Reciprocal ionic solution

Let us now consider a slightly more complex system, the system AC-BD. The ideal configurational entropy of a system like this that contains two cations A+ andB+ and two anions C and D- is readily derived as 

With Amix//m = 0 the ideal Temkin model for ionic solutions [13] is obtained. If deviations from ideality are observed, a regular solution expression for this mixture that contains two species on each of the two sub-lattices can be derived using the general procedures already discussed. The internal energy is again calculated 

The regular solution parameters are still assumed to be enthalpic in nature. In other words, the vibrational entropy is, as earlier, considered not to be affected by the mixing. The last term of eq. (9.83), the configurational entropy, is also unaffected by this modification. 

In the case of reciprocal systems, the modelling of the solution can be simplified to some degree. The partial molar Gibbs energy of mixing of a neutral component, for example AC, is obtained by differentiation with respect to the number of AC neutral entities. In general, the partial derivative of any thermodynamic function Y for a component AaCc is given by 

Using AC as an example, the chemical potential relative to the standard state (pure AC) can be shown to be 

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Figure I. The limiting ionic conductance-solvent viscosity product plotted as a function of the reciprocal ionic radii for several ions in aqueous and acetonitrile solutions at 25 C,...

Fig. 4. Splitting V4-V1 [cnr ] of monodentate perchlorate (top) and average number of uncoordinated perchlorate ions per R(III) ions, (bottom), in R(C104)3 solutions 0.05 M in anhydrous acetonitrile vs. the reciprocal ionic radii for CN = 9 (Biinzli and Kaspaiek 1991).

Fig. 11. Average coordination numbers of R(III) ions in 0.05 M R(N03)3 solutions in acetonitrile containing DMSO vs. reciprocal ionic radii (for CN = 9) / bmso [DMSO],/ [R(III], (Biinzli et al. 1990).

Fig. 12. Average coordination numbers of the R(III) ions in solutions of R(CI04)3-nDMS0 0.05 M in anhydrous acetonitrile vs. the reciprocal ionic radii forCN = 8 / DMSo = IPMSO],/[R(III], (Milicic-Tang and Biinzli 1992).

From this equation, the equilibrium volume swelling ratio, Q, i.e. the reciprocal of ds.s, can be expressed in terms of all the crosslinked structure and ionic solution... 

It was found earlier by experiment and theory that the viscosity intrinsic of polyelectrolyte solutions is nearly linear with the reciprocal square root of the ionic strength over a certain range, such as... 

The most important non-faradaic methods are conductometric analysis and (normal) potentiometric analysis in the former we have to deal essentially with the ionics and in the latter mainly with the electrodics. Strictly, one should assign a separate position to high-frequency analysis, where not so much the ionic conductance but rather the dielectric and/or diamagnetic properties of the solution are playing a role. Nevertheless, we shall still consider this techniques as a special form of conductometry, because the capacitive and inductive properties of the solution show up versus high-frequency as a kind of AC resistance (impedance) and, therefore, as far as its reciprocal is concerned, as a kind of AC conductance. 

A measurement of the ability of a buffer system to limit the change in pH of a solution upon the addition of an increment of strong base. ft is the reciprocal of the slope of the pH-neutralization curve. Consider the simple equilibrium, HA H+ -h A where K = [H+][A ]/ [HA] in which K is a practical dissociation constant determined under conditions of constant ionic strength. In such systems the practical pK is equal to the pH of solution when there are equal concentrations of the two buffer species. Since the total concentration of the two... 

From this equation it is evident that the mobility ulon of an ionic species is directly proportional to the ratio of charge to radius qlr and reciprocal to the viscosity 17 of the solution. Thus, small, highly charged ions have high mobilities, whereas large, less charged species have low mobilities. 

Impedance is a function of conductance, capacitance, and applied frequency (32). Conductance is the reciprocal of resistance, so when resistance increases, conductance decreases. An increase in the number of charged compounds, especially smaller mobile ones that easily carry a charge, results in an increase in conductance or a decrease in the resistance of current flow through a solution. When metabolism alters slightly ionic compounds, such as lactose, to higher... 

