Electrostatic interactions Debye-Huckel theory

This concept is due to Bjerrum, who in 1926 suggested that in simple electrolytes ions of the opposite charge could associate to form ion-pairs (Szwarc, 1965 Robinson Stokes, 1959). This concept of Bjerrum arose from problems with the Debye-Huckel theory, when the assumption that the electrostatic interaction was small compared with IcTwas not justified. 

When A > A the ions are free and the Debye-Huckel theory applies. When A < A the two ions tend to approach each other and form an ion-pair, and there is no contribution to the electrostatic energy from the interaction between an ion and its atmosphere. 

The increase of the -> ionic strength (I) will influence the electrostatic interactions (-> Bronsteds salt effect, -+ Bronsted-Bjerrum equation) which can be taken into account by using the Debye-Huckel theory ... 

In addition to the short-range interactions between species in all solutions, long-range electrostatic interactions are found in electrolyte solutions. The deviation from ideal solution behavior caused by these electrostatic forces is usually calculated by some variation of the Debye-Huckel theory or the mean spherical approximation (MSA). These theories do not include terms for the short-range attractive and repulsive forces in the mixtures and are therefore usually combined with activity coefficient models or equations of state in order to describe the properties of electrolyte solutions. 

In the preceding sections, we have discussed nonspecific adsorption, where long-range electrostatic forces perturb the distribution of ions near the electrode surface, and specific adsorption, where a strong interaction between the adsorbate and the electrode material causes the formation of a layer (partial or complete) on the electrode surface. The difference between nonspecific and specific adsorption is analogous to the difference between the presence of an ion in the ionic atmosphere of another, oppositely charged, ion in solution (e.g., as modeled by the Debye-Huckel theory) and the formation of a bond between the two solution species (as in a complexation reaction). 

Debye-Huckel theory A theory to explain the nonideal behaviour of electrolytes, published in 1923 by Peter Debye (1884-1966) and Erich HUckel (1896- ). It assumes that electrolytes in solution are fully dissociated and that nonideal behaviour arises because of electrostatic interactions between the ions. The theory shows how to calculate the extra free energy per ion resulting from such interactions, and consequently the activity coefficient. It gives a good description of nonideal electrolyte behaviour for very dilute solutions, but cannot be used for more concentrated electrolytes. 

Electrostatic interactions give a large deviation from ideality in equilibrium properties of solutions containing low molecular weight electrolytes. This deviation was most successfully disposed of by the Debye-Huckel theory [2]. According to this theory, the ionic species are not distributed in solution in a random manner, but form an ionic atmosphere structure, and the thermodynamic properties such as the activity coefficient of solvent (or the osmotic coefficient), the mean activity coefficient of solute, and the heat of dilution, decrease linearly with the square root of the concentration, in conformity with experimental observations. 

For weakly concentrated solutions, (< 0.01 mol 1 ), it is possible to calculate values for the individual ionic activity coefficients by a microscopic approach using the Debye-Huckel theory. This theory treats electrostatic interactions between ions as if each ion were surrounded by a cloud of ions of opposite charge [4]. The result of the calculation (2.32) shows that an individual ionic activity coefficient depends on the ionic strength of the solution J, expressed in mol 1 and defined by (2.31). 

The real behavior of systems is described by the activity coefficient y,. Instead of the concentration C of a dissolved species, one uses the activity a, = c y,. In the light of the Debye-Hiickel theory, y takes care of the electrostatic interactions of the ions. This is the main interaction for charged species in comparison with the smaller dipole and Van der Waals forces, which may be important in the case of uncharged species, but which are not included in the Debye-Huckel theory. The chemical potential p depends on the concentration according to Equation 1.37. 

Further simphfication of the SPM and RPM is to assume the ions are point charges with no hard-core correlations, i.e., du = 0. This is called the Debye-Huckel (DH) level of treatment, and an early Nobel prize was awarded to the theory of electrolytes in the infinite-dilution limit [31]. This model can capture the long-range electrostatic interactions and is expected to be valid only for dilute solutions. An analytical solution is available by solving the Pois-son-Boltzmann (PB) equation for the distribution of ions (charges). The PB equation is... 

Ionic strength appears in each of the various expressions used to calculate activity coefficients in aqueous solutions. The DeBye-Hxickel theory of interaction of ions in aqueous solution incorporates both the electrostatic interactions between ions and the thermal motion of the ions. The basic equation, called the DeBye-Huckel limiting law, was... 

Let us nov/ consider the perturbation of water structure by solutes there are three distinct types of solutes. First of all, let us discuss ions M X H20. We would like to study the environment of an ion in solution, the hydration shell. We also want to study the interaction between ions in solutions, including their hydration shells. The classical theories, based on the Debye-Huckel formalism, only deal in electrostatics, and therefore the solvent continuum only has one property, a dielectric permittivity. 

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