Determination of the Structure and Effective Dielectric Constant of Hydrated Ions

Abstract

Debye's equation for the salting in or out of nonpolar compounds, such as benzene, in aqueous salt solutions was expanded so as to determine the effective dielectric decrement and constant of the hydrated domain of an ion. For ions having an electrostatic charge per surface area less than or equal to that of the K⁺ or Cl⁻ ions, this domain consists of a single layer of water molecules loosely or negatively hydrated to the ion; i.e., the domain consists of a mono-molecular B region. For ions having an electrostatic charge per unit surface area approximately equal to that of the Na⁺ and F⁻ ions, there exists no B region and only one layer of tightly bound or positively hydrated water (a monomolecular A region). Since the electrostatic field does not appreciably influence water molecules beyond this A region, such ions have an effective dielectric constant that is near zero, as in relatively inert molecules such as hydrocarbons. For all other ions, such as H⁺, Li⁺, Mg²⁺⁰,Cr²⁺, Sr²⁺, Ba²⁺, and other multivalent ions, there exists only one monomolecular A region followed by one monomolecular B region. The effective value of the dielectric constant of such an ion is obtained from its B region, since its A region cannot be penetrated. The effective dielectric decrement or constant of any B region as measured by benzene solubility goes through a maximum as the electrostatic charge per unit surface area (C/A) is decreased because a large C/A restricts the orientation of the hydrated water molecules and a low value of C/A allows competitive interaction between surrounding water molecules. Thus both small and large values of C/A decrease the solubility of benzene, i.e., decrease i t s ability to penetrate into the medium. A decrease in the macroscopic dielectric constant of water upon the addition of salt is due to the destruction of the clusters of water by the ions, or to the addition of ions which have effective dielectric constants less than that of water, or both. All hydrated ions o r molecules which salt-in or salt -out benzene have, respectfully, effective dielectric constants greater or less than that of water.