Chapter 20, Problem 100A

(a)

Interpretation Introduction

Interpretation: The pH of the solution when the concentration of $\left[{\text{H}}^{+}\right]$ is 0.00001M is to be calculated.

Concept Introduction: pH is the measure of the acidity of a solution. It can be calculated by using the equation,

  $\text{pH}=-\log \left[{\text{H}}^{+}\right]$ .

Answer to Problem 100A

The pH of the solution when the concentration of $\left[{\text{H}}^{+}\right]$ is 0.00001M is $5$ .

Explanation of Solution

The concentration of $\left[{\text{H}}^{+}\right]$ is given and is,

  $\left[{\text{H}}^{+}\right]=0.000010\text{M}$

So,

  $\begin{array}{c}\text{pH}=-\log \left[{\text{H}}^{+}\right]\\ =-\log \left(0.000010\right)\\ =5\end{array}$

So, the pH is $5$ .

(b)

Interpretation Introduction

Interpretation: The pH of the solution when the concentration of $\left[{\text{OH}}^{-}\right]$ is $1\times {10}^{-4}\text{M}$ is to be calculated.

Concept Introduction: pH is the measure of the acidity of a solution. It can be calculated by using the equation,

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

From the ${\text{OH}}^{-}$ concentration pOH is determined by using the equation,

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

And from which pH can be calculated by using the equation,

  $\text{pOH}+\text{pH}=14$

Answer to Problem 100A

The pH of the solution when the concentration of ${\text{OH}}^{-}$ is $1\times {10}^{-4}\text{M}$ is 10.

Explanation of Solution

The concentration of ${\text{OH}}^{-}$ is given and is,

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

So pOH is,

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

So, the pOH is 4.

Now, pH can be calculated by using the equation,

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

So, the pH is 10.

(c)

Interpretation Introduction

Interpretation: The pH of the solution when the concentration of ${\text{OH}}^{-}$ is $1\times {10}^{-1}\text{M}$ is to be determined.

Concept Introduction: pH is the measure of the acidity of a solution. It can be calculated by using the equation,

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

From the ${\text{OH}}^{-}$ concentration pOH is determined by using the equation,

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

And from which pH can be calculated by using the equation,

  $\text{pOH}+\text{pH}=14$

Answer to Problem 100A

The pH of the solution when the concentration of ${\text{OH}}^{-}$ is $1\times {10}^{-1}\text{M}$ is 13.

Explanation of Solution

The concentration of ${\text{OH}}^{-}$ is given and is,

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

So pOH is,

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

So, the pOH is 1.

Now pH can be calculated by using the equation,

  $\begin{array}{c}\text{pOH}+\text{pH}=14\\ \text{pH}+1=14\\ \text{pH}=13\end{array}$

So, the pH is 13.

(d)

Interpretation Introduction

Interpretation: The pH of the solution when the concentration of $\left[{\text{H}}^{+}\right]$ is $3.0\times {10}^{-7}\text{M}$ is to be calculated.

Concept Introduction: pH is the measure of the acidity of a solution. It can be calculated by using the equation,

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

Answer to Problem 100A

The pH of the solution when the concentration of $\left[{\text{H}}^{+}\right]$ is $3.0\times {10}^{-7}\text{M}$ is 6.5.

Explanation of Solution

The concentration of $\left[{\text{H}}^{+}\right]$ is given and is,

  $\left[{\text{H}}^{+}\right]=3.0\times {10}^{-7}\text{M}$

So,

  $\begin{array}{c}\text{pH}=-\log \left[{\text{H}}^{+}\right]\\ =-\log \left(3.0\times {10}^{-7}\right)\\ =6.5\end{array}$

So the pH is 6.5.