Equivalent conductance electrical

There are many compounds which do not conduct electricity when solid or fused indicating that the bonding is neither metallic nor ionic. Lewis, in 1916. suggested that in such cases bonding resulted from a sharing of electrons. In the formation of methane CH4 for example, carbon, electronic configuration l.s 2.s 2p. uses the tour electrons in the second quantum level to form four equivalent... 

The specific heat of aqueous solutions of hydrogen chloride decreases with acid concentration (Fig. 4). The electrical conductivity of aqueous hydrogen chloride increases with temperature. Equivalent conductivity of these solutions ate summarized in Table 8. Other physicochemical data related to... 

It has already been mentioned that in an aqueous solution of KC1 at a concentration of 3.20 X 10-6 mole per liter, the equivalent conductivity was found to have a value, 149.37, that differed appreciably from the value obtained by the extrapolation of a series of measurements to infinite dilution. We may say that, even in this very dilute solution, each ion, in the absence of an electric field, does not execute a random motion that is independent of the presence of other ions the random motion of any ion is somewhat influenced by the forces of attraction and repulsion of other ions that happen to be in its vicinity. At the same time, this distortion of the random motion affects not only the electrical conductivity but also the rate of diffusion of the solute, if this were measured in a solution of this concentration. 

Consider now the observed values of the equivalent conductivity for the various species of ions given in Table 2 [disregarding the ions (OH)-and H+, which need special consideration]. If we ask, from this point of view, why such a wide variety of values is found, this must be ascribed to the wide variety in the character of the random motion executed by different species of ions in the absence of an electric field. We shall not go into the details of Einstein s theory of the Brownian motion but the liveliness of the motion for any species of particle may be expressed by assigning a value to a certain parameter for a charged particle in an... 

The electrical conduction in a solution, which is expressed in terms of the electric charge passing across a certain section of the solution per second, depends on (i) the number of ions in the solution (ii) the charge on each ion (which is a multiple of the electronic charge) and (iii) the velocity of the ions under the applied field. When equivalent conductances are considered at infinite dilution, the effects of the first and second factors become equal for all solutions. However, the velocities of the ions, which depend on their size and the viscosity of the solution, may be different. For each ion, the ionic conductance has a constant value at a fixed temperature and is the same no matter of which electrolytes it constitutes a part. It is expressed in ohnT1 cm-2 and is directly proportional to the mobilities or speeds of the ions. If for a uni-univalent electrolyte the ionic mobilities of the cations and anions are denoted, respectively, by U+ and U, the following relationships hold ... 

Arrhenius postulated in 1887 that an appreciable fraction of electrolyte in water dissociates to free ions, which are responsible for the electrical conductance of its aqueous solution. Later Kohlrausch plotted the equivalent conductivities of an electrolyte at a constant temperature against the square root of its concentration he found a slow linear increase of A with increasing dilution for so-called strong electrolytes (salts), but a tangential increase for weak electrolytes (weak acids and bases). Hence the equivalent conductivity of an electrolyte reaches a limiting value at infinite dilution, defined as... 

Fig. 2.8 The Wien effect shown by the percentage increase of equivalent conductivity in dependence on the electric field in Li3Fe(CN)6 solutions in water. Concentrations in mmol dm-3 are indicated at each curve... 

Among the two-terminal devices that can be imagined for UE [capacitors, inductors, rectifiers, negative differential resistance (NDR) devices], the simplest is a molecular wire, that is, a molecule capable of conducting electricity a nanoconductor or, equivalently, a nanoresistor. Even the most conductive of molecular wires has a minimum resistance. 

While salt is entering the membrane its electrical resistance falls progressively. If the equivalent conductance A of the salt in the membrane may be regarded as constant, which is consistent with the equilibrium conductance data to be discussed later, integration of the local resistance across the thickness of the membrane leads to... 

