Chapter 16, Problem 35A

(a)

Interpretation Introduction

Interpretation:

The concentration of ${\text{H}}^{\text{+}}$ ion in the solution having $\mathrm{p}\mathrm{O}\mathrm{H}=\text{ 4}\text{.88}$ should be calculated.

Concept Introduction:

The acidity or alkalinity of a solution is expressed by determining $\text{pH}$ of the solution. $\text{pH}$ of a solution is defined as negative logarithm of the concentration of ${\text{H}}^{\text{+}}$ ion in the solution. $\text{pH}$ is expressed as-

  $\text{pH}\text{=}\text{-}{\text{log[H}}^{\text{+}}\text{]}$

  $\text{pOH}$ of a solution is defined as negative logarithm of the concentration of hydroxyl ion $\left[{\text{OH}}^{\text{-}}\right]$ in the solution. $\text{pOH}$ is expressed as-

  $\text{pOH}=-\mathrm{l}\mathrm{o}\mathrm{g}[\mathrm{O}{\mathrm{H}}^{-}]$

Both $\text{pH}$ and $\text{pOH}$ are related to each other by this following equation-

  $\text{pH}\text{+}\text{pOH=}{\text{pK}}_{\text{w}}$

Answer to Problem 35A

The concentration of ${\text{H}}^{\text{+}}$ ion is $7.59\times {10}^{-10}\text{M}$ .

Explanation of Solution

Using the following equation to calculate concentration of ${\text{H}}^{\text{+}}$ ion in the solution,

  $\begin{array}{l}\text{pH}\text{=}\text{-}{\text{log[H}}^{\text{+}}\text{]}\\ {\text{[H}}^{\text{+}}\text{]}\text{=}{\text{10}}^{\text{-pH}}\end{array}$

The pH of the solution is calculated as:

  $\begin{array}{l}\text{pH}\text{=}\text{14}\text{-}\text{pOH}\\ =14-4.88\\ =9.12\end{array}$

Now, the concentration of hydrogen ion is calculated as:

  $\begin{array}{l}{\text{[H}}^{\text{+}}\text{]}\text{=}{\text{10}}^{\text{-pH}}\\ =10^{-9.12}=7.59\times 10^{-10}\mathrm{M}\end{array}$

The concentration of ${\text{H}}^{\text{+}}$ ion in the solution is $7.59\times {10}^{-10}\text{M}$

(b)

Interpretation Introduction

Interpretation:

The concentration of ${\text{H}}^{\text{+}}$ ion in the solution having $\mathrm{p}\mathrm{O}\mathrm{H}=\text{ 2}\text{.65}$ should be calculated.

Concept Introduction:

The acidity or alkalinity of a solution is expressed by determining $\text{pH}$ of the solution. $\text{pH}$ of a solution is defined as negative logarithm of the concentration of ${\text{H}}^{\text{+}}$ ion in the solution. $\text{pH}$ is expressed as-

  $\text{pH}\text{=}\text{-}{\text{log[H}}^{\text{+}}\text{]}$

  $\text{pOH}$ of a solution is defined as negative logarithm of the concentration of hydroxyl ion $\left[{\text{OH}}^{\text{-}}\right]$ in the solution. $\text{pOH}$ is expressed as-

  $\text{pOH}=-\mathrm{l}\mathrm{o}\mathrm{g}[\mathrm{O}{\mathrm{H}}^{-}]$

Both $\text{pH}$ and $\text{pOH}$ are related to each other by this following equation-

  $\text{pH}\text{+}\text{pOH=}{\text{pK}}_{\text{w}}$

Answer to Problem 35A

The concentration of ${\text{H}}^{\text{+}}$ ion is $4.47\times {10}^{-12}\text{M}$ .

Explanation of Solution

Using the following equation to calculate concentration of ${\text{H}}^{\text{+}}$ ion in the solution,

  $\begin{array}{l}\text{pH}\text{=}\text{-}{\text{log[H}}^{\text{+}}\text{]}\\ {\text{[H}}^{\text{+}}\text{]}\text{=}{\text{10}}^{\text{-pH}}\end{array}$

The pH of the solution is calculated as:

  $\begin{array}{l}\text{pH}\text{=}\text{14}\text{-}\text{pOH}\\ =14-2.65\\ =11.35\end{array}$

Now, the concentration of hydrogen ion is calculated as:

  $\begin{array}{l}{\text{[H}}^{\text{+}}\text{]}\text{=}{\text{10}}^{\text{-pH}}\\ =10^{-11.35}=4.47\times 10^{-12}\mathrm{M}\end{array}$

The concentration of ${\text{H}}^{\text{+}}$ ion in the solution is $4.47\times {10}^{-12}\text{M}$ .

