Question

A friend asks the following: “Consider a buffered solution made up of the weak acid HA and its salt NaA. If a strong base like NaOH is added, the HA reacts with the OH2 to form A2. Thus the amount of acid (HA) is decreased, and the amount of base (A2) is increased. Analogously, adding HCl to the buffered solution forms more of the acid (HA) by reacting with the base (A2). Thus how can we claim that a buffered solution resists changes in the pH of the solution?” How would you explain buffering to this friend?

Short answer

In short, a buffered solution resists changes in pH when small amounts of acid or base are added because of the equilibrium between the weak acid (HA) and its conjugate base (A-). When a strong base or acid is added, the weak acid and conjugate base consume the added base or acid, respectively, leading to minimal change in the concentrations of HA and A-. This equilibrium maintains the pH within a relatively narrow range, as per the Henderson-Hasselbalch equation: \[pH = pK_a + \log \frac{[A^-]}{[HA]}\]

Step-by-step solution

1. Defining Buffered Solutions

A buffered solution is a solution that resists significant changes in pH when a small amount of acid or base is added. This resistance is achieved by the presence of a weak acid and its conjugate base or a weak base and its conjugate acid. In this case, the buffered solution consists of the weak acid, HA, and its salt, NaA.

2. Buffer Components: Weak Acid and its Conjugate Base

Buffered solutions take advantage of the equilibrium between a weak acid and its conjugate base. The weak acid, HA, can donate a proton (H+) and form the conjugate base A-. The balance between HA and A- determines the pH of the buffered solution. The equilibrium expression for the dissociation of a weak acid (HA) is: \[HA \rightleftharpoons H^+ + A^-\] The pH of the solution can be determined using the Henderson-Hasselbalch equation: \[pH = pK_a + \log \frac{[A^-]}{[HA]}\] Here, \(pK_a\) is the negative log of the acid dissociation constant and represents the ability of the weak acid to donate a proton.

3. Addition of a Strong Base

When a strong base like NaOH is added to the buffered solution, the hydroxide ions (OH-) will react with the weak acid (HA), forming water (H2O) and the conjugate base (A-): \[HA + OH^- \rightarrow A^- + H_2O\] As a result, the amount of HA decreases while the amount of A- increases. This may lead to a slight shift in the pH of the buffered solution. However, due to the presence of both HA and A-, pH will not change dramatically. The buffered solution will consume the added base without affecting the pH significantly.

4. Addition of a Strong Acid

Similarly, when a strong acid like HCl is added to the buffered solution, the chloride ions (Cl-) will not participate in the buffer reaction, but excess H+ ions will react with the conjugate base (A-) to reform the weak acid (HA): \[A^- + H^+ \rightarrow HA\] The amount of A- decreases while the amount of HA increases, leading to a slight change in the pH of the solution. However, once again, due to the presence of both HA and A- in the solution, the pH will not change dramatically. The buffered solution neutralizes the added acid with minimal pH change.

5. Explaining Buffering

In conclusion, a buffered solution resists changes in pH when a small amount of acid or base is added because the weak acid (HA) and its conjugate base (A-) can consume the added acid or base without significantly altering their concentrations. Due to the equilibrium between HA and A-, adjustments in their amounts allow for the maintenance of the solution's pH within a relatively narrow range.

Key concepts

Weak Acid

A weak acid is an acid that partially ionizes in a solution. Unlike strong acids that completely dissociate in water, weak acids break down only to a small extent. This means a significant amount of the acid remains un-ionized in the solution.
For instance, consider hydrofluoric acid (HF), a common example of a weak acid. In water, HF does not fully dissociate into hydrogen ions (\(H^+\)) and fluoride ions (\(F^-\)). Instead, an equilibrium is established between HF and its ions:

• Some molecule remain as HF (unionized).
• Some dissociate into \(H^+\) and \(F^-\).

This equilibrium is a key characteristic of weak acids and plays a crucial role in buffering action.

Conjugate Base

The conjugate base is the species that results from the donation of a proton by an acid. In a buffered solution, the conjugate base works alongside its paired weak acid to maintain pH balance.
Consider the example of acetic acid (\(CH_3COOH\)). When it donates a hydrogen ion (\(H^+\)), it turns into its conjugate base, acetate (\(CH_3COO^-\)).

• The dynamic duo of weak acid and conjugate base effectively manages pH changes when external acids or bases are introduced.
• They do this by adjusting the equilibrium of the reaction, either absorbing or releasing \(H^+\) ions.

This partnership between a weak acid and its conjugate base enables the solution to resist wide shifts in pH. This mechanism is what makes a buffer system effective.

Henderson-Hasselbalch Equation

The Henderson-Hasselbalch equation is a formula used to calculate the pH of a buffered solution. It connects the concentrations of an acid and its conjugate base to the pH of the solution.
The formula is as follows:\[ pH = pK_a + \log \frac{[A^-]}{[HA]} \]Where:

• \(pK_a\) is the negative log of the acid dissociation constant, reflecting the strength of the weak acid.
• \([A^-]\) is the concentration of the conjugate base in the solution.
• \([HA]\) is the concentration of the weak acid.

This equation is very useful because it provides a straightforward way to predict how the pH will change as you alter the ratio between the acid and base levels. It explains why the buffer can neutralize small quantities of added acids or bases while maintaining a pH close to its starting point.

Acid-Base Equilibrium

In a buffered solution, acid-base equilibrium plays a pivotal role in maintaining pH balance. This equilibrium involves a balance between the weak acid and its conjugate base.
The basic principle is that the weak acid can donate protons (\(H^+\)), while the conjugate base can accept protons. This dual capability is crucial because:

• The weak acid can neutralize added bases by releasing \(H^+\) ions.
• The conjugate base can neutralize added acids by accepting \(H^+\) ions.

These interactions ensure that significant shifts in pH are avoided, creating a stable environment despite the addition of external acid or base. The system responds dynamically to restore balance, illustrating the elegant simplicity and efficiency of chemical equilibrium in buffered solutions.