Problem 143 - A Complete Resource Book in Chemistry for JEE Main

Question

Acetic acid and aq. \(\mathrm{NH}_{3}\) are weak monobasic acid and weak monobasic base respectively and \(\mathrm{Ka}\) of acetic acid is equal to \(\mathrm{K}_{\mathrm{b}}\) of aq. \(\mathrm{NH}_{3}\). Which of the following statements are incorrect? (1) If acetic acid is exactly neutralized by aq. \(\mathrm{NH}_{3}\) then \(\mathrm{pH}\) of resulting solution is equal to \(1 / 2\) pkw. (2) All the above mixing would result solution having \(\mathrm{pH}=7\) at \(25^{\circ} \mathrm{C}\) (3) If acetic acid is exactly half neutralized by \(\mathrm{NaOH}\), then \(\mathrm{pH}\) of resulting solution is equal to \(\mathrm{pKa}\). (4) If aq. \(\mathrm{NH}_{3}\) is exactly half neutralized by HCl, then pOH of resulting solution is equal to \(\mathrm{pK}_{\mathrm{b}}\). (a) 2 and 4 (b) 2 and 3 (c) 1 and 3 (d) 2 only

Step-by-Step Solution

Answer

Statement (1) is incorrect since resulting pH should be 7.

Step 1: Analyze neutralization condition for acetic acid and NH3

When acetic acid is exactly neutralized by aqueous NH3, we consider the reaction:\[ \text{CH}_3\text{COOH} + \text{NH}_3 \rightleftharpoons \text{CH}_3\text{COO}^- + \text{NH}_4^+ \]Since both acid and base have the same dissociation constants (\(\mathrm{K}_a = \mathrm{K}_b\)), at the equivalence point, the concentrations of the acetate ion and ammonium ion are equal. It results in a neutral solution with pH equal to 7 at \(25^{\circ}\mathrm{C}\). Statement (1) is therefore incorrect.

Step 2: Evaluate statement about resulting pH from mixing

The pH of the solution resulting from the exact neutralization of acetic acid by NH3 in water should be neutral due to equal dissociation constants, hence the expected pH is close to 7. Statement (2) is correct, not incorrect.

Step 3: Analyze the half-neutralization of acetic acid

When acetic acid is half neutralized by NaOH, it forms a buffer solution. In this case, the concentration of the acid equals that of its conjugate base, causing the pH to be approximately equal to the pKa of acetic acid. Statement (3) is correct, not incorrect.

Step 4: Consider ammonium hydroxide half-neutralization case

If aqueous NH3 is half-neutralized by HCl, the resulting pOH should match the pKb of NH3, since it forms a buffer solution with [NH3] = [NH4+]. Statement (4) is correct, not incorrect.

Key Concepts

Neutralization Reaction

A neutralization reaction occurs when an acid reacts with a base to form salt and water. It is a chemical reaction where the acidity and alkalinity of the reactants cancel each other out.
When acetic acid (\( \text{CH}_3\text{COOH}\) ) and aqueous ammonia (\( \text{NH}_3\) ) are mixed, they neutralize each other producing acetate and ammonium ions. This reaction can be represented using the equation: \[ \text{CH}_3\text{COOH} + \text{NH}_3 \rightleftharpoons \text{CH}_3\text{COO}^- + \text{NH}_4^+ \]

• Acetic acid is a weak monobasic acid, which means it donates one proton (H⁺) per molecule.
• Aqueous ammonia is a weak monobasic base, meaning it can accept one proton per molecule.

In this scenario, both the acetic acid and ammonia have the same dissociation constants, leading to a unique scenario where at the equivalence point the solution becomes neutral if the reaction takes place at 25°C. This equivalence also leads to a balanced reaction where the concentrations of the products are equal, producing a solution with a pH that approaches neutrality (7).

Buffer Solutions

Buffer solutions are special kinds of solutions that resist drastic changes in pH when small amounts of acid or base are added. They are made by mixing a weak acid with its conjugate base or a weak base with its conjugate acid.
When acetic acid is exactly half-neutralized by NaOH, a buffer solution is formed, comprising equal concentrations of acetic acid and its conjugate base, acetate ion. Similarly, when ammonium ions and ammonia exist in nearly equal concentrations, it also creates a buffer system.

• They help maintain a stable pH in the solution.
• Vital in maintaining biological systems' stability where pH needs to stay within tight parameters.

In the context of the exercise, the formation of a buffer is seen when half-neutralization occurs, allowing the solution to maintain a nearly constant pH. The pH or pOH in a buffer equation can be calculated using the Henderson-Hasselbalch equation.

pH Calculation

pH is a measure of the hydrogen ion concentration in a solution, determining how acidic or basic that solution is. The formula is \[ \text{pH} = -\log[\text{H}^+] \].
When acetic acid is exactly half neutralized by NaOH, the pH of the solution equals the {\( \text{p}\text{K}_a \)} of the acid. This occurs because the concentrations of the acid and its conjugate base are the same, simplifying the pH calculation:
\[ \text{pH} = \text{p}K_a + \log \left( \frac{[\text{A}^-]}{[\text{HA}]} \right) = \text{p}K_a\]
For aqueous \( \text{NH}_3\) , if half-neutralized by HCl, the pOH equals \( \text{p}K_b \), because at this point the concentrations of \( \text{NH}_3\) and \( \text{NH}_4^+ \) are equal.

• The pH can shift slightly if temperature changes, as occurring at 25°C may result in different readings compared to other temperatures.

These calculations are instrumental in chemistry, allowing us to determine concentrations and the effects of acids and bases in practical scenarios.

Dissociation Constants

Dissociation constants, \( K_a \) for acids or \( K_b \) for bases, measure the strength of an acid or a base in solution. They represent the equilibrium state where the acid or base dissociates into ions.
In our exercise, because \( K_a \) of acetic acid equals \( K_b \) of ammonium hydroxide, we find that at the point of neutralization, the pH remains neutral.

• \( K_a \) and \( K_b \) help predict how an acid or base will behave in solution and the degree to which they dissociate when dissolved in water.
• A higher \( K_a \) value means a stronger acid, whereas a higher \( K_b \) indicates a stronger base.

These constants are crucial to understanding reactions in aqueous solutions, affecting everything from industrial chemical processes to biological homeostasis in living organisms. Understanding \( K_a \) and \( K_b \) helps chemists predict reactions and the outcome of mixing various substances.