Chapter 12, Problem 12.FE

Interpretation Introduction

Interpretation:

The ${\text{pCo}}^{\text{2+}}$ should be calculated respect with given volumes of $\text{EDTA}$ and graph of ${\text{pCo}}^{\text{2+}}$ vs volume of $\text{EDTA}$ should be drawn.

Concept introduction:

In the reaction of metal with ligand, the equilibrium constant is called as formation constant or the stability constant.

${\text{MY}}^{\text{n+}}+{\text{Y}}^{\text{4-}}\underset{}{\rightleftharpoons }{\text{MY}}^{\text{n4-}}$

The formation constant for above complex reaction is,

${\text{K}}_{\text{f}}\text{=}\frac{{\text{[M}}^{\text{n+}}{\text{][Y}}^{\text{4-}}\text{]}}{{\text{[MY}}^{\text{n4-}}\text{]}}$

Where,

${\text{K}}_{\text{f}}$ is formation constant

${\text{[M}}^{\text{+}}\text{]}$ is concentration of metal ion

${\text{[Y}}^{\text{4-}}\text{]}$ is concentration of ligand

${\text{[MY}}^{\text{n4-}}\text{]}$ is concentration of the acid

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,

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