Conductivity infinite dilution

Table III.3.2 Equivalent ionic conductivities infinite dilution at 25°C...

With the knowledge now of the magnitude of the mobility, we can use equation A2.4.38 to calculate the radii of the ions thus for lithium, using the value of 0.000 89 kg s for the viscosity of pure water (since we are using the conductivity at infinite dilution), the radius is calculated to be 2.38 x 10 m (=2.38 A). This can be contrasted with the crystalline ionic radius of Li, which has the value 0.78 A. The difference between these values reflects the presence of the hydration sheath of water molecules as we showed above, the... 

L is Avagadro s constant and k is defined above. It can be seen that there are indeed two corrections to the conductivity at infinite dilution tire first corresponds to the relaxation effect, and is correct in (A2.4.72) only under the assumption of a zero ionic radius. For a finite ionic radius, a, the first tenn needs to be modified Falkenliagen [8] originally showed that simply dividing by a temr (1 -t kiTq) gives a first-order correction, and more complex corrections have been reviewed by Pitts etal [14], who show that, to a second order, the relaxation temr in (A2.4.72) should be divided by (1 + KOfiH I + KUn, . The electrophoretic effect should also... 

The salts had a high electrical conductivity, and it was claimed that the values of the molar conductances at infinite dilution showed the formation of a binary and ternary electrolyte respectively. 

The equivalent conductivity of an electrolyte is the sum of contributions of the individual ions. At infinite dilution A° = A° -f A, where A° and A are the ionic conductances of cations and anions, respectively, at infinite dilution (Table 8.35). 

Infinite dilution conductance of cation and anion cmv(gequiv-ohm) ... 

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 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. 

In Figs. 31 and 32 the ordinates give the equivalent conductivity of HC1, each point being the result of a series of measurements extrapolated to infinite dilution.1 For comparison with similar diagrams given in a later... 

In one of the two cells placed back to back, the solvent, as mentioned above, was pure water in each case. When the mixed solvent in the other cell contains only a small percentage of methanol, the resultant e.m.f. will obviously be small, and it should progressively increase with increasing difference between the solvents. In Fig. 61 abscissas are values of 1/e for the mixed solvent, running from 0.0126 for pure water to 0.0301 for pure methanol. Ordinates give the unitary part of the e.m.f. extrapolated to infinite dilution. It will be seen that for KC1, NaCl, and LiCl the curves differ only slightly from straight lines, but the curve for HC1 has quite a different shape. From the experimental results on the electrical conductivity depicted in Fig. 31 we expect the curve for HC1 to take this form. In Sec. 115 we shall discuss this result for HC1, and in Sec. 116 we shall return to the interpretation of the results obtained with the alkali chlorides. 

For strong electrolytes the molar conductivity increases as the dilution is increased, but it appears to approach a limiting value known as the molar conductivity at infinite dilution. The quantity A00 can be determined by graphical extrapolation for dilute solutions of strong electrolytes. For weak electrolytes the extrapolation method cannot be used for the determination of Ax but it may be calculated from the molar conductivities at infinite dilution of the respective ions, use being made of the Law of Independent Migration of Ions . At infinite dilution the ions are independent of each other, and each contributes its part of the total conductivity, thus ... 

It is worth mentioning that single-ion conductivities of lithium ions and anions at infinite dilution, and transference numbers of ligand-solvated lithium ions estimated therefrom, increase due to the replacement of more than one (generally four) solvent molecules. Table 6 demonstrates this beneficial feature. 

Table 6. Single-ion conductivities of solvated lithium ions and anions at 25 °C in PC at infinite dilution [13]...

Table 7 Equivalent conductances" at infinite dilution for hydrocarbon salts, [l 2 ] and [24 2 ], and related ionic species in DMSO at 25°C. ...

