A simple method for calculation of free metal ion concentrations in the presence of a chelating agent and multiple metal ions by successive approximation

Calculation of free metal ion concentrations in the presence of a chelating agent (ligand) and multiple metal ions is complicated. In this paper we describe a simple method for calculation of free ion concentrations from given total ion concentrations. The outline of this method is as follows: i) Using an arbitrarily chosen provisional value of free ligand concentration (p-Lf), calculate a total ligand concentration (Lt). ii) Divide the p-Lf by the ratio, the calculated Lt (c-Lt)/the specified Lt (s-Lt). Take the resulting value as the next p-Lf and repeat the calculation until c-Lt is close enough to s-Lt. At this point, p-Lf is supposed to be set to a good approximation of true free ligand concentration. iii) Finally, calculate free metal concentrations from the above approximation.