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The Born–Landé equation is a means of calculating the lattice energy of a crystalline ionic compound.In 1918 [1] Max Born and Alfred Landé proposed that the lattice energy could be derived from the electrostatic potential of the ionic lattice and a repulsive potential energy term.
The ionic strength of a solution is a measure of the concentration of ions in that solution. Ionic compounds, when dissolved in water, dissociate into ions. The total electrolyte concentration in solution will affect important properties such as the dissociation constant or the solubility of different salts. One of the main characteristics of a ...
The Davies equation is an empirical extension of Debye–Hückel theory which can be used to calculate activity coefficients of electrolyte solutions at relatively high concentrations at 25 °C. The equation, originally published in 1938, [ 1 ] was refined by fitting to experimental data.
For very low values of the ionic strength the value of 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. This is known as the Debye–Hückel limiting law. In this limit the equation is given as follows [14]: section 2.5.2
They can be used to calculate mixed ion activity coefficients and water activities in solutions of high ionic strength for which the Debye–Hückel theory is no longer adequate. They are more rigorous than the equations of specific ion interaction theory (SIT theory), but Pitzer parameters are more difficult to determine experimentally than ...
In practice the molar ionic conductivities are calculated from the measured ion transport numbers and the total molar conductivity. For the cation + = + +, and similarly for the anion. In solutions, where ionic complexation or associaltion are important, two different transport/transference numbers can be defined.
The calculated lattice energy gives a good estimation for the Born–Landé equation; the real value differs in most cases by less than 5%. Furthermore, one is able to determine the ionic radii (or more properly, the thermochemical radius) using the Kapustinskii equation when the lattice energy is known.
where z is the ionic charge, and F is the Faraday constant. [9] The limiting molar conductivity of a weak electrolyte cannot be determined reliably by extrapolation. Instead it can be expressed as a sum of ionic contributions, which can be evaluated from the limiting molar conductivities of strong electrolytes containing the same ions.