Problem 79 - 43 Years JEE ADVANCED (1978-2020) + JEE MAIN Chapterwise & Topicwise Solved Papers Chemistry

Question

. \(500 \mathrm{~mL}\) of \(0.2 \mathrm{M}\) aqueous solution of acetic acid is mixed with 500 \(\mathrm{mL}\) of \(0.2 \mathrm{M} \mathrm{HCl}\) at \(25^{\circ} \mathrm{C} .\) (i) Calculate the degree of dissociation of acetic acid in the resulting solution and \(\mathrm{pH}\) of the solution. (ii) If \(6 \mathrm{~g}\) of \(\mathrm{NaOH}\) is added to the above solution, determine the final \(\mathrm{pH}\). [Assume there is no change in volume on mixing; \(K_{a}\) of acetic acid is \(\left.1.75 \times 10^{-5} \mathrm{~mol} \mathrm{~L}^{-1}\right]\).

Step-by-Step Solution

Answer

Initial concentrations are: [Acetic Acid] = 0.1 M, [HCl] = 0.1 M

Step 1: Calculate initial concentrations

When mixing two solutions, the total volume is the sum of their individual volumes, so we have a total volume of 1000 mL or 1 L. The concentration of acetic acid and HCl after mixing is For acetic acid:\[ [ ext{CH}_3 ext{COOH}] = \frac{(0.2 \, ext{mol/L}) imes (0.5 \, ext{L})}{1 \, ext{L}} = 0.1 \, ext{M} \]For HCl:\[ [ ext{HCl}] = \frac{(0.2 \, ext{mol/L}) imes (0.5 \, ext{L})}{1 \, ext{L}} = 0.1 \, ext{M} \]

Key Concepts

Degree of Dissociation

The degree of dissociation (\( \alpha \)) measures how much a weak acid like acetic acid (\( \text{CH}_3\text{COOH} \)) dissociates into ions in solution. It is calculated when acetic acid is mixed with another strong acid, such as hydrochloric acid (\( \text{HCl} \)). When acetic acid partially dissociates, it forms hydrogen ions (\( \text{H}^+ \)) and acetate ions (\( \text{CH}_3\text{COO}^- \)). The degree of dissociation is expressed as:\[ \alpha = \frac{[ ext{CH}_3 ext{COO}^-]}{[ ext{CH}_3 ext{COOH}] + [ ext{CH}_3 ext{COO}^-]} \]In the presence of \( \text{HCl} \), which fully dissociates, there are more hydrogen ions available. This reduces the equilibrium concentration of acetic acid ionization products. ### Impact of Mixed Solutions - When mixed with a strong acid, the common ion effect reduces the degree of dissociation of a weak acid like acetic acid.- \( \text{HCl} \) provides additional \( \text{H}^+ \) ions, pushing the equilibrium back towards undissociated acetic acid, thus lowering \( \alpha \).Knowing the concentration of acetic acid and \( \text{HCl} \) in the solution helps in calculating precise dissociation using the formula above.

Acetic Acid

Acetic acid is a weak acid with the chemical formula \( \text{CH}_3\text{COOH} \). It is the active component of vinegar but in chemistry, it's commonly studied for its behavior in aqueous solutions. When dissolved in water, acetic acid partially ionizes into acetate ions and hydrogen ions:\[ \text{CH}_3\text{COOH} \rightleftharpoons \text{CH}_3\text{COO}^- + \text{H}^+ \]### Properties and Ionization- Acetic acid has a Ka (acid dissociation constant) of \( 1.75 \times 10^{-5} \), indicating it is a weak acid.- Only a small fraction of acetic acid molecules dissociate in water.- The ionization of acetic acid in water reaches an equilibrium, meaning the forward and reverse reactions occur at the same rate.### Reactions in Mixed SolutionsWhen mixed with a strong acid like HCl:- The additional \( \text{H}^+ \) ions from HCl suppress acetic acid's dissociation through the common ion effect.- The result is fewer acetate ions in the solution.- This behavior is essential in calculating the mixture's pH and understanding the acid-base equilibrium.

pH Calculation

Calculating the pH of a mixed acid solution involves understanding both the contributions from a weak acid and a strong acid. In the problem given, we evaluate a mixture of acetic acid and hydrochloric acid.### Strong and Weak Acid Contributions- \( \text{HCl} \) is a strong acid and dissociates completely, contributing a significant number of hydrogen ions. - Acetic acid, being a weak acid, partially dissociates and initially adds fewer hydrogen ions than HCl.To find the \( \text{pH} \) of the resulting solution:1. **Determine Initial \( \text{H}^+ \) Concentration:** - From strong acid \( \text{HCl} \), it's the same as the concentration.2. **Adjust for Weak Acid:** - Account for the reduced dissociation of acetic acid due to the additional \( \text{H}^+ \) from \( \text{HCl} \).\[ \text{pH} = -\log([\text{H}^+]) \]With such a calculation, the refined \( \text{pH} \) reflects both acids' effects. This holistic approach helps students understand how to evaluate mixed solutions' \( \text{pH} \) accurately, considering both equilibrium effects and reaction dynamics.