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 a measure of a buffer solution's resistance to pH change when an acid or base is added. A buffer capacity is typically maximized when the concentrations of the weak acid and its conjugate base are equal, or when their ratio is close to 1:1.

Step 2: Analyze Each Option

Examine each of the given compositions:(a) In option (a), the concentrations are \([HA] = 0.1 \, \text{M}\) and \([A^-] = 0.2 \, \text{M}\).(b) In option (b), the concentrations are \([HA] = 0.1 \, \text{M}\) and \([A^-] = 0.15 \, \text{M}\).(c) In option (c), the concentrations are \([HA] = 0.05 \, \text{M}\) and \([A^-] = 0.15 \, \text{M}\).(d) In option (d), the concentrations are \([HA] = 0.1 \, \text{M}\) and \([A^-] = 0.12 \, \text{M}\).

Step 3: Calculate Ratio of Conjugate Base to Acid

Find the ratio \(\frac{ [A^-] }{ [HA] }\) for each option:(a) \(\frac{ 0.2 }{ 0.1 } = 2 \)(b) \(\frac{ 0.15 }{ 0.1 } = 1.5 \)(c) \(\frac{ 0.15 }{ 0.05 } = 3 \)(d) \(\frac{ 0.12 }{ 0.1 } = 1.2 \)

Step 4: Evaluate Each Composition Based on Ratios

For maximum buffer capacity, the ideal ratio should be close to 1:1. Compare the ratios calculated: - Option (a) ratio is 2. - Option (b) ratio is 1.5. - Option (c) ratio is 3. - Option (d) ratio is 1.2. The closest ratio to 1 is with option (d), which is 1.2.

Step 5: Conclusion and Selection

Since option (d) has the ratio closest to 1:1, it will have the highest buffer capacity among the given options. Therefore, the composition that shows the maximum buffer capacity is option (d): \(0.1 \, \text{M} \, \text{CH}_3\text{COOH} + 0.12 \, \text{M} \, \text{CH}_3\text{COONa}\).

Key Concepts

Weak Acid and Conjugate Base

When we talk about buffers, the role of a weak acid and its conjugate base is crucial. A weak acid, such as acetic acid ( CH_3COOH ), only partially dissociates in a solution. This means it does not give up all of its hydrogen ions (H⁺) easily. Meanwhile, the conjugate base, like sodium acetate ( CH_3COONa ), comes from the weak acid. It is capable of accepting hydrogen ions back, making the balance between these two components essential.
A buffer solution typically includes both a weak acid and its conjugate base. The presence of both allows the solution to resist changes in pH. It's like having a team where the weak acid provides some of its hydrogen ions when a base is added to the solution, and the conjugate base picks up extra hydrogen ions when an acid is added.

pH Resistance

The concept of pH resistance is central to understanding buffer capacity. Buffer solutions act like shock absorbers for pH changes, preventing significant fluctuations. When you add a strong acid or base to a buffer solution, the weak acid and its conjugate base work together to neutralize the added substance.
For example, if a strong acid is added, the conjugate base part of the buffer will react with the hydrogen ions to reduce the change in pH. Conversely, if a strong base is added, the weak acid component will release hydrogen ions, again limiting the pH shift. This ability to resist sudden changes in pH is what defines a solution's buffer capacity.

Buffer Solution Composition

The composition of a buffer solution is a delicate balance. Creating an effective buffer depends on the concentrations of the weak acid and the conjugate base within the solution. Often, the best buffer occurs when the amounts of weak acid and conjugate base are nearly equal. This balance is critical in maintaining the desired pH.
In practical terms, equal concentrations mean there is plentiful availability of both the weak acid and its conjugate base to combat any pH changes. This balance is why we often look for compositions where their ratio is close to 1:1. Such a composition ensures the buffer has the maximum capacity to resist pH changes.

Acid-Base Ratio

The acid-base ratio is an essential parameter in determining the buffer capacity of a solution. In an ideal situation, this ratio should be close to 1. A ratio of 1:1 means the buffer can handle equal amounts of acidic and basic challenges. When the ratio skews away from 1:1, the ability of the buffer to maintain a stable pH diminishes.
The given exercise illustrates different compositions and their acid-base ratios, showing how some are better suited for buffering purposes. For example, a ratio of 1.2, as seen in option (d) of the exercise, is the closest to 1. This makes it the most effective in maintaining a stable pH compared to other options with higher ratios.