Ionic molar conductivity, limiting

In the development of the theory of ionic conductance it has been shown that the viscosity of the solvent is an important parameter determining ionic mobility. Initially, conductivity data were only available in water so that attention was focused on the effects of ionic size, structure, and charge in determining mobility and its concentration dependence. More recently, data have become available in a wide variety of non-aqueous solvents [11, 12], that is, in media with a wide range of permittivities and viscosities. On the basis of these data one may examine in more detail the role of solvent viscosity in determining the transport properties of single ions. Values of the limiting ionic molar conductance for selected monovalent cations and anions are summarized in tables 6.4 and 6.5, respectively. 

By combining the Stokes-Einstein equation (equation (6.7.27)) with equation (6.7.23), the following expression for the limiting ionic molar conductance is obtained ... 

A similar equation describes the effects of non-ideality on the limiting ionic molar conductivity, A°, for the case where the central reference ion is an anion. 

The mobilities of ions at infinite dilution, Mi , are directly proportional to the limiting ionic molar conductivities ... 

The most characteristic properties of ions are their abilities to move in solution in the direction of an electrical field gradient imposed externally. The conductivity of an electrolyte solution is readily measured accurately with a 1 kHz alternating potential in a virtually open circuit, in order to avoid electrolysis. The molar conductance of a completely dissociated electrolyte is A2 = A2°° - 2 + EC2 In C2 + J iR ) C2 — J" R")c2, where S, E, f, and f are explicit expressions, containing contributions from ionic atmosphere relaxation and electrophoretic effects, the latter two depending also on ion-distance parameters R. The infinite dilution can be split into the limiting molar ionic conductivities by using experimentally measured transport numbers extrapolated to infinite dilution, t+° and i °° = 1 - <+°°. For a binary electrolyte, Aa = 2+°° -I- and = i+ A2. Values of the limiting ionic molar conductivities in water at 298.15 K [1] are accurate to 0.01 S cm mol (S = Q ). 

The rates of movement of ions in an electric field are expressed by their mobilities Mj, measuring their speed at unit field. The mobilities at infinite dilution, m", are directly proportional to the limiting ionic molar conductivities ... 

Table 9. Ionic radii and ionic limiting molar conductivities of some anions in PC at 25°C, taken from Ref. 1211]...

While the molar conductivity of strong electrolytes A0 can be measured directly, for determination of the ionic conductivities the measurable transport numbers must be used (cf. Eq. (2.4.12)). Table 2.1 lists the values of the limiting conductivities of some ions in aqueous solutions. 

When the limiting molar conductivities are to be obtained for a series of ions in a given solvent, the first step is to get the limiting molar conductivity of an ion by one of the above methods. Then, the limiting molar conductivities for other ions can be obtained sequentially by applying Kohlrausch s law of independent ionic migration (Section 5.8). 

The limiting molar conductivities of ions in various solvents are listed in Table 7.4. The following are some general points about ionic conductivities in non-aque-ous solutions ... 

Hittorf transport method — Only at infinite dilution can the molar conductivity of a solution be split into the two limiting molar conductivities associated with the individual ions, which are independent of each other. This is because only at infinite dilution can we completely neglect interionic interactions. However, in order to determine the values of the individual ionic conductivities, an additional measurement is necessary in order to partition Ao into AJ and Ag we must determine the so-called -> transport numbers of the individual ions. The total current i, can be written as the sum of partial currents i+ and i, corresponding to the currents carried by the cations and anions. We define the transport number of the cations, t+, as t+ = -fi— = and simi-... 

A selected number of ionic mobilities at 18°C and 25°C is shown in Table 1.4. This table may be utilized for the calculation of the limiting molar conductivities of any electrolytes made up of the ions listed. Thus, for acetic acid at 25°C... 

Values of limiting molar ionic conductivities for a few common ions are shown in Table 1. The data tabulated are referred to 25°C temperature. The term limiting molar ionic conductivity is used according to lU-PAC recommendation, rather than the formerly used limiting ionic equivalent conductivity. The molar and equivalent values are interconvertible through stoichiometric coefficient z. 

The results obtained also are useful for the calculation of the ionic conductivity of nonaqueous electrolyte solutions. Several attempts exist for the calculation of the molar conductivity of associating electrolytes beyond the limiting law at the level of the MSA [3, 32, 33], where, however, only ion pairs were taken into account. Ion pairs and tetramers are electrically neutral, nonconducting species in the solution, by contrast to the ion trimers. The total concentration of charged particles is given by,... 

Estimate the molar conductivity of 0.1 M HCl at 25°C given that its limiting molar conductivity is 426.2 cm mol and assuming an ionic size parameter a of 0.45 nm. 

Use the Henderson equation to estimate the liquid junction potentials for the following systems assume that the limiting molar conductivities given in table 6.2 can be used to calculate the ionic mobility. 

This is in stark contrast to the situation where hmiting ionic conductivities are concerned (see Sections 11.11 to 11.13). Here limiting molar conductivities can be split up into individual limiting ionic conductivities for the cation and the anion, so that a table of these can be constmcted, e.g. ... 

It is used for calculating the limiting molar conductivity, JsP, of an electrolyte from tabulated individual limiting ionic conductivities, X°, i.e. for very, very low concentrations. Under such conditions, the law can handle calculations of predicted limiting molar conductivities for both strong and weak electrolytes. 

Calculate the limiting molar conductivities, A°, at 25°C for the following electrolytes NaNOa, Mg(OH)2, CaS04, K2SO4, (CH3COO)2Mg, La2(S04)3 given the following information on individual ionic conductivities at infinite dilution, i.e. A and... 

AJ is the limiting molar conductance at infinitesimal ionic strength, and the relaxation and electrophoretic parameters a and jS, respectively, are defined in eqn. 5.2.3. From eqns. 5.8.3 and 5.10.1 the transference number of a completely dissociated symmetrical electrolyte is given by... 

Na the Avogadro number. The relations between the velocity at infinitesimal ionic strength, the limiting ionic mobility and the limiting molar ionic conductance A° are taken from eqns. 5.101.5 and 5.8.2. In terms of the units commonly employed by workers in the field ... 

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