Question

The dissociation constant values of three acids \(\mathrm{A}, \mathrm{B}\) and \(\mathrm{C}\) are \(1.8 \times 10^{-5}, 1.5 \times 10^{-4}\) and \(5.2 \times 10^{-8}\) respectively. Correct order of increasing basic character of their conjugate bases is (1) \(\mathrm{A}>\mathrm{B}>\mathrm{C}\) (2) \(B>A>C\) (3) \(B

Short answer

The correct order is option (3) \(B<A<C\).

Step-by-step solution

- Understand Dissociation Constant (Ka)

The dissociation constant, denoted as Ka, is a measure of the strength of an acid in solution. It quantifies the extent to which an acid dissociates in water to form hydrogen ions (H+) and its conjugate base.

- Relate Ka to Acid Strength

A higher Ka value indicates a stronger acid because it means the acid dissociates more in solution. Conversely, a lower Ka value indicates a weaker acid.

- Determine Basic Strength of Conjugate Bases

The strength of a conjugate base is inversely related to the strength of its acid. Therefore, the weaker the acid, the stronger its conjugate base.

- Order the Acids by Ka Values

The given dissociation constant values (Ka) for acids A, B, and C are: Ka(A) = \(1.8 \times 10^{-5}\), Ka(B) = \(1.5 \times 10^{-4}\), and Ka(C) = \(5.2 \times 10^{-8}\). Order them based on their Ka values: B > A > C (since \(1.5 \times 10^{-4}\) > \(1.8 \times 10^{-5}\) > \(5.2 \times 10^{-8}\)).

- Ascertain the Basic Character

Because the basic character of the conjugate base is inversely proportional to the acid strength, order the conjugate bases by the inverse of their acids' strength: C > A > B.

- Determine the Correct Answer Option

Thus, the correct order of increasing basic character of their conjugate bases is \(B<A<C\). Therefore, the correct option is (3) \(B<A<C\).

Key concepts

Dissociation Constant (Ka)

The dissociation constant, represented as Ka, is a crucial concept when dealing with acids. It tells us how much an acid dissociates, or breaks apart, in water. This dissociation process splits an acid into hydrogen ions (H+) and its conjugate base.

Think of Ka as a measure of determination. A high Ka means the acid is very determined to separate into H+ and its conjugate base, making it a strong acid. On the other hand, a low Ka indicates that the acid is less likely to dissociate, meaning it's weaker.

For example:

• If Ka is high, the acid produces more H+ ions.
• If Ka is low, fewer H+ ions are produced.

Knowing the Ka of an acid, therefore, gives us insight into its behavior and strength in a solution.

Acid Strength

Acid strength refers to an acid's ability to donate protons (H+ ions) when dissolved in water. The stronger the acid, the more likely it is to give up its proton.

When discussing acid strength, it's essential to refer back to the dissociation constant (Ka).

Here’s a simple breakdown:

• A strong acid has a high Ka value because it dissociates completely in water, releasing many H+ ions.
• A weak acid has a low Ka value since it partially dissociates, releasing fewer H+ ions.

Using the provided example:
Consider acids A, B, and C with Ka values of \(1.8 \times 10^{-5}\), \(1.5 \times 10^{-4}\) and \(5.2 \times 10^{-8}\) respectively. We can see that:

• Acid B (Ka = \(1.5 \times 10^{-4})\) is the strongest.
• Acid A (Ka = \(1.8 \times 10^{-5})\) is intermediate.
• Acid C (Ka = \(5.2 \times 10^{-8})\) is the weakest.

This ranking helps us determine how each acid behaves in a solution.

Conjugate Bases

When an acid loses a proton (H+), it forms what's known as a conjugate base. The concept of conjugate bases is vital for understanding acid-base reactions.

The strength of the conjugate base is inversely related to the strength of the acid.

Here’s the relationship:

• A strong acid produces a weak conjugate base.
• A weak acid produces a strong conjugate base.

Let’s revisit our acids A, B, and C:

• B is the strongest acid with the highest Ka (\(1.5 \times 10^{-4})\), so it has the weakest conjugate base.
• A, with an intermediate Ka (\(1.8 \times 10^{-5})\), produces an intermediate conjugate base.
• C is the weakest acid with the lowest Ka (\(5.2 \times 10^{-8})\), implying it has the strongest conjugate base.

Thus, when we think about these conjugate bases in order of increasing basic character:
We get B’s conjugate base < A’s conjugate base < C’s conjugate base.
This matches option (3): \((B < A < C)\).

Understanding this relationship helps greatly in predicting how acids and their conjugate bases will react in different chemical environments.