Equivalent conductance , dependence

Both specific and equivalent conductances depend to a great extent on the concentration of the solution as well as on the circumstance whether the solution in question contains a weak or a strong electrolyte. 

An important feature of this equation is that it indicates that the polyion equivalent conductivity depends on the nature of the counterion. It is interesting to note that a similar dependence was predicted by Manning [7], based on quite different theoretical considerations. However, the pronounced increase of polyion conductivity in dilute solutions inherent in Manning s formula is not endorsed by the present treatment. 

Equivalent and molar conductivities are commonly used to express the conductivity of the electrolyte. Equivalent conductance depends on the concentration of the solution. If the solution is a strong electrolyte, it will completely dissociate the components in the solution to ionic forms. Kohlrauch (Macinnes, 1939) found that the equivalent conductance of a strong electrolyte was proportional to the square root of its concentration. However, if the solution is a weak electrolyte which does not completely dissociate the components in the solution to respective ions, the above observation by Kohlrauch is not applicable. 

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 and at standard concentrations, typically at 25°C. A = 1000 K/C = ) + ) = +... 

It is not usual to talk about the resistance of electrolytes, but rather about their conductance. The specific conductance (K) of an electrolyte is defined as the reciprocal of the resistance of a part of the electrolyte, 1 cm in length and 1 cm2 in cross-sectional area. It depends only on the ions present and, therefore it varies with their concentration. To take the effect of concentration into account, a function called the equivalent conductance, A, is defined. This is more commonly (and conveniently) used than the specific conductance to compare quantitatively the conductivities of electrolytes. The equivalent conductance A is the conductance of that volume of the electrolyte which contains one gram equivalent of the ions taking part in the electrolysis and which is held between parallel electrodes 1 cm apart (units ohm-1 cm4). If V cubic centimeters is the volume of the solution containing one gram equivalent, then the value of L will be 1 cm and the value of A will be V square centimeters, so that... 

In the relationship shown above, A and B are constants depending on temperature, viscosity of the solvent, and dielectric constant of the solvent, C is the concentration expressed in gram equivalents per liter, and Ac represents the equivalent conductance of the solution. A0 is the equivalent conductance at infinite dilution - that is, at C = 0, when the ions are infinitely apart from one another and there exists no interionic attraction, a represents the degree of dissociation of the electrolyte. For example, with the compound MN... 

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 ... 

Salts such as silver chloride or lead sulfate which are ordinarily called insoluble do have a definite value of solubility in water. This value can be determined from conductance measurements of their saturated solutions. Since a very small amount of solute is present it must be completely dissociated into ions even in a saturated solution so that the equivalent conductivity, KV, is equal to the equivalent conductivity at infinite dilution which according to Kohlrausch s law is the sum of ionic conductances or ionic mobilities (ionic conductances are often referred to as ionic mobilities on account of the dependence of ionic conductances on the velocities at which ions migrate under the influence of an applied emf) ... 

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... 

As shown by the measurements for the various methylbenzenes, the equivalent conductance for the same concentration of aromatic substance strongly increases with increasing number of methyl groups. This already shows qualitatively that the basicity increases in the same sense, i.e. that the formation of the aromatic cations is favoured. One further notes for the individual methylbenzenes that the equivalent conductance is very dependent on the total concentration of the aromatic substance... 

Conductance measurements also have been used for the estimation of dissociation constants of weak electrolytes. If we use acetic acid as an example, we find that the equivalent conductance A shows a strong dependence on concentration, as illustrated in Figure 20.2. The rapid decline in A with increasing concentration is largely from a decrease in the fraction of dissociated molecules. 

Furthermore, the diffusion coefficients of both reactants may also be expected to depend on solute (ionic or not) concentration. In the case of ions of charge ze, the diffusion coefficient can be estimated from the equivalent conductivity, X, as... 

The variation of the conductance of a solution (AG) depends on AK, the difference between the equivalent conductance of ion X and that of the elution ion E multiplied by the concentration Cx ... 

The migration time of mineral ions depends on the limit of their equivalent conductivity. 

Fig. 12. Dependence of equivalent conductivity on living end concentration styrene-n-butyllithium-benzene-dimethoxyethane, 25° C, DME contents (vol-%) from the top 50, 45, and 40%. Reproduced, with permission, from Ise, Hirohara, Makino, Takaya and Nakayama presented at the 17th Discussion Meeting of High Polymers, October, 1968, Matsuyama, Preprint p. 261...

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... 

The concentration dependencies of both the equivalent conductivity (A) and the chloride ion activity coefficient (fa) of the monomer DADMAC are not different... 

The plot of the equivalent conductivity vs. the polyelectrolyte concentration, however, is more suitable to demonstrate the concentration dependent changes of the polyelectrolyte conductivity [129]. Generally, the equivalent conductivity (Eq. (17)) can be written as [128]... 

The concentration dependence of this equivalent conductivity is given in Fig. 18 for the low molecular salt NaCl, the monomer DADMAC, and PDADMAC. 

Fig. 18. Concentration dependence of the equivalent conductivity A for low molecular electrolytes (NaCl, DADMAC) and PDADMAC. PDADMAC Mn= 12,000 g mol"1 T=20 °C (Data taken from [38])...

According to Kohlrausch s law of the Independent Migration of Ions the equivalent conductivity at infinite dilution of a cation (/l0+) or an anion (/l0 ) depends only on the nature of the ion and properties of the medium, such as... 

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... 

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).

The conductivity of electrolyte solutions depends on the concentration and the charge number of the ions in the solution. It is expressed as the molar or equivalent conductivity or molar conductivity, which is given by ... 

Band gap photochemical excitation of a semiconductor particle promotes an electron from the valence band to the conduction band, thus forming an electron-hole pair. Under illumination, the bands shift from their dark equilibrium positions to ones closer to the flat band condition, Scheme 9. Here the chemical potential of the electrons becomes different from that of the holes and a photovoltage develops. The concentration of free carriers, and hence of the number of available redox equivalents, will depend linearly on the incident light intensity. The free energy of these charge carriers will be related to... 

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... 

The concentration dependence of equivalent conductance is the principal source of our knowledge of ionic interactions (which generally lower mobilities). 

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