Chapter 12, Problem 12.19P

Interpretation Introduction

Interpretation:

The derivation of spreadsheet equation for auxiliary complexing agent should be explained.

Concept Information:

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,

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

The spreadsheet equation for auxiliary complexing agent for metal with ligand is,

$\varphi \text{=}\frac{{\text{1+K}}_{\text{f}}{\text{''[M]}}_{\text{free}}\text{-}\frac{{\text{[M]}}_{\text{free}}{\text{+K}}_{\text{f}}{\text{''[M]}}^{\text{2}}{}_{\text{free}}}{{\text{C}}_{\text{M}}}}{{\text{K}}_{\text{f}}{\text{''[M]}}_{\text{free}}\text{+}\frac{{\text{[M]}}_{\text{free}}{\text{+K}}_{\text{f}}{\text{''[M]}}^{\text{2}}{}_{\text{free}}}{{\text{C}}_{\text{EDTA}}}}$

The spreadsheet equation for auxiliary complexing agent for ligand with metal is,

$\varphi \text{=}\frac{{\text{1+K}}_{\text{f}}{\text{''[M]}}_{\text{free}}\text{-}\frac{{\text{[M]}}_{\text{free}}{\text{+K}}_{\text{f}}{\text{''[M]}}^{\text{2}}{}_{\text{free}}}{{\text{C}}_{\text{L}}}}{{\text{K}}_{\text{f}}{\text{''[M]}}_{\text{free}}\text{+}\frac{{\text{[M]}}_{\text{free}}{\text{+K}}_{\text{f}}{\text{''[M]}}^{\text{2}}{}_{\text{free}}}{{\text{C}}_{\text{M}}}}$

Where,

${\text{K}}_{\text{f}}\text{''}$ is Conditional formation constant at constant pH with auxiliary complexing agent.

${\text{[M]}}_{\text{free}}$ is free metal ion  concentration

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

${\text{C}}_{\text{L}}$ is total concentration of ligand ion

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