Chapter 13, Problem 69QP

(a)

Interpretation Introduction

Interpretation:

The determination of the $\text{pH}$ value from the given $\left[{\text{OH}}^{-}\right]$ concentration. Also, the respective solution is the acidic, basic or neutral is to be identified.

Explanation of Solution

The given $\left[{\text{OH}}^{-}\right]$ concentration is $1\times {10}^{-4}\text{ M}$ . The expression that shows the relation between $\text{pOH}$ and $\left[{\text{OH}}^{-}\right]$ is as follows:

$\text{pOH}=-{\log }_{10}\left[{\text{OH}}^{-}\right]$

Substitute $1\times {10}^{-4}\text{ M}$ for $\left[{\text{OH}}^{-}\right]$ .

$\begin{array}{c}\text{pOH}=-{\log }_{10}\left[1\times {10}^{-4}\right]\\ =4\end{array}$

The relation between $\text{pOH}$ and $\text{pH}$ is as follows:

$\begin{array}{c}\text{pH}+\text{pOH}=14\\ \text{pH}=14-\text{pOH}\end{array}$

Substitute $4$ for $\text{pOH}$ in the above expression.

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

As the pH of the solution is above $7$ , the solution is basic.

(b)

Interpretation Introduction

Interpretation:

The determination of the $\text{pH}$ value from the given $\left[{\text{OH}}^{-}\right]$ concentration. Also, the respective solution is the acidic, basic or neutral is to be identified.

Explanation of Solution

The given $\left[{\text{OH}}^{-}\right]$ concentration is $1\times {10}^{-7}\text{ M}$ . The expression that shows the relation between $\text{pOH}$ and $\left[{\text{OH}}^{-}\right]$ is as follows:

$\text{pOH}=-{\log }_{10}\left[{\text{OH}}^{-}\right]$

Substitute $1\times {10}^{-7}\text{ M}$ for $\left[{\text{OH}}^{-}\right]$ .

$\begin{array}{c}\text{pOH}=-{\log }_{10}\left[1\times {10}^{-7}\text{ M}\right]\\ =7\end{array}$

The relation between $\text{pOH}$ and $\text{pH}$ is as follows:

$\begin{array}{c}\text{pH}+\text{pOH}=14\\ \text{pH}=14-\text{pOH}\end{array}$

Substitute $7$ for $\text{pOH}$ in the above expression.

$\begin{array}{c}\text{pH}=14-7\\ =7\end{array}$

As the pH of the solution is $7$ , the solution is neutral.

(c)

Interpretation Introduction

Interpretation:

The determination of the $\text{pH}$ value from the given $\left[{\text{OH}}^{-}\right]$ concentration. Also, the respective solution is the acidic, basic or neutral is to be identified.

Explanation of Solution

The given $\left[{\text{OH}}^{-}\right]$ concentration is $8.2\times {10}^{-10}\text{ M}$ . The expression that shows the relation between $\text{pOH}$ and $\left[{\text{OH}}^{-}\right]$ is as follows:

$\text{pOH}=-{\log }_{10}\left[{\text{OH}}^{-}\right]$

Substitute $8.2\times {10}^{-10}\text{ M}$ for $\left[{\text{OH}}^{-}\right]$ .

$\begin{array}{c}\text{pOH}=-{\log }_{10}\left[8.2\times {10}^{-10}\text{ M}\right]\\ =9.07\end{array}$

The relation between $\text{pOH}$ and $\text{pH}$ is as follows:

$\begin{array}{c}\text{pH}+\text{pOH}=14\\ \text{pH}=14-\text{pOH}\end{array}$

Substitute $9.07$ for $\text{pOH}$ in the above expression:

$\begin{array}{c}\text{pH}=14-9.07\\ =4.93\end{array}$

As the pH of the solution is below $7$ , the solution is acidic.