Walden products

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. 

Table 2. Concentration c, conductivity

To minimize the effects of viscosity for purposes of comparing data between solvents, plots areoften made using the product of the ion mobility and the viscosity (Walden product) in place of mobility alone. A plot of the Walden product against the reciprocal of the crystallographic radii for several solvents is shown in Fig. 6. Arbitrary curves have been drawn to indicate general trends. Values in solvents for which precise transference numbers and conductance data are available, such as acetonitrile and nitromethane, give smooth curves. 

Halide ion mobilities follow the expected trends (Fig. 9). Chloride ion, with the smallest crystallographic radius of the three halides considered, is the most mobile in solvents such as nitrobenzene and dimethylformamide, where anion solvation is expected to be small. In these solvents the Walden products are large. 

A third method of estimating solvent basicity is provided by the donor number concept 14 ). The donor number of a solvent is the enthalpy of reaction, measured in kcal per mole, between the solvent and a Lewis add such as antimony (V) chloride. (Other Lewis acids, such as iodine or trimethyltin chloride, may be used, but the scale most often reported is that for SbCl5.) Available values for the SbCls donor number have been included in Table 1. Plots of the Walden product versus solvent basicity (A//SbC1 ) for several solvents are shown for lithium, sodium, and potassium ions in Fig. 10 and for the tetraalkylammon-... 

Cation Anion Tempe- rature, (K) Conduc- tivity 1, mS cm Conduc- tivity method Viscosity m. <=p Viscosity method Density (P), g cm- Density method Molar conductivity (A), cm Q mof Walden product ( ) Ref... 

To obtain the values of A0 and X0 at different temperatures we used the following equation, rather than the Walden product which is known to decrease with temperature (lb,lj ). 

We focus on the conductance data. In systems of the type considered here, the conductance is primarily determined by the degree of ion pair association a. However, at higher ion densities, substantial mobility effects come into play. In the absence of sufficiently accurate conductance theories for the region of interest, a reliable measure for estimating a. is the conductance-viscosity product Arj which is often denoted as the Walden product. Figure 7 shows isotherms for the Walden product at T Si Tc for Bu4NPic + 1-tridecanol [72] and Bu4NPic + 1-chloroheptane [137] as a function of the... 

Table 2.6 The limiting equivalent conductivities, A.00, and the Walden products, X°°r, of tetrabutylammonium and sodium ions in various solvents at 25°C (Kratochvil and Yeager 1972, Marcus 1997)... 

This equation is known as Walden s rule. The constant is called the Walden product. Although the salt contents of bulk ILs are very high (about 3-7 mol L-1), the Walden plots for a variety of ILs are similar to that of a conventional diluted system [113]. This observation indicates that ILs are ionized effectively, even in the bulk. However, ILs also contain ion aggregates which do not contribute to the ionic conductivity. Recent research shows more specifically how much ILs are ionized [114]. 

Walden product, is inversely proportional to rs (the size of the moving ion, including its solvation sphere) which in turn should be a measure of ion-solvent interactions. A comparison of Walden products (Cox, 1973) suggests that such an interpretation may be at least qualitatively reasonable. In water, K+ and Cl- have almost equal... 

Walden products, whereas in all dipolar aprotic solvents rj °(K+) 17X0 (Cl-). This suggests a large decrease in size of solvation shell of Cl-, relative to K+, on transfer from water. The quantitative significance of these electrochemical results with regard to calculated hydration numbers is in some doubt but they do appear to substantiate, at least in this particular case, conclusions drawn from thermodynamic measurements. 

Figure 21. Comparison of the temperature coefficient of the B-viscosity coefficient and that of the Walden product for various ions in water (Kay, 1968).

Some emf studies have been reported for salt solutions in sulpho-lane + water mixtures (Tommila and Belinskij, 1969). It is noteworthy that p/ a for m-nitroanilinium ions in these mixtures does not change regularly with change in solvent permittivity (Ang, 1972). Covington et al. (1974) have suggested that, in these mixtures, Cs+ ions are preferentially solvated by sulpholane. The Walden product, A°r , for KC104 has a minimum near x2 = O 2 in sulpholane + water mixtures at 298 K (D Aprano et al., 1972). 

Dawson and co-workers115) examined the Walden products for a number of ions at 40 °C. They found the products in NMA to be higher than those in water for the... 

Conductometric and spectrophotometric behavior of several electrolytes in binary mixtures of sulfolane with water, methanol, ethanol, and tert-butanol was studied. In water-sulfolane, ionic Walden products are discussed in terms of solvent structural effects and ion-solvent interactions. In these mixtures alkali chlorides and hydrochloric acid show ionic association despite the high value of dielectric constants. Association of LiCl, very high in sulfolane, decreases when methanol is added although the dielectric constant decreases. Picric acid in ethanol-sulfolane and tert-butanol-sulfolane behaves similarly. These findings were interpreted by assuming that ionic association is mainly affected by solute-solvent interactions rather than by electrostatics. Hydrochloric and picric acids in sulfolane form complex species HCl and Pi(HPi). ... 

Ionic Walden Products. Fundamental work by Kay and Evans (22) has shown that a correct interpretation of the conductometric behavior of ions in water cannot be made without considering both the complex three-dimensional structure of water and the structure-breaking, structure-making properties of ions. On the other hand, if water is an atypical... 

Regarding water-dioxane mixtures, the maxima observed in Walden products are smaller than in water-alcohol mixtures and in these mixtures too the ions having a lower structure-breaking capacity show a higher increase in Walden products than in water. 

Let us now consider inorganic ionic behavior. Na+ shows R values greater than unity throughout almost the entire range of the solvent composition with a maximum at about 30 mol % TMS. Cl" and Br", up to 60 mol % in TMS, possess nearly constant values, and are roughly equal to those in water, while I" and C104", which are the best structurebreaking ions in water, show a minimum in Walden products at about 10 mol % TMS. Therefore Na+, contrary to anions, behaves in water-TMS as it does in the mixtures studied by Kay and Broadwater. 

Figure 2. Ionic Walden products normalized to their values in water as a function of mole percent organic solvents (- ), tert-Bu0H-H20 ...

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