Chapter 16, Problem 22A

(a)

Interpretation Introduction

Interpretation:

The concentration of ${\text{H}}^{+}$ ion has to be calculated. Whether the solution is acidic or basic is to be indicated.

Concept Introduction:

The acidity or alkalinity of a solution is expressed by determining pH of the solution. pH of a solution is defined as negative logarithm of the concentration of ${\text{H}}^{+}$ ion in the solution. pH is expressed as-

  $\text{pH}=-\mathrm{l}\mathrm{o}\mathrm{g}[{\mathrm{H}}^{+}]$

pOH of a solution is defined as negative logarithm of the concentration of hydroxyl ion ( ${\text{OH}}^{-}$ ) in the solution. pOH is expressed as-

  $\text{pOH}=-\mathrm{l}\mathrm{o}\mathrm{g}[\mathrm{O}{\mathrm{H}}^{-}]$

Both pH and pOH are related to each other by this following equation-

  $\text{pH}+\text{pOH}=\mathrm{p}{\mathrm{K}}_{\mathrm{w}}$

At 25 °C the value of $\mathrm{p}{\mathrm{K}}_{\mathrm{w}}$ is 14. $\mathrm{p}{\mathrm{K}}_{\mathrm{w}}$ can be expressed as-

  $\mathrm{p}{\mathrm{K}}_{\mathrm{w}}=-\mathrm{l}\mathrm{o}\mathrm{g}[{\mathrm{K}}_{\mathrm{w}}]$

Where, ${\mathrm{K}}_{\mathrm{w}}=[{\mathrm{H}}^{+}]\times [\mathrm{O}{\mathrm{H}}^{-}]$ and at 25 °C the value of K_w is 10-14.

Answer to Problem 22A

The concentration of ${\text{H}}^{+}$ ion is4.31 × 10-11 M and the solution is basic.

Explanation of Solution

Using following equation to calculate the concentration of ${\text{H}}^{+}$ ion,

  $\begin{array}{l}{\mathrm{K}}_{\mathrm{w}}=[{\mathrm{H}}^{+}]\times [\mathrm{O}{\mathrm{H}}^{-}]\\ [{\mathrm{H}}^{+}]=\frac{{\mathrm{K}}_{\mathrm{w}}}{[\mathrm{O}{\mathrm{H}}^{-}]}=\frac{10^{-14}}{[\mathrm{O}{\mathrm{H}}^{-}]}\end{array}$

Since,

[OH^-] = 2.32 × 10-4 M

Or,

  $\begin{array}{l}[{\mathrm{H}}^{+}]=\frac{{\mathrm{K}}_{\mathrm{w}}}{[\mathrm{O}{\mathrm{H}}^{-}]}\\ =\frac{10^{-14}{\mathrm{M}}^2}{2.32\mathrm{}\times \mathrm{}10^{-4}\mathrm{M}}= 4.31\mathrm{}\times \mathrm{}10^{-11}\mathrm{M}\end{array}$

Here, concentration of H+ ion is lower than 10-7. So the solution is basic.

(b)

Interpretation Introduction

Interpretation:

The concentration of ${\text{H}}^{+}$ ion has to be calculated. Whether the solution is acidic or basic is to be indicated.

Concept Introduction:

The acidity or alkalinity of a solution is expressed by determining pH of the solution. pH of a solution is defined as negative logarithm of the concentration of ${\text{H}}^{+}$ ion in the solution. pH is expressed as-

  $\text{pH}=-\mathrm{l}\mathrm{o}\mathrm{g}[{\mathrm{H}}^{+}]$

pOH of a solution is defined as negative logarithm of the concentration of hydroxyl ion ( ${\text{OH}}^{-}$ ) in the solution. pOH is expressed as-

  $\text{pOH}=-\mathrm{l}\mathrm{o}\mathrm{g}[\mathrm{O}{\mathrm{H}}^{-}]$

Both pH and pOH are related to each other by this following equation-

  $\text{pH}+\text{pOH}=\mathrm{p}{\mathrm{K}}_{\mathrm{w}}$

At 25 °C the value of $\mathrm{p}{\mathrm{K}}_{\mathrm{w}}$ is 14. $\mathrm{p}{\mathrm{K}}_{\mathrm{w}}$ can be expressed as-

