Problem 90 - Chemistry The Molecular Science

Question

Which of these buffers involving a weak acid HA has the greater resistance to change in pH? Explain your answer. (i) \([\mathrm{HA}]=0.100 \mathrm{M}=\left[\mathrm{A}^{-}\right]\) (ii) \([\mathrm{HA}]=0.300 \mathrm{M}=\left[\mathrm{A}^{-}\right]\)

Step-by-Step Solution

Answer

Buffer (ii) has greater resistance to pH changes due to higher concentrations.

Step 1: Understanding Buffer Solutions

A buffer solution is composed of a weak acid and its conjugate base (or a weak base and its conjugate acid) in appreciable amounts. The purpose of a buffer is to maintain a relatively constant pH when small amounts of acid or base are added.

Step 2: Henderson-Hasselbalch Equation Introduction

The pH of a buffer solution can be estimated using the Henderson-Hasselbalch equation: \( \text{pH} = \text{pKa} + \log \left( \frac{[\mathrm{A}^-]}{[\mathrm{HA}]} \right) \). In buffers where \([\mathrm{HA}] = [\mathrm{A}^-]\), the pH equals pKa.

Step 3: Assessing Buffer Capacity

Buffer capacity refers to the ability of a buffer to resist changes in pH upon the addition of acid or base. It is influenced by the concentration of HA and A-. Higher concentrations of the buffer components mean a greater buffer capacity.

Step 4: Comparison of the Two Buffers

(i) has \([ ext{HA}] = 0.100 \text{ M} = [\text{A}^-]\). (ii) has \([ ext{HA}] = 0.300 \text{ M} = [\text{A}^-]\). Both have equal ratios, meaning the pH for both will be the same. However, since buffer capacity is dependent on the absolute concentrations, buffer (ii) with higher concentrations will have a greater resistance to pH changes.

Key Concepts

Buffer Solutions

Buffer solutions are fascinating and very practical mixtures. They are made up of a weak acid and its conjugate base, or a weak base and its conjugate acid. These solutions have a very special job—they help keep the pH level steady. Imagine trying to keep a seesaw perfectly balanced! When small amounts of an acid or base are added to a buffer, the buffer works its magic to stop the pH from changing too much. This is very useful in situations where it’s important to keep the pH within certain limits, such as in our blood, which is a natural buffer solution. Here are key points about buffer solutions:

• A buffer consists of a weak acid and its conjugate base.
• The main function is to neutralize small additions of acid or base.
• This means it maintains a consistent pH level, even when small amounts of external acids or bases are introduced.

The strength of a buffer solution’s resistance to pH change is called its "buffer capacity." A high buffer capacity means the solution can handle more acid or base without changing its pH significantly.

Henderson-Hasselbalch Equation

The Henderson-Hasselbalch equation is a gem in chemistry for buffer solutions. It helps us calculate and understand the pH of a buffer system. The equation is easy to remember and use: \[ \text{pH} = \text{pKa} + \log \left( \frac{[\mathrm{A}^-]}{[\mathrm{HA}]} \right) \].Let's break this down:

• \( \text{pH} \) is what we want to find, which is the measure of acidity.
• \( \text{pKa} \) is a constant for how easily the acid gives up protons, specific to each acid.
• The term \( \frac{[\mathrm{A}^-]}{[\mathrm{HA}]} \) represents the ratio of the concentration of the conjugate base to the weak acid.

A neat feature of this equation is its use when \([\mathrm{HA}] = [\mathrm{A}^-]\); in this situation, the log part equals zero, making the pH equal to the pKa. This scenario is known as the maximum buffering point where the buffer solution will have the strongest capacity to resist changes in pH.

Weak Acid and Conjugate Base

To understand buffer solutions, it's essential to grasp the concepts of weak acids and their conjugate bases. In chemistry, a weak acid doesn't fully disassociate in water. That means not every acid molecule will release a proton. As a result, you'll have lots of both the acid and its conjugate base floating around in solution.The conjugate base is what happens to the weak acid molecule when it gives up a proton. They exist in a delicate balance and this balance is crucial for buffering actions.Key characteristics:

• Weak acids only partly ionize in solution. For example, acetic acid is a weak acid.
• The conjugate base is formed once the weak acid releases a proton.
• This pair, the acid and its conjugate base, work together to neutralize added acids and bases, making them effective at maintaining pH stability.

In a buffer solution of acetic acid, \( \text{CH}_3\text{COOH} \), its conjugate base is \( \text{CH}_3\text{COO}^- \). When the solution faces an increase in H+ ions (acid), the conjugate base will react and neutralize the extra H+, preserving the buffer's pH. Similarly, if OH- ions (base) are introduced, the weak acid will react to buffer this change. This synergy is what makes buffer systems invaluable in both nature and various chemical applications.