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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In the chemistry of electrolyte solutions, an ideal solution is a solution whose colligative properties are proportional to the concentration of the solute. Real solutions show departures from this kind of ideality at all but the very lowest concentrations see, for example, Raoult’s law.
In order to accommodate these effects in the thermodynamics of solutions, the concept of activity was introduced: Activity, ais proportional to concentration, c. In an ideal electrolyte solution the activity coefficients of all the ions are equal to one. Ideality of electrolyte solution can be achieved only in very dilute solutions. Non-ideality of more concentrated solutions arises principally but not exclusively because ions of opposite charge attract each other due to electrostatic forces, while ions of the same charge repel each other.
In consequence ions are not randomly distributed throughout the solution, as they would be in an ideal solution. Activity coefficients of single ions cannot be measured experimentally because an electrolyte solution must contain both positively charged ions and negatively charged ions.
For example, with the electrolyte NaCl.
In general, the mean activity coefficient of a fully dissociated electrolyte of formula A n B m is given by . Activity coefficients are themselves functions of concentration as the amount of inter-ionic interaction increases as the concentration of the electrolyte increases.
By calculating the mean activity coefficients from them the theory could be tested against experimental data. It was found to give excellent agreement for “dilute” solutions. A snapshot of a 2-dimensional section of an idealized electrolyte solution is shown in the picture.
The ions are shown as spheres with unit electrical charge. The solvent pale blue is shown as a uniform medium, without structure. On average, each ion is surrounded more closely by ions of opposite charge than by ions of like charge.
Debye–Hückel theory – Wikipedia
The equatioon assumption is that departure from ideality is due to electrostatic interactions between ions, mediated by Coulomb’s law: The last assumption means that each cation is surrounded by a spherically symmetric cloud of other ions. The cloud has a net negative charge. Similarly each anion is surrounded by a cloud with net positive charge.
The deviation from ideality is taken to be a function of the potential energy resulting from the electrostatic interactions between ions and their surrounding clouds. To calculate this energy two steps are needed. The first step is to specify the electrostatic potential for ion j by means of Poisson’s equation.
To deby 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.
The second step is to calculate the charge density by means of a Boltzmann distribution. Nevertheless, the two equations can be combined to produce the Poisson—Boltzmann equation.
Solution of this equation is far from straightforward. The result has the form of the Helmholtz equation . This equation applies to electrolytes with equal numbers of ions of each charge.
For symmetrical electrolytes, this reduces to the modified spherical Bessel equation. This is the potential energy of a single ion in a solution. The multiple-charge generalization from electrostatics gives an expression for the potential energy debyf the entire solution see onsaget The mean activity coefficient is given by the logarithm of this quantity as follows see also: Extensions of the theory .
The most significant aspect of this result is the prediction that the mean activity coefficient is equxtion function of ionic strength rather than the electrolyte concentration. For very low values of the ionic strength the value deybe the denominator in the expression above becomes nearly equal to one. In this situation the mean activity coefficient is proportional to the square root of the ionic strength. Deviations from the theory occur at higher concentrations and with electrolytes that produce ions of higher charges, particularly unsymmetrical electrolytes.
Essentially these deviations occur because the model is hopelessly oversimplifiedso there is little to be gained making small adjustments to the model.
Moreover, ionic or is assumed to be negligible, but at higher concentrations, the ionic radius becomes comparable to the radius of the ionic atmosphere. The main extensions are the Davies equationPitzer equations and specific ion interaction theory. The theory can be applied also to dilute solutions of mixed electrolytes. Freezing point depression measurements has been used to this purpose.
The treatment given so far is for a system not subject insager an external electric field. When conductivity is measured the system is subject to an oscillating external field due to the application of an AC voltage to electrodes euation in the solution. All the postulates of the original theory were retained. In addition it was assumed that the electric field causes the charge cloud to be distorted away from spherical symmetry.
Limiting here means “at the limit of the infinite dilution”.
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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. From Wikipedia, the free encyclopedia. Lowering of freezing point and related phenomena” PDF.