Chapter 21, Problem 101A

(a)

Interpretation Introduction

Interpretation: The hydroxide ion concentration of a solution with pH value 7.0 needs to be determined.

Concept Introduction: The pH of the solution is negative log of hydronium ion in the solution. It is related to pOH of the solution as follows:

  $\text{pH}+\text{pOH}=14$

Now, pOH is negative log of hydroxide ions in the solution thus, it is represented as follows:

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

Here, $\left[{\text{OH}}^{-}\right]$ is concentration of hydroxide ions in the solution.

Explanation of Solution

The given solution has pH value 7.0. The pOH can be calculated as follows:

  $\text{pOH}=14-\text{pH}$

Or,

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

Now, from pOH the concentration of hydroxide ions can be calculated as follows:

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

Substitute the values,

  $\left[{\text{OH}}^{-}\right]={10}^{-7}$

Therefore, the concentration of hydroxide ions will be $1\times {10}^{-7}\text{ M}$ .

(b)

Interpretation Introduction

Interpretation: The hydroxide ion concentration of a solution with pH value 4.0 needs to be determined.

Concept Introduction: The pH of the solution is negative log of hydronium ion in the solution. It is related to pOH of the solution as follows:

  $\text{pH}+\text{pOH}=14$

Now, pOH is negative log of hydroxide ions in the solution thus, it is represented as follows:

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

Here, $\left[{\text{OH}}^{-}\right]$ is concentration of hydroxide ions in the solution.

Explanation of Solution

The given solution has pH value 4.0. The pOH can be calculated as follows:

  $\text{pOH}=14-\text{pH}$

Or,

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

Now, from pOH the concentration of hydroxide ions can be calculated as follows:

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

Substitute the values,

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

Therefore, the concentration of hydroxide ions will be $1\times {10}^{-10}\text{ M}$ .

(c)

Interpretation Introduction

Interpretation: The hydroxide ion concentration of a solution with pH value 9.0 needs to be determined.

Concept Introduction: The pH of the solution is negative log of hydronium ion in the solution. It is related to pOH of the solution as follows:

  $\text{pH}+\text{pOH}=14$

Now, pOH is negative log of hydroxide ions in the solution thus, it is represented as follows:

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

Here, $\left[{\text{OH}}^{-}\right]$ is concentration of hydroxide ions in the solution.

Explanation of Solution

The given solution has pH value 9.0. The pOH can be calculated as follows:

  $\text{pOH}=14-\text{pH}$

Or,

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

Now, from pOH the concentration of hydroxide ions can be calculated as follows:

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

Substitute the values,

  $\left[{\text{OH}}^{-}\right]={10}^{-5}$

Therefore, the concentration of hydroxide ions will be $1\times {10}^{-5}\text{ M}$ .