Chapter 16, Problem 100AP

. For each hydrogen or hydroxide ion concentration listed. calculate the concentration of the complementary ion and the pH and pOH of the solution.

a. $\left[{\text{H}}^{\text{+}}\right]=5.72\times {10}^{-4}M$

b. $\left[{\text{OH}}^{\text{-}}\right]=8.91\times {10}^{-5}M$c. $\left[{\text{H}}^{\text{+}}\right]=2.87\times {10}^{-12}M$d. $\left[{\text{OH}}^{\text{-}}\right]=7.22\times {10}^{-8}M$

Interpretation Introduction

(a)

Interpretation:

The concentration of complementary ion, pH and pOH of solution should be calculated.

Concept Introduction:

The concentration of hydrogen ions in a solution determines the acidity of a solution. If concentration of hydrogen ion is more than the solution is more acetic, if it is low, solution is less acidic.

The pH of solution is defined as negative log of hydrogen ion concentration thus, it can be calculated as follows:

$\text{p}\text{H}=-\text{log}\left[{\text{H}}^{+}\right]$

Here, $\left[{\text{H}}^{+}\right]$ is concentration of hydrogen ion.

Similarly, pOH of a solution is defined as negative log of hydroxide ion concentration thus, it can be calculated as follows:

$\text{p}\text{O}\text{H}=-\text{log}\left[{\text{OH}}^{-}\right]$

Here, $\left[{\text{OH}}^{-}\right]$ is concentration of hydroxide ion.

pH and pOH of a solution are related to each other as follows:

$\text{p}\text{H}+\text{p}\text{O}\text{H}=14$

In a pH scale, if the value of pH is below 7 the solution is said to be acidic in nature, if the pH value is above 7 it is said to be basic in nature. At pH 7, the solution is neutral.

Answer to Problem 100AP

For the given hydrogen ion concentration, pH, pOH and hydroxide ion concentration is 3.24, 10.76 and $1.74\times {10}^{-11}\text{ M}$ respectively.

Explanation of Solution

Given Information:

The hydrogen ion concentration is $5.72\times {10}^{-4}\text{ M}$

Calculation:

The pH of solution can be calculated as follows:

$\text{p}\text{H}=-\text{log}\left[{\text{H}}^{+}\right]$

Putting the value,

$\begin{array}{c}\text{p}\text{H}=-\text{log}\left(5.72\times {10}^{-4}\right)\\ =3.24\end{array}$

Therefore, pH of solution is 3.24.

From pH, pOH can be calculated as follows:

$\text{p}\text{O}\text{H}=14-\text{p}\text{H}$

Putting the value,

$\begin{array}{c}\text{p}\text{O}\text{H}=14-3.24\\ =10.76\end{array}$

Therefore, pOH of solution is 10.76.

Now, form pOH, hydroxide ion concentration can be calculated as follows:

$\left[{\text{OH}}^{-}\right]={10}^{-\text{p}\text{O}\text{H}}$

Putting the value,

$\begin{array}{c}\left[{\text{OH}}^{-}\right]={10}^{-10.76}\\ =1.74\times {10}^{-11}\text{ M}\end{array}$

Therefore, for the given hydrogen ion concentration, pH, pOH and hydroxide ion concentration is 3.24, 10.76 and $1.74\times {10}^{-11}\text{ M}$ respectively.

Interpretation Introduction

(b)

Interpretation:

The concentration of complementary ion, pH and pOH of solution should be calculated.

Concept Introduction:

The concentration of hydrogen ions in a solution determines the acidity of a solution. If concentration of hydrogen ion is more than the solution is more acetic, if it is low, solution is less acidic.

The pH of solution is defined as negative log of hydrogen ion concentration thus, it can be calculated as follows:

$\text{p}\text{H}=-\text{log}\left[{\text{H}}^{+}\right]$

Here, $\left[{\text{H}}^{+}\right]$ is concentration of hydrogen ion.

