Problem 197 - A Complete Resource Book in Chemistry for JEE Main

Question

Which of the following statements are correct? (a) The conjugate base of \(\mathrm{H}_{2} \mathrm{PO}_{4}^{-}\)is \(\mathrm{HPO}_{4}^{2-}\) (b) \(\mathrm{pH}\) of \(1.0 \times 10^{-8} \mathrm{M}\) aqueous solution of \(\mathrm{HCl}\) is 8 . (c) When a weak monoprotic acid solution is treated with a strong base, at half neutralization point, $$ \mathrm{pH}=\frac{1}{2} \mathrm{pK}_{\mathrm{a}} $$ (d) The autoprotolysis constant of water increases with temperature.

Step-by-Step Solution

Answer

Statements (a) and (d) are correct.

Step 1: Understand Conjugate Base Definition

A conjugate base is formed when an acid donates a proton. For the acid \(\mathrm{H}_2\mathrm{PO}_4^{-}\), when it donates a proton, we have: \(\mathrm{H}_2\mathrm{PO}_4^{-} \rightarrow \mathrm{HPO}_4^{2-} + \mathrm{H}^+\). Therefore, statement (a) is correct.

Step 2: Analyzing the pH of Dilute HCl Solution

The solution of \(1.0 \times 10^{-8} \text{ M } \mathrm{HCl}\) is very dilute, close to that of pure water. Water itself has a \(\text{pH}\) of 7. A very slightly acidic solution of \(\mathrm{HCl}\) cannot have a \(\text{pH}\) greater than 7. Thus, statement (b) is incorrect.

Step 3: Understanding the Half Neutralization Point

At the half-neutralization point of a monoprotic weak acid, the concentrations of the acid \([\mathrm{HA}]\) and its conjugate base \([\mathrm{A}^-]\) are equal. Thus, \(\text{pH} = \text{pK}_\text{a}\), not \(\frac{1}{2} \text{pK}_\text{a}\). Hence, statement (c) is incorrect.

Step 4: Examine the Autoprotolysis Constant of Water

The autoprotolysis constant \(\text{K}_\text{w}\) of water indeed increases with temperature, meaning that water's \(\text{pH}\) changes with temperature due to more dissociation. Therefore, statement (d) is correct.

Key Concepts

Conjugate Base

In the world of acid-base chemistry, understanding what a conjugate base is can deepen your comprehension of how chemical reactions work. A conjugate base is what remains after an acid donates a proton (a hydrogen ion). Every acid has a conjugate base, and they form a pair. For example, let's think about the compound \( \text{H}_2\text{PO}_4^- \). When it loses a proton, we are left with \( \text{HPO}_4^{2-} \), thus forming its conjugate base. The reaction looks like this: - \( \text{H}_2\text{PO}_4^- \rightarrow \text{HPO}_4^{2-} + \text{H}^+ \).This reaction helps to illustrate how an acid can effectively transform into its conjugate base by giving up a proton, a fundamental aspect of acid-base reactions.

pH Calculation

Calculating the pH of a solution accurately is crucial in chemistry. The pH is a measure of the acidity or basicity of a solution, which is calculated using the concentration of hydrogen ions in that solution. The pH scale is logarithmic and ranges from 0 to 14. A pH less than 7 indicates an acidic solution, whereas a pH greater than 7 indicates a basic solution.In the case of very dilute solutions, such as a \( 1.0 \times 10^{-8} \text{ M} \) \( \text{HCl} \) solution, the water's own ionic product can come into play, given that pure water has a pH of 7. Here, it’s important to remember that such dilute solutions will not significantly change the pH to exceed 7, as they're closer to pure water than a truly acidic solution. Therefore, a solution like this cannot realistically have a pH above 7.

Autoprotolysis Constant

The autoprotolysis constant, \( \text{K}_\text{w} \), is a specific term in chemistry that refers to the equilibrium constant for the self-ionization of water. In simpler terms, it describes the process by which water molecules react with each other to form hydronium ions \( (\text{H}_3\text{O}^+) \) and hydroxide ions \( (\text{OH}^-) \). This reaction can be represented as:- \( 2 \text{H}_2\text{O} \leftrightarrow \text{H}_3\text{O}^+ + \text{OH}^- \).This constant changes with temperature. As the temperature increases, \( \text{K}_\text{w} \) also increases, meaning that more water molecules dissociate at higher temperatures. This is why at higher temperatures, you'll find slight changes in the pH of water. It’s crucial to consider this when working with temperature-sensitive chemical reactions.

Weak Acid-Strong Base Titration

The titration of a weak acid with a strong base is a fascinating process often used in laboratories to determine the concentration of an acid or base in a solution. When a weak monoprotic acid is titrated with a strong base, an interesting point is reached called the half-neutralization point.At this halfway mark, exactly half of the acid present has reacted with the base to form its conjugate base. In this state, the concentration of the acid \( [\text{HA}] \) equals the concentration of its conjugate base \( [\text{A}^-] \). This is particularly significant because, at the half-neutralization point, the \( \text{pH} \) of the solution equals the \( \text{pK}_\text{a} \) of the acid, not half of it. This equivalence forms the backbone of the Henderson-Hasselbalch equation used for calculating pH during titration in buffer solutions:- \( \text{pH} = \text{pK}_\text{a} + \log\left(\frac{[\text{A}^-]}{[\text{HA}]\right)} \).Understanding this concept is key to performing accurate acid-base titrations.