Chapter 12, Problem 12.3P

(a)

Interpretation Introduction

Interpretation:

At $\text{9}\text{.0}\text{pH}$, the conditional formation constant for $\text{Mg}{\left(\text{EDTA}\right)}^{\text{2-}}$ should be calculated.

Concept Information:

Conditional Formation Constant:

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

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

The formation constant for above complex reaction is,

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

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

Degree of dissociation:

The ratio of mole of reactant that underwent to dissociating to mole of initial reactant is known as degree of dissociation.

In EDTA the degree of dissociation is,

$\begin{array}{l}\text{α}{}_{{\text{Y}}^{\text{4-}}}\text{=}\frac{{\text{[Y}}^{\text{4-}}\text{]}}{{\text{[H}}_{\text{6}}{\text{Y}}^{\text{2+}}{\text{]+[H}}_{\text{5}}{\text{Y}}^{\text{+}}{\text{]+[H}}_{\text{4}}{\text{Y]+[H}}_{\text{3}}{\text{Y}}^{\text{-}}{\text{]+[H}}_{\text{2}}{\text{Y}}^{\text{2-}}{\text{]+[H}}_{\text{3}}{\text{Y}}^{\text{3-}}{\text{]+[Y}}^{\text{4-}}\text{]}}\\ \text{=}\frac{{\text{[Y}}^{\text{4-}}\text{]}}{\text{[EDTA]}}\end{array}$

If pH is fixed, the $\text{α}{}_{{\text{Y}}^{\text{4-}}}$ is constant and ${\text{K}}_{\text{f}}$ will be ${\text{K}}_{\text{f}}\text{'}$

$\text{The formation constant}{\text{K}}_{\text{f}}\text{'=}{\text{α}}_{{\text{Y}}^{\text{4-}}}{\text{K}}_{\text{f}}\text{=}\frac{{\text{[MY}}^{\text{n-4}}\text{]}}{{\text{[M}}^{\text{n+}}\text{][EDTA]}}$

Where,

${\text{K}}_{\text{f}}\text{' is the conditional formation constant}$

(b)

Interpretation Introduction

Interpretation:

At $\text{9}\text{.0}\text{pH}$, the concentration of ${\text{Mg}}^{\text{2+}}$ ion should be calculated.

Concept Information:

Conditional Formation Constant:

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

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

The formation constant for above complex reaction is,

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

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

Degree of dissociation:

The ratio of mole of reactant that underwent to dissociating to mole of initial reactant is known as degree of dissociation.

In EDTA the degree of dissociation is,

$\begin{array}{l}\text{α}{}_{{\text{Y}}^{\text{4-}}}\text{=}\frac{{\text{[Y}}^{\text{4-}}\text{]}}{{\text{[H}}_{\text{6}}{\text{Y}}^{\text{2+}}{\text{]+[H}}_{\text{5}}{\text{Y}}^{\text{+}}{\text{]+[H}}_{\text{4}}{\text{Y]+[H}}_{\text{3}}{\text{Y}}^{\text{-}}{\text{]+[H}}_{\text{2}}{\text{Y}}^{\text{2-}}{\text{]+[H}}_{\text{3}}{\text{Y}}^{\text{3-}}{\text{]+[Y}}^{\text{4-}}\text{]}}\\ \text{=}\frac{{\text{[Y}}^{\text{4-}}\text{]}}{\text{[EDTA]}}\end{array}$

If pH is fixed, the $\text{α}{}_{{\text{Y}}^{\text{4-}}}$ is constant and ${\text{K}}_{\text{f}}$ will be ${\text{K}}_{\text{f}}\text{'}$

$\text{The formation constant}{\text{K}}_{\text{f}}\text{'=}{\text{α}}_{{\text{Y}}^{\text{4-}}}{\text{K}}_{\text{f}}\text{=}\frac{{\text{[MY}}^{\text{n-4}}\text{]}}{{\text{[M}}^{\text{n+}}\text{][EDTA]}}$

Where,

${\text{K}}_{\text{f}}\text{' is the conditional formation constant}$