Chapter 15, Problem 15.140MP

(a)

Interpretation Introduction

Interpretation:

The principal reaction is ${\text{2HA}}^{\text{-}}\stackrel{}{\rightleftharpoons }{\text{H}}_{\text{2}}{\text{A+A}}^{\text{2-}}$ has to be shown.

Concept Introduction:

Acid dissociation constant:

Consider a weak-acid equilibrium reaction,

$\text{HA}\stackrel{{\text{K}}_{\text{a}}}{\rightleftharpoons }{\text{H}}^{\text{+}}{\text{+A}}^{\text{-}}$

The acid dissociation constant ${\text{K}}_{\text{a}}$ can be given as,

${\text{K}}_{\text{a}}\text{=}\frac{\left[{\text{H}}^{\text{+}}\right]\left[{\text{A}}^{\text{-}}\right]}{\left[\text{HA}\right]}$

A weak acid is one that doesn’t undergo completion.

The negative logarithm of an equilibrium constant is called as $\text{pK}$

The ${\text{pK}}_{\text{a}}$ of weak acid is the negative logarithm of ${\text{K}}_{\text{a}}$ and can be given as,

${\text{pK}}_{\text{a}}\text{=-log}{\text{K}}_{\text{a}}$

The value of acid dissociation constant ${\text{K}}_{\text{a}}$ decreases with increase in ${\text{pK}}_{\text{a}}$

The value of ${\text{K}}_{\text{w}}$ is calculated by the formula,

${\text{K}}_{\text{w}}{\text{=K}}_{\text{a}}{\text{×K}}_{\text{b}}$

Base dissociation constant:

Consider a reaction of weak base,

${\text{B+H}}_{\text{2}}\text{O}\stackrel{{\text{K}}_{\text{b}}}{\rightleftharpoons }{\text{BH}}^{\text{+}}{\text{+OH}}^{\text{-}}$

The value of ${\text{K}}_{\text{b}}$ can be calculated as,

${\text{K}}_{\text{b}}\text{=}\frac{\left[{\text{BH}}^{\text{+}}\right]\left[{\text{OH}}^{\text{-}}\right]}{\left[\text{B}\right]}$

Where ${\text{K}}_{\text{b}}$ is called as base dissociation constant.

(b)

Interpretation Introduction

Interpretation:

The $\text{pH}$ at the first equivalence points is equal to the average of ${\text{pK}}_{\text{a1}}\text{and}{\text{pK}}_{\text{a2}}$ has to be shown.

Concept Introduction:

Acid dissociation constant:

Consider a weak-acid equilibrium reaction,

$\text{HA}\stackrel{{\text{K}}_{\text{a}}}{\rightleftharpoons }{\text{H}}^{\text{+}}{\text{+A}}^{\text{-}}$

The acid dissociation constant ${\text{K}}_{\text{a}}$ can be given as,

${\text{K}}_{\text{a}}\text{=}\frac{\left[{\text{H}}^{\text{+}}\right]\left[{\text{A}}^{\text{-}}\right]}{\left[\text{HA}\right]}$

A weak acid is one that doesn’t undergo completion.

The negative logarithm of an equilibrium constant is called as $\text{pK}$ .

The ${\text{pK}}_{\text{a}}$ of weak acid is the negative logarithm of ${\text{K}}_{\text{a}}$ and can be given as,

${\text{pK}}_{\text{a}}\text{=-log}{\text{K}}_{\text{a}}$

The value of acid dissociation constant ${\text{K}}_{\text{a}}$ decreases with increase in ${\text{pK}}_{\text{a}}$.

The value of ${\text{K}}_{\text{w}}$ is calculated by the formula,

${\text{K}}_{\text{w}}{\text{=K}}_{\text{a}}{\text{×K}}_{\text{b}}$

Base dissociation constant:

Consider a reaction of weak base,

${\text{B+H}}_{\text{2}}\text{O}\stackrel{{\text{K}}_{\text{b}}}{\rightleftharpoons }{\text{BH}}^{\text{+}}{\text{+OH}}^{\text{-}}$

The value of ${\text{K}}_{\text{b}}$ can be calculated as,

${\text{K}}_{\text{b}}\text{=}\frac{\left[{\text{BH}}^{\text{+}}\right]\left[{\text{OH}}^{\text{-}}\right]}{\left[\text{B}\right]}$

Where ${\text{K}}_{\text{b}}$ is called as base dissociation constant.

(c)

Interpretation Introduction

Interpretation:

The number of ${\text{A}}^{\text{2-}}$ ions present in $\text{50}\text{.0}\text{ml}\text{of}\text{1}\text{.0}\text{M}\text{NaHA}$ has to be calculated.