Problem 195 - A Complete Resource Book in Chemistry for JEE Main

Question

If molar concentrations of two weak acids are the same, their relative strengths can be compared by (a) \(\frac{\alpha_{1}}{\alpha_{2}}\) (b) \(\frac{\mathrm{K}_{1}}{\mathrm{~K}_{2}}\) (c) \(\sqrt{\mathrm{K}_{1} / \mathrm{K}_{2}}\) (d) \(\frac{\left[\mathrm{H}^{+}\right]_{1}}{\left[\mathrm{H}^{+}\right]_{2}}\)

Step-by-Step Solution

Answer

The correct option is (b) \(\frac{\mathrm{K}_{1}}{\mathrm{~K}_{2}}\).

Step 1: Understanding Weak Acid Dissociation

The strength of a weak acid is determined by its extent of ionization in water. The higher the dissociation constant (K), the stronger the acid. Each weak acid will have a specific dissociation constant, labeled as \(K_1\) and \(K_2\) for the two acids here.

Step 2: Using Dissociation Constant (K)

Comparing the dissociation constants \(K_1\) and \(K_2\) provides a direct way to determine the relative strengths of two acids at the same concentration. The acid with the larger K value dissociates more in solution, indicating a stronger acid.

Step 3: Applying the Formula for Comparison

Given that we need to compare the strengths of two acids, the appropriate method is to directly compare their dissociation constants. The option \(\frac{\mathrm{K}_{1}}{\mathrm{~K}_{2}}\) provides this direct comparison.

Step 4: Selecting the Correct Option

Reviewing the provided options, choice (b) \(\frac{\mathrm{K}_{1}}{\mathrm{~K}_{2}}\) is the correct answer as it directly compares the dissociation constants, reflecting relative acid strength.

Key Concepts

Dissociation Constant

The dissociation constant, commonly denoted as \( K_a \), is a crucial value used to understand how well an acid dissociates into its ions in water. For weak acids, this constant helps indicate how strong the acid is by showing the equilibrium concentration of ions in solution. An acid with a high dissociation constant has a greater tendency to lose protons and dissociate more in solution.
When comparing two weak acids, their dissociation constants (\( K_1 \) and \( K_2 \)) can be directly related to their acid strength. A larger \( K_a \) value signifies a stronger acid because it implies a higher concentration of

• Ionized ions, such as \( H^+ \) and the conjugate base \( A^- \),
• Acid dissociation in solution

Understanding this allows for a straightforward comparison of acid strengths by examining their \( K_a \) values.

Ionization in Water

Acid ionization in water is a process where water molecules interact with acid molecules, leading the acid to release hydrogen ions (\( H^+ \)). For weak acids, this process does not go to completion but reaches an equilibrium where both dissociated and undissociated molecules exist.

• In water, the acid \( HA \) dissociates as \( HA \rightleftharpoons H^+ + A^- \).
• The extent of this ionization is dependent on the dissociation constant \( K_a \).

The more an acid ionizes, the more it contributes \( H^+ \) ions to the solution, influencing the solution's acidity. Since weak acids do not fully dissociate, observing their ionization extent provides significant insight. The equilibrium concentration of ions is critical in gauging the strength of the acid, and hence its behavior in an aqueous solution.

Comparative Acid Strength

To compare the strength of two weak acids, consider their dissociation constants \( K_1 \) and \( K_2 \). The main indicator of comparative strength is given by the ratio \( \frac{K_1}{K_2} \). This ratio directly tells us which of the acids is stronger based on how much each can dissociate in water.
A higher \( K_1 \) value, compared to \( K_2 \), indicates that acid 1 is stronger than acid 2 within the same concentration. This is because a larger \( K_a \) suggests more effective ionization and more contributed \( H^+ \) ions, leading to a more potent acidic character.
Using the \( \frac{K_1}{K_2} \) comparison not only simplifies the evaluation process of acid strengths at equal concentrations but also ensures accurate conclusions.

• Option (b), \( \frac{K_1}{K_2} \), is widely recognized as the standard method for comparing weak acids.
• Helps predict the acid's behavior in reactions and solutions.

This comparative analysis is essential for understanding how different weak acids can influence chemical environments.