Properties of Electrolyte Solutions

i should be 1 for all nonelectrolytes. For strong electrolytes such as NaCl and KNO3, i should be 2, and for strong electrolytes such as Na2S04 and CaCl2, i should be 3. Consequently, the equations for colligative properties must be modified as 

Every unit of NaCl or KNO3 that cissociates yields two ions (/ = 2) every unit of Na2S04 or MgCIa that (issociates produces three ions (/ = 3). 

Tacobus Hendricus van t Hoff (1852-1911). Dutch chemist One of the most prominent chemists of his time, van t Hoff did significant work in diermodyn nics, molecular structure and optical activity, and solution chemistry. In 1901 he received the first Nobel Prize in Chemistry. 

Indicate which compound in each of the following groups has a greater tendency to form ion pairs in water (a) NaQ or Nt S04, (b) MgCl2 or MgS04, (c) LiBr or KBr. 

The osmotic pressure of a 0.010 M potassium iodide (KI) solution at 25°C is 0.465 atm. Calculate the van t Hoff factor for KI at this concentration. 

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In the last two decades experimental evidence has been gathered showing that the intrinsic properties of the electrolytes determine both bulk properties of the solution and the reactivity of the solutes at the electrodes. Examples covering various aspects of this field are given in Ref. [16]. Intrinsic properties may be described with the help of local structures caused by ion-ion, ion-solvent, and solvent-solvent interactions. An efficient description of the properties of electrolyte solutions up to salt concentrations significantly larger than 1 mol kg 1 is based on the chemical model of electrolytes. 

Fuoss, R. M. Kraus, C. A. (1933). Properties of electrolytic solutions. IV. The conductance minimum and the formation of triple ions due to the action of Coulomb forces. Journal of the American Chemical Society, 55, 2387-99. 

The parameters of molar conductivity of the electrolyte, A = a/c,, and molar conductivity of ions, Xj = ZjFuj (units S cm /mol), are also used to describe the properties of electrolyte solutions (A is used only in the case of binary solutions). With Eq. (1.14), we can write for a binary solution... 

The theory of electrolytic dissociation was not immediately recognized universally, despite the fact that it could qualitatively and quantitatively explain certain fundamental properties of electrolyte solutions. For many scientists the reasons for spontaneous dissociation of stable compounds were obscure. Thus, an energy of about 770kJ/mol is required to break up the bonds in the lattice of NaCl, and about 430kJ/mol is required to split H l bonds during the formation of hydrochloric acid solution. Yet the energy of thermal motions in these compounds is not above lOkJ/mol. It was the weak point of Arrhenius s theory that this mismatch could not be explained. 

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. 

As in the nonelectrolyte case, the problem of representing the thermodynamic properties of electrolyte solutions is best regarded as that of finding a suitable expression for the non-ideal part of the chemical potential, or the excess Gibbs energy, as a function of composition, temperature, dielectric constant and any other relevant variables. 

The second period, from 1890 to around 1920, was characterized by the idea of ionic dissociation and the equilibrium between neutral and ionic species. This model was used by Arrhenius to account for the concentration dependence of electrical conductivity and certain other properties of aqueous electrolytes. It was reinforced by the research of Van t Hoff on the colligative properties of solutions. However, the inability of ionic dissociation to explain quantitatively the properties of electrolyte solutions was soon recognized. 

King, E. J. "Acid-Base Equilibria in "The International Encyclopedia of Physical Chemistry and Chemical Physics Topic 15, Equilibrium Properties of Electrolyte Solutions" Vol. 4, Robinson, R. A., Ed., Pergamon Press, 1965 (distributed by The MacMillan Co., New York). ... 

Friedman (1962) has used the cluster theory of Mayer (1950) to derive equations which give the thermodynamic properties of electrolyte solutions as the sum of convergent series. The first term in these series is identical to and thus confirms the Debye-Huckel limiting law. The second term is an I2.nl term whose coefficient is, like the coefficient in the Debye-Huckel limiting law equation, a function of the charge type of the salt and the properties of the solvent. From this theory, as well as from others referred to above, a higher order limiting law can be written as... 

