Chapter 17, Problem 1KSP

Which of the acids in Table 16.6 can be used to prepare a buffer of pH 6.5? (Select all that apply.)

(a)

hydrofluoric acid

(b)

benzoic acid

(c)

hydrocyanic acid

(d)

phenol

(e)

none

Interpretation Introduction

Interpretation:

The acidthat can be used to preparea buffersolution with apH value of $6.5$ is to be identified.

Concept introduction:

The $\text{pH}$ of a solution is calculated by using the Henderson–HasselBalch equation, which is given as follows:

$\text{pH}=p{K}_a+\log \frac{\left[\text{conjugate base}\right]}{\left[\text{acid}\right]}$

Here, $\left[\text{acid}\right]$ and $\left[\text{conjugate base}\right]$ are the concentrations ofthe acid and the conjugate base.

Answer to Problem 1KSP

Correct answer:Option (e).

Explanation of Solution

Reason for correct option:

The term $\log \frac{\left[\text{conjugate base}\right]}{\left[\text{acid}\right]}$ in the expression for the value ofpHlieswithin the range of $-1$ to $+1$.

Therefore, the pH of the solution formed from the given acid is given by the expression as follows:

$\text{pH}=p{K}_a\pm 1$

Forhydrochloric acid,

The acid ionization constant of hydrofluoric acid is $7.1\times {10}^{-4}$.

The value of $p{K}_a$ for hydrofluoric acid is calculated as follows:

$\begin{array}{c}p{K}_a=-\log \left[7.1\times {10}^{-4}\right]\\ =3.15\end{array}$

The pH of the buffer solution formed from hydrofluoric acid is calculated as follows:

$\begin{array}{c}\text{pH}=pKa\pm 1\\ =3.15\pm 1\\ =4.15\left(\text{or}\right)2.15\end{array}$

Forbenzoic acid,

The acid ionization constant of benzoic acid is $6.5\times {10}^{-5}$.

The value of $p{K}_a$ forbenzoic acid is calculated as follows:

$\begin{array}{c}p{K}_a=-\log \left[6.5\times {10}^{-5}\right]\\ =4.19\end{array}$

The pH of the buffer solution formed from benzoic acid is calculated as follows:

$\begin{array}{c}\text{pH}=p{K}_a\pm 1\\ =4.19\pm 1\\ =5.19\left(\text{or}\right)3.19\end{array}$

For hydrocyanic acid,

The acid ionization constant of hydrocyanic acid is $4.9\times {10}^{-10}$.

The value of $p{K}_a$ forhydrocyanic acid is calculated as follows:

$\begin{array}{c}pKa=-\log \left[4.9\times {10}^{-10}\right]\\ =9.30\end{array}$

The pH of the buffer solution formed from hydrocyanic acid is calculated as follows:

$\begin{array}{c}\text{pH}=pKa\pm 1\\ =9.30\pm 1\\ =10.30\left(\text{or}\right)8.30\end{array}$

For phenol,

The acid ionization constant of phenol is $1.3\times {10}^{-10}$.

The value of $p{K}_a$ forphenol is calculated as follows:

$\begin{array}{c}pKa=-\log \left[1.3\times {10}^{-10}\right]\\ =9.89\end{array}$

The pH of the buffer solution formed from phenol is calculated as follows:

$\begin{array}{c}\text{pH}=pKa\pm 1\\ =9.89\pm 1\\ =10.89\left(\text{or}\right)8.89\end{array}$

Therefore, a buffer solution with apH value of $6.5$ is not obtained from the given acids.

Hence, option (e) is correct.

Reason for incorrect option:

Option (a) is incorrect because, according to above explanation, a buffer solution with a pH value between $2.15$ and $4.15$ can be prepared from hydrofluoric acid. So, it is an incorrect option.

Option (b) is incorrect because, according to above explanation, a buffer solution with a pH value between $3.19$ and $5.19$ can be prepared from benzoic acid. So, it is an incorrect option.

Option (c) is incorrect because, according to above explanation, a buffer solution with a pH value between $8.30$ and $10.30$ can be prepared from hydrocyanic acid. So, it is an incorrect option.

Option (d) is incorrect because, according to above explanation, a buffer solution with a pH value between $10.89$ and $8.89$ can be prepared from phenol. So, it is an incorrect option.

Hence, options (a), (b), (c), and (d) are incorrect.