Chapter 21, Problem 100A

(a)

Interpretation Introduction

Interpretation: The pH of solution containing $1\times {10}^{-8}\text{ M}$ hydrogen ion concentration needs to be determined.

Concept Introduction: For a given solution, pH can be calculated as follows:

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

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

Explanation of Solution

The given concentration of hydrogen ion is $1\times {10}^{-8}\text{ M}$ .

The pH of solution can be calculated as follows:

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

Substitute the values,

  $\begin{array}{c}\text{pH}=-\log \left(1\times {10}^{-8}\text{ M}\right)\\ =8\end{array}$

Thus, the pH of solution is 8.

(b)

Interpretation Introduction

Interpretation: The pH of solution containing $0.000010\text{ M}$ hydrogen ion concentration needs to be determined.

Concept Introduction: For a given solution, pH can be calculated as follows:

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

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

Explanation of Solution

The given concentration of hydrogen ion is $0.000010\text{ M}$ .

The pH of solution can be calculated as follows:

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

Substitute the values,

  $\begin{array}{c}\text{pH}=-\log \left(0.000010\right)\\ =5\end{array}$

Thus, the pH of solution is 5.

(c)

Interpretation Introduction

Interpretation: The pH of solution containing $1\times {10}^{-4}\text{ M}$ hydroxide ion concentration needs to be determined.

Concept Introduction: For a given solution, pH can be calculated as follows:

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

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

Similarly, pOH can be calculated as follows:

  $\text{pH}=-\log \left[{\text{OH}}^{-}\right]$

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

The relation between pH and pOH of solution is represented as follows:

  $\text{pH}+\mathrm{pOH}=14$

Explanation of Solution

The given concentration of hydroxide ion is $1\times {10}^{-4}\text{ M}$ . From hydroxide ion concentration, pH is calculated from pOH value. Here, pOH is calculated as follows:

  $\text{pH}=-\log \left[{\text{OH}}^{-}\right]$

Substitute the values,

  $\begin{array}{c}\text{pOH}=-\log \left(1\times {10}^{-4}\text{ M}\right)\\ =4\end{array}$

Now, pH is calculated from pOH as follows:

  $\text{pH}=14-\text{pOH}$

Substitute the value,

  $\begin{array}{c}\text{pH}=14-4\\ \text{= 10}\end{array}$

Therefore, the pH of solution is 10.

(d)

Interpretation Introduction

Interpretation: The pH of solution containing $1\times {10}^{-9}\text{ M}$ hydroxide ion concentration needs to be determined.

Concept Introduction: For a given solution, pH can be calculated as follows:

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

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

Similarly, pOH can be calculated as follows:

  $\text{pH}=-\log \left[{\text{OH}}^{-}\right]$

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

The relation between pH and pOH of solution is represented as follows:

  $\text{pH}+\mathrm{pOH}=14$

Explanation of Solution

The given concentration of hydroxide ion is $1\times {10}^{-9}\text{ M}$ . From hydroxide ion concentration, pH is calculated from pOH value. Here, pOH is calculated as follows:

  $\text{pH}=-\log \left[{\text{OH}}^{-}\right]$

Substitute the values,

  $\begin{array}{c}\text{pOH}=-\log \left(1\times {10}^{-9}\text{ M}\right)\\ =9\end{array}$

Now, pH is calculated from pOH as follows:

  $\text{pH}=14-\text{pOH}$

Substitute the value,

  $\begin{array}{c}\text{pH}=14-9\\ \text{= 5}\end{array}$

Thus, pH of solution is 5.