  $\mathrm{p}{\mathrm{K}}_{\mathrm{w}}=-\mathrm{l}\mathrm{o}\mathrm{g}[{\mathrm{K}}_{\mathrm{w}}]$

Where, ${\mathrm{K}}_{\mathrm{w}}=[{\mathrm{H}}^{+}]\times [\mathrm{O}{\mathrm{H}}^{-}]$ and at 25 °C the value of K_w is 10-14.

Answer to Problem 22A

The concentration of H+ ion is1.11 × 10-5 M and the solution is acidic.

Explanation of Solution

Using following equation to calculate the concentration of H+ ion,

  $\begin{array}{l}{\mathrm{K}}_{\mathrm{w}}=[{\mathrm{H}}^{+}]\times [\mathrm{O}{\mathrm{H}}^{-}]\\ [{\mathrm{H}}^{+}]=\frac{{\mathrm{K}}_{\mathrm{w}}}{[\mathrm{O}{\mathrm{H}}^{-}]}=\frac{10^{-14}}{[\mathrm{O}{\mathrm{H}}^{-}]}\end{array}$

Data given: [OH^-] = 8.99 × 10-10 M

  $\begin{array}{l}[{\mathrm{H}}^{+}]=\frac{{\mathrm{K}}_{\mathrm{w}}}{[\mathrm{O}{\mathrm{H}}^{-}]}\\ =\frac{10^{-14}{\mathrm{M}}^2}{8.99\mathrm{}\times \mathrm{}10^{-10}\mathrm{M}}= 1.11\mathrm{}\times \mathrm{}10^{-5}\mathrm{M}\end{array}$

Here, concentration of H+ ion is higher than 10-7. So the solution is acidic.

(c)

Interpretation Introduction

Interpretation:

The concentration of H+ ion has to be calculated. Whether the solution is acidic or basic is to be indicated.

Concept Introduction:

The acidity or alkalinity of a solution is expressed by determining pH of the solution. pH of a solution is defined as negative logarithm of the concentration of ${\text{H}}^{+}$ ion in the solution. pH is expressed as-

  $\text{pH}=-\mathrm{l}\mathrm{o}\mathrm{g}[{\mathrm{H}}^{+}]$

pOH of a solution is defined as negative logarithm of the concentration of hydroxyl ion ( ${\text{OH}}^{-}$ ) in the solution. pOH is expressed as-

  $\text{pOH}=-\mathrm{l}\mathrm{o}\mathrm{g}[\mathrm{O}{\mathrm{H}}^{-}]$

Both pH and pOH are related to each other by this following equation-

  $\text{pH}+\text{pOH}=\mathrm{p}{\mathrm{K}}_{\mathrm{w}}$

At 25 °C the value of $\mathrm{p}{\mathrm{K}}_{\mathrm{w}}$ is 14. $\mathrm{p}{\mathrm{K}}_{\mathrm{w}}$ can be expressed as-

  $\mathrm{p}{\mathrm{K}}_{\mathrm{w}}=-\mathrm{l}\mathrm{o}\mathrm{g}[{\mathrm{K}}_{\mathrm{w}}]$

Where, ${\mathrm{K}}_{\mathrm{w}}=[{\mathrm{H}}^{+}]\times [\mathrm{O}{\mathrm{H}}^{-}]$ and at 25 °C the value of K_w is 10-14.

Answer to Problem 22A

The concentration of H+ ion is 2.30 × 10-9 M and the solution is basic.

