Molar conductivity calculation

Fig. 7.1 (A - Aca ) vs c >2 relations for lithium halide solutions in sulfolane at 30°C, where A is the experimental molar conductivity and A i the molar conductivity calculated from Eq. (7.1) [la].

The existence of dynamical inhomogeneity also explains certain measurements for self-diffusion in ILs that have previously been attributed to ion pairing. Watanabe and co-workers [165-170] conducted studies on a range of ILs, comparing the molar conductivities calculated via PGSE-NMR (nuclear magnetic resonance) measurement against those obtained via electrochemical... 

The temperature dependence of molar conductivity, calculated from ionic conductivity determined from complex impedance measurements and molar concentrations, and the VFT fitting curves are shown Figure 5.8. The VFT equation for molar conductivity is... 

The shape of specific conductivity relation on composition of the binary mixed solvent depends on conductivity of the components and some other parameters discussed below. Because of molar conductivity calculation of binary mixed solvent system, the ion associate concentration should be taken into account (eq. [9.7]). This quantity is known in very rare instances,therefore, the conductivity of interacting mixed solvent is most often expressed in specific conductivity terms. 

Pu W, He X, Lu J, Jiang C, Wan C (2005) Molar conductivity calculation of Li-ion battery electrolyte based on mode coupling theory. J Chem Phys 123 231105... 

Due to the fact that K2TaF7 - KF is considered to be part of the TaF5 - KF binary system, while the K2TaF7 - KCI system is a component of the interconnected ternary system K+, Ta5+//F", Cl", the single-molecule conductivity and activation energy of the systems was calculated based on density and specific conductivity data [322, 324]. Molar conductivity (p) depends on the absolute temperature (T), according to the following exponential equation ... 

Such a model of the melt structure does not contradict conductivity data [324], if plotted against the composition of the KF - TaF5 system. Fig. 63 presents isotherms of molar conductivity, in which molar conductivity of the ideal system was calculated using Markov s Equation [315], and extrapolation... 

Positive deviations of molar conductivity from the values calculated for the ideal system correspond to the interaction of ionic and associated components of the system. Dissolution of KF in TaF5 and the solution generated as a result, cause the dissociation of the (TaF5)n polyanionic structure in to separate groups, leading to the ionization of the system, which undoubtedly leads in turn to an increase in its conductivity. 

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 ... 

Danek and his group have independently proposed a quite similar model, which they call the dissociation modeV - For this model Olteanu and Pavel have presented a versatile numerical method and its computing program. However, they calculated only the electrical conductivity or the molar conductivity of the mixtures, and the deviation of the internal mobilities of the constituting cations from the experimental data is consequently vague. 

In aqueous solutions, concentrations are sometimes expressed in terms of normality (gram equivalents per liter), so that if C is concentration, then V = 103/C and a = 103 K/C. To calculate C, it is necessary to know the formula of the solute in solution. For example, a one molar solution of Fe2(S04)3 would contain 6 1CT3 equivalents cm-3. It is now clear as to why A is preferred. The derivation provided herein clearly brings out the fact that A is the measure of the electrolytic conductance of the ions which make up 1 g-equiv. of electrolyte of a particular concentration - thereby setting conductance measurements on a common basis. Sometimes the molar conductance am is preferred to the equivalent conductance this is the conductance of that volume of the electrolyte which contains one gram molecule (mole) of the ions taking part in the electrolysis and which is held between parallel electrodes 1 cm apart. 

The value for k will normally decrease as the concentration of the solution decreases but the value for A will increase because of the increased dissociation of molecules in dilute solutions. A value for the molar conductance at infinite dilution (A,)) can be determined by plotting the calculated values for A against the molar concentration of the solution used and determining the plateau value for A. From such investigations it is possible to determine the ionic mobilities of ions (Table 4.3) and calculate the molar conductance of an... 

