Problem 104 - A Complete Resource Book in Chemistry for JEE Main

Question

Which represents the correct decreasing order of dissociation constants \(\mathrm{K}_{1}, \mathrm{~K}_{2}\) and \(\mathrm{K}_{3}\) for \(\mathrm{HNO}_{2}, \mathrm{~N}_{3} \mathrm{H}\) and \(\mathrm{HNO}_{3}\) respectively? (a) \(\mathrm{K}_{2}>\mathrm{K}_{1}>\mathrm{K}_{3}\) (b) \(\mathrm{K}_{1}>\mathrm{K}_{2}>\mathrm{K}_{3}\) (c) \(\mathrm{K}_{3}>\mathrm{K}_{1}>\mathrm{K}_{2}\) (d) \(\mathrm{K}_{3}>\mathrm{K}_{2}>\mathrm{K}_{1}\)

Step-by-Step Solution

Answer

Option (c) \(\mathrm{K}_3 > \mathrm{K}_1 > \mathrm{K}_2\) is correct.

Step 1: Understanding Dissociation Constants

Dissociation constants, often denoted as \(K_a\), measure the tendency of an acid to donate a proton. A higher \(K_a\) value means the acid dissociates more completely in solution, indicating it is a stronger acid.

Step 2: Identifying Acid Strengths

Let's identify the acids and their likely dissociation strengths: \(\mathrm{HNO}_3\) is a strong acid, \(\mathrm{HNO}_2\) is a weaker acid compared to \(\mathrm{HNO}_3\), and \(\mathrm{N}_3\mathrm{H}\) is an even weaker acid. Hence, their dissociation constants will follow the trend of \(K_3 > K_1 > K_2\).

Step 3: Choosing the Correct Option

Based on the analysis of acid strengths, the correct decreasing order of dissociation constants is \(K_3 > K_1 > K_2\). Therefore, the appropriate option that reflects this order is (c) \(\mathrm{K}_3 > \mathrm{K}_1 > \mathrm{K}_2\).

Key Concepts

Understanding Acid Strength

Acid strength refers to the ability of an acid to donate a proton (H⁺) to a base. Strong acids such as nitric acid (\(\mathrm{HNO}_3\)) completely dissociate in water, releasing a large number of hydrogen ions. They have high dissociation constants (\(K_a\)) indicating strong acidity.
Weaker acids like nitrous acid (\(\mathrm{HNO}_2\)) and hydrazoic acid (\(\mathrm{N}_3\mathrm{H}\)) dissociate to a lesser extent, resulting in a smaller \(K_a\) value.
Thus, the acid strength is assessed based on the magnitude of \(K_a\): higher values indicate stronger acids.

• Strong acids: High \(K_a\), extensive dissociation.
• Weak acids: Low \(K_a\), limited dissociation.

Exploring Acid Dissociation

Acid dissociation is the process where an acid releases its proton (H⁺) into a solution. This event is crucial in determining the acid's strength.
In the context of dissociation, the equilibrium established is between the undissociated acid molecules and the ions formed.
The dissociation constant (\(K_a\)) quantifies this equilibrium.
For a general acid HA dissociating into H⁺ and A⁻, the reaction equation is:
\[\mathrm{HA}_{(aq)} \rightarrow \mathrm{H}^+_{(aq)} + \mathrm{A}^-_{(aq)}\]The larger the \(K_a\) value, the more the equilibrium lies towards the right, indicating more proton release.

• High \(K_a\): Equilibrium favors dissociation, strong acid.
• Low \(K_a\): Equilibrium favors the undissociated form, weak acid.

Interpreting Chemical Equilibrium

Chemical equilibrium is a dynamic state where the rates of the forward and reverse reactions are equal. In the case of acid dissociation, this means the rate at which the acid donates protons equals the rate at which protons are accepted back.
This balance is crucial for understanding the dissociation process and the behavior of acids in a solution.
The position of equilibrium, therefore, is essential to determine whether an acid is strong or weak, heavily relying on its dissociation constant (\(K_a\)).
It tells us the extent of dissociation and thus, the acid strength.

• Equilibrium favoring products: Stronger acid.
• Equilibrium favoring reactants: Weaker acid.

Protolyte Chemistry Explained

Protolyte chemistry revolves around the transfer of protons between molecules. This concept is core to understanding acids and bases in solution.
A protolyte is a compound that can donate or accept protons, making it central to acid-base reactions.
In this framework, acids are seen as protolytes that donate protons, while bases are protolytes that accept protons.

• Acids (proton donors): Stronger with higher dissociation constants.
• Bases (proton acceptors): Characterized by their ability to take up protons.

Understanding protolyte chemistry is essential for grasping the concept of acid dissociation and the equilibrium that governs these processes.