Explanation of Solution

Using following equation to calculate the concentration of ${\text{H}}^{+}$ on,

  $\begin{array}{l}{\mathrm{K}}_{\mathrm{w}}=[{\mathrm{H}}^{+}]\times [\mathrm{O}{\mathrm{H}}^{-}]\\ [{\mathrm{H}}^{+}]=\frac{{\mathrm{K}}_{\mathrm{w}}}{[\mathrm{O}{\mathrm{H}}^{-}]}=\frac{10^{-14}}{[\mathrm{O}{\mathrm{H}}^{-}]}\end{array}$

Here,

[OH^-] = 4.34 × 10-6 M

Thus,

  $\begin{array}{l}[{\mathrm{H}}^{+}]=\frac{{\mathrm{K}}_{\mathrm{w}}}{[\mathrm{O}{\mathrm{H}}^{-}]}\\ =\frac{10^{-14}{\mathrm{M}}^2}{4.34\mathrm{}\times \mathrm{}10^{-6}\mathrm{M}}= 2.30\mathrm{}\times \mathrm{}10^{-9}\mathrm{M}\end{array}$

Here, concentration of H+ ion is lower than 10-7. So the solution is basic.

(d)

Interpretation Introduction

Interpretation:

The concentration of ${\text{H}}^{+}$ ion has to be calculated. Whether the solution is acidic or basic is to be indicated.

Concept Introduction:

Concept Introduction:

The acidity or alkalinity of a solution is expressed by determining pH of the solution. pH of a solution is defined as negative logarithm of the concentration of ${\text{H}}^{+}$ ion in the solution. pH is expressed as-

  $\text{pH}=-\mathrm{l}\mathrm{o}\mathrm{g}[{\mathrm{H}}^{+}]$

pOH of a solution is defined as negative logarithm of the concentration of hydroxyl ion ( ${\text{OH}}^{-}$ ) in the solution. pOH is expressed as-

  $\text{pOH}=-\mathrm{l}\mathrm{o}\mathrm{g}[\mathrm{O}{\mathrm{H}}^{-}]$

Both pH and pOH are related to each other by this following equation-

  $\text{pH}+\text{pOH}=\mathrm{p}{\mathrm{K}}_{\mathrm{w}}$

At 25 °C the value of $\mathrm{p}{\mathrm{K}}_{\mathrm{w}}$ is 14. $\mathrm{p}{\mathrm{K}}_{\mathrm{w}}$ can be expressed as-

  $\mathrm{p}{\mathrm{K}}_{\mathrm{w}}=-\mathrm{l}\mathrm{o}\mathrm{g}[{\mathrm{K}}_{\mathrm{w}}]$

Where, ${\mathrm{K}}_{\mathrm{w}}=[{\mathrm{H}}^{+}]\times [\mathrm{O}{\mathrm{H}}^{-}]$ and at 25 °C the value of K_w is 10-14.

Answer to Problem 22A

The concentration of ${\mathrm{H}}^{+}$ ion is1.61 × 10-3 M and the solution is acidic.

Explanation of Solution

Using following equation to calculate the concentration of ${\mathrm{H}}^{+}$ ion,

  $\begin{array}{l}{\mathrm{K}}_{\mathrm{w}}=[{\mathrm{H}}^{+}]\times [\mathrm{O}{\mathrm{H}}^{-}]\\ [{\mathrm{H}}^{+}]=\frac{{\mathrm{K}}_{\mathrm{w}}}{[\mathrm{O}{\mathrm{H}}^{-}]}=\frac{10^{-14}}{[\mathrm{O}{\mathrm{H}}^{-}]}\end{array}$

Here,

  $[{\text{OH}}^{-}]=6.22\times {10}^{-12}\text{M}$

Now,

  $\begin{array}{l}[{\mathrm{H}}^{+}]=\frac{{\mathrm{K}}_{\mathrm{w}}}{[\mathrm{O}{\mathrm{H}}^{-}]}\\ =\frac{10^{-14}{\mathrm{M}}^2}{6.22\mathrm{}\times \mathrm{}10^{-12}\mathrm{M}}= 1.61\mathrm{}\times \mathrm{}10^{-3}\mathrm{M}\end{array}$

Here, concentration of H+ ion is higher than 10-7. So the solution is acidic.