Problem 186 - A Complete Resource Book in Chemistry for JEE Main

Question

Hydrolysis constant \(\mathrm{K}_{\mathrm{A}}\) and \(\mathrm{K}_{\mathrm{B}}\) of two salts of weak acids HA and \(\mathrm{HB}\) are \(10^{-8}\) and \(10^{-6}\) respectively. If the dissociation constant of third acid \(\mathrm{HC}\) is \(10^{-2}\). The order of acidic strengths of three acids will be (a) \(\mathrm{HA}>\mathrm{HB}>\mathrm{HC}\) (b) \(\mathrm{HB}>\mathrm{HA}>\mathrm{HC}\) (c) \(\mathrm{HC}>\mathrm{HA}>\mathrm{HB}\) (d) \(\mathrm{HA}=\mathrm{HB}=\mathrm{HC}\)

Step-by-Step Solution

Answer

The order of acidic strengths is (a) \( \mathrm{HA} > \mathrm{HB} > \mathrm{HC} \).

Step 1: Understanding Hydrolysis Constants

The hydrolysis constant \( K_A \) is the inverse of the acid dissociation constant \( K_a \) for a weak acid. Similarly, \( K_B \) is for a base's equivalent, but we use \( K_a \) here for acid strength. Thus, \( K_a = \frac{1}{K_A} \). For \( \mathrm{HA} \), given \( K_A = 10^{-8} \), \( K_{a(\mathrm{HA})} = 10^{8} \). For \( \mathrm{HB} \), \( K_B = 10^{-6} \), \( K_{a(\mathrm{HB})} = 10^{6} \). These calculations show the acid strengths.

Step 2: Compare Given Dissociation Constants

For \( \mathrm{HC} \), the dissociation constant \( K_{a(\mathrm{HC})} \) is directly given as \( 10^{-2} \). Now, we have: \( K_{a(\mathrm{HA})} = 10^{8} \), \( K_{a(\mathrm{HB})} = 10^{6} \), and \( K_{a(\mathrm{HC})} = 10^{-2} \). These values represent their respective acidic strengths if higher \( K_a \) means a stronger acid.

Step 3: Determine the Order of Acidic Strength

Compare all \( K_a \) values: \( K_{a(\mathrm{HA})} = 10^{8} \), \( K_{a(\mathrm{HB})} = 10^{6} \), \( K_{a(\mathrm{HC})} = 10^{-2} \). Acidic strength increases with larger \( K_a \), so \( \mathrm{HC} \) has a significantly lower \( K_a \), making it much weaker than \( \mathrm{HA} \) and \( \mathrm{HB} \). Thus, \( \mathrm{HA} > \mathrm{HB} > \mathrm{HC} \).

Key Concepts

Hydrolysis Constant

The hydrolysis constant, represented as either \( K_A \) for acids or \( K_B \) for bases, measures how a salt derived from a weak acid or base dissociates in water to produce the original acid or base. In simple terms, it's an indicator of the reverse reaction of dissociation.
For weak acids, the hydrolysis constant \( K_A \) is defined as the reciprocal of the dissociation constant \( K_a \). This means \( K_a = \frac{1}{K_A} \). A smaller \( K_A \) indicates a stronger acid, as it means a larger \( K_a \), reflecting more dissociation.
Understanding the hydrolysis constants is key when ranking acidic strengths. Here's why:

• If you have a large \( K_a \) (and therefore a small \( K_A \)), the acid dissociates more in water, meaning it's a stronger acid.
• This concept is crucial when dealing with complex chemistry problems that compare acid strengths using these constants.

Dissociation Constant

The dissociation constant \( K_a \) is fundamental in understanding an acid's strength. It quantitatively describes how well an acid dissociates into its ions in water. The larger the \( K_a \), the more an acid will dissociate and, consequently, the stronger it is.
To grasp this:

• Think of \( K_a \) as the measure of an acid's ionization in a solution. More ions mean the acid is stronger, hence a larger \( K_a \) number.
• Strong acids dissociate almost completely, resulting in a high \( K_a \).
• Weak acids partially dissociate, leading to a lower \( K_a \).

Compare dissociation constants when determining acid strength. For example, if you're given \( K_a \) values like \( 10^8 \), it suggests a strong acid compared to a \( K_a \) of \( 10^{-2} \), indicating a weak acid. This principle helps you sort acids based on their dissociation ability.

Weak Acids

Weak acids are acids that do not fully dissociate in water, meaning they partially break into ions. This characteristic leads to a low \( K_a \), which indicates weaker acidity compared to strong acids.
Let's break it down:

• In a solution, weak acids establish an equilibrium between the undissociated acid and the ions it forms. This equilibrium favors the undissociated form.
• Thus, weak acids have \( K_a \) values that are considerably less than those of strong acids.
• In practical terms, if you have a weak acid with a hydrolysis constant \( K_A \) (large in value), its \( K_a \) will be smaller, indicating less dissociation and therefore a weaker acid.

Understand that weak acids are common and important in chemistry, affecting pH and reactions in different environments. Their behavior can be predicted and contrasted based on their dissociation and hydrolysis constants.