Problem 53 - A Complete Resource Book in Chemistry for JEE Main

Question

Which one of the following is true for any diprotic acid, \(\mathrm{H}_{2} \mathrm{X} ?\) (a) \(\mathrm{Ka}_{2}=\mathrm{Ka}_{1}\) (b) \(\mathrm{Ka}_{2}>\mathrm{Ka}_{1}\) (c) \(\mathrm{Ka}_{1}>\mathrm{Ka}_{2}\) (d) \(\mathrm{Ka}_{2}=1 / \mathrm{Ka}_{1}\)

Step-by-Step Solution

Answer

Option (c) \( \mathrm{Ka}_1 > \mathrm{Ka}_2 \) is true for any diprotic acid.

Step 1: Understanding Diprotic Acids

A diprotic acid can donate two protons, which means it has two dissociation constants: \( \mathrm{Ka}_1 \) for the first proton dissociation and \( \mathrm{Ka}_2 \) for the second proton dissociation.

Step 2: Comparing Dissociation Constants

In general, for any diprotic acid, the first dissociation constant \( \mathrm{Ka}_1 \) is always larger than the second dissociation constant \( \mathrm{Ka}_2 \). This is because it is easier to remove the first proton than the second one.

Step 3: Evaluate the Options

Given the understanding that \( \mathrm{Ka}_1 > \mathrm{Ka}_2 \) for any diprotic acid, the correct choice must reflect this relationship. Among all the provided options, (c) \( \mathrm{Ka}_1 > \mathrm{Ka}_2 \) is the correct expression.

Key Concepts

Dissociation Constants

When exploring the behavior of diprotic acids, an important concept to grasp is dissociation constants. These constants, represented as Ka values, indicate how easily an acid ionizes in solution. Essentially, they measure the strength of an acid by showing its tendency to donate hydrogen ions (protons).

Each proton donation has its unique dissociation constant, with diprotic acids having two such constants: one for each step of proton dissociation. Understanding these constants is crucial because they help predict how an acid behaves in different chemical environments. For students, recognizing this concept means gaining insights into chemical reactivity and behavior.

Ka1 and Ka2

In the realm of chemical reactions, particularly those involving diprotic acids, the terms \( K_a1 \) and \( K_a2 \) have significant roles. They represent the dissociation constants for the first and second proton donations, respectively.

• \( K_a1 \): Represents the ionization strength when the first proton is lost.
• \( K_a2 \): Represents the ionization strength for the second proton loss.

Generally, \( K_a1 \) is greater than \( K_a2 \). Why? Because it typically requires less energy to lose the first proton than the second one.

This hierarchy of proton release in acids reflects molecular stability and the environment's impact, influencing pH levels and the rate of reaction. Recognizing the order of \( K_a \) values is key to predicting reaction outcomes, and in this exercise, understanding this helped us choose the right answer.

Proton Donation

A fascinating aspect of acid behavior is proton donation, especially for diprotic acids like \( H_2X \). These acids don't give away both protons at once. Instead, they do so in steps, each step having its unique characteristics and challenges.

The process can be summarized as follows:

• First Proton Donation: Characterized by \( K_a1 \), this is generally the more straightforward step.
• Second Proton Donation: Occurs under \( K_a2 \), often requiring more intricate conditions and greater energy.

Understanding proton donation gives insight into why some acids behave more aggressively than others. More importantly, it shows the natural progression of chemical reactions in dynamic environments. Seeing how protons are donated sequentially allows chemists to manipulate conditions to steer reactions efficiently. This process is a cornerstone of acid-base chemistry, illustrating the delicate balance at play in chemical dynamics.