Ionic equivalent conductivity, defined

Debye length (3.1.10b), mean free path of a gas molecule (3.1.114), filter coefficient (7.2.187), parameter for a dialyzer (8.1.399), parameter for a distillation plate/stage (8.3.38), latent heat of vaporization/condensation molecular conformation coordinate (3.3.89c) electrode spacings (7.3.18) retention parameter for species i (7.3.213), ionic equivalent conductance of ion i (3.1.108r) value of Xi for a cation value of A, for an anion value of A, at infinite dilution (Table 3.A.8) defined by (5.4.100) equivalent conductance of a salt (an electrolyte) (3.1.108s)... 

Conductometric titrations. Van Meurs and Dahmen25-30,31 showed that these titrations are theoretically of great value in understanding the ionics in non-aqueous solutions (see pp. 250-251) in practice they are of limited application compared with the more selective potentiometric titrations, as a consequence of the low mobilities and the mutually less different equivalent conductivities of the ions in the media concerned. The latter statement is illustrated by Table 4.7108, giving the equivalent conductivities at infinite dilution at 25° C of the H ion and of the other ions (see also Table 2.2 for aqueous solutions). However, in practice conductometric titrations can still be useful, e.g., (i) when a Lewis acid-base titration does not foresee a well defined potential jump at an indicator electrode, or (ii) when precipitations on the indicator electrode hamper its potentiometric functioning. 

The quantity lOOOac is the concentration of A ions (and also of B ions) in mol m 9 = N e is the Faraday constant (96485.31 C equiv ), and C/, is the ionic mobility of charged species i. Note that the mobility is defined as the migration speed of an ion under the influence of unit potential gradient and hence has the units m s V. It is now convenient to define a new quantity, the equivalent conductance A, by... 

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... 

It would be awkward to have to refer to the concentration every time one wished to state the value of the equivalent conductivity of an electrolyte. One should be able to define some reference value for the equivalent conductivity. Here, the facts of the experimental variation of equivalent conductivity with concentration come to one s aid as the electrolytic solution is made more dilute, the equivalent conductivity approaches a limiting value (Fig. 4.57). This limiting value should form an excellent basis for comparing the conducting powers of different electrolytes, for it is the only value in which the effects of ionic concentration are removed. The limiting value will be called the equivalent conductivity at infinite dilution, designated by the symbol /1° (Table 4.12). 

Determination of the Degree of Dissociation.—The determination of the degree of dissociation involves the evaluation of the quantity A at the given concentration, as defined by equation (44) as seen previously, A is the equivalent conductance the electrolyte would have if the solute were completely dissociated at the same ionic concentration as in the experimental solution. Since the definition of A involves a, whereas A is required in order to calculate a, it is evident that the former quantity can be obtained only as the result of a series of approximations. Two of the methods that have been used will be described here. 

In order to test the reliability of equation (99) it is necessary to know the value of the degree of dissociation at various concentrations of the electrolyte MA in his classical studies of dissociation constants Ostwald, following Arrhenius, assumed that a at a given concentration was equal to the conductance ratio A/Ao, where A is the equivalent conductance of the electrolyte at that concentration and Ao is the value at infinite dilution. As already seen (p. 95), this is approximately true for weak electrolytes, but it is more correct, for electrolytes of all types, to define a as A/A where A is the conductance of 1 equiv. of free ions at the same ionic concentration as in the given solution. It follows therefore, by substituting this value of a in equation (95), that... 

Conductivity measurements only define the sum of the equivalent ionic conductances no information about their individual values can be derived. However, it is known that the equivalent conductances of ions may differ significantly. According to Kohlrausch s law of independent ion drift, all ions move independent of each other in an infinitely diluted solution. Since the equivalent conductances of ions differ, they contribute differently to the current transport. The contribution of an ionic species i to the total current is called the transport number... 

The above theory can also be applied to account for the concentration dependence of transport numbers, especially in dilute solutions. Since the transport number can be defined as a ratio of the equivalent conductance of the given ion to the total ionic conductance (equation (6.7.6)), it is clear that a non-linear relationship can be derived describing the concentration dependence using equations (6.9.23) and (6.9.24). 

With these equations we may define the ionic and solution equivalent conductivities Ai, Ap, and A. 

For solutions of simple, pure electrolytes (i.e., one positive and one negative ionic species), such as KCl, CaCl2, and HNO3, conductance is often quantified in terms of the equivalent conductivity. A, which is defined by... 

