Chapter 16, Problem 25A

(a)

Interpretation Introduction

Interpretation:

The concentration that represents more basic solution should be selected from the following:

  $[{\mathrm{H}}^{+}]=1.59\times {10}^{-7}\mathrm{M}$ or $[{\mathrm{H}}^{+}]=1.04\times {10}^{-8}\mathrm{M}$

Concept Introduction:

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

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

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

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

Answer to Problem 25A

Solution having concentration $[{\mathrm{H}}^{+}]=1.04\times {10}^{-8}\mathrm{M}$ is more basic.

Explanation of Solution

The pH for both the solution is calculated as:

  $\begin{array}{l}\text{pH}=-\mathrm{l}\mathrm{o}\mathrm{g}[{\mathrm{H}}^{+}]\\ =-\mathrm{l}\mathrm{o}\mathrm{g}[1.59\mathrm{}\times \mathrm{}10^{-7}]\\ =6.8\end{array}$

  $\begin{array}{l}\text{pH}=-\mathrm{l}\mathrm{o}\mathrm{g}[{\mathrm{H}}^{+}]\\ =-\mathrm{l}\mathrm{o}\mathrm{g}[1.04\mathrm{}\times \mathrm{}10^{-8}]\\ =7.98\end{array}$

The solution having pH greater than 7 represents basic solution so, the solution having concentration $[{\mathrm{H}}^{+}]=1.04\times {10}^{-8}\mathrm{M}$ is more basic.

(b)

Interpretation Introduction

Interpretation:

The concentration that represents more basic solution should be selected from the following:

  $[{\mathrm{H}}^{+}]=5.69\times {10}^{-8}\mathrm{M}$ or $[\mathrm{O}{\mathrm{H}}^{-}]=4.49\times {10}^{-6}\mathrm{M}$

Concept Introduction:

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

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

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

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

Answer to Problem 25A

Solution having concentration $[\mathrm{O}{\mathrm{H}}^{-}]=4.49\times {10}^{-6}\mathrm{M}$ is more basic.

Explanation of Solution

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

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

So,

  $\begin{array}{l}[{\mathrm{H}}^{+}]=\frac{{\mathrm{K}}_{\mathrm{w}}}{[\mathrm{O}{\mathrm{H}}^{-}]}\\ =\frac{10^{-14}{\mathrm{M}}^2}{4.49\mathrm{}\times \mathrm{}10^{-6}\mathrm{M}}= 2.23\mathrm{}\times \mathrm{}10^{-9}\mathrm{M}\end{array}$

The pH is calculated as:

  $\begin{array}{l}\text{pH}=-\mathrm{l}\mathrm{o}\mathrm{g}[{\mathrm{H}}^{+}]\\ =-\mathrm{l}\mathrm{o}\mathrm{g}[2.23\mathrm{}\times \mathrm{}10^{-9}]\\ =8.65\end{array}$

The pH is calculated as:

  $\begin{array}{l}\text{pH}=-\mathrm{l}\mathrm{o}\mathrm{g}[{\mathrm{H}}^{+}]\\ =-\mathrm{l}\mathrm{o}\mathrm{g}[5.69\mathrm{}\times \mathrm{}10^{-8}]\\ =7.24\end{array}$

Since the pH of both the solutions is greater than 7 so, both are basic in nature but the solution having greater value of pH represents more basic solution so, the solution having concentration $[\mathrm{O}{\mathrm{H}}^{-}]=4.49\times {10}^{-6}\mathrm{M}$ is more basic.

(c)

Interpretation Introduction

Interpretation:

The concentration that represents more basic solution should be selected from the following:

  $[{\mathrm{H}}^{+}]=5.99\times {10}^{-8}\mathrm{M}$ or ${\text{[OH}}^{\text{-}}\text{] =6}{\text{.01 × 10}}^{\text{-7}}\text{M}$

Concept Introduction:

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

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

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

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

Answer to Problem 25A

Solution having concentration ${\text{[OH}}^{\text{-}}\text{] =6}{\text{.01 × 10}}^{\text{-7}}\text{M}$ is more basic.

Explanation of Solution

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

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

So,

  $\begin{array}{l}[{\mathrm{H}}^{+}]=\frac{{\mathrm{K}}_{\mathrm{w}}}{[\mathrm{O}{\mathrm{H}}^{-}]}\\ =\frac{10^{-14}{\mathrm{M}}^2}{6.01\mathrm{}\times \mathrm{}10^{-7}\mathrm{M}}= 1.66\mathrm{}\times \mathrm{}10^{-8}\mathrm{M}\end{array}$

The pH is calculated as:

  $\begin{array}{l}\text{pH}=-\mathrm{l}\mathrm{o}\mathrm{g}[{\mathrm{H}}^{+}]\\ =-\mathrm{l}\mathrm{o}\mathrm{g}[1.66\mathrm{}\times \mathrm{}10^{-8}]\\ =7.78\end{array}$

  $\begin{array}{l}\text{pH}=-\mathrm{l}\mathrm{o}\mathrm{g}[{\mathrm{H}}^{+}]\\ =-\mathrm{l}\mathrm{o}\mathrm{g}[5.99\mathrm{}\times \mathrm{}10^{-8}]\\ =7.22\end{array}$

Since the pH of both the solutions is greater than 7 so, both are basic in nature but the solution having greater value of pH represents more basic solution so, the solution having concentration ${\text{[OH}}^{\text{-}}\text{] =6}{\text{.01 × 10}}^{\text{-7}}\text{M}$ is more basic.