Chapter 17, Problem 1DE

(a)

Interpretation Introduction

To determine: A set of experiments or calculations to test the given hypotheses.

Concept Introduction: The replacement of the hydrogen atom by chlorine in the methyl group of the acetic acid increases the polarity of the $\text{O}-\text{H}$ bond and chlorine group stabilizes the carboxylate ion formed after the donation of the proton and, hence increasing the acidity.

As the $\text{p}{K}_{\text{a}}$ of the acid lowers, the acid becomes stronger and hence its solubility in the low $\text{pH}$ solution increases. The weaker is the acid, the higher is its $\text{p}{K}_{\text{a}}$ and the lower is it solubility in acidic solution.

Answer to Problem 1DE

Solution: Due to the presence of chlorine atom, the acidity of trichloroacetic acid is more than that of chloroacetic acid and acetic acid.

Explanation of Solution

The $\text{p}{K}_{\text{a}}$ of acetic acid is 4.74 and that of chloroacetic acid and trichloroacetic acid is 2.86 and 0.66 respectively.

Now, comparing the O-H bond polarity of all the three acids, since, chlorine is electronegative in nature, if it is attached to the carbonyl carbon, the polarity of O-H bond increases, the O-H bond become weak making the compound more acidic.

Due to the presence of 3 chlorine atoms, trichloroacetic acid is more acidic than the chloroacetic acid which is then more acidic than acetic acid.

The $\text{p}{K}_{\text{a}}$ of an acid is defined as negative log of the acid dissociation constant.

It is mathematically represented as follows:

  $\text{p}{K}_{\text{a}}=-\log K_{\text{a}}$

Here, $K_{\text{a}}$ is acid dissociation constant of an acid.

Taking example of dissociation of acetic acid, the reaction will be as follows:

  ${\text{CH}}_{\text{3}}\text{COOH}\rightleftharpoons {\text{CH}}_{\text{3}}{\text{COO}}^{-}+{\text{H}}^{+}$

The expression for acid dissociation constant can be written as follows:

  $K_a=\frac{\left[{\text{CH}}_{\text{3}}{\text{COO}}^{-}\right]\left[{\text{H}}^{+}\right]}{\left[{\text{CH}}_{\text{3}}\text{COOH}\right]}$

More the value of $\text{p}{K}_{\text{a}}$ , less will be the acidity. Thus, trichloroacetic acid will be more acetic.

The solution of the known concentration of the acetic acid, chloroacetic acid and trichloroacetic acid in different flask and the $\text{pH}$ of the solution is determined by using $\text{pH}$ meter.

The concentration of the proton ion is calculated by the formula:

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

The concentration of the proton is same as that of the conjugate base of the acids. Also the concentrations of the acids are known.

Thus, the equilibrium concentration of the acid is calculated by the formula:

  $K_{\text{a}}=\frac{\text{Concentration}\text{of}\text{conjugate}\text{base}\times \text{Concentration}\text{of}\text{the}\text{proton}}{\text{Concentration}\text{of}\text{the}\text{acid}}$

Hence, using the $K_{\text{a}}$ values, the $\text{p}{K}_{\text{a}}$ of the acids are calculated as:

  $\text{p}{K}_{\text{a}}=-\log K_{\text{a}}$

Conclusion

The $\text{p}{K}_{\text{a}}$ of the acids are calculated as:

  $\text{p}{K}_{\text{a}}=-\log K_{\text{a}}$

(b)

Interpretation Introduction

To determine: An experiment to determine the solubility of acetic acid, chloroacetic acid and trichloroacetic acid.

Answer to Problem 1DE

Solution: As the value of $\text{p}{K}_{\text{a}}$ increases, the acidity of the acids and the solubility of the salt formed from these acids decreases.

Explanation of Solution

The solubility of any salt depends on its concentration, which is related to pH and $\text{p}{K}_{\text{a}}$ of acid as follows:

  $pH=p{k}_a+\log \frac{\left[\text{salt}\right]}{\left[\text{acid}\right]}$

The above equation is Henderson-Hasselbach equation.

From the above equation, if the pH of solution decreases, the acid concentration increases and that of salt decreases.

Since, the acidity of acetic acid is least thus, its solution has maximum pH value and its sodium salt has maximum solubility.

The trichloroacetic acid is strongest acid and has minimum pH thus, its sodium salt has minimum solubility.

Conclusion

As the value of $\text{p}{K}_{\text{a}}$ increases, the acidity of the acids and the solubility of the salt formed from these acids decreases.