The Determination of Consecutive Formation Constants of Complex Ions from Polarographic Data

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

• Introduction
• Experimental Technique
• Principal Reactions
• Experimental Results
• Fundamental Equations
• Current Application
• Conclusions
• Questions

3
Introduction

• This paper describes a method of mathematical
  analysis of the shift of half-wave potential with
  ligand concentrations
• This analysis makes possible
• the identification of the successive complex
  ions formed between a metal and a ligand
• the evaluation of the corresponding formation
  constants

4
Experimental Technique

• Voltammetry is utilized to obtain the necessary
  polarographic data, which is a measure of current
  vs. potential

• Principles of voltammetry
• a potential is applied between a reference and
  working electrode for a definite time
• a redox reaction takes place on the working
  electrode
• the electrons exchanged produce a current that is
  measured by an auxiliary electrode

5
Principal Reactions

• The reduction of a metal complex to the metallic
  state (amalgam) at the working electrode

Solution
diffusion
dissociation
redox
MLn
MLn
Mz nL-z/n
Mz nL-z/n
ze- Mz
electrode
M
compact layer
reaction layer
diffusion layer
6
Experimental Results

• Typical results
• As 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 surface
• The magnitude of the diffusion current is
  directly proportional to the analyte
  concentration in solution

I
Half-wave Potential E1/2
Diffusion Current, Id
E
7
Fundamental Equations

• Electrical Potential- assuming the electrode
  reactions are reversible
• Formation Reaction- assuming the formation of the
  complexes is rapid and reversible

8
Fundamental Equations (cont)

• Summing the formation reactions for the
  individual complexes and rearranging
• Current- concentrations of the complex and metal
  amalgam can be directly related to the current
• diffusion current electrode current

9
Fundamental Equations (cont)

• 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 metal ion (assuming g1)

10
Fundamental Equations (cont)

• 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 F0(X) with respect to
  CLgL is given by

11
Current Application

• Luther et al. (1996)
• Similar to before, the n1th derivative of F0(X)
  is
• Or

12
Conclusions

• The mathematical form of the F-Functions is very
  useful in
• establishing the number of complexes formed in a
  given system
• providing a qualitative check on the validity of
  the data
• determining the consecutive formation constants
  of metal-ligand complexes

13
Questions

• ?