Chapter 17, Problem 19CR

Interpretation Introduction

(a)

Interpretation:

The concentration of ${\text{H}}^{+}$ ion in the given solution that contains $2.11\times {10}^{-4}\text{M}{\text{OH}}^{-}$ ion is to be calculated.

Concept Introduction:

The ionic product of water is the product of concentration of ${\text{OH}}^{-}$ and ${\text{H}}^{+}$ ion in water at a given temperature. The ionic product of water is represented as,

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

Where,

• $\left[{\text{OH}}^{-}\right]$ represents the concentration of ${\text{OH}}^{-}$ ions in the solution.
• $\left[{\text{H}}^{+}\right]$ represents the concentration of ${\text{H}}^{+}$ ions in the solution.
• ${\text{K}}_{\text{w}}$ represents the ionic product of water.

Answer to Problem 19CR

The value of $\left[{\text{H}}^{+}\right]$ in the solution that contains $2.11\times {10}^{-4}\text{M}{\text{OH}}^{-}$ ion is $4.74\times {10}^{-11}\text{M}$.

Explanation of Solution

The concentration of ${\text{OH}}^{-}$ in the solution is $2.11\times {10}^{-4}\text{M}$.

The value of ionic product of water at $25°\text{C}$ is $1.00\times {10}^{-14}{\text{M}}^2$.

The ionic product of water is represented as,

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

Where,

• $\left[{\text{OH}}^{-}\right]$ represents the concentration of ${\text{OH}}^{-}$ ions in the solution.
• $\left[{\text{H}}^{+}\right]$ represents the concentration of ${\text{H}}^{+}$ ions in the solution.
• ${\text{K}}_{\text{w}}$ represents the ionic product of water.

Rearrange the above equation for the value of $\left[{\text{H}}^{+}\right]$.

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

Substitute the value of $\left[{\text{OH}}^{-}\right]$ and ${\text{K}}_{\text{w}}$ in the above equation.

$\begin{array}{c}\left[{\text{H}}^{+}\right]=\frac{1.00\times {10}^{-14}{\text{M}}^2}{2.11\times {10}^{-4}\text{M}}\\ =4.74\times {10}^{-11}\text{M}\end{array}$

Therefore, the concentration of ${\text{H}}^{+}$ in the solution is $4.74\times {10}^{-11}\text{M}$.

Interpretation Introduction

(b)

Interpretation:

The $\text{pH}$ of the given solution that contains $7.34\times {10}^{-6}\text{M}{\text{OH}}^{-}$ ion is to be calculated.

Concept Introduction:

The term $\text{pH}$ referred to the power of hydrogen. The $\text{pH}$ of a solution is mathematically equal to the negative logarithm of concentration of ${\text{H}}^{+}$ ion in solution. The $\text{pH}$ of a solution is represented as,

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

Where,

• $\left[{\text{H}}^{+}\right]$ represents the concentration of ${\text{H}}^{+}$ ions in the solution.

Answer to Problem 19CR

The $\text{pH}$ of the solution is $8.87$.

Explanation of Solution

The concentration of ${\text{OH}}^{-}$ in the solution is $7.34\times {10}^{-6}\text{M}$.

The value of ionic product of water at $25°\text{C}$ is $1.00\times {10}^{-14}{\text{M}}^2$.

The ionic product of water is represented as,

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

Where,

• $\left[{\text{OH}}^{-}\right]$ represents the concentration of ${\text{OH}}^{-}$ ions in the solution.
• $\left[{\text{H}}^{+}\right]$ represents the concentration of ${\text{H}}^{+}$ ions in the solution.
• ${\text{K}}_{\text{w}}$ represents the ionic product of water.

Rearrange the above equation for the value of $\left[{\text{H}}^{+}\right]$.

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

Substitute the value of $\left[{\text{OH}}^{-}\right]$ and ${\text{K}}_{\text{w}}$ in the above equation.

$\begin{array}{c}\left[{\text{H}}^{+}\right]=\frac{1.00\times {10}^{-14}{\text{M}}^2}{7.34\times {10}^{-6}\text{M}}\\ =1.36\times {10}^{-9}\text{M}\end{array}$

Therefore, the concentration of ${\text{H}}^{+}$ in the solution is $1.36\times {10}^{-9}\text{M}$.

The $\text{pH}$ of a solution is represented as,

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

Where,

• $\left[{\text{H}}^{+}\right]$ represents the concentration of ${\text{H}}^{+}$ ions in the solution.

Substitute the value of $\left[{\text{H}}^{+}\right]$ ions in the above equation.

$\begin{array}{c}\text{pH}=-\text{log}\left(1.36\times {10}^{-9}\text{M}\right)\\ =8.87\end{array}$

Therefore, the $\text{pH}$ of the solution is $8.87$.

Interpretation Introduction

(c)

Interpretation:

The $\text{pOH}$ of the given solution that contains $9.81\times {10}^{-8}\text{M}{\text{OH}}^{-}$ ion is to be calculated.

