the diffuse edl part has collapsed against the metal surface. This is the explanation why electrokinetic processes develop only in dilute electrolyte solutions. 

Hu, W., Hasebe, K., Tanaka, K., and Haddad, P R., Electrostatic ion chromatography of polarizable anions in saline waters with N- 2-[acetyl(3-sulfopro-pyl)aminoethyl -N,N-dimethyldodecanaminium hydroxide (ammonium sulfobetaine-1) as the stationary phase and a dilute electrolytic solution as the mobile phase, /. Chromatogr. A, 850, 161, 1999. 

Consider a dilute electrolyte solution containing s components (nonelectrolytes and various ionic species) in which concentration gradients of the components and an electric field are present. The material flux of the ith component is then given by a combination of Eqs (2.3.11) to (2.3.20) ... 

Consider a solid surface in contact with a dilute electrolyte solution. The plane where motion of the liquid can commence is parallel to the outer Helmholtz plane but shifted in the direction into the bulk of the solution. The electric potential in this plane with respect to the solution is termed the electrokinetic potential ( = 02 ). 

Rate constants for the dissolution and precipitation of quartz, for example, have been measured in deionized water (Rimstidt and Barnes, 1980). Dove and Crerar (1990), however, found that reaction rates increased by as much as one and a half orders of magnitude when the reaction proceeded in dilute electrolyte solutions. As well, reaction rates determined in the laboratory from hydrothermal experiments on clean systems differ substantially from those that occur in nature, where clay minerals, oxides, and other materials may coat mineral surfaces and hinder reaction. 

There is no certainty, furthermore, that the reaction or reaction mechanism studied in the laboratory will predominate in nature. Data for reaction in deionized water, for example, might not apply if aqueous species present in nature promote a different reaction mechanism, or if they inhibit the mechanism that operated in the laboratory. Dove and Crerar (1990), for example, showed that quartz dissolves into dilute electrolyte solutions up to 30 times more quickly than it does in pure water. Laboratory experiments, furthermore, are nearly always conducted under conditions in which the fluid is far from equilibrium with the mineral, although reactions in nature proceed over a broad range of saturation states across which the laboratory results may not apply. 

The necessary components of oral rehydration therapy (ORT) solutions include glucose, sodium, potassium, chloride, and water (Table 39-2). The American Academy of Pediatrics recommends rehydration with an electrolyte-concentrated rehydration phase followed by a maintenance phase using dilute electrolyte solutions and larger volumes. 

This latter expression allows us to compute all the excess properties of dilute electrolytic solutions for instance, the excess osmotic pressure is determined by Eq. (138). The most remarkable result is of course that all these thermodynamic properties are non-anaiytic functions of the concentration ... 

Electrostatic and statistical mechanics theories were used by Debye and Hiickel to deduce an expression for the mean ionic activity (and osmotic) coefficient of a dilute electrolyte solution. Empirical extensions have subsequently been applied to the Debye-Huckel approximation so that the expression remains approximately valid up to molal concentrations of 0.5 m (actually, to ionic strengths of about 0.5 mol L ). The expression that is often used for a solution of a single aqueous 1 1, 2 1, or 1 2 electrolyte is... 

Experimenters would do well to avoid any unnecessary changes in the ionic composition of reaction samples within a series of experiments. If possible, chose a standard set of reaction conditions, because one cannot readily correct data from one set of experimental conditions in any reliable manner that reveals the reactivity under a different set of conditions. Maintenance of ionic strength and solvent composition is desirable, and correction to constant ionic strength often effectively minimizes or ehminates electrostatic effects. Even so, remember that Debye-Hiickel theory only applies to reasonably dilute electrolyte solutions. Another important fact is that ion effects and solvent effects on the activity coefficients of polar transition states may be more significant than more modest effects on reactants. 

However, it should be noted that using diluted electrolyte solutions imply lowering ionic strength and buffering capacity, leading to a variety of drawbacks that will be discussed later in this chapter. 

Equations 3-131a,b to 3-134e are exact relations for infinite dilute electrolyte solutions and have been used to obtain diffusivity data from conductivity and vice versa. 

Distances within the double layer are considered large or small, depending on their magnitude relative to k-1. Thus in dilute electrolyte solutions, in which k is large, the surface of shear —which is close to the particle surface even in absolute units —may be safely regarded as coinciding with the surface in units relative to the double-layer thickness. Therefore, in the case for which k is large (or k small), Equation (21) becomes... 

Figure 5.38 shows an electrolyte solution between two plane electrodes. The conductivity of the solution (ic) is expressed by k=L/AR, where L is the distance between the two electrodes (cm), A the electrode area (cm2), and R the electrical resistance of the solution (fi). For dilute electrolyte solutions, the conductivity k is proportional to the concentrations of the constituent ions, as in Eq. (5.39) ... 

The potential of mean force due to the solvent structure around the reactants and equilibrium electrolyte screening can also be included (Chap. 2). Chapter 9, Sect. 4 details the theory of (dynamic) hydro-dynamic repulsion and its application to dilute electrolyte solutions. Not only can coulomb interactions be considered, but also the multipolar interactions, charge-dipole and charge-induced dipole, but these are reserved until Chap. 6—8, and in Chaps. 6 and 7 the problems of germinate radical or ion pair recombination (of species formed by photolysis or high-energy radiolysis) are considered. 

In 1923, Peter Debye and Erich Hiickel developed a classical electrostatic theory of ionic distributions in dilute electrolyte solutions [P. Debye and E. Hiickel. Phys. Z 24, 185 (1923)] that seems to account satisfactorily for the qualitative low-ra nonideality shown in Fig. 8.3. Although this theory involves some background in statistical mechanics and electrostatics that is not assumed elsewhere in this book, we briefly sketch the physical assumptions and mathematical techniques leading to the Debye-Hiickel equation (8.69) to illustrate such molecular-level description of thermodynamic relationships. 

Vol. 33 G.A. Martynov, R.R. Salem, Electrical Double Layer at a Metal-dilute Electrolyte Solution Interface. VI, 170 pages. 1983. 

For a given solute, different solvents show different departures from ideal behaviour, both in terms of the concentration required to observe the onset of such deviations and in terms of their direction and magnitude. It is first necessary to specify the composition scale employed. For aqueous solutions the molality scale, moles of solute per kg of water, denoted by m, is frequently used. This scale becomes less useful when several solvents are compared, since in one kg batches of diverse solvents there are a variable number of moles of solvent (1 /[Ml kg mol 1]) and they occupy different volumes (l/[molality scale is in common use for dilute electrolyte solutions in solvents used for electrochemical purposes as it is for their aqueous solutions. However, even the change from water to heavy water, D20, requires caution in this respect, and the... 

GHz. A detailed study of the internal conductivity of erythrocytes revealed the intracellular ionic mobility to be identical with that of ions in dilute electrolyte solutions if appropriate allowance is made for internal friction with suspended macromolecules (5). Tissue conductivities near 100 or 200 MHz, sufficiently high that cell membranes do not affect tissue electrical properties, are comparable to the conductivity of blood and to somewhat similar protein suspensions in electrolytes of physiological strength. Hence, it appears that the mobility of ions in the tissue fluids is not noticeably different from their mobility in water. 

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