Learn basic and advanced concepts of Debye Huckel Onsager Equation to clear IIT JEE Main, Advanced & BITSAT exam at Embibe, prepared by ✓ IIT Faculty. The verification of the Debye-Huckel-Onsager equation is more difficult for in the derivation of the Onsager equation holds good only for ions in dilute solution. Notes on Debye-Hückel Theory. We seek: µi = µi o + RT ln simple expression for ψi. One of the fundamental laws of electrostatics (Maxwell’s first equation) is.

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For example, with the electrolyte Equatoon. This is the potential energy of a single ion in a solution. The solvent pale blue is shown as a uniform medium, without structure. To apply this formula it is essential that the cloud has spherical symmetry, that is, the charge density is a function only of distance from the central ion as this allows the Poisson equation to be cast in terms of spherical coordinates with no angular dependence.

Ideality of electrolyte solution can be achieved only in very dilute solutions. For very low values of the ionic strength the value of the denominator in the expression above becomes nearly equal to one.

Debye–Hückel theory

Activity coefficients are themselves functions of concentration as the amount of inter-ionic interaction increases as the concentration of the electrolyte increases. The cloud has a net negative charge.

Limiting here means “at the limit of the infinite dilution”. The last assumption means that each cation is surrounded by a spherically symmetric cloud of other ions. Deviations from the theory occur at higher concentrations and with electrolytes that produce ions of higher charges, particularly unsymmetrical electrolytes.


The most significant aspect of this result is the prediction that the mean activity coefficient is a function of ionic strength rather than the electrolyte concentration. In consequence ions are not randomly distributed throughout the solution, as they would be in an ideal solution. The ions are shown as spheres with unit electrical charge.

The second step is to calculate the charge density by means of a Boltzmann distribution. The multiple-charge generalization from electrostatics gives an expression for the potential energy of the entire solution see also: In general, the mean activity coefficient of a fully dissociated electrolyte of formula A n B m is given by [4].

When conductivity is measured the system is subject to an oscillating external dsbye due to the application of an AC voltage to electrodes immersed in the solution. By using this site, you agree to the Terms of Use and Privacy Policy. Freezing point depression measurements has been used to this purpose. Retrieved from ” https: By calculating the mean cebye coefficients from them the theory could be tested against experimental data.

Real solutions show departures from this kind of ideality at all but the very lowest concentrations see, for example, Raoult’s law.

Debye–Hückel theory – Wikipedia

Ddebye treatment given so far huckep for a system not subject to an external electric field. The mean activity coefficient is given by the logarithm of this quantity as follows see also: The principal assumption is that departure from ideality is due to electrostatic interactions between ions, mediated by Coulomb’s law: Activity coefficients of eqkation ions cannot be measured experimentally because an electrolyte solution must contain both positively charged ions and negatively charged ions.

For symmetrical electrolytes, this reduces to the modified spherical Bessel equation. Moreover, ionic radius is assumed to be negligible, but at higher concentrations, the ionic radius becomes comparable to the radius of the ionic atmosphere. However, this equation only applies to very dilute solutions and has been largely superseded by other equations due to Fuoss and Onsager, and and later.


The result has the form of the Helmholtz equation [10]. Thermodynamic models Electrochemistry Equilibrium chemistry Peter Debye. In this situation the mean activity coefficient is proportional to the square root of the ionic strength.

The first step is to specify the electrostatic potential for ion j by means of Poisson’s equation. On average, each ion is surrounded more closely by ions of opposite charge than by ions of like charge.

Activity, ais proportional to concentration, c. In an ideal electrolyte solution the activity coefficients of all the ions debyr equal to one. In addition it was assumed that the electric field causes the charge cloud to be distorted away from spherical symmetry.

To calculate this energy two steps are needed.

Similarly each anion is surrounded by a cloud with net positive charge. This equation applies to electrolytes with equal numbers of ions of degivation charge. The theory can be applied also to dilute solutions of mixed electrolytes. Essentially these deviations occur because the model is hopelessly oversimplifiedso there is little to be gained making small adjustments to the model.