Question

Define buffering capacity. How do the following buffers differ in buffering capacity? How do they differ in pH? $$\begin{aligned} &\text { Buffer a: } 0.01 \mathrm{M} \mathrm{Na}_{2} \mathrm{HPO}_{4} \text { and } 0.01 \mathrm{M} \mathrm{NaH}_{2} \mathrm{PO}_{4}\\\ &\text { Buffer b: } 0.10 \mathrm{M} \mathrm{Na}_{2} \mathrm{HPO}_{4} \text { and } 0.10 \mathrm{M} \mathrm{NaH}_{2} \mathrm{PO}_{4}\\\ &\text { Buffer c: } 1.0 \mathrm{M} \mathrm{Na}_{2} \mathrm{HPO}_{4} \text { and } 1.0 \mathrm{M} \mathrm{NaH}_{2} \mathrm{PO}_{4} \end{aligned}$$

Short answer

Buffering capacity: Buffer c > Buffer b > Buffer a. pH is the same for all buffers.

Step-by-step solution

- Define Buffering Capacity

Buffering capacity refers to the ability of a buffer solution to resist changes in pH upon the addition of small amounts of an acid or a base.

- Determine Buffering Capacities

Buffering capacity is proportional to the concentration of the acidic and basic components of the buffer. Therefore, the higher the concentration, the greater the buffering capacity. From this information:- Buffer a has the lowest concentration (0.01 M each of Na₂HPO₄ and NaH₂PO₄).- Buffer b has a moderate concentration (0.10 M each of Na₂HPO₄ and NaH₂PO₄).- Buffer c has the highest concentration (1.0 M each of Na₂HPO₄ and NaH₂PO₄).Thus, Buffer c has the highest buffering capacity, followed by Buffer b, and then Buffer a.

- Examine pH Values

The pH of a buffer solution is determined by the acid and base pair used and their concentrations. Since all three buffers use the same acid (NaH₂PO₄) and conjugate base (Na₂HPO₄), and their concentrations are at a 1:1 ratio, they have the same pH value. The ratio of acid to conjugate base in each buffer being equal ensures that the pH remains constant.

Conclusion - Compare Buffers

To summarize, the buffering capacities differ among the buffers due to their differing concentrations: Buffer c > Buffer b > Buffer a. However, the pH remains the same across all three buffers due to the constant ratio of acid to conjugate base.

Key concepts

Buffer Solution

A buffer solution is a special type of solution that resists changes in its pH when small amounts of an acid or a base are added. This is crucial in many biological and chemical processes where maintaining a stable pH is essential. Buffers usually consist of a weak acid and its conjugate base or a weak base and its conjugate acid. These components work together to neutralize added acids or bases, ensuring that the pH remains relatively stable. In the given exercise, the buffers are made from mixtures of Na₂HPO₄ (a weak base) and NaH₂PO₄ (its conjugate acid). This specific mixture helps maintain the pH level despite external additions. Conditions such as enzymatic reactions in our body rely on buffers to maintain the desired pH levels.
Here are some key points about buffer solutions:

• Buffers are crucial in maintaining pH in biological systems.
• They function by neutralizing the addition of small amounts of acids or bases.
• The weak acid and conjugate base or weak base and conjugate acid are the main components.

pH

pH is a measure of how acidic or basic a solution is. It is a scale ranging from 0 to 14, with values below 7 indicating an acidic solution, values above 7 indicating a basic solution, and a value of 7 being neutral. The pH scale is logarithmic, meaning that each whole number on the scale corresponds to a tenfold increase or decrease in acidity or basicity. In the context of the buffers in the exercise, even though the concentrations of the buffers vary, the pH remains the same because the ratio of the weak acid (NaH₂PO₄) to its conjugate base (Na₂HPO₄) is maintained at 1:1. It's the ratio that plays a crucial role in determining the pH of the buffer solution.
Here are some quick notes about pH:

• pH is a measure of acidity or basicity of a solution.
• The pH scale ranges from 0 (most acidic) to 14 (most basic).
• A pH of 7 is neutral, such as pure water.

Concentration

Concentration refers to the amount of a substance in a given volume of solution. It is typically expressed in molarity (M), which is moles of solute per liter of solution. In the context of buffers, concentration is directly linked to buffering capacity. A higher concentration of the buffer components results in a greater ability to resist pH changes when an acid or base is added. In the provided exercise, buffers a, b and c differ in their concentrations (0.01 M, 0.10 M, and 1.0 M respectively). Therefore, Buffer c, with the highest concentration of components, can neutralize more added acid or base compared to Buffer a. This contributes to Buffer c having the highest buffering capacity.
Some important aspects of concentration in this context include:

• Concentration is measured in molarity (M).
• Higher concentration means greater buffering capacity.
• It influences how well a buffer can maintain the pH level.

Acid-Base Pair

An acid-base pair consists of two substances related by the loss or gain of a single hydrogen ion. In the case of buffer solutions discussed in the exercise, the acid-base pair involved are NaH₂PO₄ (acid) and Na₂HPO₄ (base). The acid, NaH₂PO₄, can donate a hydrogen ion (H⁺) to neutralize bases, while the base, Na₂HPO₄, can accept a hydrogen ion to neutralize acids. This pairing is essential for the buffering action. By keeping the ratio of these two components constant, the buffer maintains the pH level even when acids or bases are introduced into the solution.
Important points about acid-base pairs:

• An acid-base pair consists of two substances that can donate or accept H⁺ ions.
• They work together to maintain the buffer's pH level.
• In a buffer system, these pairs help neutralize added acids or bases efficiently.