Question

Buffered solutions are mixtures of a weak acid and its conjugate base. Explain why a mixture of a strong acid and its conjugate base (such as \(\mathrm{HCl}\) and \(\mathrm{Cl}^{-}\) ) is not buffered.

Short answer

A mixture of a strong acid and its conjugate base, such as HCl and Cl-, is not a buffered solution because the strong acid is fully ionized, and its conjugate base is a weak base that does not readily accept protons. As a result, the mixture does not have the capacity to neutralize added acids or bases and maintain a constant pH.

Step-by-step solution

Understanding Buffered Solutions

A buffered solution is a mixture containing a weak acid and its conjugate base or a weak base and its conjugate acid. The purpose of a buffered solution is to maintain a relatively constant pH when small amounts of acids or bases are added.

Buffered Solutions and Weak Acids/Bases

In a buffered solution, the weak acid and its conjugate base are in equilibrium, and they can absorb or neutralize a small amount of added acid or base. This ability to maintain a constant pH is due to the fact that the weak acid is not fully ionized, and the conjugate base is not fully deprotonated, allowing them to react with added acids or bases. For example, in a solution containing acetic acid (\(\mathrm{CH_3COOH}\)) and its conjugate base, acetate (\(\mathrm{CH_3COO^-}\)), the following equilibrium exists: \[\mathrm{CH_3COOH \rightleftharpoons CH_3COO^- + H^+}\] If an acid (such as HCl) is added to this solution, the excess \(\mathrm{H^+}\) ions will react with the acetate ions to form acetic acid: \[\mathrm{CH_3COO^- + H^+ \rightarrow CH_3COOH}\] Similarly, if a base (such as NaOH) is added, the \(\mathrm{OH^-}\) ions will react with the acetic acid to produce more acetate ions and water: \[\mathrm{CH_3COOH + OH^- \rightarrow CH_3COO^- + H_2O}\] In both cases, the pH of the solution remains relatively constant because the weak acid and its conjugate base are able to neutralize the added acid or base.

Strong Acid and Conjugate Base Mixture

Now let's consider a mixture containing a strong acid, such as HCl, and its conjugate base, Cl-. In this mixture, HCl is almost completely ionized: \[\mathrm{HCl \rightarrow H^+ + Cl^-}\] When adding an acid or a base to this mixture, the Cl- ions will not react with the added \(\mathrm{H^+}\) ions to a meaningful extent, nor will the HCl molecules react with \(\mathrm{OH^-}\) ions. This is because the strong acid, HCl, has completely ionized, and its conjugate base, Cl-, is a very weak base that does not readily accept protons. As a result, the pH of the solution will change significantly upon addition of an acid or base, and it does not have the buffering capacity of a weak acid-conjugate base mixture.

Conclusion

A mixture of a strong acid and its conjugate base, such as HCl and Cl-, is not a buffered solution because the strong acid is fully ionized, and its conjugate base is a weak base that does not readily accept protons. As a result, the mixture does not have the capacity to neutralize added acids or bases and maintain a constant pH.

Key concepts

Weak acid-conjugate base equilibrium

At the heart of a buffered solution is the delicate balance between a weak acid and its conjugate base. This equilibrium allows the solution to effectively resist changes in pH when small amounts of acid or base are introduced. The primary reason this works is that the weak acid does not fully dissociate in water. This means some of its molecules remain intact and can react with additional bases, while its conjugate base can react with acids.

For example, consider acetic acid (\( \mathrm{CH_3COOH} \)) and its conjugate base, acetate (\( \mathrm{CH_3COO^-} \)). In this solution, the following equilibrium expression is established:
\[\mathrm{CH_3COOH \rightleftharpoons CH_3COO^- + H^+}.\]

• The acetic acid can donate a proton to neutralize OH⁻ ions from a base.
• The acetate ion can pick up H⁺ ions from an added acid.

This balance ensures that both added acids and bases are neutralized, keeping the pH relatively constant.

Strong acids vs weak acids

Understanding the difference between strong and weak acids is vital in explaining why strong acid solutions do not buffer. A strong acid, like hydrochloric acid (\( \mathrm{HCl} \)), ionizes completely in water:
\[\mathrm{HCl \rightarrow H^+ + Cl^-}.\]In contrast, weak acids partially ionize. This complete ionization in strong acids means there's little to no presence of the un-ionized acid form to "soak up" added bases. Moreover, the conjugate base of a strong acid, such as chloride ion (\( \mathrm{Cl^-} \)), is a very weak base and does not readily accept protons.

This inability to react further with added acids or bases means a solution of a strong acid and its conjugate base lacks the buffering capacity.

• Strong acids: Fully ionize, have weak conjugate bases.
• Weak acids: Partially ionize, maintain equilibrium with their conjugate base.

pH stability

Achieving pH stability is the cornerstone of any buffered solution. This stability arises from the equilibrium that occurs between a weak acid and its conjugate base, as previously described. When the system is disturbed by the addition of an external acid or base, the prevailing equilibrium manipulates itself to counter this change and maintain the overall hydrogen ion concentration.

Adding an acid to a buffered solution causes the conjugate base to react with the surplus \( \mathrm{H^+} \) ions, forming the weak acid:

• The weak acid increases slightly in concentration, offsetting the added acid.

Introducing a base induces a reaction with the weak acid, producing more of its conjugate base:

• The conjugate base increases slightly in concentration, balancing the addition of the base.

This dynamic nature preserves the pH within a desirable range, unlike the drastic shifts seen in unbuffered strong acid or base solutions.