Molar conductivity Ratio

Figure 5.9 Molar conductivity ratios (A/Anmr) piotted against temperature for EMIBF4, EMiTFSi, BPBF4, and BPTFSi.

Figure 5. (a) The ( A, SO,) anion symmetric streching mode of polypropylene glycol)- LiCF,SO, for 0 M ratios of 2000 1 and 6 1. Solid symbols represent experimental data after subtraction of the spectrum corre-ponding to the pure polymer. Solid curves represent a three-component fit. Broken curves represent the individual fitted components, (b) Relative Raman intensities of the fitted profiles for the ( Aj, SO,) anion mode for this system, plotted against square root of the salt concentration, solvated ions ion pairs , triple ions, (c) The molar conductivity of the same system at 293 K. Adapted from A. Ferry, P. Jacobsson, L. M. Torell, Electrnchim. Acta 1995, 40, 2369 and F. M. Gray, Solid State Ionics 1990, 40/41, 637. 

At salt concentration below those shown in Fig. 5, molar conductivity behavior has been identified with the formation of electrically neutral ion pairs [8]. Between concentration of 0.01 and 0.1 mol L 1 (up to an 0 M ratio of -50 1) the molar conductivity rises and this can be explained by the formation of mobile... 

The conductometric titrations of the non-conducting solution of trimethyl-tin iodide in nitrobenzene (at c 7.10 2) with different donors reveal that conducting solutions are formed. The molar conductivity at a given mole ratio D (CH3 )3 SnI generally increases with increasing donicity of the donor10 (Fig. 9),... 

Fig. 9. Molar conductivities of (O SnHn nitrobenzene as a function of the nature of D and the molar ratio...

The electrolyte concentration is very important when it comes to discussing mechanisms of ion transport. Molar conductivity-concentration data show conductivity behaviour characteristic of ion association, even at very low salt concentrations (0.01 mol dm ). Vibrational spectra show that by increasing the salt concentration, there is a change in the environment of the ions due to coulomb interactions. In fact, many polymer electrolyte systems are studied at concentrations greatly in excess of 1.0 mol dm (corresponding to ether oxygen to cation ratios of less than 20 1) and charge transport in such systems may have more in common with that of molten salt hydrates or coulomb fluids. However, it is unlikely that any of the models discussed here will offer a unique description of ion transport in a dynamic polymer electrolyte host. Models which have been used or developed to describe ion transport in polymer electrolytes are outlined below. 

As far as the determination of the composition of the complex is concerned, this can be obtained from the variation of electrical conductance of an ionic solution titrated with a solution of the neutral receptor as a result of the different mobilities of the species in solution. Plots of molar conductances, Am, against the ratio of the concentrations of the receptor and anion can provide useful information regarding the strength of anion-receptor interaction. In fact, several conclusions can be drawn from the shape of the conductometric titration curves. 

Kohlrausch discovered, in the last century, that the molar conductivity of aqueous solutions of electrolytes increases with dilution, and reaches a limiting value at very great dilutions. The increase of molar conductivity, in line with the Arrhenius theory, results from the increasing degree of dissociation the limiting value corresponds to complete dissociation. This limiting value of the molar conductivity is denoted here by A0 (the notation A C is also used), while its value at a concentration c will be denoted by Ac. The degree of dissociation can be expressed as the ratio of these two molar conductivities... 

Sn(CH3)3l dissolved in nitrobenzene as a function of concentration of various EPD solvents added (35). In noncoordinating or weakly coordinating solvents, such as hexane, earbon tetrachloride, 1,2-dichloroethane, nitrobenzene, or nitromethane, Sn(CH3)3l is present in an unionized state (tetrahedral molecules). Addition of a stronger EPD solvent to this solution provokes ionization, presumably with formation of trigonal bipju amidal cations [Sn(CH3)3 (EPD)2J. Table II reveals that the molar conductivities at a given mole ratio EPD Sn(CH3)3l are (with the exception of pyridine) in accordance with the relative solvent donicities. No relationship appears to exist between conductivities and the dipole moments or the dielectric constants of the solvents. 

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. 

