1. The Determination of Consecutive Formation Constants of Complex Ions from Polarographic Data Paper by: Donald D. DeFord and David N. Hume Presentation by: Molly Finster 02/04/99

2. Contents b Introduction b Experimental Technique b Principal Reactions b Experimental Results b Fundamental Equations b Current Application b Conclusions b Questions

3. Introduction b This paper describes a method of mathematical analysis of the shift of half-wave potential with ligand concentrations b This analysis makes possible: the identification of the successive complex ions formed between a metal and a ligandthe identification of the successive complex ions formed between a metal and a ligand the evaluation of the corresponding formation constantsthe evaluation of the corresponding formation constants

4. Experimental Technique b Principles of voltammetry a potential is applied between a reference and working electrode for a definite timea potential is applied between a reference and working electrode for a definite time a redox reaction takes place on the working electrodea redox reaction takes place on the working electrode the electrons exchanged produce a current that is measured by an auxiliary electrodethe electrons exchanged produce a current that is measured by an auxiliary electrode b Voltammetry is utilized to obtain the necessary polarographic data, which is a measure of current vs. potential

5. Principal Reactions b The reduction of a metal complex to the metallic state (amalgam) at the working electrode: electrode ML n M +z + nL -z/n ML n M +z + nL -z/n diffusiondissociation Solution ze - + M +z redox M reaction layer diffusion layer compact layer

6. Experimental Results b Typical results: As reduction commences, the current increasesAs reduction commences, the current increases After a steep increase in current, the current is limited by the rate at which the metal ions can diffuse from the solution to the working electrode surfaceAfter a steep increase in current, the current is limited by the rate at which the metal ions can diffuse from the solution to the working electrode surface The magnitude of the diffusion current is directly proportional to the analyte concentration in solutionThe magnitude of the diffusion current is directly proportional to the analyte concentration in solution Half-wave Potential E 1/2 Diffusion Current, I d I E

7. Fundamental Equations b Electrical Potential- assuming the electrode reactions are reversible: b Formation Reaction- assuming the formation of the complexes is rapid and reversible:

8. Fundamental Equations (con’t) b Summing the formation reactions for the individual complexes and rearranging: b Current- concentrations of the complex and metal amalgam can be directly related to the current: diffusion current:electrode current:diffusion current:electrode current:

9. Fundamental Equations (con’t) b Substituting the above equations in to the electrical potential, one gets the half-wave potentials of: the reducible ion in the presence of the complex forming ligand:the reducible ion in the presence of the complex forming ligand: the metal ion (assuming  =1):the metal ion (assuming  =1):

10. Fundamental Equations (con’t) b Finally, by combining and rearranging the two half-wave potential equations, one can get an expression consisting of experimentally measurable quantities:  The the first derivative of with respect to is given by:  The the first derivative of F 0 (X) with respect to C L  L is given by:

11. Current Application b Luther et al. (1996)  Similar to before, the n+1 th derivative of is:  Similar to before, the n+1 th derivative of F 0 (X) is: b Or:

12. Conclusions b The mathematical form of the F-Functions is very useful in: establishing the number of complexes formed in a given systemestablishing the number of complexes formed in a given system providing a qualitative check on the validity of the dataproviding a qualitative check on the validity of the data determining the consecutive formation constants of metal-ligand complexesdetermining the consecutive formation constants of metal-ligand complexes

13. Questions ?