Fig. 10.15 Conductance per ion pair of metal-ammonia solutions. The ratio of electrical conductivity to the concentration of metal (equivalent conductance) is shown as a function of concentration. O represent data of Kraus (1921) and data of Dye et al. (I960), both at 240 K and in Na-NH3 solutions. + and x represent the equivalent conductances assigned to positive and negative carriers respectively by Dye on the basis of transference-number measurements. From Cohen and Thompson (1968).

Lower Conductivity. The equivalent conductance of nonaqueous solutions a( infinite dilution is often comparable to that of aqueous systems, but it decreases with an increase in concentration more rapidly than the corresponding aqueous systems (the effect of the lower dielectric constant). Since the specific conductivity, K (that which determines the resistance between cathode and anode) is proportional to Ac, the equivalent conductance, the IR drop between the electrodes of a cell in which deposition from nonaqueous solutions is to lake place will be greater than that in aqueous solution (see Section 4.8.7). The electricity needed to deposit a given mass of metal is proportional to the total E between the electrodes, and this includes the IR between the electrodes, which is much greater in the nonaqueous than in the aqueous cases. Hence, nonaqueous deposition will be more costly in electricity (more kilowatt hours per unit of weight deposited) than a corresponding deposition in aqueous solution. The difference may be prohibitive. 

The triple ion formation can be checked by the electric conductivity data. In Fig. 12, the equivalent conductance (A) is given as a function... 

Electrolytes, depending upon their strength, dissociate to a greater or less extenl in polar solvents. The extent to which a weak electrolyte dissociates may be determined by electrical conductance, electromotive force, and freezing point depression methods. The electrical conductance method is the most used because of its accuracy and simplicity. Arrhenius proposed that the degree of dissociation, a. of a weak electrolyte at any concentration in solution could be found from the rutio of the equivalent conductance. A. of the electrolyte at the concentration in question to (he equivalent conductance at infinite dilution A0 of the electrolyte. Thus... 

Table IV also reports the mathematical expressions useful to estimate such resistances, where the electric conductivity of the solutions involved was expressed in terms of equivalent conductance. For the sake of simplicity, the resistances of the boundary layers adjacent to any membrane were estimated by expressing the equivalent conductance as a linear function of the square root of solute concentration, that is, by neglecting the contribution of the empirical coefficients i2 and j83 of Eq. 4.

The electrical conductance shows a weaker concentration dependence above than below the CMC corresponding to a decrease in the equivalent conductance (Fig. 2.10). The transport number of the surfactant ion rises sharply at the CMC while that of the counterion may become negative. This as well as electrophoretic mobilities may yield information on micellar charge. At high concentrations, conductance anisotropies have been observed for flowing systems. This, as well as flow birefringence, is useful for the demonstration of nonspherical micelle shape. 

The conductivity of precipitation samples depends on the concentrations of various ion species and their different abilities to transport electric charges in solution, that is, the equivalent conductivity of the... 

As with any electrolyte, various aggregate species are expected to form as the concentration of solute increases. In particular, both the electrical conductivity and (metal) NMR data (Fig. 4) signal the appearance of neutral species at metal concentrations in excess of 103 MPM (37), the conductivity via a Morse-like behavior in the equivalent conductance, the magnetic resonance via a finite Knight (contact) shift... 

Fig. 4. The concentration dependence of various electronic properties of metal-ammonia solutions, (a) The ratio of electrical conductivity to the concentration of metal-equivalent conductance, as a function of metal concentration (240 K). [Data from Kraus (111).] (b) The molar spin (O) and static ( ) susceptibilities of sodium-ammonia solutions at 240 K. Data of Hutchison and Pastor (spin, Ref. 98) and Huster (static, Ref. 97), as given in Cohen and Thompson (37). The spin susceptibility is calculated at 240 K for an assembly of noninteracting electrons, including degeneracy when required (37).