The various physical methods in use at present involve measurements, respectively, of osmotic pressure, light scattering, sedimentation equilibrium, sedimentation velocity in conjunction with diffusion, or solution viscosity. All except the last mentioned are absolute methods. Each requires extrapolation to infinite dilution for rigorous fulfillment of the requirements of theory. These various physical methods depend basically on evaluation of the thermodynamic properties of the solution (i.e., the change in free energy due to the presence of polymer molecules) or of the kinetic behavior (i.e., frictional coefficient or viscosity increment), or of a combination of the two. Polymer solutions usually exhibit deviations from their limiting infinite dilution behavior at remarkably low concentrations. Hence one is obliged not only to conduct the experiments at low concentrations but also to extrapolate to infinite dilution from measurements made at the lowest experimentally feasible concentrations. 

While the condition of stoichiometric neutrality invariably must hold for a macroscopic system such as a space-network polyelectrolyte gel, its application to the poly electrolyte molecule in an infinitely dilute solution may justifiably be questioned. In a polyelectrolyte gel of macroscopic size the minute excess charge is considered to occur in the surface layer (the gel being conductive), which is consistent with the assumption that the potential changes abruptly at the surface. This change is never truly abrupt, for it must take place throughout a layer extending to a depth which is of the order of magnitude of the... 

From results of conductance measurements it has been found that although the conductance of an electrolyte becomes progressively smaller with decreasing concentration, the values of equivalent conductance increase as the concentration decreases or the solution dilution increases until a maximum limiting value is finally obtained. The limiting value of the equivalent conductance which is attained with decreasing concentration or increasing solution dilution is termed the equivalent conductance at infinite dilution, and is denoted Aq-... 

A comparison of the equivalent conductance at some finite concentration (Ac) with that at infinite dilution (AJ gives a measure of the fraction of electrolyte dissociation at the higher concentration. One introduces a, the degree of dissociation or ionization, and writes... 

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... 

It has been seen above that the value of A, extrapolated to zero concentration provides A0, the equivalent conductance at infinite dilution, for strong electrolytes, HC1 and KC1. A similar operation for the determination of A, for the weak electrolytes will just not hold simply because, as it has been seen, weak electrolytes feature the fact their Ac rise steeply at high dilutions. The experimental determinations become very uncertain in these situations. 

Table 6.8 Equivalent conductance (AJ of some of the electrolytes at 25 °C at infinite dilution.

It may finally be recounted that Kohlrausch found that, at infinite dilution, each ion in the electrolyte contributes a characteristic amount to the equivalent conductance of the electrolyte, so that for the electrolyte containing the salt MN ... 

It may be added that Kohlrausch s law does not lead to any method of deducing the contributions of the individual ions. The immediate practical application of Kohlrausch s law of independent contributions of the ions at infinite dilution is a method for deducing the limiting equivalent conductance, A0, of weak electrolytes. This will be illustrated by taking a specific example of a weak electrolyte. 

In a weak electrolyte such as CH3COOH, the A values rise steeply with decreasing concentration because more of the electrolyte ionizes according to the principle of equilibrium, and ionization is complete at infinite dilution. The sharp rise in the A value at lower concentration occurs because of a sharp increase in the number of ions in solution. Kohlrausch s law may be used in the determination of A0 for acetic acid or any weak electrolyte. According to this law, A0 for acetic acid is the sum of the ionic conductivities of H+ and CHjCOCT at infinite dilution... 

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 ... 

A+ = N A0. Thus, the ionic conductance of an ion is obtained by multiplying the equivalent conductivity at infinite dilution of any strong electrolyte containing that ion by its transport number. In this manner the ionic mobilities of the two ions present in the weak electrolyte can be calculated, and finally its equivalent conductivity at infinite dilution can be calculated by summing these two values. 

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) ... 

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... 

Sometimes in the literature the equivalent ionic conductivity at infinite dilution is erroneously termed ion mobility however, eqn. 2.17 clearly shows the interesting linear relationship between both properties with the faraday as a factor. 

EQUIVALENT IONIC CONDUCTIVITIES AND ION MOBILITIES AT INFINITE DILUTION IN AQUEOUS SOLUTIONS AT 25° C... 

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. 

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