Chapter 16.5, Problem 8PPA

Calculate the concentration of HNO₃ in a solution at 25°C that has pH (a) 2.06, (b) 1.77, and (c) 6.01.

Interpretation Introduction

Interpretation:

The concentration of ${\text{HNO}}_{\text{3}}$ in a solution at ${\text{25}}^{\circ }\text{C}$ with the given pH has to be calculated

Concept Information:

Strong acids:

In strong acids, the ionization of acid is complete. This implies that the concentration of the hydrogen ion or hydronium ion will be equal to the initial concentration of the acid at equilibrium.

pH definition:

The concentration of hydrogen ion is measured using $\text{pH}$ scale.  The acidity of aqueous solution is expressed by $\text{pH}$ scale.

The $\text{pH}$ of a solution is defined as the negative base-10 logarithm of the hydrogen or hydronium ion concentration.

$\text{pH}\text{=}{\text{-log[H}}_{\text{3}}{\text{O}}^{\text{+}}\text{]}$

On rearranging, the concentration of hydrogen ion ${\text{[H}}^{+}\text{]}$ can be calculated using pH as follows,

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

To calculate: The concentration of ${\text{HNO}}_{\text{3}}$ solution with the pH=2.06

Answer to Problem 8PPA

Answer

The concentration of ${\text{HNO}}_{\text{3}}$ solution with the given pH is $8.7\times {10}^{-3}M$

Explanation of Solution

${\text{HNO}}_{\text{3}}$ is a strong acid.

In a strong acid solution, the molar concentration of hydrogen ion is equal to the acid concentration

The pH of the given ${\text{HNO}}_{\text{3}}$ solution is 2.06

The concentration of hydrogen ion can be calculated as follows,

$\begin{array}{l}{\text{[H}}^{+}\text{]}\text{=}{\text{10}}^{\text{-pH}}\\ {\text{ =10}}^{\text{-2}\text{.06}}\\ \text{ =}8.7\times {10}^{-3}M\end{array}$

The concentration of hydrogen ion is $8.7\times {10}^{-3}M$

Therefore, the concentration of the given ${\text{HNO}}_{\text{3}}$ solution is $8.7\times {10}^{-3}M$

Interpretation Introduction

Interpretation:

The concentration of ${\text{HNO}}_{\text{3}}$ in a solution at ${\text{25}}^{\circ }\text{C}$ with the given pH has to be calculated

Concept Information:

Strong acids:

In strong acids, the ionization of acid is complete. This implies that the concentration of the hydrogen ion or hydronium ion will be equal to the initial concentration of the acid at equilibrium.

pH definition:

The concentration of hydrogen ion is measured using $\text{pH}$ scale.  The acidity of aqueous solution is expressed by $\text{pH}$ scale.

The $\text{pH}$ of a solution is defined as the negative base-10 logarithm of the hydrogen or hydronium ion concentration.

$\text{pH}\text{=}{\text{-log[H}}_{\text{3}}{\text{O}}^{\text{+}}\text{]}$

On rearranging, the concentration of hydrogen ion ${\text{[H}}^{+}\text{]}$ can be calculated using pH as follows,

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

To calculate: The concentration of ${\text{HNO}}_{\text{3}}$ solution with the pH=1.77

Answer to Problem 8PPA

Answer

The concentration of ${\text{HNO}}_{\text{3}}$ solution with the given pH is $1.7\times {10}^{-2}M$

Explanation of Solution

${\text{HNO}}_{\text{3}}$ is a strong acid.

In a strong acid solution, the molar concentration of hydrogen ion is equal to the acid concentration

The pH of the given ${\text{HNO}}_{\text{3}}$ solution is 1.77

The concentration of hydrogen ion can be calculated as follows,

$\begin{array}{l}{\text{[H}}^{+}\text{]}\text{=}{\text{10}}^{\text{-pH}}\\ {\text{ =10}}^{\text{-1}\text{.77}}\\ \text{ =}1.7\times {10}^{-2}M\end{array}$

The concentration of hydrogen ion is $1.7\times {10}^{-2}M$

Therefore, the concentration of the given ${\text{HNO}}_{\text{3}}$ solution is $1.7\times {10}^{-2}M$

Interpretation Introduction

Interpretation:

The concentration of ${\text{HNO}}_{\text{3}}$ in a solution at ${\text{25}}^{\circ }\text{C}$ with the given pH has to be calculated

Concept Information:

Strong acids:

In strong acids, the ionization of acid is complete. This implies that the concentration of the hydrogen ion or hydronium ion will be equal to the initial concentration of the acid at equilibrium.

pH definition:

The concentration of hydrogen ion is measured using $\text{pH}$ scale.  The acidity of aqueous solution is expressed by $\text{pH}$ scale.

The $\text{pH}$ of a solution is defined as the negative base-10 logarithm of the hydrogen or hydronium ion concentration.

$\text{pH}\text{=}{\text{-log[H}}_{\text{3}}{\text{O}}^{\text{+}}\text{]}$

On rearranging, the concentration of hydrogen ion ${\text{[H}}^{+}\text{]}$ can be calculated using pH as follows,

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

To calculate: The concentration of ${\text{HNO}}_{\text{3}}$ solution with the pH=6.01

Answer to Problem 8PPA

Answer

The concentration of ${\text{HNO}}_{\text{3}}$ solution with the given pH is $9.8\times {10}^{-7}M$

Explanation of Solution

${\text{HNO}}_{\text{3}}$ is a strong acid.

In a strong acid solution, the molar concentration of hydrogen ion is equal to the acid concentration

The pH of the given ${\text{HNO}}_{\text{3}}$ solution is 6.01

The concentration of hydrogen ion can be calculated as follows,

$\begin{array}{l}{\text{[H}}^{+}\text{]}\text{=}{\text{10}}^{\text{-pH}}\\ {\text{ =10}}^{\text{-6}\text{.01}}\\ \text{ =}9.8\times {10}^{-7}M\end{array}$

The concentration of hydrogen ion is $9.8\times {10}^{-7}M$

Therefore, the concentration of the given ${\text{HNO}}_{\text{3}}$ solution is $9.8\times {10}^{-7}M$