C. High-Pressure PVT Properties. Three methods are presently being used to measure the high-pressure PVT properties of electrolyte solutions volumetric methods, (26,32,106) high pressure magnetic float systems, (36,107,108) and high pressure speed of sound systems (109,110,111,112). I will not attempt to review all the modifications made to these systems. 

The long-range electrostatic term is expressed by mean spherical approximations which is a very promising method for describing the thermodynamic properties of electrolyte solutions [192,193] ... 

There are many sources of this paradoxical situation, in which a theoretical understanding lags far behind experiment in such a practically relevant area as electro-diffusion. There was a period of intense qualitative development in this area in the 1920s until the early 1950s when the modern classics of chemical physics developed the theory of electrolytic conductance and related phenomena [11]—[13]. These works were mainly concerned with the mean field approach to microscopic mechanisms determining such properties of electrolyte solutions as ion diffusivity, dielectric susceptibility, etc. in particular, they were concerned with the effects of an externally applied stationary and alternating electric field upon the above properties... 

ELECTRONEUTRALITY, If one describes the properties of electrolytic solutions in terms of ionic species, one has to take account of the fact that the concentrations of all species are not independent because the solution as a whole is neutral. 

Note that the MCT treatment presented above is quite general and can be extended to describe relaxation in many different systems, such as orientational relaxation in dipolar liquids [54]. This approach can also be extended to multicomponent systems, in particular to describe transport properties of electrolyte solutions [55]. The usefulness and the simplicity of the expressions lies in the separation between the single particle and collective dynamics (as in Eq. 98). Actually this sepration allows one to make connections with hydrodynamic (or continuum frameowrk) models where only the collective dynamics is included but the single particle motion is ignored. However, the same separation is also the reason for the failure... 

Solutions are usually classified as nonelectrolyte or electrolyte depending upon whether one or more of the components dissociates in the mixture. The two types of solutions are often treated differently. In electrolyte solutions properties like the activity coefficients and the osmotic coefficients are emphasized, with the dilute solution standard state chosen for the solute.c With nonelectrolyte solutions we often choose a Raoult s law standard state for both components, and we are more interested in the changes in the thermodynamic properties with mixing, AmjxZ. In this chapter, we will restrict our discussion to nonelectrolyte mixtures and use the change AmjxZ to help us understand the nature of the interactions that are occurring in the mixture. In the next chapter, we will describe the properties of electrolyte solutions. 

The special properties of electrolyte solutions present both advantages and disadvantages as we attempt to describe these mixtures. A disadvantage is that significant deviations from limiting law solution behavior occur at much lower concentrations for electrolyte solutes than for nonelectrolyte solutes. An advantage is that the coulombic attractions and repulsions in the electrolyte solution dominate other types of interactions. The result is that theoretical descriptions of electrolyte solutions can concentrate on the coulombic interactions. 

Chapter 18 describes electrolyte solutions that are too concentrated for the Debye-Hiickel theory to apply. Gugenheim s equations are presented and the Pitzer and Brewer tabulations, as a method for obtaining the thermodynamic properties of electrolyte solutions, are described. Next, the complete set of Pitzer s equations from which all the thermodynamic properties can be calculated, are presented. This discussion ends with an example of the extension of Pitzer s equations to high temperatures and high pressures. Three-dimensional figures show the change in the thermo-... 

The three appendices in this volume give selected sets of thermodynamic data (Appendix 5), review the statistical calculations covered in Principles and Applications (Appendix 6), and summarize the equations and parameters required to calculate the properties of electrolyte solutions, principally from Pitzer s equations (Appendix 7). 

Thermodynamic nonidealities are considered both in the transport equations (A10) and in the equilibrium relationships at the phase interface. Because electrolytes are present in the system, the liquid-phase diffusion coefficients should be corrected to account for the specific transport properties of electrolyte solutions. 

The treatment of all those properties of electrolyte solutions, where selective solvation of ions in mixed solvents may play a major role, would result in an accumulation of data hard to follow up. Therefore, only those theoretical treatments of ion solvation have been mentioned in the following whose results have been used to ... 

