1. Unit 3: Metal ligand equilibria in solution
Stepwise and overall formation constants and their interactions By: Ankit Petwal Id: 18-Cy-07 Program: Integrated M.Sc. Chemistry

2. Formation constants:
The formation constant or stability constant may be defined as the equilibrium constant for the formation of a complx in solution.
Measure of the strength of the interaction between the ligands, which come in contact to form the complex, and the metal center.
Example:
[Fe(OH2)6]3+ (aq) + SCN- (aq) ⇌ [Fe(SCN)(OH2)5]2+ (aq) + H20 (l)
Kf = [Fe(SCN)(OH2)5]2+ / [Fe(OH2)6]3+ [SCN- ]
The equilibrium constant,Kf of this reaction is called the formation constant of the complex.
The value of Kf indicates the strength of binding of the ligand relative to H20.
If Kf is large, the incoming ligand binds more strongly than solvent H20 .
If Kf is small , the incoming ligand binds more weakly than H20

3. Stepwise Formation constant:
According to the J. Bjerrum, the solution proceeds by the stepwise addition of the ligands to the central metal atom.
Thus, the formation of complex MLn by the stepwise formation method can be given as: ,
M + L Kn ⇌ ML K1 = [ML]/ [M][L]
ML + L ⇌ ML K2 = [ML2]/[ML][L]
ML2 + L ⇌ ML K3= [ML3]/[ML2][L] .
MLn-1 + L ⇌ MLn Kn = [MLn]/[MLn-1][L]
Where K1, K2, K3,- - - Kn are stepwise formation or stability constant for the complexes
formed in the corresponding steps.
The magnitude of these individual equilibrium constants indicates the extent of the formation of different species in a particular step.

4. Overall formation constant:
The formation of the complex MLn may also be expressed by the following steps and equilibrium constants.
M + L ⇌ ML β1 = [ML] / [M][L]
M+2L ⇌ ML β2 = [ML2] / [M][L]2
M+3L ⇌ ML β3 = [ML3] / [M][L]3 .
M+nL ⇌ MLn βn = [MLn]/[M][L]n
The equilibrium constant β1 , β2 , β3 ……. βn are called Overall formation or Stability constant for the complexes formed in corresponding Reactions.
βn = overall formation constant for MLn complex.

5. Relationship between stepwise formation constant and overall formation constant :
Consider the overall formation constant for complex [ML3]
β3 = [ML3] / [M][L]3
multiplying both numerator and denominator by [ML][ML2]
β3 = [ML3] [ML][ML2]/ [M][L]3 [ML][ML2]
β3 = [ML]/[M][L] × [ML2]/[ML][L] × [ML3]/[ML2][L]
β3= K1 × K2 × K3
In general ;
βn= K1× K2× K3× ………..×Kn
Thus, from the above equation, it is observed that the product of stepwise formation constant is always equal to the overall formation constant for any particular complex.