Chapter 18, Problem 18.128P

(a)

Interpretation Introduction

Interpretation:

The following salts have to be ranked in order of increasing $\text{pH}$ of their $\text{0}\text{.1}\text{M}$ aqueous solutions:

  ${\text{KNO}}_{\text{3}}\text{,}{\text{K}}_{\text{2}}{\text{SO}}_{\text{3}}\text{,}{\text{K}}_{\text{2}}\text{S,}{\text{Fe(NO}}_{\text{3}}{\text{)}}_{\text{2}}$

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

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

The dissociation of a base can be given as

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

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

  $\begin{array}{l}{\text{K}}_{\text{b}}{\text{ = [BH}}^{\text{+}}{\text{][OH}}^{\text{-}}\text{] / [B]}\\ \\ {\text{pK}}_{\text{b}}{\text{= -log K}}_{\text{b}}\\ \\ {\text{pH = pK}}_{\text{b}}{\text{ = -logK}}_{\text{b}}\end{array}$

The ${\text{K}}_{\text{a}}$ and ${\text{K}}_{\text{b}}$ are related to each other through the ion constant of water.

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

As ${\text{K}}_{\text{a}}$ and ${\text{K}}_{\text{b}}$ are equal, if one increases, the other decreases.

The larger ${\text{K}}_{\text{a}}$ value gives the lower $\text{pH}$ and the larger ${\text{K}}_{\text{b}}$ value gives the higher $\text{pH}$.

(b)

Interpretation Introduction

Interpretation:

The following salts have to be ranked in order of increasing $\text{pH}$ of their $\text{0}\text{.1}\text{M}$ aqueous solutions:

  ${\text{NH}}_{\text{4}}{\text{NO}}_{\text{3}}\text{,}{\text{NaHSO}}_{\text{4}}\text{,}{\text{NaHCO}}_{\text{3}}\text{,}{\text{Na}}_{\text{2}}{\text{CO}}_{\text{3}}$

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

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

The dissociation of a base can be given as

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

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

  $\begin{array}{l}{\text{K}}_{\text{b}}{\text{ = [BH}}^{\text{+}}{\text{][OH}}^{\text{-}}\text{] / [B]}\\ \\ {\text{pK}}_{\text{b}}{\text{= -log K}}_{\text{b}}\\ \\ {\text{pH = pK}}_{\text{b}}{\text{ = -logK}}_{\text{b}}\end{array}$

The ${\text{K}}_{\text{a}}$ and ${\text{K}}_{\text{b}}$ are related to each other through the ion constant of water.

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

As ${\text{K}}_{\text{a}}$ and ${\text{K}}_{\text{b}}$ are equal, if one increases, the other decreases.

The larger ${\text{K}}_{\text{a}}$ value gives the lower $\text{pH}$ and the larger ${\text{K}}_{\text{b}}$ value gives the higher $\text{pH}$.