Chapter 19.2, Problem 15SP

(a)

Interpretation Introduction

Interpretation: The hydrogen ion concentration of a solution with a pH value of 4.00 needs to be calculated.

Concept Introduction: The pH of the solution is calculated from hydrogen ion concentration as follows:

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

The above relation can be rearranged to calculate the hydrogen ion concentration.

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

Explanation of Solution

The pH of the solution is given 4.00. It is related to hydrogen ion concentration as follows:

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

Thus, hydrogen ion concentration can be calculated from pH value as follows:

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

Substitute the value,

  $\left[{\text{H}}^{+}\right]={10}^{-4}$

Thus, the hydrogen ion concentration of the solution is $1\times {10}^{-4}\text{ M}$ .

(b)

Interpretation Introduction

Interpretation: The hydrogen ion concentration of a solution with a pH value of 11.55 needs to be calculated.

Concept Introduction: The pH of the solution is calculated from hydrogen ion concentration as follows:

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

The above relation can be rearranged to calculate the hydrogen ion concentration.

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

Explanation of Solution

The pH of the solution is given 11.55. It is related to hydrogen ion concentration as follows:

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

Thus, hydrogen ion concentration can be calculated from pH value as follows:

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

Substitute the value,

  $\begin{array}{c}\left[{\text{H}}^{+}\right]={10}^{-11.55}\\ =2.82\times {10}^{-12}\text{ M}\end{array}$

Thus, the hydrogen ion concentration of the solution is $2.82\times {10}^{-12}\text{ M}$ .