Chapter 12, Problem 12.22P

Interpretation Introduction

Interpretation:

The titration curve and plot for the given $\text{EDTA}$ titration should be drawn.

Concept introduction:

The titration curves and plot:

The observed values, which is recorded from the titration is plotted in a graph sheet is known as titration plot and the variation of plotted values result the curved graph line, the end point of the titration is determined from this graph line, where the maximum difference is results.

Spreadsheet equation for auxiliary complexing agent:

In the EDTA titration, the titration curve is drawn by a single equation, it is known as spreadsheet equation for auxiliary complexing agent and it applies whole titration because the reaction is carried out by at constant pH.

The spreadsheet equation for auxiliary complexing agent is,

$\varphi \text{=}\frac{{\text{C}}_{\text{EDTA}}{\text{V}}_{\text{EDTA}}}{{\text{C}}_{\text{M}}{\text{V}}_{\text{M}}}$

Where,

${\text{C}}_{\text{M}}$ is total concentration of metal ion

${\text{C}}_{\text{EDTA}}$ is concentration of metal EDTA

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,

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