# For the complex $M{{L}_{2}}$ stepwise formation constants for$M+L\rightleftharpoons ML$$ML+L\rightleftharpoons M{{L}_{2}}$ Are 4 and 3.Hence, overall stability constant for:$M+2L\rightleftharpoons M{{L}_{2}}$ is?   (A) 12  (B) 7  (C) 1.33  (D) 0.75

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Hint: The stability constant can be defined as the equilibrium constant for the formation of a complex in solution and an overall or cumulative constant,(β) is the constant for the formation of a complex from reagents. The overall stability constant can be obtained by multiplying the individual formation constants.

- Let’s start with the concept of stability constant. They are also called formation constants or, binding constants .It can be defined as the equilibrium constant for the formation of a complex in solution. It provides the information needed to calculate the concentration of the complex in a solution.
- The stability constant is a measure of the strength of the interaction between the reagents which come together to form a complex and there are mainly two kinds of complex: supramolecular complexes, such as host–guest complexes and complexes of anions and compounds formed by the interaction of a metal ion with a ligand.
- A overall or cumulative constant,(β) is the constant for the formation of a complex from reagents. Generally the cumulative constant for the formation of $M{{L}_{2}}$ is given by
$M+2L\rightleftharpoons M{{L}_{2}};{{\beta }_{12}}=\dfrac{\left[ M{{L}_{2}} \right]}{\left[ M \right]{{\left[ L \right]}^{2}}}$
The stepwise constants, ${{K}_{1}}$ and${{K}_{2}}$ refers to the formation of the complexes one step at a time
$M+L\rightleftharpoons ML;{{K}_{1}}=\dfrac{\left[ ML \right]}{\left[ M \right]\left[ L \right]}$
$ML+L\rightleftharpoons M{{L}_{2}};{{K}_{2}}=\dfrac{\left[ M{{L}_{2}} \right]}{\left[ ML \right]\left[ L \right]}$
A cumulative constant (β) can be expressed as the product of stepwise constants (${{K}_{1}}$ and ${{K}_{2}}$) and we can write as follows
${{\beta }_{12}}={{K}_{1}}{{K}_{2}}$
In the question the values of ${{K}_{1}}$ and${{K}_{2}}$ are given as 4 and 3 respectively. We are asked to find the overall stability constant (β or${{K}_{eff}}$) and it can be obtained by multiplying ${{K}_{1}}$ and${{K}_{2}}$.
${{K}_{eff}}={{K}_{1}}\times {{K}_{2}}=4\times 3=12$

Therefore the answer is option (A).12.

Note:
Keep in mind that the overall stability constant can also be expressed in terms of logarithmic scale as log β. The thermodynamic stability of the metal complexes can be calculated by the overall formation constant and if the value of log β is greater than 8, then the complex is considered as thermodynamically stable.