Chapter 8, Problem 8.72AP

(a)

Interpretation Introduction

Interpretation:

The $\left[{\text{H}}_{\text{3}}{\text{O}}^{\text{+}}\right]$ value of ${\text{10}}^{\text{-12}}\text{M}$ has to be calculated and the solution has to be determined as acidic or basic.

Concept Introduction:

The ion-product constant for water $\left({\text{K}}_{\text{w}}\right)$ is calculated using the formula,

  ${\text{K}}_{\text{w}}\text{=}\left[{\text{H}}_{\text{3}}{\text{O}}^{\text{+}}\right]\left[{\text{OH}}^{\text{-}}\right]$

The value of ${\text{K}}_{\text{w}}$ is $\text{1}{\text{.0×10}}^{\text{-14}}$ for all aqueous solution at ${\text{25}}^{\text{o}}\text{C}\text{.}$

For a solution to be acidic, $\left[{\text{H}}_{\text{3}}{\text{O}}^{\text{+}}\right]\text{>}\left[{\text{OH}}^{\text{-}}\right].$

For a solution to be basic, $\left[{\text{OH}}^{\text{-}}\right]\text{>}\left[{\text{H}}_{\text{3}}{\text{O}}^{\text{+}}\right].$

Answer to Problem 8.72AP

The value of $\left[{\text{H}}_{\text{3}}{\text{O}}^{\text{+}}\right]$ is ${\text{10}}^{\text{-2}}\text{M}\text{.}$

The solution is acidic.

Explanation of Solution

Given,

$\begin{array}{l}\left[{\text{OH}}^{-}\right]{\text{=10}}^{\text{-12}}\text{M}\\ {\text{K}}_{\text{w}}\text{=1}{\text{.0×10}}^{\text{-14}}\end{array}$

The concentration of ${\text{H}}_{\text{3}}{\text{O}}^{\text{+}}$ is calculated as,

  $\begin{array}{l}\left[{\text{H}}_{\text{3}}{\text{O}}^{\text{+}}\right]\text{=}\frac{{\text{K}}_{\text{w}}}{\left[{\text{OH}}^{\text{-}}\right]}\\ \left[{\text{H}}_{\text{3}}{\text{O}}^{\text{+}}\right]\text{=}\frac{\text{1}{\text{.0×10}}^{\text{-14}}}{{\text{10}}^{\text{-12}}}\\ \left[{\text{H}}_{\text{3}}{\text{O}}^{\text{+}}\right]\text{=1}{\text{.0×10}}^{\text{-2}}\text{M}\end{array}$

The value of $\left[{\text{H}}_{\text{3}}{\text{O}}^{\text{+}}\right]$ is ${\text{10}}^{\text{-2}}\text{M}\text{.}$

The solution is said to be acidic, since $\left[{\text{H}}_{\text{3}}{\text{O}}^{\text{+}}\right]$ is greater than the concentration of hydroxide ions.

(b)

Interpretation Introduction

Interpretation:

The $\left[{\text{H}}_{\text{3}}{\text{O}}^{\text{+}}\right]$ value of $\text{5}{\text{.0×10}}^{\text{-10}}\text{M}$ has to be calculated and the solution has to be determined as acidic or basic.

Concept Introduction:

Refer to part (a).

Answer to Problem 8.72AP

The value of $\left[{\text{H}}_{\text{3}}{\text{O}}^{\text{+}}\right]$ is $\text{2}{\text{.0×10}}^{\text{-5}}\text{M}\text{.}$

The solution is acidic.

Explanation of Solution

Given,

$\begin{array}{l}\left[{\text{OH}}^{-}\right]\text{=5}\text{.0}\times {\text{10}}^{\text{-10}}\text{M}\\ {\text{K}}_{\text{w}}\text{=1}{\text{.0×10}}^{\text{-14}}\end{array}$

The concentration of ${\text{H}}_{\text{3}}{\text{O}}^{\text{+}}$ is calculated as,

  $\begin{array}{l}\left[{\text{H}}_{\text{3}}{\text{O}}^{\text{+}}\right]\text{=}\frac{{\text{K}}_{\text{w}}}{\left[{\text{OH}}^{\text{-}}\right]}\\ \left[{\text{H}}_{\text{3}}{\text{O}}^{\text{+}}\right]\text{=}\frac{\text{1}{\text{.0×10}}^{\text{-14}}}{\text{5}{\text{.0×10}}^{\text{-10}}}\\ \left[{\text{H}}_{\text{3}}{\text{O}}^{\text{+}}\right]\text{=2}{\text{.0×10}}^{\text{-5}}\text{M}\end{array}$

The value of $\left[{\text{H}}_{\text{3}}{\text{O}}^{\text{+}}\right]$ is $\text{2}{\text{.0×10}}^{\text{-5}}\text{M}\text{.}$

The solution is said to be acidic, since $\left[{\text{H}}_{\text{3}}{\text{O}}^{\text{+}}\right]$ is greater than the concentration of hydroxide ions.