Marcus, Y. On the relation between thermodynamic, transport and structural properties of electrolyte solutions. Russ. J. Electrochem., 2008,44,16-27. 

Barthel, J. J. Temperature dependence of the properties of electrolyte solutions I a semi-phenomenological approach to an electrolyte theory including short range forces. Ber. Bunsen Ges. Phys. Chem. 1979, 83, 252-257. 

Attention should be drawn to the fact that there has been a degree of inconsistency in the treatments of ionic clouds (Chapter 3) and the elementary theory of ionic drift (Section 4.4.2). When the ion atmosphere was described, the central ion was considered—from a time-averaged point of view—at rest. To the extent that one seeks to interpret the equilibrium properties of electrolytic solutions, this picture of a static central ion is quite reasonable. This is because in the absence of a spatially directed field acting on the ions, the only ionic motion to be considered is random walk, the characteristic of which is that the mean distance traveled by an ion (not the mean square distance see Section 4.2.5) is zero. The central ion can therefore be considered to remain where it is, i.e., to be at rest. 

The colligative properties of electrolyte solutions are described by including the van t Hoff factor in the appropriate equation. For example, for changes in freezing and boiling points the modified equation is... 

Many properties of electrolytic solutions are additive functions of the properties of the respective ions this is at once evident from the fact that the chemical properties of a salt solution are those of its constituent ions. For example, potassium chloride in solution has no chemical reactions which are characteristic of the compound itself, but only those of potassium and chloride ions. These properties are possessed equally by almost all potassium salts and all chlorides, respectively. Similarly, the characteristic chemical properties of acids and alkalis, in aqueous solution, are those of hydrogen and hydroxyl ions, respectively. Certain physical properties of electrolytes are also additive in nature the most outstanding example is the electrical conductance at infinite dilution. It will be seen in Chap. II that conductance values can be ascribed to all ions, and the appropriate conductance of any electrolyte is equal to the sum of the values for the individual ions. The densities of electrolytic solutions have also been found to be additive functions of the properties of the constituent ions. The catalytic effects of various acids and bases, and of mixtures with their salts, can be accounted for by associating a definite catalytic coefl5.cient with each type of ion since undissociated molecules often have appreciable catalytic properties due allowance must be made for their contribution. 

The basic effects responsible for the properties of electrolyte solutions are ion solvation, ion 2issociation to ion pairs and higher ion aggregates with and without inclusion of solvent molecules. FTIR (Fourier transform infrared) and MW (microwave) spectra are a valuable source of information on ion-solvent and ion-ion interactions and yield factual knowledge on the structure and dynamics of electrolyte solutions. The efficiency of these methods is exemplified for solvation in aptotic and protic solvents, hydrophobic solvation, association to charged and neutral ion aggregates, and stability of ion pairs. 

In addition to the short-range interactions between species in all solutions, long-range electrostatic interactions are found in electrolyte solutions. The deviation from ideal solution behavior caused by these electrostatic forces is usually calculated by some variation of the Debye-Huckel theory or the mean spherical approximation (MSA). These theories do not include terms for the short-range attractive and repulsive forces in the mixtures and are therefore usually combined with activity coefficient models or equations of state in order to describe the properties of electrolyte solutions. 

Abstract Analytical solution of the associative mean spherical approximation (AMSA) and the modified version of the mean spherical approximation - the mass action law (MSA-MAL) approach for ion and ion-dipole models are used to revise the concept of ion association in the theory of electrolyte solutions. In the considered approach in contrast to the traditional one both free and associated ion electrostatic contributions are taken into account and therefore the revised version of ion association concept is correct for weak and strong regimes of ion association. It is shown that AMSA theory is more preferable for the description of thermodynamic properties while the modified version of the MSA-MAL theory is more useful for the description of electrical properties. The capabilities of the developed approaches are illustrated by the description of thermodynamic and transport properties of electrolyte solutions in weakly polar solvents. The proposed theory is applied to explain the anomalous properties of electrical double layer in a low temperature region and for the treatment of the effect of electrolyte on the rate of intramolecular electron transfer. The revised concept of ion association is also used to describe the concentration dependence of dielectric constant in electrolyte solutions. 

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