Combined with densities, molecular weights, and transference numbers (fractions of the current carried by the various ionic constituents), the conductivity yields the relative velocities of the ionic constituents under the influence of an electric field. The mobilities (velocity per unit electric field, cm2 s-1 V-1) depend on the size and charge of the ion, the ionic concentration, temperature, and solvent medium. In dilute aqueous solutions of dissociated electrolytes, ionic mobilities decrease slightly as the concentration increases. The equivalent conductance extrapolated to zero electrolyte concentration may be expressed as the sum of independent equivalent conductances of the constituent ions... 

When the neutralization has been very carefully carried out, so that exactly equivalent quantities of acid and base have been used, the resulting solution shows none of the characteristic properties or either acid or base. It still conducts electricity strongly, showing that it contains ions if it is evaporated a solid salt is left. 

The equivalent conductance thus represents the quantity of electrical charge transferred per unit of time by ions present in a volume of solution of a given concentration containing one gram-equivalent of the electrolyte placed between two electrodes set 1 cm apart and at unit potential difference across them. 

Both anions and cations take part in the transport of electricity so that the conductance of an electrolyte equals the sum of conductances of both species of ions. The conductance of each ion depends on the magnitude of elementary ionic charge e, the quantity of ions within the given volume of the solution (n+, n ), their respective valencies (z+, z ) and absolute velocities (t>+, ) at a potential gradient of 1 V/cm. The contribution of cations A to the total conductance of the solution is thus given by the product (en+z+jq) and the contribution of anions B by the product (en z v )- The summary equivalent conductance of the solution may then be expressed by following sum ... 

Ah already stated the liquid junction potential results from the different mobility of ions. Consequently no diffusion potential can result at the junction of the electrolyte solution the ions of which migrate with the same velocity. It is just this principle on which the salt bridge, filled by solutions of those salts the ions of which have approximately the same mobilities, is based (the equivalent conductivities of ions Kf and Cl- at infinite dilution at 25 °C are 73.5 and 70.3 respectively and the conductivities of ions NH+ and NOg are 73.4 and 71.4 respectively). Because ions of these salts have approximately the same tendency to transfer their charge to the more diluted solution during diffusion, practically no electric double layer is formed and thus no diffusion potential either. The effect of the salt bridge on t he suppression of the diffusion potential will be better, the more concentrated the salt solution is with which it is filled because the ions of the salt are considerably in excess at the solution boundary and carry, therefore, almost exclusively the eleotric current across this boundary. 

The best-developed way to measure the association of ions is through the measurement of electrical conductance of dilute solutions. As mentioned, this realization occurred in the nineteenth century to Arrhenius and Ostwald. An elaborate development of conductance equations suitable to a range of ion concentrations of millimolar and lower by many authors (see Refs. 5, 33 and 34 for critical reviews) has made the determination of association constants common. Unfortunately, in dealing with solutions this dilute, the presence of impurities becomes very difficult to control and experimenters should exercise due caution, since this has been the source of many incorrect results. For example, 20 ppm water corresponds to 1 mM water in PC solution, so the effect of even small contaminants can be profound, especially if they upset the acid-base chemistry of association. The interpretation of these conductance measurements leads, by least squares analysis of the measurements, to a determination of the equivalent conductance at infinite dilution, Ao, the association constant for a positively and negatively charged ion pair, KA, and a distance of close approach, d, using a conductance equation of choice. One alternative is to choose the Bjerrum parameter for the distance, which is defined by... 

The electrical conductivity of molten salts can be expressed in two ways equivalent conductivity A (ohm-1 cm2 cquiv ) and specific conductivity k (ohm-1 cm-1), and between these terms there is the relation... 

Equivalent conductivities (and ionic mobilities) of the melts are similar to that of aqueous solutions. Very high specific conductivities are typical for molten salts, as seen in Table 1 [49], The reason for this is the fact that molten salts are very concentrated solutions (for example, the concentration of molten LiF is about 65 molar the concentration of molten KC1 is about 20 molar, etc.). The electrical conductivities of various molten salts cannot be compared at constant temperature because of their different melting points. Therefore, in Table 1 the values of conductivities were selected at 50° above the melting point of each salt. 