Considering these different limiting forms of the recombination term an Important tentative conclusion emerges the concentration dependence of the reciprocal relaxation time is a direct measure of the main ionic recombination process and yields therefore information on the ionic species present in solution. A linear dependence on total ion-pair concentration would therefore indicate unilateral triple ion formation or, if both kinds of triple ions are present as indicated by conductance, a sufficient difference in their stability. At this point it should be noted that the usual method of Fuoss and Draus... 

Experimentally all the limiting cases of the recombination term are encountered in all systems investigated up to now. In solutions of tetraalkylammonium salts in benzene the reciprocal relaxation time is even dependent on the square of total concentration (but here the quadrupoles may be comparable in concentration with ion-pairs) which would indicated a preponderance of quintuple and triple ions in the ionic recombination. 

The area per molecule as which appears in the preceding equation is evaluated at a distance d from the surface in contact with water and is curvature dependent. Expressions for ag are given by eq 7.15. The distance <5 is estimated as the distance from the surface in contact with water to the surface where the center of the counterion is located. k is the reciprocal Debye length, na is the number of counterions in solution per cubic centimeter, Cuon is the molar concentration of the singly dispersed ionic surfactant molecules in water, Cadd is the molar concentration of the salt added to the surfactant solution, andA Av is Avogadro s number. The last term in the right-hand side of eq 7.17 provides a curvature correction to the ionic interaction energy. For normal droplets, Cg = 2/(7 w + d) for reverse droplets, Cg = —2/(7 w — <5) and for flat layers, Cg = 0. 

Conductivity, Electrical Conductometry and Conductometric Titrations. Electrical conductivity is thequality or ability of a substance to transmit electrical energy. If it deals with the conductivity of an electrolyte in solution, it is then called electrolytic conductivity. Conductometry deals with analyses by measuring electrolytic conductivity, based on the fact that ionic substances in many solvents conduct electricity. Conductometric titrations are quantative analysis based on the fact that with the addn of the titrating agent to a soln being titrated, the specific conductivity (reciprocal of specific resistance in mhos) changes at a different rate before and after the end point (Comp with Potentiometric Analysis) Refs 1 )Kirk Othmer 4 (L 949), 325-33 (Conductometry) 2)W.G.Berl, Edit, "Physical Methods... 

Partial molar entropies of ions can, for example, be calculated assuming S (H+) = 0. Alternatively, because K+ and Cl ions are isoelectronic and have similar radii, the ionic properties of these ions in solution can be equated, e.g. analysis of B-viscosity coefficients (Gurney, 1953). In other cases, a particular theoretical treatment which relates solvation parameters to ionic radii indicates how the subdivision could be made. For example, the Bom equation requires that AGf (ion) be proportional to the reciprocal of the ionic radius (Friedman and Krishnan, 1973b). However, this approach involves new problems associated with the definition of ionic radius (Stem and Amis, 1959). In another approach to this problem, the properties of a series of salts in solution are plotted in such a way that the value for a common ion is obtained as the intercept. For example, when the partial molar volumes of some alkylammonium iodides, V (R4N+I ) in water (Millero, 1971) are plotted against the relative molecular mass of the cation, M+, the intercept at M + = 0 is equated to Ve (I-) (Conway et al., 1966). This procedure has been used to... 

Defined as the reciprocal of resistance (siemens, ft-1) conductance is a measure of ionic mobility in solution when the ions are subjected to a potential gradient. The equivalent conductance A of an ion is defined as the conductance of a solution of unspecified volume containing one gram-equivalent and measured between electrodes I cm apart. Due to interionic effects, A is concentration dependent, and the value, A0, at infinite dilution is used for comparison purposes. The magnitude of A0 is determined by the charge, size and degree of hydration of the ion values for a number of cations and anions at 298.15K are given in table 6.6. It should be noted that HjO and... 

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