Dilution, electrolytes

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)... 

In concentrated electrolytes the electric current appHed to a stack is limited by economic considerations, the higher the current I the greater the power consumption W in accordance with the equation W = P where is the electrical resistance of the stack. In relatively dilute electrolytes the electric current that can be appHed is limited by the abflity of ions to diffuse to the membranes. This is illustrated in Eigure 4 for the case of an AX membrane. When a direct current is passed, a fraction (t 0.85-0.95) is carried by anions passing out of the membrane—solution interface region and... 

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

Our final focus in this review is on charged quenched-annealed fluid systems. Very recently Bratko, Chakraborty and Chandler have addressed this problem [34-36]. A set of grand canonical computer simulation results for infinitely diluted electrolyte adsorbed in an electroneutral matrix of ions has been presented and an attempt to describe them at the level of... 

The hardness of the film is markedly affected by the conditions of anodising. By means of special methods involving dilute electrolytes at low temperatures and relatively high voltages , with or without superimposed alternating current, it is possible to produce compact abrasion-resistant films with thicknesses of 50-75/im and hardnesses of 200-500 VPN, for special applications. 

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. 

They concluded, thereby, that Ag2Te formation is governed by the initial amount of silver deposit. It is worth noting that the present method, involving dilute electrolytic baths of the compound precursors, deviates from the typical, initially proposed by Panicker et al., method of employing high concentration ratios of the metal to the chalcogen precursor. 

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. 

In addition, the effect of ionic screening was analyzed [89] using Eqs. (67). The ionic concentrations considered (1.0 M, 0.1 M, 0.01 M) correspond to Debye lengths Ijj = 0.3,1 and 3 nm. The results for /o = 3 nm, the most dilute electrolyte, where ionic screening is least effective, are presented in Table 3. 

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. 

The first satisfactory explanation of these effects was given, in the twenties, by Debye, Hiickel, Onsager, and Falkenhagen (see, for instance, Ref. 8). Using a remarkably clever combination of microscopic and macroscopic concepts, they were able to describe the behavior of dilute electrolytes by the famous limiting laws . 

It is remarkable that Eq. (124) itself tells us that the approximation (122) is not rigorous indeed, the superposition principle of electrostatics indicates that the potential due to a system of charges has to be given by the sum of the potentials created by each single charge this is not the case for Eq. (124). However, if we limit ourselves to the simple case of a dilute electrolyte, we... 

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 ... 

This completes our macroscopic description of the limiting conductance in dilute electrolytes. 

While these two approximations are heuristic, the cases treated in Sections V-C and V-E correspond to well defined mathematical limiting procedures. In both models, one considers a dilute electrolyte (see Eq. (393)) with heavy ions (see Eq. (394)) the difference lies in the relation connecting these two limits. The small friction case, Eq. (395), corresponds to the plasma-dynamic model (Eq. (361)) ... 

The use of surface charge to provide colloid stability to particles dispersed in dilute electrolytes in aqueous solution, or even in media of intermediate polarity, is an effective means of stabilising particles against van der Waals forces of attraction. Figure 3.16 shows typical potential... 

It should be noted that the local composition model is not consistent with the commonly accepted solvation theory. According to the solvation theory, ionic species are completely solvated by solvent molecules. In other words, the local mole fraction of solvent molecules around a central ion is unity. This becomes unrealistic when applied to high concentration electrolyte systems since the number of solvent molecules will be insufficient to completely solvate ions. With the local composition model, all ions are, effectively, completely surrounded by solvent molecules in dilute electrolyte systems and only partially surrounded by solvent molecules in high concentration electrolyte systems. Therefore, the local composition model is believed to be closer to the physical reality than the solvation theory. 

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