Problem 183 - A Complete Resource Book in Chemistry for JEE Main

Question

\(0.1 \mathrm{M}\) solution of three different sodium salts \(\mathrm{NaX}, \mathrm{NaY}\) and \(\mathrm{NaZ}\) have \(\mathrm{pH}\) values \(7.0,9.0\) and \(11.0\) respectively. The correct order of dissociation constant values of these acids is (a) \(\mathrm{K}_{\mathrm{HX}}<\mathrm{K}_{\mathrm{HY}}<\mathrm{K}_{\mathrm{Hz}}\) (b) \(\mathrm{K}_{\mathrm{HX}}>\mathrm{K}_{\mathrm{HY}}>\mathrm{K}_{\mathrm{Hz}}\) (c) \(\mathrm{K}_{\mathrm{HX}}>\mathrm{K}_{\mathrm{Hz}}>\mathrm{K}_{\mathrm{HY}}\) (d) \(\mathrm{K}_{\mathrm{HX}}<\mathrm{K}_{\mathrm{HY}}<\mathrm{K}_{\mathrm{HZ}}\)

Step-by-Step Solution

Answer

(b) \(\text{K}_{\text{HX}}>\text{K}_{\text{HY}}>\text{K}_{\text{HZ}}\).

Step 1: Understand the Problem

We are given the pH values of solutions of three sodium salts formed with different acids, and we need to determine the relative order of the dissociation constants (\(K_a\)) of these acids. The salts are \(\text{NaX}\), \(\text{NaY}\), and \(\text{NaZ}\) with \(\text{pH}\) values of 7.0, 9.0, and 11.0, respectively. We know that higher \(\text{pH}\) implies the salt forms from a weaker acid because the acid is less dissociated.

Step 2: Interpret the Connection Between pH and Ka

The pH of the salt solution is related to the strength of the parent acid. Specifically, the \pH\ increases as the acid becomes weaker because the solution becomes more basic. Thus, a solution with a higher pH implies the corresponding acid is weaker and has a smaller dissociation constant \(K_a\).

Step 3: Order the pH Values

The given pH values are: \(\text{NaX: pH 7.0}\), \(\text{NaY: pH 9.0}\), \(\text{NaZ: pH 11.0}\). We can see that \(\text{pH of NaZ} > \text{pH of NaY} > \text{pH of NaX}\), indicating that \(\text{HX}\) is the strongest acid because it leaves the least basic (neutral \(\text{pH 7.0}\)) solution, while \(\text{HZ}\) is the weakest acid.

Step 4: Determine the Order of Ka Values

Since \(\text{HX}\) is the strongest acid, it will have the largest \(K_a\), and \(\text{HZ}\) being the weakest acid will have the smallest \(K_a\). Thus, the order of dissociation constant values will be \(\text{K}_\text{HX} > \text{K}_\text{HY} > \text{K}_\text{HZ}\).

Step 5: Select the Correct Answer

Comparing with the given options: (a) \(\text{K}_{\text{HX}}<\text{K}_{\text{HY}}<\text{K}_{\text{HZ}}\) (b) \(\text{K}_{\text{HX}}>\text{K}_{\text{HY}}>\text{K}_{\text{HZ}}\) (c) \(\text{K}_{\text{HX}}>\text{K}_{\text{HZ}}>\text{K}_{\text{HY}}\) (d) \(\text{K}_{\text{HX}}<\text{K}_{\text{HY}}<\text{K}_{\text{HZ}}\) The correct answer is (b) \(\text{K}_{\text{HX}}>\text{K}_{\text{HY}}>\text{K}_{\text{HZ}}\).

Key Concepts

pH and acidity

The pH of a solution is a crucial measure which tells us how acidic or basic that solution is. It's a numeric scale ranging from 0 to 14, where lower numbers indicate higher acidity (more hydrogen ions, H+) and higher numbers indicate higher basicity (more hydroxide ions, OH-). For instance, pure water is neutral with a pH of 7.
When we talk about the pH of a solution involving sodium salts, such as NaX, NaY, and NaZ, the pH reflects the strength of the parent acids, HX, HY, and HZ, respectively. If a salt solution has a lower pH, it suggests that its parent acid is stronger — it dissociates more completely in water, releasing more hydrogen ions.
- **Lower pH (<7):** More acidic, indicating a stronger acid. - **Neutral pH (7):** Neither acidic nor basic. - **Higher pH (>7):** More basic, suggesting a weaker acid because fewer hydrogen ions are released.

sodium salt solutions

Sodium salts, like those in our example, are often used to infer properties of the acids from which they derive. These salts are formed when an acid reacts with a sodium base, typically sodium hydroxide (NaOH). The reaction looks like this:
\[ \text{HA} + \text{NaOH} \rightarrow \text{NaA} + \text{H}_2\text{O} \] Here, HA represents the acid and NaA the resulting sodium salt.
These salts strongly influence the pH of their solutions. We use the relationship between the pH of the salt solution to understand the acidity/basicity of the parent acid:

• A sodium salt like NaZ resulting in a highly basic solution (pH 11) suggests a weak parent acid HZ.
• Conversely, a relatively neutral salt solution like NaX (pH 7) indicates a stronger parent acid HX.

This means that, if we know the pH of these sodium salt solutions, we can infer important details about their parent acids.

chemical equilibrium concepts

Chemical equilibrium refers to the condition in which reactants and products of a chemical reaction are present in concentrations which have no further tendency to change with time. Typically, this occurs in a closed system.
In the context of our sodium salt solutions, we examine the equilibrium between the dissociation of the acid and the formation of its corresponding ions in solution:
\[ \text{HA} \rightleftharpoons \text{H}^+ + \text{A}^- \]
The acid dissociation constant, \( K_a \), quantifies the strength of an acid in this equilibrium. A higher \( K_a \) value indicates a stronger acid that dissociates more completely:

• **Strong acids:** Large \( K_a \), leading to more H+ and A- ions at equilibrium.
• **Weak acids:** Small \( K_a \), less ion dissociation and fewer H+ ions.

In our exercise, acids HX, HY, and HZ have different pH levels when forming sodium salts. Understanding these equilibria and how they relate to the pH allows us to determine which acid has the highest \( K_a \). This helps in correctly estimating the strength of each acid based on the concentration of resulting ions in solution.