Problem 161 - A Complete Resource Book in Chemistry for JEE Main

Question

Which of the following composition shows maximum buffer capacity? (a) \(0.1 \mathrm{M} \mathrm{CH}_{3} \mathrm{COOH}+0.2 \mathrm{M} \mathrm{CH}_{3} \mathrm{COONa}\) (b) \(0.1 \mathrm{M} \mathrm{CH}_{3} \mathrm{COOH}+0.15 \mathrm{M} \mathrm{CH}_{3} \mathrm{COONa}\) (c) \(0.05 \mathrm{M} \mathrm{CH}_{3} \mathrm{COOH}+0.15 \mathrm{M} \mathrm{CH}_{3} \mathrm{COONa}\) (d) \(0.1 \mathrm{M} \mathrm{CH}_{3} \mathrm{COOH}+0.12 \mathrm{M} \mathrm{CH}_{3} \mathrm{COONa}\)

Step-by-Step Solution

Answer

Option (d) has the maximum buffer capacity.

Step 1: Understanding Buffer Capacity

Buffer capacity is the ability of a buffer solution to resist changes in pH. It is highest when the concentrations of the acid and its conjugate base are equal, or when they are close to each other, allowing them to neutralize added acids or bases effectively.

Step 2: Identifying Buffer Components

All options presented are buffer solutions composed of a weak acid, acetic acid ( CH_3COOH ), and its conjugate base, sodium acetate ( CH_3COONa ). The effectiveness of a buffer is maximized when the concentration of the acid and conjugate base are equal or almost equal.

Step 3: Analyzing the Concentrations of Acid and Base

(a) 0.1 M CH_3COOH and 0.2 M CH_3COONa : The concentrations are not equal. (b) 0.1 M CH_3COOH and 0.15 M CH_3COONa : The concentrations are closer, but the base is still more concentrated. (c) 0.05 M CH_3COOH and 0.15 M CH_3COONa : The concentrations are far apart. (d) 0.1 M CH_3COOH and 0.12 M CH_3COONa : These concentrations are the closest to each other among the options.

Step 4: Selecting the Maximum Buffer Capacity Option

Option (d), with 0.1 M of CH_3COOH and 0.12 M of CH_3COONa , has the concentrations of the acid and its conjugate base closest to being equal, out of all the given options. Therefore, option (d) exhibits the highest buffer capacity.

Key Concepts

Acetic Acid

Acetic acid is a simple organic compound with the formula \( \text{CH}_3\text{COOH} \). It is a weak acid that is commonly used in vinegar. In the context of buffers, it plays a crucial role. A buffer solution can resist changes in pH when acids or bases are added, mainly because of the presence of both a weak acid and its conjugate base.

In a buffer solution with acetic acid, the weak acid partially dissociates in solution. This dissociation is represented by the equilibrium:

• \( \text{CH}_3\text{COOH} \rightleftharpoons \text{CH}_3\text{COO}^- + \text{H}^+ \)

This equilibrium is vital because it determines how acetic acid interacts with its environment. When extra hydrogen ions are added, they are neutralized by the acetate ions \( (\text{CH}_3\text{COO}^-) \), derived from the conjugate base, minimizing pH fluctuation.
On the flip side, when hydroxide ions are introduced, they react with existing hydrogen ions to form water, shifting the equilibrium towards more acetate ions. This further strengthens the buffer against pH change.

This functionality is the key to buffer capacity—it's all about balance and equilibrium! Acetic acid is central to maintaining this essential chemical balance.

Conjugate Base

A conjugate base is an ion or molecule that results when an acid loses its hydrogen ion. In the case of acetic acid, the conjugate base is the acetate ion \( (\text{CH}_3\text{COO}^-) \). The concept of a conjugate base is pivotal in understanding buffer solutions.

When we mix a weak acid like acetic acid with its conjugate base, they form a buffer solution capable of resisting pH changes. The role of the conjugate base in this setup is to neutralize added acids. Here is how the mechanism works:

• When an external acid is introduced, the conjugate base reacts with the added hydrogen ions:
• \( \text{CH}_3\text{COO}^- + \text{H}^+ \rightarrow \text{CH}_3\text{COOH} \)

This reaction helps maintain the pH by reducing the free hydrogen ions in the solution.

Similarly, if a base is added, causing an increase in hydroxide ions \( (\text{OH}^-) \), the weak acid part of the buffer neutralizes them:

• \( \text{CH}_3\text{COOH} + \text{OH}^- \rightarrow \text{CH}_3\text{COO}^- + \text{H}_2\text{O} \)

Hence, the conjugate base not only supports the buffering action but is integral in maintaining the chemical equilibrium necessary for the buffer's function.

Sodium Acetate

Sodium acetate \( (\text{CH}_3\text{COONa}) \) is often used along with acetic acid to create buffer solutions. It is a salt formed from sodium \( (\text{Na}^+) \) and the conjugate base of acetic acid, acetate ion \( (\text{CH}_3\text{COO}^-) \). Its role in buffer solutions is critical because it is the source of the acetate ions.

When dissolved in water, sodium acetate dissociates completely:

• \( \text{CH}_3\text{COONa} \rightarrow \text{CH}_3\text{COO}^- + \text{Na}^+ \)

This dissociation increases the availability of acetate ions, which are key to the buffering action.

By including sodium acetate in a buffer solution, you ensure that there are sufficient acetate ions present to respond to any pH changes effectively. They do so by neutralizing additional acids, as previously discussed. The presence of sodium acetate makes the buffer solution more efficient in resisting pH changes, especially when the concentration of sodium acetate is close to that of acetic acid.
In an ideal buffer system, the concentrations of acetic acid and sodium acetate are nearly equal, which maximizes the buffer capacity. This directly ties back to the concept of buffer capacity being highest when the weak acid and its conjugate base are in close equilibrium—a harmony essential for effective buffering.