Concept Introduction:

The $\text{pOH}$ of a solution is used to measure the alkalinity of the solution. The $\text{pOH}$ of a solution is mathematically equal to the negative logarithm of concentration of ${\text{OH}}^{-}$ ion in solution. The $\text{pOH}$ of a solution is represented as,

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

Where,

• $\left[{\text{OH}}^{-}\right]$ represents the concentration of ${\text{OH}}^{-}$ ions in the solution.

Answer to Problem 19CR

The $\text{pOH}$ of the given solution that contains $9.81\times {10}^{-8}\text{M}{\text{OH}}^{-}$ ion is $7.01$.

Explanation of Solution

The concentration of ${\text{OH}}^{-}$ ions in the solution is $9.81\times {10}^{-8}\text{M}$.

The $\text{pOH}$ of a solution is represented as,

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

Where,

• $\left[{\text{OH}}^{-}\right]$ represents the concentration of ${\text{OH}}^{-}$ ions in the solution.

Substitute the value of $\left[{\text{OH}}^{-}\right]$ in the above equation.

$\begin{array}{c}\text{pOH}=-\text{log}\left(9.81\times {10}^{-8}\text{M}\right)\\ =7.01\end{array}$

Therefore, the value of $\text{pOH}$ is $7.01$.

Interpretation Introduction

(d)

Interpretation:

The $\text{pOH}$ of the given solution that have $9.81\text{pH}$ is to be calculated.

Concept Introduction:

The $\text{pOH}$ of a solution is used to measure the alkalinity of the solution. The $\text{pOH}$ of a solution is mathematically equal to the negative logarithm of concentration of ${\text{OH}}^{-}$ ion in solution. The $\text{pOH}$ of a solution is represented as,

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

Where,

• $\left[{\text{OH}}^{-}\right]$ represents the concentration of ${\text{OH}}^{-}$ ions in the solution.

Answer to Problem 19CR

Explanation of Solution

The $\text{pH}$ of the solution is $9.32$.

The relation between $\text{pH}$ and $\text{pOH}$ of a solution is given as,

$\text{pOH}=\text{14}-\text{pH}$

Substitute the value of $\text{pH}$ in the above equation.

$\begin{array}{c}\text{pOH}=\text{14}-9.32\\ =4.68\end{array}$

Therefore, the $\text{pOH}$ of the solution is $4.68$.

Interpretation Introduction

(e)

Interpretation:

The $\text{pH}$ of the given solution that contains $5.87\times {10}^{-11}\text{M}{\text{H}}^{+}$ ion is to be calculated.

Concept Introduction:

The term $\text{pH}$ referred to the power of hydrogen. The $\text{pH}$ of a solution is mathematically equal to the negative logarithm of concentration of ${\text{H}}^{+}$ ion in solution. The $\text{pH}$ of a solution is represented as,

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

Where,

• $\left[{\text{H}}^{+}\right]$ represents the concentration of ${\text{H}}^{+}$ ions in the solution.

Answer to Problem 19CR

The $\text{pH}$ of the given solution that contains $5.87\times {10}^{-11}\text{M}{\text{H}}^{+}$ ion is $10.23$.

Explanation of Solution

The concentration of ${\text{H}}^{+}$ ions in the solution is $5.87\times {10}^{-11}\text{M}$.

The $\text{pH}$ of a solution is represented as,

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

Where,

• $\left[{\text{H}}^{+}\right]$ represents the concentration of ${\text{H}}^{+}$ ions in the solution.

Substitute the value of $\left[{\text{H}}^{+}\right]$ ions in the above equation.

$\begin{array}{c}\text{pH}=-\text{log}\left(5.87\times {10}^{-11}\text{M}\right)\\ =10.23\end{array}$

Therefore, the $\text{pH}$ of the solution is $10.23$.

Interpretation Introduction

(f)

Interpretation:

The concentration of ${\text{H}}^{+}$ ions in the given solution that has $5.83\text{pH}$ is to be calculated.

Concept Introduction:

The term $\text{pH}$ referred to the power of hydrogen. The $\text{pH}$ of a solution is mathematically equal to the negative logarithm of concentration of ${\text{H}}^{+}$ ion in solution. The $\text{pH}$ of a solution is represented as,

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

Where,

• $\left[{\text{H}}^{+}\right]$ represents the concentration of ${\text{H}}^{+}$ ions in the solution.

Answer to Problem 19CR

The concentration of ${\text{H}}^{+}$ ions in the given solution that has $5.83\text{pH}$ is $1.48\times {10}^{-6}\text{M}$.

Explanation of Solution

The $\text{pH}$ of the solution is $5.83$.

The $\text{pH}$ of a solution is represented as,

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

Where,

• $\left[{\text{H}}^{+}\right]$ represents the concentration of ${\text{H}}^{+}$ ions in the solution.

Rearrange the above equation for the value of $\left[{\text{H}}^{+}\right]$.

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

Substitute the value $\text{pH}$ in the above equation.

$\begin{array}{c}\left[{\text{H}}^{+}\right]={10}^{-\left(5.83\right)}\\ =1.48\times {10}^{-6}\text{M}\end{array}$

The concentration of ${\text{H}}^{+}$ ions in the solution is $1.48\times {10}^{-6}\text{M}$.