# Salt concentration and electrical permittivity of water

We know that the electric flux density $$D$$ can be related to electric field intensity $$E$$ as

$$D = \epsilon(\omega) E$$

where

$$\epsilon(\omega) = \epsilon_0 \epsilon_r(\omega)$$

and $$\epsilon_0$$ is the permittivity of vacuum and $$\epsilon_r(\omega)$$ is the relative permittivity of the material.

At the low-frequency limit, I would like to know how the value of $$\epsilon_r (\omega)$$ of water changes with temperature and salt ($$\ce{NaCl}$$) concentration. Please explain,

1. the rationale of the variation (from quantum mechanics or statistical mechanics etc)

2. observed trend holds good for any liquid or only for highly polar solvents

3. any references that you know of which talks in detail about these variations

The relative electric permittivity of water at $20^oC$ under the effect of a static or low frequency is $\epsilon_r\approx80$. Hasted (1948) conducted an experimental study on the dielectric properties of salt-water solutions and observed a dielectric decrement with salt concentration. That is, the addition of sodium chloride to water results in a drop in electrical permittivity.

Source: Hasted, Ritson and Collie (1948).

This can be understood by examining the following diagram.

The sodium and chloride ions dissociate in solution, resulting in an an electric field between them (shown in bold line). The water molecules, which are polarised, get oriented under the effect of the electric field so that their oxygen atoms (carrying a partial negative charge) face toward the sodium ion and their hydrogens (carrying partial positive charges) face toward the chloride ion. This orientation of the polar water molecules causes its own electric field (dashed lines), which cancels out most of the electric field that would exist if the ions were in a vacuum. The end result is that the sodium and chloride ions are effectively 'sheilded' by a 'hydration shell' of polarized water molecules which effectively lowers their to the applied external field and hence lowering the dielectric constant (electric permittivity) as the ionic concentration increases ().

In dilute solution (less than 2.0M) the dielectric decrement is linear. At higher salt concentrations, the dielectric decrement is observed to saturate at about $\epsilon_r=45$. The effect of sodium chloride concentration on electric permittivity is shown in the graph below at various temperatures.

Source: Gavish and Promislow (2012).

The above graph indicates that for a given salt concentration below about 3M, the electric permittivity decreases with temperature.

REFERENCES:

Hasted, J.B., Ritson, D.M., Collie, C.H., "Dielectric Properties of Aqueous Ionic Solutions. Parts I and II." Journal of Chemical Physics 16, 1 (1948). http://dx.doi.org/10.1063/1.1746645

Gavish, N., Promislow, K, "Dependence of the dielectric constant of electrolyte solutions on ionic concentration", http://arxiv.org/pdf/1208.5169.pdf

• Excellent answer. Just to clarify, this decrease is mainly due to the polarization of water molecules. If i use a non polar solvent can i expect electrical permittivity to NOT change as a function of concentration? – WanderingMind Nov 6 '14 at 19:46