Chapter 19.2, Problem 11SP

Interpretation Introduction

Interpretation: The hydroxide ion concentration of the solution is $1\times {10}^{-3}\text{ M}$ , the concentration of hydrogen ion that needs to be determined. Also, if the solution is acidic, basic, or neutral needs to be determined.

Concept Introduction: For a given solution, pH can be calculated as follows:

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

Here, $\left[{\text{H}}^{+}\right]$ is the hydrogen ion concentration.

Similarly, pOH can be calculated as follows:

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

Here, $\left[{\text{OH}}^{-}\right]$ is the hydroxide ion concentration.

The relation between pH and pOH of the solution is represented as follows:

  $\text{pH}+\mathrm{pOH}=14$

Explanation of Solution

The given concentration of hydroxide ion is $1\times {10}^{-3}\text{ M}$ . From hydroxide ion concentration, pH is calculated from the pOH value. Here, pOH is calculated as follows:

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

Substitute the values,

  $\begin{array}{c}\text{pOH}=-\log \left(1\times {10}^{-3}\text{ M}\right)\\ =3\end{array}$

Now, pH is calculated from pOH as follows:

  $\text{pH}=14-\text{pOH}$

Substitute the value,

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

From the pH of the solution, hydrogen ion concentration can be calculated as follows:

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

Or,

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

Substitute the value,

  $\left[{\text{H}}^{+}\right]={\text{10}}^{-}{}^{11}$

Thus, the concentration of hydrogen ions is ${\text{10}}^{-}{}^{11}$ .

Since the pH of the solution is more than 7, the solution will be basic in nature.