The Determination of The Determination of Consecutive Formation Consecutive Formation
Constants of Complex Ions Constants of Complex Ions from Polarographic Datafrom Polarographic Data
Paper by: Donald D. DeFord and David Paper by: Donald D. DeFord and David N. HumeN. Hume
Presentation by: Molly FinsterPresentation by: Molly Finster
02/04/9902/04/99
ContentsContents
IntroductionIntroduction Experimental TechniqueExperimental Technique Principal ReactionsPrincipal Reactions Experimental ResultsExperimental Results Fundamental EquationsFundamental Equations Current ApplicationCurrent Application ConclusionsConclusions QuestionsQuestions
IntroductionIntroduction
This paper describes a method of This paper describes a method of mathematical analysis of the shift of mathematical analysis of the shift of half-wave potential with ligand half-wave potential with ligand concentrationsconcentrations
This analysis makes possible:This analysis makes possible:•the identification of the successive the identification of the successive complex ions formed between a metal and complex ions formed between a metal and a liganda ligand•the evaluation of the corresponding the evaluation of the corresponding formation constantsformation constants
Experimental TechniqueExperimental Technique
Principles of Principles of voltammetryvoltammetry• a potential is applied between a a potential is applied between a
reference and working reference and working electrode for a definite timeelectrode for a definite time
• a redox reaction takes place on a redox reaction takes place on the working electrodethe working electrode
• the electrons exchanged the electrons exchanged produce a current that is produce a current that is measured by an auxiliary measured by an auxiliary electrodeelectrode
Voltammetry is utilized to obtain the Voltammetry is utilized to obtain the necessary polarographic data, which is a necessary polarographic data, which is a measure of current vs. potentialmeasure of current vs. potential
Principal ReactionsPrincipal Reactions
The reduction of a metal complex to the metallic The reduction of a metal complex to the metallic state (amalgam) at the working electrode:state (amalgam) at the working electrode:
elec
trod
e
MLn
M+z + nL-z/n
MLn
M+z + nL-z/n
diffusiondissociation
Solution
ze- + M+z
redox
M
reaction layerdiffusion layer
compact layer
Experimental ResultsExperimental Results
Typical results:Typical results:
• As reduction commences, the current increasesAs reduction commences, the current increases• After a steep increase in current, the current is limited After a steep increase in current, the current is limited
by the rate at which the metal ions can diffuse from the by the rate at which the metal ions can diffuse from the solution to the working electrode surfacesolution to the working electrode surface
• The magnitude of the diffusion current is directly The magnitude of the diffusion current is directly proportional to the analyte concentration in solutionproportional to the analyte concentration in solution
Half-wave Potential
E1/2
Diffusion Current, Id
I
E
Fundamental EquationsFundamental Equations
Electrical PotentialElectrical Potential- assuming the - assuming the electrode reactions are reversible:electrode reactions are reversible:
Formation ReactionFormation Reaction- assuming the - assuming the formation of the complexes is rapid and formation of the complexes is rapid and reversible:reversible:
MM
aaae C
C
nF
RTEE
0
00 ln
iL
iLMMjMLjMLj CCKC )()(
Fundamental Equations Fundamental Equations (con’t)(con’t)
Summing the formation reactions for the Summing the formation reactions for the individual complexes and rearranging:individual complexes and rearranging:
CurrentCurrent- concentrations of the complex - concentrations of the complex and metal amalgam can be directly and metal amalgam can be directly related to the current:related to the current:• diffusion current:diffusion current: electrode current:electrode current:
j MLj
jL
jLMMj
jMLj
MM CCK
C
C
)()(
0
0
j
MLjcd CkIi 0aMe CkIi
Fundamental Equations Fundamental Equations (con’t)(con’t)
Substituting the above equations in to Substituting the above equations in to the electrical potential, one gets the the electrical potential, one gets the half-wave potentials of:half-wave potentials of:• the reducible ion in the presence of the the reducible ion in the presence of the
complex forming ligand:complex forming ligand:
• the metal ion (assuming the metal ion (assuming =1):=1):
j MLj
jL
jL
M
cac
Ck
I
I
nF
RTEE
)()(
ln)( 0
21
M
sas I
I
nF
RTEE ln)( 0
21
Fundamental Equations Fundamental Equations (con’t)(con’t)
Finally, by combining and rearranging Finally, by combining and rearranging the two half-wave potential equations, the two half-wave potential equations, one can get an expression consisting of one can get an expression consisting of experimentally measurable quantities:experimentally measurable quantities:
The the first derivative of The the first derivative of F0(X) with with respect to respect to CLL is given by: is given by:
c
scs
j MLj
jL
jLj
I
IEE
RT
nFCKXF log)()(435.0log)( 0
21
0
21
10
LL
s
C
KXF
XF
00
1
)(
)(
Current ApplicationCurrent Application
Luther et al. Luther et al. (1996)(1996)
Similar to Similar to before, the before, the n+1n+1th th derivative derivative of of F0(X) is:is:
Or:Or:
LL
s
nn
n C
KXF
XF
)(
)(1
s
nLLnn
KCXFXF
)()( 1
ConclusionsConclusions
The mathematical form of the F-The mathematical form of the F-Functions is very useful in:Functions is very useful in:• establishing the number of complexes establishing the number of complexes
formed in a given systemformed in a given system• providing a qualitative check on the validity providing a qualitative check on the validity
of the dataof the data• determining the consecutive formation determining the consecutive formation
constants of metal-ligand complexesconstants of metal-ligand complexes
QuestionsQuestions
??
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