Chapter 18, Problem 18.22P

(a)

Interpretation Introduction

Interpretation:

In a $\text{0}\text{.1 M}$ solution of an acid with ${\text{K}}_{\text{a}}{\text{= 1×10}}^{\text{-4}}$ or with ${\text{K}}_{\text{a}}{\text{= 4×10}}^{\text{-5}}$, the solution with higher $\text{pH}$ has to be given with explanation.

Concept Introduction:

The dissociation of an acid can be given as

  ${\text{HA + H}}_{\text{2}}\text{O}\rightleftharpoons {\text{A}}^{\text{-}}{\text{ + H}}_{\text{3}}{\text{O}}^{\text{+}}$

The relationship between $\text{pH}$ and ${\text{K}}_{\text{a}}$ can be given as

  $\begin{array}{l}{\text{K}}_{\text{a}}{\text{ = [H}}^{\text{+}}{\text{][A}}^{\text{-}}\text{] / [HA]}\\ \\ {\text{pK}}_{\text{a}}{\text{= -log K}}_{\text{a}}\\ \\ {\text{pH = pK}}_{\text{a}}{\text{ = -logK}}_{\text{a}}\end{array}$

At lower concentrations of hydronium ions (${\text{H}}_{\text{3}}{\text{O}}^{\text{+}}$), $\text{pH}$ is higher.

The $\text{pH}$ value increases with decrease in ${\text{K}}_{\text{a}}$ or the molarity of acid.

The $\text{pH}$ value decreases with increase in ${\text{K}}_{\text{a}}$ or the molarity of acid.

(b)

Interpretation Introduction

Interpretation:

In a $\text{0}\text{.1 M}$ solution of an acid with ${\text{pK}}_{\text{a}}\text{= 3}\text{.0}$ or with ${\text{pK}}_{\text{a}}\text{= 3}\text{.5}$, the solution with higher $\text{pH}$ has to be given with explanation.

Concept Introduction:

The dissociation of an acid can be given as

  ${\text{HA + H}}_{\text{2}}\text{O}\rightleftharpoons {\text{A}}^{\text{-}}{\text{ + H}}_{\text{3}}{\text{O}}^{\text{+}}$

The relationship between $\text{pH}$ and ${\text{K}}_{\text{a}}$ can be given as

  $\begin{array}{l}{\text{K}}_{\text{a}}{\text{ = [H}}^{\text{+}}{\text{][A}}^{\text{-}}\text{] / [HA]}\\ \\ {\text{pK}}_{\text{a}}{\text{= -log K}}_{\text{a}}\\ \\ {\text{pH = pK}}_{\text{a}}{\text{ = -logK}}_{\text{a}}\end{array}$

At lower concentrations of hydronium ions (${\text{H}}_{\text{3}}{\text{O}}^{\text{+}}$), $\text{pH}$ is higher.

The $\text{pH}$ value increases with decrease in ${\text{K}}_{\text{a}}$ or the molarity of acid.

The $\text{pH}$ value decreases with increase in ${\text{K}}_{\text{a}}$ or the molarity of acid.

(c)

Interpretation Introduction

Interpretation:

In a $\text{0}\text{.1 M}$ solution or $\text{0}\text{.01 M}$ of a weak acid, the solution with higher $\text{pH}$ has to be given with explanation.

Concept Introduction:

The dissociation of an acid can be given as

  ${\text{HA + H}}_{\text{2}}\text{O}\rightleftharpoons {\text{A}}^{\text{-}}{\text{ + H}}_{\text{3}}{\text{O}}^{\text{+}}$

The relationship between $\text{pH}$ and ${\text{K}}_{\text{a}}$ can be given as

  $\begin{array}{l}{\text{K}}_{\text{a}}{\text{ = [H}}^{\text{+}}{\text{][A}}^{\text{-}}\text{] / [HA]}\\ \\ {\text{pK}}_{\text{a}}{\text{= -log K}}_{\text{a}}\\ \\ {\text{pH = pK}}_{\text{a}}{\text{ = -logK}}_{\text{a}}\end{array}$

At lower concentrations of hydronium ions (${\text{H}}_{\text{3}}{\text{O}}^{\text{+}}$), $\text{pH}$ is higher.