When the molar conductivity is related to the unity of the amount of positive or negative charge we get equivalent conductivity. This enables direct comparison of the mobility of ions of different valence. The equivalent conductivity is the ratio k/cz. 

Since ratios are involved in the Henderson equation, the molar conductivities may be used directly instead of the mobility... 

We can extrapolate the curves back to zero concentration and obtain a quantity known as Aq, the molar conductivity at infinite dilution, or zero concentration. With weak electrolytes this extrapolation may be unreliable, and an indirect method, explained on p. 285, is usually employed. It is convenient to denote the ratio of A at any concentration to Ao by the symbol a ... 

Another electrochemical factor of great importance is the molar conductivity A, which is a ratio of electric conductivity and mass quantity in 1 m (concentration c) ... 

There is still one last problem to discuss Although we are actually interested in the transport numbers t or t at infinite dilution in order to calculate the characteristic molar conductivities for individual types of ions, nature only allows us to experiment using a real solution having finite dilution. As concentration increases, the ionic conductivity as well as the molar conductivity of the electrolytes continuously decrease. As a result, the concentration dependency largely cancels out when we calculate the ratio. At concentrations that are not too high (below 10 mol m ), we have approximately t+ = t or t = t . 

Figure 1.3 Molar conductivity of various alkali halides atT = 1100 K (fluorites atT = 1270 K) versus the ratio of the bond energy of individual and complex ions A U to the internal energy of the melt AU (according to Khokhlov ). (Reproduced with permission from Ref. [18], 1998 by Trans Tech Publications.)...

Some authors define the molar conductivity A b of the salt AB by the ratio A b = k/cab. or the equivalent conductivity A b of an ion as A b = Zb F eB Because they easily lead to confusion, these quantities will not be used in this text. 

The conductance of an electrolyte solution is a property that determines the extent of movement of all ionic species in the solution upon the application of an electric field, resulting in the flow of the current through the solution. A complementary property is defined, the trans-ferance number, which expresses the relative extent to which only one kind of ion contributes to the charge transport. The conductance is the sum of the ionic conductances, whereas the transferance numbers depend on their ratio. Conductance yields unique information as to the nature of the structure of electrolytes, their equilibria and the ionic composition of liquids. Conductance depends on concentration and on external parameters, temperature and pressure. The concentration dependence of conductance indicates the ion-ion interactions such as the ion-pair formation and dissociation equilibria. On the other hand, the limiting values of the molar conductance (conductance/concentration) obtained by extrapolation for an infinitesimal dilution are functions only of the ion-solvent interactions. 

The symbols p (ohm m) and k (ohm" m ) denote the specific resisitivity and conductivity, respectively. According to Eq. (31) G depends on the geometric configuration of a conductometric cell, whereas p and k are intrinsic properties of the solution at given external conditions. The ratio of //A is the cell constant which is not determined from physical dimensions but is measured when the cell is filled with one of the standard solutions of a well-defined specific conductivity. Since k reflects not only the characteristics of the solute but also its concentration, it is more practical to define the molar conductance as... 

Nernst s equations were soon adopted by other workers although they often multiplied the ratio of concentrations by the ratio of molar conductances to allow for incomplete dissociation (even for strong electrolytes). Only in 1920 did Macinnes and Beattie (1 ) replace concentrations by activities and use the emf equation in its proper differential form. A more general equation in terms of ion-constituent transference numbers and applicable also to electrodes reversible to a complex ion was later derived by the present author (H). In 1935 Brown and Macinnes (92) initiated the converse procedure of calculating activity coefficients from the accurate m.b. transference numbers then available and the emfs of cells with transference, an approach that required only one type of reversible electrode. 

Determination of the degree of dissociation of weak electrolytes is a common application of conductivity measurements. This approach will be briefly outlined here with a sample calculation illustrating the utility of the method. From the data presented in the next section, the limiting molar conductivity of acetic acid can be seen to be 389.9 S cm mol (from addition of the limiting values for the proton and the acetate ion). At finite concentrations, this weak acid will only be partially deprotonated. The ratio of observed to predicted electrolytic conductivity can be used to determine the degree of dissociation, a. At 0.01 M, the observed molar conductivity of acetic acid was found to be 14.30 S cm mol . Thus... 

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