Debye-Huckel theory: How to calculate activity coefficient for ions and strong electrolytes in solution?

The Debye -Huckel equation is used to calculate ionic strength of ions in solution. It is based on the following:

1. Strong electrolytes completely ionize in dilute solutions.
2. Electrostatic interactions of oppositely charged ions lead to deviations from ideal solution behavior.

The Debye-Huckel equation for an ion i in solution is expressed as the following:

Where, Ɣi is the activity coefficient of an ion in solution, A is a constant that depends on temperature and dielectric constant of the solvent (A = 0.51 for water at 25 ºC), zi is the valence of the ion i, and µ is the ionic strength of the solution. The equation for a binary electrolyte in solution is expressed as the following:

Where, Ɣe is the mean ionic activity coefficient of an electrolyte in solution, z+ and z- are the valencies of the positively charged ion and the negatively charged ion respectively.

Example. Calculate activity coefficient for sodium ions (Na⁺) and the mean ionic activity coefficient for sodium chloride (NaCl) in an aqueous solution with an ionic strength value of 0.03 at 25 ºC.

For sodium ions:

log Ɣi = - 0.51 × 1² × sqrt(0.03) = -0.088

Ɣi = 10^-0.088 = 0.82

For sodium chloride:

log Ɣe = - 0.51 × 1 × 1 × sqrt(0.03) = -0.088

Ɣe = 10^-0.088 = 0.82