(c)

Interpretation Introduction

Interpretation:

The $\left[{\text{H}}_{\text{3}}{\text{O}}^{\text{+}}\right]$ value of $\text{6}{\text{.0×10}}^{\text{-4}}\text{M}$ has to be calculated and the solution has to be determined as acidic or basic.

Concept Introduction:

Refer to part (a).

Answer to Problem 8.72AP

The value of $\left[{\text{H}}_{\text{3}}{\text{O}}^{\text{+}}\right]$ is $\text{1}\text{.67}\times {\text{10}}^{\text{-11}}\text{M}\text{.}$

The solution is said to be basic.

Explanation of Solution

Given,

$\begin{array}{l}\left[{\text{OH}}^{-}\right]\text{=6}\text{.0}\times {\text{10}}^{\text{-4}}\text{M}\\ {\text{K}}_{\text{w}}\text{=1}{\text{.0×10}}^{\text{-14}}\end{array}$

The concentration of ${\text{H}}_{\text{3}}{\text{O}}^{\text{+}}$ is calculated as,

  $\begin{array}{l}\left[{\text{H}}_{\text{3}}{\text{O}}^{\text{+}}\right]\text{=}\frac{{\text{K}}_{\text{w}}}{\left[{\text{OH}}^{\text{-}}\right]}\\ \left[{\text{H}}_{\text{3}}{\text{O}}^{\text{+}}\right]\text{=}\frac{\text{1}{\text{.0×10}}^{\text{-14}}}{\text{6}\text{.0}\times {\text{10}}^{\text{-4}}}\\ \left[{\text{H}}_{\text{3}}{\text{O}}^{\text{+}}\right]\text{=1}{\text{.66×10}}^{\text{-11}}\text{M}\end{array}$

The value of $\left[{\text{H}}_{\text{3}}{\text{O}}^{\text{+}}\right]$ is $\text{1}\text{.67}\times {\text{10}}^{\text{-11}}\text{M}\text{.}$

The value of $\left[{\text{OH}}^{-}\right]\text{=6}\text{.0}\times {\text{10}}^{\text{-4}}\text{M}$

The solution is said to be basic, since $\left[{\text{OH}}^{\text{-}}\right]$ is greater than the hydronium ions.

(d)

Interpretation Introduction

Interpretation:

The $\left[{\text{H}}_{\text{3}}{\text{O}}^{\text{+}}\right]$ value of $\text{8}{\text{.9×10}}^{\text{-11}}\text{M}$ has to be calculated and the solution has to be determined as acidic or basic.

Concept Introduction:

Refer to part (a).

Answer to Problem 8.72AP

The value of $\left[{\text{H}}_{\text{3}}{\text{O}}^{\text{+}}\right]$ is $1.136\times {\text{10}}^{-4}\text{M}\text{.}$

The solution is acidic.

Explanation of Solution

Given,

$\begin{array}{l}\left[{\text{OH}}^{-}\right]\text{=8}\text{.9}\times {\text{10}}^{\text{-11}}\text{M}\\ {\text{K}}_{\text{w}}\text{=1}{\text{.0×10}}^{\text{-14}}\end{array}$

The concentration of ${\text{H}}_{\text{3}}{\text{O}}^{\text{+}}$ is calculated as,

  $\begin{array}{l}\left[{\text{H}}_{\text{3}}{\text{O}}^{\text{+}}\right]\text{=}\frac{{\text{K}}_{\text{w}}}{\left[{\text{OH}}^{\text{-}}\right]}\\ \left[{\text{H}}_{\text{3}}{\text{O}}^{\text{+}}\right]\text{=}\frac{\text{1}{\text{.0×10}}^{\text{-14}}}{8.8\times {\text{10}}^{\text{-11}}}\\ \left[{\text{H}}_{\text{3}}{\text{O}}^{\text{+}}\right]\text{=1}{\text{.136×10}}^{\text{-4}}\text{M}\end{array}$

The value of $\left[{\text{H}}_{\text{3}}{\text{O}}^{\text{+}}\right]$ is $1.136\times {\text{10}}^{-4}\text{M}\text{.}$

The solution is acidic, since $\left[{\text{H}}_{\text{3}}{\text{O}}^{\text{+}}\right]$ is greater than the concentration of hydroxide ions.