Chapter 13, Problem 70QP

(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 $6.4\times {10}^{-4}\text{ M}$ . 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 $6.4\times {10}^{-4}\text{ M}$ for $\left[{\text{OH}}^{-}\right]$ .

$\begin{array}{c}\text{pOH}=-{\log }_{10}\left[6.4\times {10}^{-4}\right]\\ =3.19\end{array}$

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 $3.19$ for $\text{pOH}$ in the above expression.

$\begin{array}{c}\text{pH}=14-3.19\\ =10.81\end{array}$

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

$\begin{array}{c}\text{pOH}=-{\log }_{10}\left[1\right]\\ =0\end{array}$

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 $0$ for $\text{pOH}$ in the above expression.

$\begin{array}{c}\text{pH}=14-0\\ =14\end{array}$

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

(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 $2.7\times {10}^{-10}\text{ M}$ . 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 $2.7\times {10}^{-10}\text{ M}$ for $\left[{\text{OH}}^{-}\right]$ .

$\begin{array}{c}\text{pOH}=-{\log }_{10}\left[2.7\times {10}^{-10}\right]\\ =9.57\end{array}$

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 $9.57$ for $\text{pOH}$ in the above expression.

$\begin{array}{c}\text{pH}=14-9.57\\ =4.43\end{array}$

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