The break-seal on A is then crushed, the sample to be investigated diluted with the solvent in C, and the optical density of the resulting solution determined in the appropriate optical cell. The solution is then transferred to conductivity cell H, and its resistance is measured. The optical density is redetermined, and thereafter about two thirds of the solution is transferred to C. The solvent from C is distilled into the chilled ampoule G and used to dilute the residual solutions left in H. The conductivity and the optical density of this solution are determined as described previously thereafter, two thirds is again transferred to C, and the remaining one third is diluted by the above-described procedure. In this way the conductivities are determined for decreasing concentrations of living polymer, so that the molar conductivity A can be calculated as a function of [living polymer] down to about 10" M. 

Tab. 6.5 Ionic molar conductivities (A00) in some organic solvents and LJPs between solutions in the same solvent (Ej) calculated by the Henderson equation...

Here, c is the total concentration of MA, KA is the association constant, a is the degree of dissociation of the ion-pair M2+A2h and y is the average activity coefficient of free ions of concentration ca. Because the ion-pairs do not conduct electricity, the molar conductivity A in the presence of ion association is less than in its absence. In Fig. 7.1, the difference between the experimental molar conductivity (A) and the value calculated from Eq. (7.1), /lcai, are plotted against c1/2 for lithium halides in sulfolane [la]. For Lil, the difference between A and /lcai is small because ion association is not appreciable (KA=5.(> mol-11). For LiBr (KA = 278 mol-11) and LiCl (KA= 13860 mol-11), however, A is much smaller than... 

As mentioned in Section 7.1, if we determine the molar conductivity of an electrolyte as a function of its concentration and analyze the data, we can get the value of limiting molar conductivity A°° and quantitative information about ion association and triple-ion formation. If we determine the limiting molar conductivity of an ion (7 °) by one of the methods described in Section 7.2, we can determine the radius of the solvated ion and calculate the solvation number. It is also possible to judge the applicability of Walden s rule to the ion under study. These are the most basic applications of conductimetry in non-aqueous systems and many studies have been carried out on these problems [1-7]. 

Sometimes, the conductivity of the solution may decrease due to the formation of electroneutral ion pairs. Under these conditions, the Fuoss-Onsager equation can be used to calculate the molar conductivity (A) of associated electrolytes [57] ... 

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... 

If c or V is known and a is determined by one of the experimental methods mentioned in Section 1.10, K can be calculated by these equations. These equations are often referred to as Ostwald s dilution law, as they express the correlation between dilution and the degree of dissociation. As the latter is proportional to the molar conductivity of the solution, the above correlation describes the particular shapes of the conductivity curves shown in Fig. 1.3. 

Table 1.7 Calculation of the dissociation equilibrium constant of acetic acid from measured values of molar conductivity...

The Nernst-Einstein equation is applied to calculate molar conductivity (A mr) from the PGSE-NMR diffiision coefficients ... 

Since the mode of ionization of the salt is not known, it is not possible to determine the equivalent weight and hence the equivalent conductance cannot be calculated it is necessary, therefore, to make use of the molar conductance, as defined on p. 31. In the simple case of a series of salts all of which have one univalent ion, either the cation or anion, whereas the other ion has a valence of z, the gram molecule contains z gram equivalents the molar conductance is thus z-timcs the equivalent conductance. If the mean equivalent conductance of all ions is taken as 60, the equivalent conductance of any salt is 120 ohms cm., and the molar conductance is 120 z ohms" cm. The approximate results for a number of salts of different valence types with one univalent ion at 25 are given in Table XXL The observed molar conductances of the platinosammine... 

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,... 

By listing the ratios of the molar conductivities versus the conductivities calculated from the NMR self-diffusion coefficients A m /ANV(R, they were able to propose a useful parameter to characterize various properties of ILs with different anions, such as quantitative information on how much individual ions contribute to ionic conduction. 

The calculation procedure is as follows For the chosen values of the dissociation degrees of the pure components oi and ao2, the values of ai and 2 are calculated according to Eqs. (8.29) and (8.30) for each composition of the mixture with a known value of the molar conductivity, A, exp. The theoretical value of the molar conductivity, i, calc is calculated according to Eq. (8.36), in such a way for each couple of oi and 02 that a set of theoretical values of molar conductivities for the given composition is obtained. The criterion for selection of the right values of aoi and ao2 is given by the relation... 

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