Effects of Ions on the Relaxation Times of the Solvents in Their Solutions

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There are three new "effects" related to the properties of relaxation time that arise when ions are added to water.

First, the solution's relaxation time appears to change. If solvent molecules are far away, say more than 1000 pm distant from an ion, the ion's effect on the relaxation time will be negligible. Conversely, water molecules bound to ions will be what is called dielectrically saturated; they will be so tightly held in the ion's local electric field that they will not be affected by the applied electric field used to measure the dielectric constant of the solution. The average relaxation time of all the waters will be increased, because the water molecules attached to the ions now have, in effect, an infinite relaxation time.

The second effect is related to the formation of ion pairs. If ion pairs or other ionic aggregates are present, they will introduce a new relaxation time above that exhibited by the pure solvent.

Figure 4.100 shows the Argand diagram1'of water (curve 1) and the permittivity for 0.8 M KC1 (curve 2) in water. The "structural" part of the spectrum is represented by curve 3. The difference of curves 2 and 3 is the result of electrolytic conductance.

*An Argand diagram (also called a Cole-Cole plot) is a diagram of the real e' and imaginary e" components of the dielectric constant of the system.

Fig. 4.100. Argand diagrams of a completely dissociated electrolyte and its pure solvent. Full circles: experimental data from frequency domain measurements on aqueous potassium chloride solutions at 25 °C. Curve 1: Argand diagram of pure water. Curve 2: Argand diagram, 0" = f(e')t of an 0.8 Maqueous KCI solution, Curve 3: Argand diagram, e"=f(e'), obtained from curve 2. (Reprinted from P. Turq, J. Barthel, and M. Chemla, in Transport, Relaxation and Kinetic Processes in Electrolyte Solutions, Springer-Verlag, Berlin, 1992, p. 78).

The permittivity of ionic solutions, is less than that of the pure solvent and decreases linearly with an increase in concentration. The reason for this has already been discussed (Section 2.12.1): water dipoles held by the very strong local field of an ion cannot orient against the weak applied field used in measuring the dielectric constant. The average is therefore decreased.

The linear relation found between dielectric constant and concentration can be interpreted in a first approximation as the result of a number of "irrotationally bound" waters. Such waters would constitute the primary hydration water referred to in Section 2.4.

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