Molar conductivity.

Conductivity as a practical quantity has restricted use since it is not possible to compare values for different electrolyte concentrations owing to the sec- 

Imagine two electrodes held at a separation of 1 m. If a solution has a concentration C mol m , then the volume of solution containing one mole = 1/C and both electrodes would have to have this area, for a separation of 1 m, if one equivalent of electrolyte were to be held between them at concentration C. The molar conductivity is thus given by the conductivity, k, multiplied by the volume which contains one mole of electrolyte, i.e. by 

Important information about the nature of solutions has been provided by measurements of their conductivities. A solution of sucrose in water has the same electrical conductivity as water itself, while a solution of sodium chloride or acetic acid has a much higher conductivity. The latter substances are known as electrolytes, since their solutions in water and in other solvents contain ions. By contrast, sucrose is a non electrolyte, its molecules being present intact in solution. 

Aqueous solutions of sodium chloride and cupric sulfate of, say, 1 M concentration conduct electricity much better than a 1 M solution of acetic acid. This suggests that the sodium chloride and cupric sulfate exist in solution to a greater extent as ions than does acetic acid. More detailed investigations have indicated that certain substances, including sodium chloride and cupric sulfate, occur almost entirely as ions when in aqueous solution. Such substances are known as strong electrolytes. Other substances are present only partially as ions. Acetic acid, for example, exists in solution partly as CH3COOH and partly as CHaCOO -f These are known as weak electrolytes. 

According to Ohm s law, the resistance Rota slab of material is equal to the potential V in volts (V), divided by the current / in amperes (A)  

The proportionality constant k is now known as the electrolytic conductivity (formerly specific conductivityX and its units are O cm h It is the conductance of a I cm cube. 

Kohlrausch realized that the electrolytic conductivity is not a suitable quantity for comparing the conductivities of different solutions. If a solution of one electrolyte is much more concentrated than another, it may well have a higher conductivity simply because it contains more ions the value of the electrolytic conductivity thus does not immediately tell us anything of significance about the solution. What is needed instead is a property in which there has been some compensation for the differences in concentrations. Such a property, first defined and used by Kohlrausch, is now called the molar conductivity and given the symbol A (lambda). It can be 

---

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. 

Ionic liquid System Cation Anion(s) Temperature, (X Conduc- tivity (k), mS cm Conduc- tivity method Viscosity (n), cP Viscosity method Density (p), gcm Density method Molar conductivity fAJ, cm iT mor Walden product (An) Ref. 

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 ... 

Table 53 presents coefficients of the molar conductivity of molten systems K2TaF7 - KF and K2TaF7 - KCI. 

Table 53. Molar conductivity (p, cm2ohm mot1) and conductivity activation energy (U of molten systems KF - K2TaF7 and KCl - K2TaF7. Reproduced from [324], A. I. Agulyansky, P. T. Stangrit, V. I. Konstantinov, Zh. Prikl. Khim. 51 (1978) 2720, Copyright 1978, with permission of Nauka (Russian Academy of Sciences) publishing.

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... 

Fig. 63. Isotherms (800°C) of the molar conductivity of molten systems KF -KfTaFj (1), KCl - K FaF7 (2) and an ideal system versus the concentration of TaFs.

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. 

As a whole, the KF — TaF5 system forms melts that are characterized by a decrease in molar volume and increase in molar conductivity, as demonstrated in Fig. 64. This behavior enables classification of the system as a lib-type... 

Methyl iso-butyl ketone, 279-281 Microcalorimetry, 237 Molar conductivity, 155, 160 Molar volume, 156, 160... 

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 ... 

Mohr procedure exptl. details of, 349, 351 Molar absorption coefficient 649 Molar conductivity 520 Molar extinction coefficient see Molar absorption coefficient Molar solution definition, 260 Molarity 259 Mole 259... 

Conductivity measurements yield molar conductivities A (Scm2 mol-1) at salt concentration c (mol L-1). A set of data pairs (Af, c,), is evaluated with the help of non linear fits of equations [89,93,94] consisting of the conductivity equation, Eq. (7), the expression for the association constant, Eq. (3), and an equation for the activity coefficient of the free ions in the solution, Eq.(8) the activity coefficient of the ion pair is neglected at low concentrations. 

Table 4. Molar conductivities of LiBF4 in DME at zero concentration and their standard deviations at 25 °C according to different methods...

Conductivities k of electrolytes are related to molar conductivities A, ion conductivities A, and ionic mobilities w(- by Eq. (57)... 

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

Radii of anions of lithium salts and limiting molar conductivities in solvents of... 

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... 

A,. limiting molar conductivity of electrolyte in presence of ligand III.7 ... 

They measured the formation of ionic species in the pulse radiolysis of a 10"3 m MTMSO aqueous solution saturated by N20 gas at pH 5.6 by conductivity detection and found an increase in conductivity. Assuming the molar conductivity of CH3SCH2S02 to be the same as that measured for CH3S02- 45, it is found that G(CH3SCH2S02") = 2.7. 

The terms specifie conductivity and equivalent conductivity were previously used. However, these terms are not recommended for use as the SI units. They should be replaced by molar conductivity according to the SI recommendation, which states as follows, When the mole is used, the elementary entities must be specified and may be atoms, molecules, ions, electrons, other particles, or specified groups of such particles. Thus, when we previously used equivalent conductivity, we should now use molar conductivity, where we define the molar unit so that it is equal to the equivalent unit previously used. For example, we define (l/2)Ca, (l/3)La, (l/2)CO and Alj/jF as molar units. 

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. 

The parameters of molar conductivity of the electrolyte, A = a/c,, and molar conductivity of ions, Xj = ZjFuj (units S cm /mol), are also used to describe the properties of electrolyte solutions (A is used only in the case of binary solutions). With Eq. (1.14), we can write for a binary solution... 

For the change of molar conductivity of the ions which occurs with increasing concentration, only the mobility decrease is responsible in dilute solutions a limiting value of X° = ZjFuf is attained. A limiting value of molar conductivity A° implies limiting values X° as well as complete dissociation ... 

These terms are no longer recommended. Instead, we consider the molar conductivities of electrolytes and ions as defined above and where necessary indicate the electrolyte units to which the concentrations refer for example, A(MgCl2) or A( MgCl2), A(Ca"+) or A( Ca +). We evidently have A( MgCl2) = -lAIMgCy. 

In electrolyte solutions the molecules dissociate into ions spontaneously, so that the solution becomes conductive. Different electrolytes exhibit different degrees of dissociation, a, which will influence the actual values of molar conductivity A the two parameters are interrelated as... 

---