Chapter 14, Problem 60E

Interpretation Introduction

(a)

Interpretation:

The molar hydroxide ion concentration with $\text{pH}=0.90$ is to be calculated.

Concept introduction:

The $\text{pH}$ scale tells about the strength of an acid and a base. It measures the concentration of the hydrogen ions. There is an inverse relationship between the $\text{pH}$ value and the concentration of the hydrogen ion. Higher the concentration of hydrogen ions, lesser the value of $\text{pH}$. There is an inverse relationship between the $\text{pOH}$ value and the concentration of the hydroxide ion. Higher the concentration of hydroxide ions, lesser the value of $\text{pOH}$.

Answer to Problem 60E

The molar hydroxide ion concentration with $\text{pH}=0.90$ is $8.0\times {10}^{-14}M$.

Explanation of Solution

The relationship between $\text{pH}$ and hydrogen ion concentration is equal to $10$ raised to the power negative value of $\text{pH}$. It is represented as shown below.

$\left[{\text{H}}^{+}\right]={10}^{-\text{pH}}$ …(1)

The given value of $\text{pH}$ is $0.90$.

Substitute the value of $\text{pH}$ in equation (1) as shown below.

$\begin{array}{rll}\left[{\text{H}}^{+}\right]& =& {10}^{-0.90}\\ \left[{\text{H}}^{+}\right]& =& {10}^{-\left(1-0.10\right)}\\ & =& {\text{10}}^{0.10}\times {10}^{-1}M\\ & =& \text{1}\text{.25}\times {10}^{-1}M\end{array}$

The relation between hydrogen ion concentration and hydroxide ion concentration is shown below.

$\left[{\text{H}}^{+}\right]\left[{\text{OH}}^{-}\right]={10}^{-14}$ …(2)

Substitute the value of $\left[{\text{H}}^{+}\right]$ in equation (2) as shown below.

$\begin{array}{rll}\left[{\text{H}}^{+}\right]\left[{\text{OH}}^{-}\right]& =& {10}^{-14}\\ \left(\text{1}\text{.25}\times {10}^{-1}M\right)\left[{\text{OH}}^{-}\right]& =& {10}^{-14}\\ \left[{\text{OH}}^{-}\right]& =& \frac{{10}^{-14}}{\text{1}\text{.25}\times {10}^{-1}M}\\ & =& 8.0\times {10}^{-14}M\end{array}$

Therefore, the calculated molar hydroxide ion concentration with $\text{pH}=0.90$ is calculated as $8.0\times {10}^{-14}M$.

Conclusion

The molar hydroxide ion concentration with $\text{pH}=0.90$ is calculated as $8.0\times {10}^{-14}M$.

Interpretation Introduction

(b)

Interpretation:

The molar hydroxide ion concentration with $\text{pH}=\text{1}\text{.62}$ is to be calculated.

Concept introduction:

The $\text{pH}$ scale tells about the strength of an acid and a base. It measures the concentration of the hydrogen ions. There is an inverse relationship between the $\text{pH}$ value and the concentration of the hydrogen ion. Higher the concentration of hydrogen ions, lesser the value of $\text{pH}$. There is an inverse relationship between the $\text{pOH}$ value and the concentration of the hydroxide ion. Higher the concentration of hydroxide ions, lesser the value of $\text{pOH}$.

Answer to Problem 60E

The molar hydrogen ion concentration with $\text{pH}=\text{1}\text{.62}$ is $4.18\times {10}^{-13}M$.

Explanation of Solution

The relationship between $\text{pH}$ and hydrogen ion concentration is equal to $10$ raised to the power negative value of $\text{pH}$. It is represented as shown below.

$\left[{\text{H}}^{+}\right]={10}^{-\text{pH}}$ …(1)

The value of $\text{pH}$ is $\text{1}\text{.62}$.

Substitute the value of $\text{pH}$ in equation (1) as shown below.

$\begin{array}{rll}\left[{\text{H}}^{+}\right]& =& {10}^{-\text{1}\text{.62}}\\ & =& {10}^{-\left(2.0-0.38\right)}M\end{array}$

Therefore, the above equation can be written as shown below.

$\begin{array}{rll}\left[{\text{H}}^{+}\right]& =& {10}^{-\left(2.0-0.38\right)}\\ & =& {\text{10}}^{0.38}\times {10}^{-2}M\\ & =& \text{2}\text{.39}\times {10}^{-2}M\end{array}$

The relation between hydrogen ion concentration and hydroxide ion concentration is shown below.

$\left[{\text{H}}^{+}\right]\left[{\text{OH}}^{-}\right]={10}^{-14}$ …(2)

Substitute the value of $\left[{\text{H}}^{+}\right]$ in equation (2) as shown below.

$\begin{array}{rll}\left[{\text{H}}^{+}\right]\left[{\text{OH}}^{-}\right]& =& {10}^{-14}\\ \left(\text{2}\text{.39}\times {10}^{-2}M\right)\left[{\text{OH}}^{-}\right]& =& {10}^{-14}\\ \left[{\text{OH}}^{-}\right]& =& \frac{{10}^{-14}}{\text{2}\text{.39}\times {10}^{-2}M}\\ & =& 4.18\times {10}^{-13}M\end{array}$

Therefore, the molar hydroxide ion concentration with $\text{pH}=\text{1}\text{.62}$ is calculated as $4.18\times {10}^{-13}M$.

Conclusion

The molar hydroxide ion concentration with $\text{pH}=\text{1}\text{.62}$ is calculated as $4.18\times {10}^{-13}M$.