Electrolyte conductivity depends on three factors the ion charges, mobilities, and concentrations of ionic species present. First, the number of electrons each ion carries is important, because A, for example, carries twice as much charge as A . Second, the speed with which each ion can travel is termed its mobility. The mobility of an ion is the limiting velocity of the ion in an electric field of unit strength. Factors that affect the mobility of the ion include (1) the solvent (e.g., water or organic), (2) the applied voltage, (3) the size of the ion (the larger it is, the less mobile it will be), and (4) the nature of the ion (if it becomes hydrated, its effective size is increased). The mobility is also affected by the viscosity and temperature of the solvent. Under standard conditions the mobility is a reproducible physical property of the ion. Because in electrolytes the ion concentration is an important variable, it is usual to relate the electrolytic conductivity to equivalent conductivity. This is defined by... 

Conductivities have units of ohm m Resistivities or conductivities are extremely easy to measure experimentally using modern electrical equipment. However, as one might expect, they are quite variable because p would depend not only on the charge on the ions but on the concentration of the solution. It is better to define a quantity that takes these factors into account. The equivalent conductance of an ionic solute, A, is defined as... 

The equivalent conductance of a solution is a convenient chemical quantity. It is defined as the hypothetical conductance of one chemical equivalent of a dissolved substance A = a iV ixe, where a is the fraction of the dissolved substance (solute) in the ionic form, and iV , A, and e are, respectively, Avogadro s number, the ionic mobility, and the elementary charge. The equivalent conductance is related to the conductance a = /xe hy the relation A = 1000 a/c, where c is the solute concentration in moles per liter. With solvents of dielectric constant greater than 30, solutions of simple electrolytes generally may be expectd to be fully ionized at all concentrations, i.e., a = 1. Upon dilution of concentrated solutions in which the mobility of the ions is reduced by interionic forces, the variation of A with concentration follows the general limiting law ... 

Under the prerequisite that the cell constant and the equivalent ionic conductances of eluent anions and eluent cations are known, Eq. (181) makes it possible to calculate the conductivity of typical eluents for this kind of detection method. To determine the cell constant, the conductance of a potassium chloride solution with defined concentration is usually measured, as the equivalent ionic conductances of potassium and chloride ions are known with 74 S cm2 vaf1 and 76 S cm2 val-1, respectively (see Table 6-1). 

We normally define the energy level of electrons in a solid in terms of the Fermi level, eF, which is essentially equivalent to the electrochemical potential of electrons in the solid. In the case of metals, the Fermi level is equal to the highest occupied level of electrons in the partially filled frontier band. In the case of semiconductors of covalent and ionic solids, by contrast, the Fermi level is situated within the band gap where no electron levels are available except for localized ones. A semiconductor is either n-type or p-type, depending on its impurities and lattice defects. For n-type semiconductors, the Fermi level is located close to the conduction band edge, while it is located close to the valence band edge for p-type semiconductors. For examples, a zinc oxide containing indium as donor impurities is an n-type semiconductor, and a nickel oxide containing nickel ion vacancies, which accept electrons, makes a p-type semiconductor. In semiconductors, impurities and lattice defects that donate electrons introduce freely mobile electrons in the conduction band, and those that accept electrons leave mobile holes (electron vacancies) in the valence band. Both the conduction band electrons and the valence band holes contribute to electronic conduction in semiconductors. 

This observation suggests that the ionic transport can be related to the defect energy, which is defined by the interaction between the acceptors and oxygen sublattice. This interaction results in the barrier for ion hopping between equivalent positions in the lattice. Therefore, there has been considerable effort to optimize the ionic conductivity of stabilized zirconia by controlling the acceptors concentration and their size [1, 3]. 

Using the defined complex PdCl2[P(OPh)3]2 as a catalyst, alkynones were produced in low to moderate yields at 1 bar of CO (Scheme 5.15). When the reaction was conducted in an ionic liquid, the catalyst could be reused in four consecutive catalytic runs with high activity. Notably, benzyl bromide was reported as a substrate for the first time, but 2 equivalents of acetylenes were required for this system. 

Recent recommendations on units and symbols define the mobility of an ion, u, as its velocity under unit potential gradient. Most writers in the past, however, have used the term as a convenient synonym for the equivalent ionic conductivity, A. The relation between the two is Ai = Fui, and this should be remembered when consulting the literature. 

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