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 \(\mathrm{NaOH}\) is added, the HA reacts with the \(\mathrm{OH}^{-}\) to form \(\mathrm{A}^{-}\). Thus the amount of acid (HA) is decreased, and the amount of base \(\left(\mathrm{A}^{-}\right)\) is increased. Analogously, adding \(\mathrm{HCl}\) to the buffered solution forms more of the acid (HA) by reacting with the base \(\left(\mathrm{A}^{-}\right) .\) Thus how can we claim that a buffered solution resists changes in the \(\mathrm{pH}\) of the solution?' How would you explain buffering to this friend?

Short answer

In short, a buffered solution resists changes in pH because it contains a weak acid (HA) and its conjugate base (A⁻) that can neutralize small amounts of added strong acids or bases. When a strong acid or base is added, the equilibrium between the weak acid and its conjugate base shifts to consume the added ions, maintaining a relatively constant pH. This buffering action is due to the large reservoirs of both HA and A⁻ in the solution, which allows the equilibrium to compensate for the addition of strong acids or bases, preventing significant pH changes.

Step-by-step solution

Introduction to Buffered Solutions

A buffered solution is a mixture of a weak acid (HA) and its conjugate base (A⁻) or a weak base and its conjugate acid. The buffering action comes from the ability of the weak acid and its conjugate base to neutralize small amounts of added strong acids or bases. As a result, the pH of the solution remains relatively constant, even when small amounts of strong acids or bases are added.

Weak Acid and Conjugate Base Equilibrium

In a buffered solution made up of a weak acid (HA) and its conjugate base (A⁻), the following equilibrium is established: \[ HA \rightleftharpoons H^+ + A^-\] When a strong base like NaOH is added, the OH⁻ ions will react with the H⁺ ions present in the solution.

Reaction with a Strong Base (NaOH)

When NaOH is added to the buffered solution, the following reaction occurs: \[ OH^- + HA \rightarrow H_2O + A^-\] The OH⁻ ions react with the weak acid HA, converting it into its conjugate base (A⁻) and water (H₂O). This reaction consumes the added OH⁻ ions, preventing a significant change in pH. Since there's a large reservoir of both HA and A⁻ in the solution, the equilibrium can shift to compensate for the addition of the strong base, keeping the pH relatively constant.

Reaction with a Strong Acid (HCl)

When HCl is added to the buffered solution, the following reaction occurs: \[ H^+ + A^- \rightarrow HA\] The H⁺ ions from HCl react with the conjugate base (A⁻) in the solution to form more of the weak acid (HA). This reaction consumes the added H⁺ ions, preventing a significant change in pH. Similar to the reaction with the strong base, there's a large reservoir of both HA and A⁻ in the solution, so the equilibrium can shift to compensate for the addition of the strong acid, keeping the pH relatively constant.

Conclusion

To summarize, a buffered solution contains a weak acid and its conjugate base (or a weak base and its conjugate acid), which can neutralize small amounts of added strong acids or bases. When a strong acid or base is added to the solution, the equilibrium between the weak acid and its conjugate base can shift to consume the added ions, keeping the pH relatively constant. That's how a buffered solution resists changes in pH when a strong acid or base is added.

Key concepts

Acid-Base Equilibrium

Understanding acid-base equilibrium is crucial to decipher how buffered solutions work. This concept pertains to the relationship between acids, bases, and their respective ions in solution. It's like a dance between the molecules, where weak acids (such as HA) and weak bases exist in harmony with their charged ions (H⁺ for acids and A⁻ for bases). In a solution at equilibrium, the rates of the forward and reverse reactions are equal, keeping the concentrations of the reactants and products constant.

For a weak acid HA in water, the equilibrium can be represented as:
\[\begin{equation}HA \rightleftharpoons H^+ + A^-\end{equation}\]This reversible process is pivotal because the acid HA can donate a proton (H⁺) to become its conjugate base (A⁻), and vice versa. This delicate balance ensures that when you add a strong acid or base, the equilibrium position adjusts to accommodate the change, thus moderating shifts in pH.

Weak Acid and Conjugate Base

The magic of buffering lies in the partnership of a weak acid and its conjugate base. A weak acid is like an introverted party guest – it doesn't fully dissociate in water, but rather, prefers to release some protons (H⁺) and reabsorb them from time to time. Its sidekick, the conjugate base, is what the acid becomes after donating a proton.

Consider our example of the weak acid HA and its sidekick, the conjugate base A⁻. They exist in equilibrium. The presence of both allows the solution to have a 'buffer' against pH changes because each part is ready to jump into action. If a strong base is added, the weak acid will react with it, limiting the increase in pH. If a strong acid is introduced, the conjugate base will neutralize it, keeping the pH from dropping significantly. This balancing act is what makes a buffered solution so resistant to pH changes.

Neutralization Reaction

When acids and bases meet, they can participate in a neutralization reaction. It's like a molecular handshake, where the acid says goodbye to its proton and passes it to the base.

In our buffered solution scenario, when NaOH, a strong base, is introduced, it seeks out protons to 'shake hands' with and finds them in the form of H⁺ from the weak acid HA:
\[\begin{equation}OH^- + HA → H_2O + A^-\end{equation}\]The product is water and the conjugate base A⁻. This reaction essentially 'consumes' the OH⁻ from the NaOH, preventing the pH from skyrocketing. The reverse happens when we add a strong acid like HCl; its protons find their partners in the conjugate base A⁻, making more HA and thus counteracting the pH decrease.

pH Stabilization

The pH stabilization prowess of buffered solutions is their crowning glory. pH refers to how acidic or basic a solution is. In less technical terms, you can think of it as a mood ring for the solution, where every small change is noticeable. However, buffered solutions wear a special 'coat' that keeps their 'mood' stable, even when strong acids or bases try to 'irritate' them.

Thanks to our dynamic duo, the weak acid HA and the conjugate base A⁻, buffered solutions absorb the added strong acid or base through a neutralization reaction, which we've discussed earlier. The capacity of the buffer to hold its pH in the face of these additions is remarkable; it's like a large reservoir that can absorb the 'rain' or 'drought' of outside influences without 'flooding' or 'drying up' its pH levels. This is why buffered solutions are indispensable in many biological and chemical applications where maintaining a stable pH is vital.