Chapter 12, Problem 12.17P

(a)

Interpretation Introduction

Interpretation:

The derivations of given ${\text{α}}_{\text{M}}$ and ${\text{α}}_{\text{M2}}$ expressions should be explained.

Concept Information:

Fraction of free metal ion:

In the metal ligand equilibria the number of moles of metal and ligand are equilibrium with number of mole of complex formed.

$\begin{array}{l}\text{M+}\text{L}\underset{}{\rightleftharpoons }\text{ML}{\text{β}}_1\text{=}\frac{\text{[ML]}}{\text{[M][L]}}\\ \text{M+}2\text{L}\underset{}{\rightleftharpoons }{\text{ML}}_2{\text{β}}_2\text{=}\frac{{\text{[ML}}_2\text{]}}{{\text{[M][L]}}^2}\\ \text{M+}\text{nL}\underset{}{\rightleftharpoons }{\text{ML}}_{\text{n}}{\text{β}}_{\text{n}}\text{=}\frac{{\text{[ML}}_{\text{n}}\text{]}}{{\text{[M][L]}}^{\text{n}}}\end{array}$

Where,

${\text{β}}_{\text{n}}$ is cumulative formation constant

Fraction of free metal ion ${\text{α}}_{\text{M}}$ is,

${\text{α}}_{\text{M}}\text{=}\frac{\text{[M]}}{{\text{[M}}_{\text{tot}}\text{]}}$

$\begin{array}{l}{\text{α}}_{\text{M}}\text{=}\frac{\text{[M]}}{{\text{[M]{1+β1[L]+β}}_{\text{2}}{\text{[L]}}^{\text{2}}\text{}}}\\ =\frac{1}{{\text{1+β1[L]+β}}_{\text{2}}{\text{[L]}}^{\text{2}}}\end{array}$

Where,

$\text{M}\text{is free metal ion}$

(b)

Interpretation Introduction

Interpretation:

The values of ${\text{α}}_{\text{M}}$ and ${\text{α}}_{\text{M2}}$ should be calculated.

Concept Information:

Fraction of free metal ion:

In the metal ligand equilibria the number of moles of metal and ligand are equilibrium with number of mole of complex formed.

$\begin{array}{l}\text{M+}\text{L}\underset{}{\rightleftharpoons }\text{ML}{\text{β}}_1\text{=}\frac{\text{[ML]}}{\text{[M][L]}}\\ \text{M+}2\text{L}\underset{}{\rightleftharpoons }{\text{ML}}_2{\text{β}}_2\text{=}\frac{{\text{[ML}}_2\text{]}}{{\text{[M][L]}}^2}\\ \text{M+}\text{nL}\underset{}{\rightleftharpoons }{\text{ML}}_{\text{n}}{\text{β}}_{\text{n}}\text{=}\frac{{\text{[ML}}_{\text{n}}\text{]}}{{\text{[M][L]}}^{\text{n}}}\end{array}$

Where,

${\text{β}}_{\text{n}}$ is cumulative formation constant

Fraction of free metal ion ${\text{α}}_{\text{M}}$ is,

${\text{α}}_{\text{M}}\text{=}\frac{\text{[M]}}{{\text{[M}}_{\text{tot}}\text{]}}$

$\begin{array}{l}{\text{α}}_{\text{M}}\text{=}\frac{\text{[M]}}{{\text{[M]{1+β1[L]+β}}_{\text{2}}{\text{[L]}}^{\text{2}}\text{}}}\\ =\frac{1}{{\text{1+β1[L]+β}}_{\text{2}}{\text{[L]}}^{\text{2}}}\end{array}$

Where,

$\text{M}\text{is free metal ion}$