In this applet we explore several aspects of the Debye-Hückel theory of ionic solutions, including the concept of a shielded Coulomb potential, the Debye-Hückel limiting law, and the extended Debye-Hückel law.
A central concept in the development of the Debye-Hückel theory of ionic solutions is that of an ionic atmosphere, a time-averaged, spherical haze around a central ion that has a net charge equal in magnitude but opposite in sign to that of the central ion. The ionic atmosphere causes the electric potential to decay with distance more sharply than the Coulomb potential implies. The Coulomb potential,, has the form
Where eC is the elementary charge (1.602177 x 10-19 C), z is the charge number of the ion, r is distance (m), and is the medium permittivity (J-1 C2 m-1).
The ionic atmosphere shields the charge of the central ion. This effect is taken into account by replacing the Coulomb potential with the shielded Coulomb potential, , which is expressed in terms of the parameter rD, the Debye length.
To graph these equations select the appropriate tab and hit New Plot. Up to 5 plots can be displayed at one time. The Clear button will remove all plots. To see the parameters for each plot hit the Legend on/off button. The Redraw button will refresh the graph. This is useful when the function domain has been changed. To see the value of each plot at a given point, move your cursor to the desired location then click and hold.
The energy, and therefore the chemical potential of any central ion is lowered as a result of its interaction with the ionic atmosphere. This lowering of energy appears as the difference between the molar Gibbs energy and the ideal value of the solute, and hence can be identified with RT ln , where is the mean activity coefficient. The Debye-Hückel limiting law states that, for dilute aqueous solutions at 25 °C,
Where zcation is the absolute value of the charge number for the cation, zanion is the absolute value of the charge number for the anion, and I is the ionic strength.
When the ionic strength of the solution is too high for the limiting law to be valid, the activity coefficient may be estimated by the extended Debye-Hückel law:
where B is an empirical parameter.
To compare these two laws graphically click the Comparison tab.