In the following text the general term electrical conductivity means the property of a molten salt to conduct the electric current, and when necessary the specific and equivalent conductivities will be specified. 

There are numerous data in the literature [59] which demonstrate that for molten halides the equivalent conductivity calculated by means of the Nernst-Einstein relation is significantly higher than the directly measured conductivity value. This is due to the fact that the structural entities of molten salts make unequal contributions to diffusion and electrical conductivity. 

The electrical conductivity of molten salts has been used to elucidate the structure of the salts. Generally the variation of that property was measured as a function of composition and temperature. The isotherm of the ideal equivalent conductivity of a binary system is additive, and it can be calculated by the relationship... 

Here, Ry and ay are the active resistance and the corresponding electric conductance of the circuit fragment between points i and j. Note that in kinetic equation (1.31), thermodynamic rushes fr of the reactant groups behave as electric potentials in the points, while parameter Ey is equivalent to electric conductance ay. 

The previous definitions can be interpreted in terms of ionic-species diffusivities and conductivities. The latter are easily measured and depend on temperature and composition. For example, the equivalent conductance A is commonly tabulated in chemistry handbooks as the limiting (infinite dilution) conductance A and at standard concentrations, typically at 25°C. A = 1000 K/C = X+ + X = A + flC), (cmVohm gequiv) K = a/R = specific conductance, (ohm cm) C = solution concentration, (gequiv/ ) a = conductance cell constant (measured), (cm ) R = solution electrical resistance, which is measured (ohm) and/(C) = a complicated function of concentration. The resulting equation of the electrolyte diffusivity is... 

Use the infinite-dilution equality between the accelerative force for ions under an applied electric field and the viscous drag to calculate the hydration number of Cl in HCl aqueous solution, using the result that the transport number of the cation is 0.83, while the equivalent conductivity at infinite dilution is 304 S cm mol" (25 °C). Take the radius of water as 170 pm and the corresponding viscosity of water as 0.01 poise. 

What does Eq. (4.163) reveal It shows that the equivalent conductivity will be a constant independent of concentration only if the electrical mobility does not vary with concentration. It will be seen, however, that ion-ion interactions (which have been shown in Section 3.3.8 to depend on concentration) prevent the electrical mobility from being a constant. Hence, the equivalent conductivity must be a function of concentration. 

The Einstein relation also permits experiments on diffusion to be linked up with other phenomena involving the mobility of ions, i.e., phenomena in which there are forces that produce drift velocities. Two such forces are the force experienced by an ion when it overcomes the viscous drag of a solution and the force arising from an applied electric field. Thus, the diffusion coefficient may be linked up to the viscosity (the Stokes-Einstein relation) and to the equivalent conductivity (the Nernst-Einstein relation). 

We learned early on that equivalent conductivity and specific conductivity differed in that the former was not directly proportional to concentration but only secondarily so. However, it turned out that this secondary dependence was considerable and arose because the mobility of the ion itself decreased with an increase in concentration. Thus, as ions get near enough to feel each other through the interaction of their electric fields, they slow down. 

Ohm s law implies that the equivalent conductivity is independent of the strength of the applied electric field. This is certainly so for a very wide variety of applied fields, 1 to 10 V cm, in fact. Howevo, Wien showed that (with appropriate precaution taken against heating of the solution, etc.), the equivalent conductivity of electrolytes undergoes a substantial increase at about 10 V cm . By appropriate consideration of the ionic atmosphere and its time of relaxation, show that a credible model to explain the above is that the high applied field... 

Consider, for instance, the electrical conductance of fused CdClj and KCl mixtures. If the equivalent conductivity of the mixtures (at a fixed temperature) were given by a simple additivity relation, then a linear variation of equivalent conductivity with the mole fraction of KCl should be observed (dashed line in Fig. 5.53). The straight line should run from the equivalent conductivity of pure liquid CdClj at a particular temperature to that of pure liquid KCl at the same temperature. Some binary mixtures of single ionic liquids do indeed exhibit the simple additivity implied by the dashed line of Fig. 5.53. 

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