Similarly, pOH of a solution is defined as negative log of hydroxide ion concentration thus, it can be calculated as follows:

$\text{p}\text{O}\text{H}=-\text{log}\left[{\text{OH}}^{-}\right]$

Here, $\left[{\text{OH}}^{-}\right]$ is concentration of hydroxide ion.

pH and pOH of a solution are related to each other as follows:

$\text{p}\text{H}+\text{p}\text{O}\text{H}=14$

In a pH scale, if the value of pH is below 7 the solution is said to be acidic in nature, if the pH value is above 7 it is said to be basic in nature. At pH 7, the solution is neutral.

Answer to Problem 100AP

For given hydroxide ion concentration, pOH, pH and hydrogen ion concentration is 4.05, 9.95 and $1.12\times {10}^{-10}\text{ M}$ respectively.

Explanation of Solution

Given Information:

The hydroxide ion concentration is $8.91\times {10}^{-5}\text{ M}$.

Calculation:

From the hydroxide ion concentration, first pOH can be calculated as follows:

$\text{p}\text{O}\text{H}=-\text{log}\left[{\text{OH}}^{-}\right]$

Putting the value,

$\begin{array}{c}\text{p}\text{O}\text{H}=-\text{log}\left(8.91\times {10}^{-5}\right)\\ =4.05\end{array}$

From pOH of solution, pH can be calculated as follows:

$\text{p}\text{H}+\text{p}\text{O}\text{H}=14$

On rearranging,

$\text{p}\text{H}=14-\text{p}\text{O}\text{H}$

Putting the values,

$\begin{array}{c}\text{p}\text{H}=14-4.05\\ =9.95\end{array}$

Therefore, pH of solution is 9.95.

Now, from pH, hydrogen ion concentration can be calculated as follows:

$\left[{\text{H}}^{+}\right]={10}^{-\text{p}\text{H}}$

Putting the value,

$\begin{array}{c}\left[{\text{H}}^{+}\right]={10}^{-9.95}\\ =1.12\times {10}^{-10}\text{ M}\end{array}$

Therefore, for given hydroxide ion concentration, pOH, pH and hydrogen ion concentration is 4.05, 9.95 and $1.12\times {10}^{-10}\text{ M}$ respectively.

Interpretation Introduction

(c)

Interpretation:

The concentration of complementary ion, pH and pOH of solution should be calculated.

Concept Introduction:

The concentration of hydrogen ions in a solution determines the acidity of a solution. If concentration of hydrogen ion is more than the solution is more acetic, if it is low, solution is less acidic.

The pH of solution is defined as negative log of hydrogen ion concentration thus, it can be calculated as follows:

$\text{p}\text{H}=-\text{log}\left[{\text{H}}^{+}\right]$

Here, $\left[{\text{H}}^{+}\right]$ is concentration of hydrogen ion.

Similarly, pOH of a solution is defined as negative log of hydroxide ion concentration thus, it can be calculated as follows:

$\text{p}\text{O}\text{H}=-\text{log}\left[{\text{OH}}^{-}\right]$

Here, $\left[{\text{OH}}^{-}\right]$ is concentration of hydroxide ion.

pH and pOH of a solution are related to each other as follows:

$\text{p}\text{H}+\text{p}\text{O}\text{H}=14$

In a pH scale, if the value of pH is below 7 the solution is said to be acidic in nature, if the pH value is above 7 it is said to be basic in nature. At pH 7, the solution is neutral.

Answer to Problem 100AP

For the given hydrogen ion concentration, pH, pOH and hydroxide ion concentration is 11.54, 2.46 and $3.47\times {10}^{-3}\text{ M}$ respectively.

Explanation of Solution

Given Information:

The hydrogen ion concentration is $2.87\times {10}^{-12}\text{ M}$

Calculation:

The pH of solution can be calculated as follows:

$\text{p}\text{H}=-\text{log}\left[{\text{H}}^{+}\right]$

Putting the value,

$\begin{array}{c}\text{p}\text{H}=-\text{log}\left(2.87\times {10}^{-12}\right)\\ =11.54\end{array}$

Therefore, pH of solution is 11.54.

