Electrolyte solution, calculation

Another valuable quality test for electrolyte solution calculations is based upon the zeroth and second moment conditions of Stillinger and Lovett. To apply these conditions, the first of which is equivalent to the requirement of local electroneutralitywe define the zeroth and second moment defects for an ion of species a as follows ... 

Sorensen, T.S. and Sloth, P., Ion and potential distribution in charged and non-charged primitive spherical pores in equilibrium with primitive electrolyte solution calculated by grand canonical ensemble Monte Carlo simulation, J. Chem. Soc. Faraday Trans., 88 (4), 571-589, 1992. 

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]. 

Rasaiah J C, Card D N and Valleau J 1972 Calculations on the restricted primitive model for 1-1-electrolyte solutions J. Chem. Phys. 56 248... 

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. 

Although ED is more complex than other membrane separation processes, the characteristic performance of a cell is, in principle, possible to calculate from a knowledge of ED cell geometry and the electrochemical properties of the membranes and the electrolyte solution. 

Most of the methods we have described so far give the activity of the solvent. Often the activity of the solute is of equal or greater importance. This is especially true of electrolyte solutions where the activity of the ionic solute is of primary interest, and in Chapter 9, we will describe methods that employ electrochemical cells to obtain ionic activities directly. We will conclude this chapter with a discussion of methods based on the Gibbs-Duhem equation that allow one to calculate activities of one component if the activities of the other are known as a function of composition. 

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

Vitanov and Popov et al.156 660-662 have studied Cd(0001) electrolyti-cally grown in a Teflon capillary in an aqueous surface-inactive electrolyte solution. The E is independent of ce) and v. The capacity dispersion is less than 5%, and the electrode resistance dispersion is less than 3%. The adsorption of halides increases in the order Cl" < Br" < I".661 A comparison with other electrodes shows an increase in adsorption in the sequence Cd(0001) < pc-Cd < Ag( 100) < Ag(l 11). A linear Parsons-Zobel plot with /pz = 1.09 has been found at a = 0. A slight dependence has been found for the Cit a curves on ce, ( 5%) in the entire region of a. Theoretical C, E curves have been calculated according to the GCSG model. 

Nucleation Consider an idealized spherical nucleus of a gas with the radius on the surface of an electrode immersed in an electrolyte solution. Because of the small size of the nucleus, the chemical potential, of the gas in it will be higher than that ( To) in a sufficiently large phase volume of the same gas. Let us calculate this quantity. 

The beginning of the twentieth century also marked a continuation of studies of the structure and properties of electrolyte solution and of the electrode-electrolyte interface. In 1907, Gilbert Newton Lewis (1875-1946) introduced the notion of thermodynamic activity, which proved to be extremally valuable for the description of properties of solutions of strong electrolytes. In 1923, Peter Debye (1884-1966 Nobel prize, 1936) and Erich Hiickel (1896-1981) developed their theory of strong electrolyte solutions, which for the first time allowed calculation of a hitherto purely empiric parameter—the mean activity coefficients of ions in solutions. 

Le Hung presented a general theoretical approach for calculating the Galvani potential Ajyj at the interface of two immiscible electrolyte solutions, e.g., aqueous (w) and organic solvent (s) [25]. Le Hung s approach allows the calculation of when the initial concentration (Cj), activity coefficients (j/,) and standard energies of transfer of ions (AjG ) are known in both solutions. 

The above equation allows the calculation of Galvani potentials at the interfaces of immiscible electrolyte solutions in the presence of any number of ions with any valence, also including the cases of association or complexing in one of the phases. Makrlik [26] described the cases of association and formation of complexes with participation of one of the ions but in both phases. In a later work [27] Le Hung extended his approach and also considered any mutual interaction of ions and molecules present in both phases. Buck and Vanysek performed the detailed analysis of various practical cases, including membrane equilibria, of multi-ion distribution potential equations [28,29]. 

It would be desirable to extend this model to electrolyte solutions, but it is extremely difficult to calculate a free-energy functional that accounts for the presence of ions. 

The Leclanche cell (also known as the dry cell) is frequently used to power flashlights, watches, calculators, and a number of other portable devices. Despite the name dry cell, this battery does contain an electrolyte solution but only in the form of dense paste. There are two versions of this cell, the acid version and the alkaline version. 

Activity coefficient models offer an alternative approach to equations of state for the calculation of fugacities in liquid solutions (Prausnitz ct al. 1986 Tas-sios, 1993). These models are also mechanistic and contain adjustable parameters to enhance their correlational ability. The parameters are estimated by matching the thermodynamic model to available equilibrium data. In this chapter, vve consider the estimation of parameters in activity coefficient models for electrolyte and non-electrolyte solutions. 

We consider Pitzer s model for the calculation of activity coefficients in aqueous electrolyte solutions (Pitzer, 1991). It is the most widely used thermodynamic model for electrolyte solutions. 

---