Chapter 13, Problem 78QP

(a)

Interpretation Introduction

Interpretation:

The $\left[{\text{OH}}^{-}\right]$ concentration is to be determined and also, the acidic, basic or neutral nature of the solution is to be identified.

Explanation of Solution

The given value of $\text{pH}$ is $5$ .

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

$\text{pH}+\text{pOH}=14$

Substitute $5$ for $\text{pH}$ in the above expression:

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

The expression that is used to calculate the $\text{pOH}$ of the solution is:

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

Substitute $9$ for $\text{pOH}$ in the above expression:

$\begin{array}{l}\left[{\text{OH}}^{-}\right]={10}^{-\text{pOH}}\text{ M}\\ \left[{\text{OH}}^{-}\right]=1\times {10}^{-9}\text{ M}\end{array}$

At neutral condition, the value of $\left[{\text{OH}}^{-}\right]$ is $1\times {10}^{-7}\text{ M}$ . As the concentration of $\left[{\text{OH}}^{-}\right]$ is less than $1\times {10}^{-7}\text{ M}$ , thus the solution is acidic in nature.

(b)

Interpretation Introduction

Interpretation:

The $\left[{\text{OH}}^{-}\right]$ concentration is to be determined and also, the acidic, basic or neutral nature of the solution is to be identified.

Explanation of Solution

The given value of $\text{pH}$ is $11$ .

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

$\text{pH}+\text{pOH}=14$

Substitute $11$ for $\text{pH}$ in the above expression:

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

The expression that is used to calculate the $\text{pOH}$ of the solution is:

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

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

$\left[{\text{OH}}^{-}\right]=1\times {10}^{-3}\text{ M}$

At neutral condition, the value of $\left[{\text{OH}}^{-}\right]$ is $1\times {10}^{-7}\text{ M}$ . As the concentration of $\left[{\text{OH}}^{-}\right]$ is greater than $1\times {10}^{-7}\text{ M}$ , thus the solution is basic in nature.

(c)

Interpretation Introduction

Interpretation:

The $\left[{\text{OH}}^{-}\right]$ concentration is to be determined and also, the acidic, basic or neutral nature of the solution is to be identified.

Explanation of Solution

The given value of $\text{pH}$ is $12.8$ .

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

$\text{pH}+\text{pOH}=14$

Substitute $12.8$ for $\text{pH}$ in the above expression:

$\begin{array}{l}\text{pOH}=14-\text{pH}\\ \text{pOH}=14-12.8\\ \text{pOH}=1.2\end{array}$

The expression that is used to calculate the $\text{pOH}$ of the solution is:

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

Substitute $1.2$ for $\text{pOH}$ in the above expression:

$\begin{array}{l}\left[{\text{OH}}^{-}\right]={10}^{-1.2}\text{ M}\\ \left[{\text{OH}}^{-}\right]=6.31\times {10}^{-2}\text{ M}\end{array}$

At neutral condition, the value of $\left[{\text{OH}}^{-}\right]$ is $1\times {10}^{-7}\text{ M}$ . As the concentration of $\left[{\text{OH}}^{-}\right]$ is greater