Electrolytes, solution theory

Among other applications of electrolyte solution theory to defect problems should be mentioned the application of the Debye-Hiickel activity coefficients by Harvey32 to impurity ionization problems in elemental semiconductors. Recent reviews by Anderson7 and by Lawson45 emphasizing the importance of Debye-Hiickel effects in oxide semiconductors and in doped silver halides, respectively, and the book by Kroger41 contain accounts of other applications to defect problems. However, additional quantum-mechanical problems arise in the treatment of semiconductor systems and we shall not mention them further, although the studies described below are relevant to them in certain aspects. 

Two chapters are devoted to silicate melts. One is an introduction to petro-genetic diagrams, extensively treated in petrology. Aqueous solutions are covered in a single chapter that basically deals with electrolyte solution theory and its applications, since any further subdivision seemed unnecessary. A single chapter was deemed sufficient to describe the up-to-date information about gases. The decision not to treat chemistry and equilibria in the earth s atmosphere was dic-... 

Support for that portion of this work dealing with electrolyte solution theory has been provided to J.E. by the National Science Foundation (CBT-8811789) and by a grant of Cray X-MP time at the National Center for Supercomputing Applications. The authors wish to express appreciation for assistance provided by Nr. John Potter with the development of computer software used in the production of a movie of a nucleation event shown at this symposium. 

Duer W. C., Leung W. H., Oglesby G. B., and Millero F. J. (1976) Seawater. A test for multicomponent electrolyte solution theories II. Enthalpy of mixing and dilution of the major sea salts. J. Solut. Chem. 5, 509—528. 

In 1923 Peter Debye and Erich HUckel published two remarkable papers that described an a priori method of calculating the activity coefficient of electrolytic solutes in dilute solution. Without doubt this was one of the major breakthroughs in electrolyte solution theory. 

Karraker, K.A. and Radke, C.J., Disjoining pressures, zeta potentials and surface tensions of aqueous non ionic surfactant electrolyte solutions theory and comparison to experiment, Adv. Colloid Inter/. Sci., 96, 231-264, 2002. 

Yang, J.Z. (2005). Medium effect of an organic solvent on the activity coefficients of HCl consistent with Pitzer s electrolyte solution theory, /. Solution Chem, Vol. 1, No. 1, pp. 71-76, ISSN 0095-9782... 

Ionic transport properties like ion mobilities and the related conductivities and diffusion coefficients Di are measurable quantities that permit the development of helpful concepts of electrolyte solution theories. At dilute and moderate concentrations, the models in use are very satisfying, whereas at high concentrations they still... 

Covington, A.K. and Ferra, M.I.A., 1994, A Pitzer mixed electrolyte solution theory approach to assignment pH to standard buffer solutions, J. Solution Chem., 23, 1. 

A probable cause for this variation in A is that the electrolyte solution theory used to calculate electrical potentials in the double layer is only valid for dilute solutions of monovalent ions. Whereas, in this study, the ionic concentrations were high and divalent ions were also used. An approach which partially compensates for this deficiency in the electrolyte theory is the introduction of a Stern layer of adsorbed counterions at the particle/solution interface. These counterions void a portion of the charges due to the surfactant. 

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]. 

The situation for electrolyte solutions is more complex theory confimis the limiting expressions (originally from Debye-Htickel theory), but, because of the long-range interactions, the resulting equations are non-analytic rather than simple power series.) It is evident that electrolyte solutions are ideally dilute only at extremely low concentrations. Further details about these activity coefficients will be found in other articles. 

Outhwaite C W 1974 Equilibrium theories of electrolyte solutions Specialist Periodical Report (London Chemical Society)... 

Rasaiah J C 1987 Theories of electrolyte solutions The Liquid State and its Electrical Properties (NATO Advanced Science Institute Series Vol 193) ed E E Kunhardt, L G Christophous and L H Luessen (New York Plenum)... 

Wlien describing the interactions between two charged flat plates in an electrolyte solution, equation (C2.6.6) cannot be solved analytically, so in the general case a numerical solution will have to be used. Several equations are available, however, to describe the behaviour in a number of limiting cases (see [41] for a detailed discussion). Here we present two limiting cases for the interactions between two charged spheres, surrounded by their counterions and added electrolyte, which will be referred to in further sections. This pair interaction is always repulsive in the theory discussed here. 

Huckel was a German physi cal chemist Before his theo retical studies of aromaticity Huckel collaborated with Peter Debye in developing what remains the most widely accepted theory of electrolyte solutions... 

A finite time is required to reestabUsh the ion atmosphere at any new location. Thus the ion atmosphere produces a drag on the ions in motion and restricts their freedom of movement. This is termed a relaxation effect. When a negative ion moves under the influence of an electric field, it travels against the flow of positive ions and solvent moving in the opposite direction. This is termed an electrophoretic effect. The Debye-Huckel theory combines both effects to calculate the behavior of electrolytes. The theory predicts the behavior of dilute (<0.05 molal) solutions but does not portray accurately the behavior of concentrated solutions found in practical batteries. 

SFA has been traditionally used to measure the forces between modified mica surfaces. Before the JKR theory was developed, Israelachvili and Tabor [57] measured the force versus distance (F vs. d) profile and pull-off force (Pf) between steric acid monolayers assembled on mica surfaces. The authors calculated the surface energy of these monolayers from the Hamaker constant determined from the F versus d data. In a later paper on the measurement of forces between surfaces immersed in a variety of electrolytic solutions, Israelachvili [93] reported that the interfacial energies in aqueous electrolytes varies over a wide range (0.01-10 mJ/m-). In this work Israelachvili found that the adhesion energies depended on pH, type of cation, and the crystallographic orientation of mica. 

A. L. Kholodenko, A. L. Beyerlein. Theory of symmetric electrolyte solutions Field theoretic approach. Phys Rev A 54 3309-3324, 1986. 

Recent developments of the chemical model of electrolyte solutions permit the extension of the validity range of transport equations up to high concentrations (c 1 mol L"1) and permit the representation of the conductivity maximum Knm in the framework of the mean spherical approximation (MSA) theory with the help of association constant KA and ionic distance parameter a, see Ref. [87] and the literature quoted there in. 

Calculation of the Thermodynamic Properties of Strong Electrolyte Solutes The Debye-Hiickel Theory... 

Equation (7.45) is a limiting law expression for 7 , the activity coefficient of the solute. Debye-Htickel theory can also be used to obtain limiting-law expressions for the activity a of the solvent. This is usually done by expressing a in terms of the practical osmotic coefficient

electrolyte solute, it is defined in a general way as... 

Chapters 7 to 9 apply the thermodynamic relationships to mixtures, to phase equilibria, and to chemical equilibrium. In Chapter 7, both nonelectrolyte and electrolyte solutions are described, including the properties of ideal mixtures. The Debye-Hiickel theory is developed and applied to the electrolyte solutions. Thermal properties and osmotic pressure are also described. In Chapter 8, the principles of phase equilibria of pure substances and of mixtures are presented. The phase rule, Clapeyron equation, and phase diagrams are used extensively in the description of representative systems. Chapter 9 uses thermodynamics to describe chemical equilibrium. The equilibrium constant and its relationship to pressure, temperature, and activity is developed, as are the basic equations that apply to electrochemical cells. Examples are given that demonstrate the use of thermodynamics in predicting equilibrium conditions and cell voltages. 

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