Equivalent conductance concentration dependence

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... 

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 = ) + ) = +... 

Figure 4. Concentration-dependent ion channel blockade by (R)-JV-methylanatoxinol. The patterns identified as bursts and separated by long (>8 msec) closed intervals are indicated with a bar, the figure was designed to show approximately 2 bursts per trace. The dose-related decrease in mean channel open time resulted from the blockade of the open channel by the (R)-A -methylanatoxinol. The channel amplitude is related to membrane voltage (as was given in Figure 3) by the slope conductance such that 1 pA is equivalent to 30 mV. Continued on next page.

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... 

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 ... 

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])...

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 ... 

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). 

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. 

The dependence of the equivalent conductance on the concentration of the solution is due to the dissociation of the electrolyte on one hand and to mutual interaction of ions on the other. The first factor is of primary importance in the case of weak electrolytes. As the degree of dissociation increases with increasing dilution, the decrease of specific conductance x is slower than would correspond to the decrease of the analytical concentration c. Therefore equivalent conductance rises with decreasing concentration of the solution as will be seen from the equation A = 1000 x/ce. The other factor, namely mutual interaction of ions, manifests itself at higher concentrations of solutions only. 

The conductivity k depends on the equivalent concentrations and the mobilities of the ions present. Consider a single electrolyte A giving ions and B - and having fractional ionization a at a solute concentration c in moles per liter. The concentration in equivalents per liter for the positive ions (and also for the negative ions) is vac, where V = V+Z+ = v z denotes the number of equivalents of positive or negative ions per mole of the electrolyte. The conductivity is given 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... 

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... 

Anticipating the atomistic treatment of conduction that follows, it may be mentioned that at very low ionic concentrations, the ions are too far apart to exert appreciable interionic forces on each other. Only under these conditions does one obtain the pristine version of equivalent conductivity, i.e., values unperturbed by ion-ion interactions, which have been shown in Chapter 3 to be concentration dependent. The state of infinite dilution therefore is not only the reference state for the study of equilibrium properties (Section 3.3), it is also the reference state for the study of the nonequilibrium (irreversible) process, which is called ionic conduction, or migration (see Section 4.1). 

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