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 \(1 / 2 \mathrm{pkw}\). (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 \(\mathrm{HCl}\), then \(\mathrm{pOH}\) 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

The incorrect statements are (1) and none others.

Step 1: Analyze Statement 1

When acetic acid is exactly neutralized by aqueous NH₃, the resulting solution is a salt solution of either ammonium acetate or acetate ions and ammonium ions in water. Since the Ka of the acid and the Kb of the base are equal, the pH of the solution should be neutral, i.e., equal to 7 at 25°C. Statement 1 claims the pH is equal to 1/2 pKw, which is incorrect because 1/2 pKw equals 7 only at 25°C.

Step 2: Evaluate Statement 2

According to Statement 2, all mixtures result in a solution with pH = 7 at 25°C. Since the neutralization results in a neutral salt solution and both the acid and base have equal strength (Ka = Kb), this statement is correct at 25°C, as the pH of the resulting solution should indeed be 7.

Step 3: Examine Statement 3

If acetic acid is exactly half neutralized by NaOH, the resulting solution will be a buffer, composed of acetic acid and acetate ions. The pH of such a buffer solution is given by pH = pKa + log([A⁻]/[HA]). When half-neutralized, [A⁻] = [HA] and thus pH = pKa. Statement 3 is correct as per buffer solution characteristics.

Step 4: Assess Statement 4

If aqueous NH₃ is exactly half neutralized by HCl, the resulting solution is a buffer composed of NH₄⁺ and NH₃. The pOH of this buffer is given by pOH = pKb + log([B⁻]/[BH⁺]). When half-neutralized, [B⁻] = [BH⁺], and thus pOH = pKb. Thus, Statement 4 is correct.

Step 5: Determine Incorrect Statements

Based on our evaluation above, Statement 1 is incorrect because the pH cannot be equal to 1/2 pKw unless at special conditions, usually associated with both Ka and Kb being significantly different. In neutralization of equal strengths, the neutral solution is expected. Statement 2, 3, and 4 are consistent with known chemical principles at standard conditions.

Key Concepts

Buffer Solutions

A buffer solution is an important concept in acid-base chemistry. It is a solution that resists changes in pH when small amounts of an acid or a base are added. Buffer solutions are typically composed of a weak acid and its conjugate base (or a weak base and its conjugate acid). This means that the solution can neutralize small additions of H⁺ or OH⁻ ions by converting them into more of the weak acid or base, maintaining a relatively stable pH.

• A classic buffer system is composed of acetic acid (\(\text{CH}_3\text{COOH}\)) and its conjugate base, acetate ions (\(\text{CH}_3\text{COO}^-\)).
• When you add OH⁻, it reacts with acetic acid to form water and acetate ions, minimizing any pH change.
• Likewise, adding H⁺ ions will react with acetate ions to form more acetic acid, again keeping the pH quite consistent.

Buffer solutions are especially useful in many biological and industrial processes where maintaining a stable pH is necessary.

Neutralization Reactions

Neutralization reactions are a fundamental part of acid-base chemistry. They involve an acid and a base reacting to form water and a salt.
A neutralization reaction can be shown as follows: \[\text{Acid} + \text{Base} \rightarrow \text{Salt} + \text{Water}\] In these reactions, the hydrogen ions (\(\text{H}^{+}\)) from the acid combine with the hydroxide ions (\(\text{OH}^{-}\)) from the base to form water. This reaction reduces the acidity or alkalinity of the solution.

• An example is acetic acid reacting with ammonium hydroxide, where the strength of the acid and base are comparable, leading to a solution that can be neutral.
• Neutralization can vary depending on the strength of the acids and bases involved; when both have similar strength (Ka = Kb), the resulting solution can be neutral with a pH of 7.

It's important to note that neutralization does not always result in a neutral pH (7); the final pH depends on the strength and concentration of the acids and bases involved.

pH and pOH Calculations

Understanding pH and pOH is crucial for predicting the acidity or basicity of a solution. The pH measures the concentration of hydrogen ions (\(\text{H}^{+}\)), while pOH measures the concentration of hydroxide ions (\(\text{OH}^{-}\)).

The formulas to calculate pH and pOH are as follows:

• pH = -\(\log[\text{H}^+]\)
• pOH = -\(\log[\text{OH}^-]\)

There is an important relation given by the expression: \[\text{pH} + \text{pOH} = \text{pK}_W = 14\] When acetic acid and ammonium hydroxide are used together as buffers, or in neutralization processes, their interactions directly relate to these calculations.

• In buffer solutions like acetic acid and its conjugate base, when the concentrations of the acid and its conjugate base are equal, pH = pKa.
• Similarly, in a buffer of NH₃ and NH₄⁺, when their concentrations are equal, pOH = pKb.

These calculations help chemists understand and predict the behaviors of solutions under various conditions.