Debye–Hückel equation

The Debye- Hückel theory (after Peter Debye and Erich Hückel ) describes the electrostatic interactions of ions in electrolyte solutions. This Coulomb attraction and repulsion forces lead to a deviation of the activity ( effective concentration, formerly "active mass ") of the ion species of their molar concentration according. The Debye- Hückel theory provides equations that the individual activity coefficient can be calculated as a function of concentration, temperature and dielectric constant of the solvent.

• 2.1 Activity coefficient f of the ion species
• 2.2 radius of the ion cloud
• 2.3 Debye- Hückel limiting law
• 2.4 Mean activity coefficient and Debye- Hückel limiting law

Basics

Model concept

Oppositely charged ions attract each other, homonymous charged ions repel each other. For these reasons, ions are not randomly distributed in a solution, but have a certain short range order, can be found in the anions rather near cations and vice versa ( Figure ). Electroneutrality of the solution is maintained here. In contrast to the ionic lattice ions can not be completely arranged regularly in solution because solvent molecules weaken as the dielectric Coulomb interactions, followed by the thermal motion leads to a greater distribution of the ions. Averaged over time, but each ion is located in the center of a cloud of oppositely charged ions ( in the figure by circles indicated ). This ion clouds shield the charge of the central ion, what is the reason for the introduction of the activity as " effective concentration " at ions.

Important parameters

Based on these conceptual models have P. Debye and E. Hückel derived some often used in electrochemistry equations by combining the Poisson equation with the Boltzmann statistics to describe the ion distribution. For simplicity, they used it, the following abbreviations

Results

Activity coefficient f of the ion species

Radius of the ion cloud

It turned out, that can be interpreted as the reciprocal of the radius of the ion cloud.

This radius is also called screening length or Debye length.

Debye- Hückel limiting law

Where A = is 0.509 kg1 / 2 mol -1/2 to put, when water is used at 25 ° C as the solvent. For other temperatures and / or solvent must be calculated according to the equation given above.

This is the most commonly quoted for practical purposes equation that results in the approximation. Thus, it applies to ion clouds, which are substantially larger than the enclosed ion. As a rule, the very dilute solutions with mol · dm- third

Mean activity coefficient and Debye- Hückel limiting law

Individual activity coefficients (or activities ) can indeed be calculated, but are not measured due to the electroneutrality condition. For the measurable mean activity coefficient of an electrolyte

For details, see activity.

For the calculation of the conductance coefficient for determining the equivalent conductance, the Debye-Hückel 's law can also be used, however, the discharge is more complicated. Activity and conductivity coefficients of a solution differ significantly. The activity coefficient, for example, the law of mass action, in the determination of the solubility product, used the boiling point elevation, but not for conductivity determinations.

Debye- Hückel - Onsager law for the conductivity of ions

Onsager (1927), the theory has been used for conductivity measurements. The oppositely charged ion cloud around the central ion slows down the rate of migration of the central ion Debye - Hückel. The viscosity of the solvent has important impact on the magnitude of the deceleration. With a directional movement in an electric field now occurs, a disturbance of the symmetry of the ion cloud. The time period until the ions rearrange again called relaxation time. The force generated by movement of the central asymmetry with braking effect is called relaxation or Wien effect.

Originally established by Kohlrausch and Ostwald theory of ion mobilities ( cal Ostwald 's dilution law, Kohlrausch cal square root law ) was held by the Debye - Hückel - Onsager theory improvements. The ion mobility and the equivalent conductivity are concentration dependent.

For the solvent is water, at 25 ° C, the following relationship can be established for (strong ) of 1,1- electrolytes:

For 2,1- electrolytes (e.g., Na2SO4) about applies in water at 25 ° C:

1,2- electrolytes (e.g., MgCl2) applies approximately in water at 25 ° C:

For 2,2 - electrolytes in water at 25 ° C applies:

For 3,1 - electrolytes in water at 25 ° C applies:

However, the above formulas are only for dilute (up to 0.01 mol / liter) solutions applicable

Improvements of the theory came through the mathematical descriptions of double, cation-anion under E. Vickie M. Eigen. With these models, the Debye- Hückel - Onsager law was extended to more concentrated solutions (up to 1 mol / liter).

At high frequencies corresponding to the relaxation time, eliminating the electrostatic retarding effect of the ion motion.