Chemistry Reference
In-Depth Information
The equilibrium constant for this reaction is given by:
K = [M(H
2
O)
n−1
L] [H
2
O]/[M(H
2
O)
n
][L]
(3.39)
The expression can be simplified by removing constants. The number of water mol-
ecules attached to each metal ion is constant, and in dilute solutions the concentra-
tion of water is essentially constant. The expression becomes
K = [ML]/[M][L].
(3.40)
The stepwise coordination of a ligand L to a metal M to form a complex ML
n
, can
be represented as:
M + L ⇌ ML
K
1
= [ML]/[M][L]
(3.41)
ML + L ⇌ ML
2
K
2
= [ML
2
]/[ML][L]
(3.42)
ML
2
+ L ⇌ ML
3
K
3
= [ML
3
]/[ML
2
][L]
(3.43)
...
Or, in the general form,
ML
n−1
+ L ⇌ ML
n
K
n
= [ML
n
][ML
n−1
][L]
(3.44)
where the K
1
, K
2,
…, Kn represent individual stability constants.
An alternative representation may be the following:
M + L ⇌ ML
β
1
= [ML]/[M][L]
(3.45)
M + 2L ⇌ ML
2
β
2
= [ML
2
]/[M][L]
2
(3.46)
M + 3L ⇌ ML
3
β
3
= [ML
3
]/[M][L]
3
(3.47)
…
M + nL ⇌ ML
n
β
n
= [ML
n
]/[M][L]
n
(3.48)
where the β
1
, β
2
, …, β
n
represent overall stability constants.
The relationship that connects β
n
and K
n
:
β
1
= K
1
(3.49)
β
2
= K
1
·K
2
(3.50)
β
3
= K
1
·K
2
·K
3
(3.51)
…
β
n
= K
1
·K
2
….K
n
(3.52)
