Problem 141 - A Complete Resource Book in Chemistry for JEE Main

Question

If the equilibrium constant of the reaction of weak acid HA with strong base is \(10^{9}\), then \(\mathrm{pH}\) of \(0.1 \mathrm{M} \mathrm{NaA}\) is (a) 3 (b) 9 (c) 7 (d) 6

Step-by-Step Solution

Answer

The pH of 0.1 M NaA is 9.

Step 1: Understand the Problem

We are dealing with the reaction of a weak acid (HA) with a strong base to produce a salt (NaA) that is dissociated in water. We need to find the pH of a 0.1 M solution of this salt, given the equilibrium constant.

Step 2: Identify the Chemical Reaction

The weak acid HA dissociates in water to form H+ and A-. The equilibrium reaction is \( \text{HA} \stackrel{K_a}{\rightleftharpoons} \text{H}^+ + \text{A}^- \), where \( [\text{A}^-] = 0.1 \text{ M} \) due to the NaA salt dissociation.

Step 3: Apply the Concept of Equilibrium Constant

The reaction implies that \( K = \frac{[\text{A}^-][\text{H}^+]}{[\text{HA}]} = 10^9 \). Since NaA completely dissociates, the concentration of A- is 0.1 M. We assume x M of HA is present at equilibrium.

Step 4: Solve the Equilibrium Expression

Assume practically all HA is ionized due to the strong base presence, practically negligible reverse reaction (Ka is small). Therefore, \( [\text{H}^+] = 10^{-9} \).

Step 5: Calculate the pH

Using \( \text{pH} = - \log[\text{H}^+] \), substitute \( [\text{H}^+] = 10^{-9} \) to get \( \text{pH} = 9 \).

Step 6: Verify the Solution

Ensure that calculations and assumptions align with the equilibrium process and nature of weak acids and their salts. Re-evaluate if necessary to confirm \( \text{pH} = 9 \).

Key Concepts

Equilibrium Constant

In chemistry, the equilibrium constant (K) helps us understand the balance achieved at equilibrium during a chemical reaction. It provides insight into the ratio of the concentration of products to reactants at equilibrium. For the dissociation of a weak acid HA in water, the equilibrium equation is generally represented as:

• \( ext{HA} \leftrightharpoons ext{H}^+ + ext{A}^- \)

The equilibrium constant is expressed by the formula:

• \( K_a = \frac{[ ext{H}^+][ ext{A}^-]}{[ ext{HA}]} \)

When the equilibrium constant has a large value, as in this case \(10^9\), it indicates that the reaction extensively favors the formation of products. This is important in determining the pH of solutions involving weak acids and their salts.
Understanding the equilibrium constant is crucial for accurate pH calculations, as it essentially dictates how much a weak acid dissociates in solution.

Weak Acid

A weak acid is an acid that only partially dissociates in water to produce hydrogen ions (H+) and its conjugate base (A^-). Unlike strong acids, which dissociate completely, weak acids achieve an equilibrium between the undissociated acid and the ions

• \( ext{HA} \leftrightharpoons ext{H}^+ + ext{A}^- \)

The small equilibrium constant \(K_a\) associated with weak acids implies limited ionization in water. This partial ionization is key when calculating the pH of solutions that contain weak acids or their salts.
A weak acid like HA may react with a strong base such as NaOH, forming a salt like NaA, which can affect the pH depending on its dissociation characteristics. Grasping the nature of weak acids aids in understanding how they interact in varying chemical environments.

Strong Base

Strong bases fully dissociate in water, releasing hydroxide ions \( ( ext{OH}^-) \). This complete dissociation means the base's presence significantly affects the equilibrium of reactions involving acids.

• For instance, a strong base like NaOH dissociates completely to Na\(^+\) and OH\(^-\) ions.

The strong base's influence on weak acids is pivotal in formation and dissociation of salts such as NaA. This complete dissociation effectively drives the equilibrium reaction of a weak acid such as HA towards its products.

• Thus, the presence of a strong base encourages the full deprotonation of the weak acid, implying significant dissociation into H\(^+\) and A\(^-\) ions.

This understanding is vital in achieving accurate pH calculations, particularly when handling reactions between weak acids and strong bases.

Salt Dissociation

Salt dissociation refers to the process where a salt, such as NaA, dissolves in water to release its constituent ions. In the process of a weak acid reacting with a strong base, a salt emerges as a product that easily dissociates in aqueous solution.

The reaction can be illustrated as follows:

• \( ext{HA} + ext{NaOH} \rightarrow ext{NaA} + ext{H}_2 ext{O} \)

Upon dissolving in water, NaA splits into \( ext{Na}^+ \) and \( ext{A}^- \) ions. The \( ext{A}^- \) ions play a crucial role in determining the pH of the solution because they can interact with water molecules in a hydrolysis reaction:

• \( ext{A}^- + ext{H}_2 ext{O} \leftrightharpoons ext{HA} + ext{OH}^- \)

The resulting equilibrium affects the pH value, tending to make it more basic if the base derived from the salt is strong enough.
Comprehending how salt dissociation impacts pH is essential for predicting the behavior of solutions containing salts from reactions between weak acids and strong bases.