Chapter 13, Problem 56QP

(a)

Interpretation Introduction

Interpretation:

The determination of $\left[{\text{OH}}^{-}\right]$ concentration from the given $\left[{\text{H}}_3{\text{O}}^{+}\right]$ concentration. Also, the acidic, basic, or neutral nature of the solution is to be identified.

Explanation of Solution

The given concentration of $\left[{\text{H}}_3{\text{O}}^{+}\right]$ is $1\times {10}^{-3}\text{ M}$ .

Now,

$\begin{array}{c}\left[{\text{OH}}^{-}\right]\times \left[{\text{H}}_3{\text{O}}^{+}\right]=1\times {10}^{-14}{\text{ M}}^2\\ \left[{\text{OH}}^{-}\right]=\frac{1\times {10}^{-14}{\text{ M}}^2}{\left[{\text{H}}_3{\text{O}}^{+}\right]}\end{array}$

Substitute $1\times {10}^{-3}\text{ M}$ for $\left[{\text{H}}_3{\text{O}}^{+}\right]$ .

$\begin{array}{c}\left[{\text{OH}}^{-}\right]=\frac{1\times {10}^{-14}{\text{ M}}^2}{1\times {10}^{-3}\text{ M}}\\ =1\times {10}^{-11}\text{M}\end{array}$

The hydroxide ion concentration is less than $1\times {10}^{-7}$ and hence, the solution is acidic.

(b)

Interpretation Introduction

Interpretation:

The determination of $\left[{\text{OH}}^{-}\right]$ concentration from the given $\left[{\text{H}}_3{\text{O}}^{+}\right]$ concentration. Also, the acidic, basic, or neutral nature of the solution is to be identified.

Explanation of Solution

The given concentration of $\left[{\text{H}}_3{\text{O}}^{+}\right]$ is $1\times {10}^{-5}\text{ M}$ .

Now,

$\begin{array}{c}\left[{\text{OH}}^{-}\right]\times \left[{\text{H}}_3{\text{O}}^{+}\right]=1\times {10}^{-14}{\text{ M}}^2\\ \left[{\text{OH}}^{-}\right]=\frac{1\times {10}^{-14}{\text{ M}}^2}{\left[{\text{H}}_3{\text{O}}^{+}\right]}\end{array}$

Substitute $1\times {10}^{-5}\text{ M}$ for $\left[{\text{H}}_3{\text{O}}^{+}\right]$

$\begin{array}{c}\left[{\text{OH}}^{-}\right]=\frac{1\times {10}^{-14}{\text{ M}}^2}{1\times {10}^{-5}\text{ M}}\\ =1\times {10}^{-9}\text{M}\end{array}$

The hydroxide ion concentration is less than $1\times {10}^{-7}$ and hence, the solution is acidic.

(c)

Interpretation Introduction

Interpretation:

The determination of $\left[{\text{OH}}^{-}\right]$ concentration from the given $\left[{\text{H}}_3{\text{O}}^{+}\right]$ concentration. Also, the acidic, basic, or neutral nature of the solution is to be identified.

Explanation of Solution

The given concentration of $\left[{\text{H}}_3{\text{O}}^{+}\right]$ is $7.3\times {10}^{-10}\text{ M}$ .

Now,

$\begin{array}{c}\left[{\text{OH}}^{-}\right]\times \left[{\text{H}}_3{\text{O}}^{+}\right]=1\times {10}^{-14}{\text{ M}}^2\\ \left[{\text{OH}}^{-}\right]=\frac{1\times {10}^{-14}{\text{ M}}^2}{\left[{\text{H}}_3{\text{O}}^{+}\right]}\end{array}$

Substitute $7.3\times {10}^{-10}\text{ M}$ for $\left[{\text{H}}_3{\text{O}}^{+}\right]$ .

$\begin{array}{c}\left[{\text{OH}}^{-}\right]=\frac{1\times {10}^{-14}{\text{ M}}^2}{7.3\times {10}^{-10}\text{ M}}\\ =1.4\times {10}^{-5}\text{M}\end{array}$

The hydroxide ion concentration is more than $1\times {10}^{-7}$ and hence, the solution is basic.