From pH, pOH can be calculated as follows:

$\text{p}\text{O}\text{H}=14-\text{p}\text{H}$

Putting the value,

$\begin{array}{c}\text{p}\text{O}\text{H}=14-11.54\\ =2.46\end{array}$

Therefore, pOH of solution is 2.46.

Now, form pOH, hydroxide ion concentration can be calculated as follows:

$\left[{\text{OH}}^{-}\right]={10}^{-\text{p}\text{O}\text{H}}$

Putting the value,

$\begin{array}{c}\left[{\text{OH}}^{-}\right]={10}^{-2.46}\\ =3.47\times {10}^{-3}\text{ M}\end{array}$

Therefore, for the given hydrogen ion concentration, pH, pOH and hydroxide ion concentration is 11.54, 2.46 and $3.47\times {10}^{-3}\text{ M}$ respectively.

Interpretation Introduction

(d)

Interpretation:

The concentration of complementary ion, pH and pOH of solution should be calculated.

Concept Introduction:

The concentration of hydrogen ions in a solution determines the acidity of a solution. If concentration of hydrogen ion is more than the solution is more acetic, if it is low, solution is less acidic.

The pH of solution is defined as negative log of hydrogen ion concentration thus, it can be calculated as follows:

$\text{p}\text{H}=-\text{log}\left[{\text{H}}^{+}\right]$

Here, $\left[{\text{H}}^{+}\right]$ is concentration of hydrogen ion.

Similarly, pOH of a solution is defined as negative log of hydroxide ion concentration thus, it can be calculated as follows:

$\text{p}\text{O}\text{H}=-\text{log}\left[{\text{OH}}^{-}\right]$

Here, $\left[{\text{OH}}^{-}\right]$ is concentration of hydroxide ion.

pH and pOH of a solution are related to each other as follows:

$\text{p}\text{H}+\text{p}\text{O}\text{H}=14$

In a pH scale, if the value of pH is below 7 the solution is said to be acidic in nature, if the pH value is above 7 it is said to be basic in nature. At pH 7, the solution is neutral.

Answer to Problem 100AP

For the given hydrogen ion concentration, pH, pOH and hydroxide ion concentration is 11.54, 2.46 and $3.47\times {10}^{-3}\text{ M}$ respectively.

Explanation of Solution

Given Information:

The hydroxide ion concentration is $7.22\times {10}^{-8}\text{ M}$.

For given hydroxide ion concentration, pOH, pH and hydrogen ion concentration is 7.14, 6.86 and $1.38\times {10}^{-7}\text{ M}$ respectively.

Calculation:

From the hydroxide ion concentration, first pOH can be calculated as follows:

$\text{p}\text{O}\text{H}=-\text{log}\left[{\text{OH}}^{-}\right]$

Putting the value,

$\begin{array}{c}\text{p}\text{O}\text{H}=-\text{log}\left(7.22\times {10}^{-8}\right)\\ =7.14\end{array}$

From pOH of solution, pH can be calculated as follows:

$\text{p}\text{H}+\text{p}\text{O}\text{H}=14$

On rearranging,

$\text{p}\text{H}=14-\text{p}\text{O}\text{H}$

Putting the values,

$\begin{array}{c}\text{p}\text{H}=14-7.14\\ =6.86\end{array}$

Therefore, pH of solution is 6.86.

Now, from pH, hydrogen ion concentration can be calculated as follows:

$\left[{\text{H}}^{+}\right]={10}^{-\text{p}\text{H}}$

Putting the value,

$\begin{array}{c}\left[{\text{H}}^{+}\right]={10}^{-6.86}\\ =1.38\times {10}^{-7}\text{ M}\end{array}$

Therefore, for given hydroxide ion concentration, pOH, pH and hydrogen ion concentration is 7.14, 6.86 and $1.38\times {10}^{-7}\text{ M}$ respectively.