Problem 19 - Chemistry: The Central Science

Question

Which of the following solutions is a buffer? (a) \(0.10 \mathrm{M}\) \(\mathrm{CH}_{3} \mathrm{COOH}\) and \(0.10 \mathrm{MCH}_{3} \mathrm{COONa}\), (b) \(0.10 \mathrm{M} \mathrm{CH}_{3} \mathrm{COOH}\), (c) \(0.10 \mathrm{M} \mathrm{HCl}\) and \(0.10 \mathrm{M} \mathrm{NaCl}\), (d) both a and \(c_{1}\) (e) all of a, b, and \(c\).

Step-by-Step Solution

Answer

The correct option is (a) \(0.10 \mathrm{M}\) \(\mathrm{CH}_{3} \mathrm{COOH}\) and \(0.10 \mathrm{MCH}_{3} \mathrm{COONa}\), as it contains a weak acid and its conjugate base, which can act as a buffer.

Step 1: Understand the criteria for a buffer solution

A buffer solution should contain a weak acid and its conjugate base or a weak base and its conjugate acid. This means that the solution must be able to resist changes in pH when small amounts of acid or base are added.

Step 2: Analyze solution (a)

Solution (a) contains 0.10 M CH3COOH (acetic acid) and 0.10 M CH3COONa (sodium acetate). Acetic acid is a weak acid and sodium acetate is the conjugate base of acetic acid. Since this solution contains a weak acid and its conjugate base, it can act as a buffer.

Step 3: Analyze solution (b)

Solution (b) contains 0.10 M CH3COOH (acetic acid) only. Since this solution does not contain any conjugate base of the weak acid, it cannot act as a buffer.

Step 4: Analyze solution (c)

Solution (c) contains 0.10 M HCl (hydrochloric acid) and 0.10 M NaCl (sodium chloride). Hydrochloric acid is a strong acid and is not suitable for buffer formation as it will not resist pH changes when a small amount of acid or base is added. Sodium chloride is a neutral salt and the chloride ion is the conjugate base of a strong acid, which does not contribute to buffering capacity. Therefore, this solution cannot act as a buffer.

Step 5: Determine the correct option

From our analysis, we know that solution (a) can act as a buffer while solutions (b) and (c) cannot. Thus, the correct option is (a) \(0.10 \mathrm{M}\) \(\mathrm{CH}_{3} \mathrm{COOH}\) and \(0.10 \mathrm{MCH}_{3} \mathrm{COONa}\).

Key Concepts

Weak Acids

Weak acids are a key player in the formation of buffer solutions. They do not completely dissociate into ions in water, which is why they are termed 'weak'. Instead, they partially ionize, meaning they release some, but not all, of their hydrogen ions (or protons) into the solution. This partial ionization is what makes them weak compared to strong acids, which completely dissociate in water.

One classic example of a weak acid is acetic acid (\(\mathrm{CH}_3\mathrm{COOH}\)). Unlike strong acids such as hydrochloric acid (\(\mathrm{HCl}\)), the ionization process of acetic acid is reversible:

• \[\mathrm{CH}_3\mathrm{COOH} \rightleftharpoons \mathrm{CH}_3\mathrm{COO}^- + \mathrm{H}^+\]

This reversible nature allows the weak acid to establish an equilibrium with its ions in the solution. This is an essential aspect of buffering capacity as it provides the means to respond to pH changes. Because these acids don't completely dissociate, their presence allows for the absorption or release of protons when the pH shifts, thereby stabilizing the pH of the solution.

Conjugate Base

The conjugate base is what remains after a weak acid donates a proton. It's important in buffering solutions because it can act in the reverse capacity, accepting protons back into the molecule. This dual action is crucial for maintaining a stable pH environment.

Take for example acetic acid, \(\mathrm{CH}_3\mathrm{COOH}\). When it donates a proton, it forms acetate, the conjugate base \(\mathrm{CH}_3\mathrm{COO}^-\). These two molecules, acetic acid and acetate ion, work together in a buffer system. When more acid (protons) is added to the solution, the conjugate base can absorb these additional protons, converting back to the weak acid:

• \[\mathrm{CH}_3\mathrm{COO}^- + \mathrm{H}^+ \rightarrow \mathrm{CH}_3\mathrm{COOH}\]

Alternatively, if the system encounters a base (which removes protons), acetic acid can donate protons to counteract this change:

• \[\mathrm{CH}_3\mathrm{COOH} \rightarrow \mathrm{CH}_3\mathrm{COO}^- + \mathrm{H}^+\]

This dynamic interplay between the weak acid and its conjugate base ensures the stability of the buffer solution, as both additions and depletions of protons are counteracted.

pH Resistance

In buffer solutions, pH resistance is an ability to maintain a stable pH despite the addition of small amounts of acids or bases. This characteristic is what makes buffers essential in many chemical and biological processes. Buffers work on the principle of dynamic equilibrium, where the weak acid and its conjugate base work together to neutralize any added protons (\(\mathrm{H}^+\)) or hydroxide ions (\(\mathrm{OH}^-\)).

For a buffer to be effective, the amounts of the weak acid and its conjugate base must be sufficient to counteract the disturbances. This means a buffer solution needs to have a significant concentration of both components. During a disturbance:

• If an acid is added, the solution's \(\mathrm{H}^+\) concentration would rise, but the conjugate base can "soak up" these additional protons, forming more of the weak acid, thereby minimizing any change in pH.
• If a base is added, \(\mathrm{OH}^-\) ions would react with \(\mathrm{H}^+\), converting to water. The weak acid can release protons to replace them, maintaining the pH balance.

The Henderson-Hasselbalch equation helps predict the pH of a buffer solution:

• \[\text{pH} = \text{pKa} + \log\left(\frac{[\text{Conjugate Base}]}{[\text{Weak Acid}]}\right)\]

This equation demonstrates how the ratio of concentration between the conjugate base and the weak acid determines the pH of the buffer. By carefully adjusting these concentrations, pH resistance is achieved, keeping the environment stable even in the face of potential disruptions.