Chapter 13, Problem 72QP

(a)

Interpretation Introduction

Interpretation:

The determination of the $\text{pH}$ value from the given concentration of the solution. Also, the respective solution is acidic, basic or neutral nature of the solution is to be identified.

Explanation of Solution

The given concentration of $\left[\text{KOH}\right]$ is $0.001\text{ M}$ .

$\left[\text{KOH}\right]$ is a strong base, the $\left[{\text{OH}}^{-}\right]$ concentration is equal to the concentration of $\left[\text{KOH}\right]$ .

Therefore, the concentration of $\left[{\text{OH}}^{-}\right]$ is $0.001\text{ M}$ .

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 $0.001\text{ M}$ for $\left[{\text{OH}}^{-}\right]$ .

$\begin{array}{c}\text{pOH}=-{\log }_{10}\left[0.001\right]\\ =3\end{array}$

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 $3$ for $\text{pOH}$ in the above expression.

$\begin{array}{c}\text{pH}=14-3\\ =11\end{array}$

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 concentration of the solution. Also, the respective solution is acidic, basic or neutral nature of the solution is to be identified.

Explanation of Solution

The given concentration of $\left[\text{NaOH}\right]$ is $0.005\text{ M}$ .

$\left[\text{NaOH}\right]$ is a strong base, the $\left[{\text{OH}}^{-}\right]$ concentration is equal to the concentration of $\left[\text{NaOH}\right]$ .

Therefore, the concentration of $\left[{\text{OH}}^{-}\right]$ is $0.005\text{ M}$ .

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 $0.005\text{ M}$ for $\left[{\text{OH}}^{-}\right]$ .

$\begin{array}{c}\text{pOH}=-{\log }_{10}\left[0.005\right]\\ =2.3\end{array}$

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 $2.3$ for $\text{pOH}$ in the above expression.

$\begin{array}{c}\text{pH}=14-2.3\\ =11.7\end{array}$

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 concentration of the solution. Also, the respective solution is acidic, basic or neutral nature of the solution is to be identified.

Explanation of Solution

The given concentration of $\left[\text{HCl}\right]$ is $0.001\text{ M}$ .

$\left[\text{HCl}\right]$ is a strong acid, the $\left[{\text{H}}_3{\text{O}}^{+}\right]$ concentration is equal to the concentration of $\left[\text{HCl}\right]$ .

Therefore, the concentration of $\left[{\text{H}}_3{\text{O}}^{+}\right]$ is $0.001\text{ M}$ .

The expression that shows the relation between $\text{pH}$ and $\left[{\text{H}}_3{\text{O}}^{+}\right]$ is as follows:

$\text{pH}=-{\log }_{10}\left[{\text{H}}_3{\text{O}}^{+}\right]$

Substitute $0.001\text{ M}$ for $\left[{\text{H}}_3{\text{O}}^{+}\right]$ .

$\begin{array}{c}\text{pH}=-{\log }_{10}\left[0.001\right]\\ =3\end{array}$

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