(c)

Interpretation Introduction

Interpretation:

The concentration of ${\text{H}}^{\text{+}}$ ion in the solution having $\mathrm{p}\mathrm{O}\mathrm{H}=\text{ 11}\text{.13}$ should be calculated.

Concept Introduction:

The acidity or alkalinity of a solution is expressed by determining $\text{pH}$ of the solution. $\text{pH}$ of a solution is defined as negative logarithm of the concentration of ${\text{H}}^{\text{+}}$ ion in the solution. $\text{pH}$ is expressed as-

  $\text{pH}\text{=}\text{-}{\text{log[H}}^{\text{+}}\text{]}$

  $\text{pOH}$ of a solution is defined as negative logarithm of the concentration of hydroxyl ion $\left[{\text{OH}}^{\text{-}}\right]$ in the solution. $\text{pOH}$ is expressed as-

  $\text{pOH}=-\mathrm{l}\mathrm{o}\mathrm{g}[\mathrm{O}{\mathrm{H}}^{-}]$

Both $\text{pH}$ and $\text{pOH}$ are related to each other by this following equation-

  $\text{pH}\text{+}\text{pOH=}{\text{pK}}_{\text{w}}$

Answer to Problem 35A

The concentration of ${\text{H}}^{\text{+}}$ ion is $1.35\times {10}^{-3}\text{M}$ .

Explanation of Solution

Using the following equation to calculate concentration of ${\text{H}}^{\text{+}}$ ion in the solution,

  $\begin{array}{l}\text{pH}\text{=}\text{-}{\text{log[H}}^{\text{+}}\text{]}\\ {\text{[H}}^{\text{+}}\text{]}\text{=}{\text{10}}^{\text{-pH}}\end{array}$

The pH of the solution is calculated as:

  $\begin{array}{l}\text{pH}\text{=}\text{14}\text{-}\text{pOH}\\ =14-11.13\\ =2.87\end{array}$

Now, the concentration of hydrogen ion is calculated as:

  $\begin{array}{l}{\text{[H}}^{\text{+}}\text{]}\text{=}{\text{10}}^{\text{-pH}}\\ =10^{-2.87}=1.35\times 10^{-3}\mathrm{M}\end{array}$

The concentration of ${\text{H}}^{\text{+}}$ ion in the solution is $1.35\times {10}^{-3}\text{M}$ .

(d)

Interpretation Introduction

Interpretation:

The concentration of ${\text{H}}^{\text{+}}$ ion in the solution having $\mathrm{p}\mathrm{O}\mathrm{H}=\text{ 6}\text{.29}$ should be calculated.

Concept Introduction:

The acidity or alkalinity of a solution is expressed by determining $\text{pH}$ of the solution. $\text{pH}$ of a solution is defined as negative logarithm of the concentration of ${\text{H}}^{\text{+}}$ ion in the solution. $\text{pH}$ is expressed as-

  $\text{pH}\text{=}\text{-}{\text{log[H}}^{\text{+}}\text{]}$

  $\text{pOH}$ of a solution is defined as negative logarithm of the concentration of hydroxyl ion $\left[{\text{OH}}^{\text{-}}\right]$ in the solution. $\text{pOH}$ is expressed as-

  $\text{pOH}=-\mathrm{l}\mathrm{o}\mathrm{g}[\mathrm{O}{\mathrm{H}}^{-}]$

Both $\text{pH}$ and $\text{pOH}$ are related to each other by this following equation-

  $\text{pH}\text{+}\text{pOH=}{\text{pK}}_{\text{w}}$

Answer to Problem 35A

The concentration of ${\text{H}}^{\text{+}}$ ion is $1.95\times {10}^{-8}\text{M}$ .

Explanation of Solution

Using the following equation to calculate concentration of ${\text{H}}^{\text{+}}$ ion in the solution,

  $\begin{array}{l}\text{pH}\text{=}\text{-}{\text{log[H}}^{\text{+}}\text{]}\\ {\text{[H}}^{\text{+}}\text{]}\text{=}{\text{10}}^{\text{-pH}}\end{array}$

The pH of the solution is calculated as:

  $\begin{array}{l}\text{pH}\text{=}\text{14}\text{-}\text{pOH}\\ \text{=}\text{14}\text{-}\text{6}\text{.29}\\ \text{=}\text{7}\text{.71}\end{array}$

Now, the concentration of hydrogen ion is calculated as:

  $\begin{array}{l}{\text{[H}}^{\text{+}}\text{]}\text{=}{\text{10}}^{\text{-pH}}\\ =10^{-7.71}=1.95\times 10^{-8}\mathrm{M}\end{array}$

The concentration of ${\text{H}}^{\text{+}}$ ion in the solution is $1.95\times {10}^{-8}\text{M}$ .