Chapter 16, Problem 16.35QP

(a)

Interpretation Introduction

Interpretation: The $\text{pH}$ of the given buffer solutions at the given conditions is to be calculated.

Concept introduction: The $\text{pH}$ of the given buffer solution is calculated by using the formula,

$\text{pH}=p{K}_{\text{a}}+\log \frac{\left[\text{Conjugate}\text{Base}\right]}{\left[\text{Acid}\right]}$

To determine: The $\text{pH}$ of the given buffer solution consisting of ${\text{HNO}}_2$ and ${\text{NaNO}}_2$.

Answer to Problem 16.35QP

Solution

The $\text{pH}$ of the given buffer solution consisting of ${\text{HNO}}_2$ and ${\text{NaNO}}_2$ is $\underset{\_}{3.49}$.

Explanation of Solution

Explanation

Given

The concentration of ${\text{HNO}}_2$ solution is $0.120\text{M}$.

The concentration of ${\text{NaNO}}_2$ solution is $0.150\text{M}$.

The $\text{pH}$ of the given buffer solution is calculated by using the formula,

$\text{pH}=p{K}_{\text{a}}+\log \frac{\left[{\text{NaNO}}_2\right]}{\left[{\text{HNO}}_2\right]}$

Where,

• $\text{pH}$ is the hydrogen content of solution.
• $p{K}_{\text{a}}$ is the dissociation constant of acid.
• $\left[{\text{NaNO}}_2\right]$ is the concentration of sodium nitrate solution.
• $\left[{\text{HNO}}_2\right]$ is the concentration of nitrous acid.

Substitute the values of $\left[{\text{NaNO}}_2\right]$, $\left[{\text{HNO}}_2\right]$ and $p{K}_{\text{a}}$ in the above equation.

$\begin{array}{c}\text{pH}=3.39+\log \frac{0.150}{0.120}\\ \text{pH}=\underset{\_}{3.49}\end{array}$

(b)

Interpretation Introduction

To determine: The $\text{pH}$ of the solution after addition of $1.00\text{mL}$ of given hydrochloric acid to the given buffer solution.

Answer to Problem 16.35QP

Solution

The $\text{pH}$ of the buffer after addition of hydrochloric acid solution is $\underset{\_}{3.41}$.

Explanation of Solution

Explanation

Given

The volume of hydrochloric acid in the solution is $1.00\text{mL}\left(=0.001\text{L}\right)$

The concentration of hydrochloric acid solution is $11.6\text{M}$.

The concentration of ${\text{HNO}}_2$ solution is $0.120\text{M}$.

The concentration of ${\text{NaNO}}_2$ solution is $0.150\text{M}$.

The number of moles of hydrochloric acid present in the given solution is calculated by using the formula,

$\begin{array}{l}M=\frac{n}{V}\\ n=M\cdot V\end{array}$

Where,

• $M$ is the molarity of the solution.
• $n$ is the number of moles of solute.
• $V$ is the volume of solution in liters.

Substitute the values of $M$ and $V$ in above equation.

$\begin{array}{c}n=11.6\text{M}\times 0.001\text{L}\\ =0.0116\text{mol}\end{array}$

The addition of acid to the given buffer solution increases the concentration of acid by the given number of moles and reduces the concentration of salt equal to the added moles of acid. Therefore, the concentration of ${\text{HNO}}_2$ and ${\text{NaNO}}_2$ after addition of hydrochloric acid is calculated as,

For concentration of ${\text{NaNO}}_2$,

$\begin{array}{c}\text{Concentration}\text{of}{\text{NaNO}}_2=\left(0.150-0.0116\right)\text{M}\\ =0.1384\text{M}\end{array}$

For concentration of ${\text{HNO}}_2$,

$\begin{array}{c}\text{Concentration}\text{of}{\text{HNO}}_2=\left(0.120+0.0116\right)\text{M}\\ =0.1316\text{M}\end{array}$

The $\text{pH}$ of the given buffer solution is calculated by using the formula,

$\text{pH}=p{K}_{\text{a}}+\log \frac{\left[{\text{NaNO}}_2\right]}{\left[{\text{HNO}}_2\right]}$

Where,

• $\text{pH}$ is the hydrogen content of solution.
• $p{K}_{\text{a}}$ is the dissociation constant of acid.
• $\left[{\text{NaNO}}_2\right]$ is the concentration of sodium nitrate solution.
• $\left[{\text{HNO}}_2\right]$ is the concentration of nitrous acid.

Substitute the values of $\left[{\text{NaNO}}_2\right]$, $\left[{\text{HNO}}_2\right]$ and $p{K}_{\text{a}}$ in the above equation.

$\begin{array}{c}\text{pH}=3.39+\log \frac{0.1384}{0.1316}\\ \text{pH}=\underset{\_}{3.41}\end{array}$

Conclusion

1. a. The $\text{pH}$ of the given buffer solution consisting of ${\text{HNO}}_2$ and ${\text{NaNO}}_2$ is $\underset{\_}{3.49}$.
2. b. The $\text{pH}$ of the buffer after addition of hydrochloric acid solution is $\underset{\_}{3.41}$