The $\text{pH}$ value increases with decrease in ${\text{K}}_{\text{a}}$ or the molarity of acid.

The $\text{pH}$ value decreases with increase in ${\text{K}}_{\text{a}}$ or the molarity of acid.

(d)

Interpretation Introduction

Interpretation:

In a $\text{0}\text{.1 M}$ solution of a weak acid or a $\text{0}\text{.1 M}$ solution of a strong acid, the solution with higher $\text{pH}$ has to be given with explanation.

Concept Introduction:

The dissociation of an acid can be given as

  ${\text{HA + H}}_{\text{2}}\text{O}\rightleftharpoons {\text{A}}^{\text{-}}{\text{ + H}}_{\text{3}}{\text{O}}^{\text{+}}$

The relationship between $\text{pH}$ and ${\text{K}}_{\text{a}}$ can be given as

  $\begin{array}{l}{\text{K}}_{\text{a}}{\text{ = [H}}^{\text{+}}{\text{][A}}^{\text{-}}\text{] / [HA]}\\ \\ {\text{pK}}_{\text{a}}{\text{= -log K}}_{\text{a}}\\ \\ {\text{pH = pK}}_{\text{a}}{\text{ = -logK}}_{\text{a}}\end{array}$

At lower concentrations of hydronium ions (${\text{H}}_{\text{3}}{\text{O}}^{\text{+}}$), $\text{pH}$ is higher.

The $\text{pH}$ value increases with decrease in ${\text{K}}_{\text{a}}$ or the molarity of acid.

The $\text{pH}$ value decreases with increase in ${\text{K}}_{\text{a}}$ or the molarity of acid.

(e)

Interpretation Introduction

Interpretation:

In a $\text{0}\text{.1 M}$ solution of an acid or a $\text{0}\text{.01 M}$ solution of a base, the solution with higher $\text{pH}$ has to be given with explanation.

Concept Introduction:

The dissociation of an acid can be given as

  ${\text{HA + H}}_{\text{2}}\text{O}\rightleftharpoons {\text{A}}^{\text{-}}{\text{ + H}}_{\text{3}}{\text{O}}^{\text{+}}$

The relationship between $\text{pH}$ and ${\text{K}}_{\text{a}}$ can be given as

  $\begin{array}{l}{\text{K}}_{\text{a}}{\text{ = [H}}^{\text{+}}{\text{][A}}^{\text{-}}\text{] / [HA]}\\ \\ {\text{pK}}_{\text{a}}{\text{= -log K}}_{\text{a}}\\ \\ {\text{pH = pK}}_{\text{a}}{\text{ = -logK}}_{\text{a}}\end{array}$

At lower concentrations of hydronium ions (${\text{H}}_{\text{3}}{\text{O}}^{\text{+}}$), $\text{pH}$ is higher.

The $\text{pH}$ value increases with decrease in ${\text{K}}_{\text{a}}$ or the molarity of acid.

The $\text{pH}$ value decreases with increase in ${\text{K}}_{\text{a}}$ or the molarity of acid.

(f)

Interpretation Introduction

Interpretation:

In a solution of $\text{pOH 6}\text{.0}$ or a solution of $\text{pOH 8}\text{.0}$, the solution with higher $\text{pH}$ has to be given with explanation.

Concept Introduction:

The $\text{pOH}$ value of the solution is the concentration of hydroxide ions.

  ${\text{pOH = -log [OH}}^{\text{-}}\text{]}$

  $\begin{array}{l}{\text{K}}_{\text{w}}{\text{= [H}}_{\text{3}}{\text{O}}^{\text{+}}{\text{][OH}}^{\text{-}}\text{] = 1}{\text{.0 × 10}}^{\text{-14}}\\ \\ {\text{pK}}_{\text{w}}\text{ = pH + pOH = 14}\text{.00}\end{array}$