*5.2.5 Bjerrum's method*

For a successive metal complex formation, use this method. If ligand is protonate and the produced complex has maximum number of donate atoms of ligands, a selective light is absorbed by this complex, while for determination of stability constant, it is just known about the composition of formed species.

Bjerrum (1941) used the method stepwise addition of the ligands to coordination sphere for the formation of complex. So, complex metal–ligand-n forms as the following steps [22]. The equilibrium constants, K1, K2, K3, … Kn are called stepwise stability constants. The formation of the complex metal-ligandn may also be expressed by the following steps and equilibrium constants.

Where:

M = central metal cation

L = monodentate ligand

N = maximum coordination number for the metal ion M for the ligand

$$\text{Metal} + \text{Ligand} \leftrightharpoons \text{Metal} - \text{Ligand K}\_1 = \frac{(ML)}{[M][L]} \tag{34}$$

$$\text{Metal} - \text{Ligmoid} \leftrightharpoons \text{Metal} - \text{Ligmoid}\_2 \text{ K}\_2 = \frac{(ML\_2)}{[ML][L]} \tag{35}$$

$$\text{Metal} - \text{Ligmoid}\_2 \leftrightharpoons \text{Metal} - \text{Ligmoid}\_3 \text{ K}\_3 = \frac{(ML\_3)}{[ML\_2][L]} \tag{36}$$

$$\text{Thus } \text{Metal} - \text{Ligand}\_{n-1} + \text{Ligand} \Leftrightarrow \text{Metal} - \text{Ligand}\_{n} \text{K}\_{n} = \frac{(\text{ML}\_{n})}{[\text{ML}\_{n-1}][L]} \tag{37}$$

#### *5.2.6 Isotopic dilution method*

If a complex ion is slow to reach equilibrium, it is often possible to apply the method of isotopic dilution to determine the equilibrium concentration of one or more of the species. Most often radioactive isotopes are used.

#### *5.2.7 Conductance measurement method*

This method was extensively used by Werner and others to study metal complexes. In the case of a series of complexes of Co(III) and Pt(IV), Werner assigned the correct formulae on the basis of their molar conductance values measured in freshly prepared dilute solutions. In some cases, the conductance of the solution increased with time due to a chemical change, e.g.,

$$\left[\text{Co}(\text{NH}\_3)\_4\text{Br}\_2\right]^+ + 2\text{H}\_2\text{O} \left[\text{Co}(\text{NH}\_3)\_4(\text{H}\_2\text{O})\_2\right]^{\mathfrak{J}+} + 2\text{Br}^-\tag{38}$$

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