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): \( \mathrm{K}_{3} > \mathrm{K}_{1} > \mathrm{K}_{2} \).

Step 1: Identify the substances involved

We need to consider three substances: 1. \( \mathrm{HNO}_{2} \), known as nitrous acid.2. \( \mathrm{N}_{3} \mathrm{H} \), commonly known as hydrazoic acid.3. \( \mathrm{HNO}_{3} \), known as nitric acid.

Step 2: Understand dissociation constants

\( \mathrm{K}_1 \), \( \mathrm{K}_2 \), and \( \mathrm{K}_3 \) are the dissociation constants for \( \mathrm{HNO}_{2} \), \( \mathrm{N}_{3} \mathrm{H} \), and \( \mathrm{HNO}_{3} \) respectively. The strength of an acid is directly proportional to its dissociation constant. Thus, a larger dissociation constant means the acid dissociates more in solution, indicating a stronger acid.

Step 3: Arrange acids by strength

Nitric acid (\( \mathrm{HNO}_3 \)) is a strong acid and dissociates almost completely in solution, so it will have the highest dissociation constant among the three. Nitrous acid (\( \mathrm{HNO}_2 \)) is a weaker acid than nitric acid but stronger than hydrazoic acid, so it will have the second highest dissociation constant. Hydrazoic acid (\( \mathrm{N}_3 \mathrm{H} \)) is the weakest and will have the smallest dissociation constant.

Step 4: Rank the dissociation constants

Based on the strength of the acids: - \( \mathrm{HNO}_3 \) \( (\mathrm{K}_3) \) > \( \mathrm{HNO}_2 \) \( (\mathrm{K}_1) \) > \( \mathrm{N}_3 \mathrm{H} \) \( (\mathrm{K}_2) \). This order represents the decreasing order of the dissociation constants.

Step 5: Select the correct option

The correct decreasing order of dissociation constants is \( \mathrm{K}_{3} > \mathrm{K}_{1} > \mathrm{K}_{2} \). Thus, the correct answer is option (c).

Key Concepts

Acid Strength

Acid strength is a critical concept in chemistry, referring to an acid's ability to donate protons to a base. This ability is quantitatively measured using the dissociation constant, often represented by the symbol \( K_a \). The larger the dissociation constant, the stronger the acid is, because it dissociates more completely in solution.

When an acid is strong, it means it can lose its hydrogen ions easily, whereas a weak acid holds onto its hydrogen ions more tightly. This distinction is important when comparing the reactivity and characteristics of different acids.

Key points to remember about acid strength include:

• Acids with a larger \( K_a \) are stronger, as they dissociate more in water.
• Strong acids dissociate completely, while weak acids only partially dissociate.
• The strength of an acid influences its chemical behavior and reactions with other substances.

Nitric Acid

Nitric acid, or \( \mathrm{HNO}_3 \), is a powerful and corrosive strong acid. Among the three acids in our exercise, it has the highest dissociation constant (\( K_3 \)). This means it dissociates almost completely in solution, releasing its hydrogen ions effectively.

This characteristic makes nitric acid valuable in various industrial applications such as manufacturing fertilizers, explosives, and in metal processing.

Additionally, because of its strength, nitric acid is also used in chemical labs for experiments and synthesis, as it reacts readily with metals and inorganic materials. However, due to its potency, careful handling is essential to prevent harm.

Nitrous Acid

Nitrous acid, denoted as \( \mathrm{HNO}_2 \), is a weaker acid compared to nitric acid and has a lower dissociation constant (\( K_1 \)). Although it does dissociate in water, it does so less completely than nitric acid.

This weaker dissociation means that nitrous acid is less reactive, making it suitable for different applications than those of stronger acids. For example, it's often used in the generation of diazonium salts, important in dye manufacturing.

Understanding its position relative to other acids helps us comprehend how it behaves in different chemical environments and informs decisions in both laboratory and industrial settings.

Hydrazoic Acid

Hydrazoic acid, also known as \( \mathrm{N}_3 \mathrm{H} \), is the weakest among the three acids discussed, with the smallest dissociation constant (\( K_2 \)). As a result, it dissociates the least in solution.

Despite its relatively low strength, hydrazoic acid is notable for its reactivity due to its chemical instability. It is used as a precursor to certain explosives and as a reagent in organic chemistry.

While it plays a specific role in chemical synthesis, caution must be exercised when handling hydrazoic acid, given its potential volatility and the toxicity of its vapors. Comparing its acid strength with other acids aids in understanding its behavior and safe usage.