Question

Explain the buffering action of a liter of \(0.10 \mathrm{M}\) acetic acid containing \(0.1\) mole of sodium acetate. In the explanation, use ionic equations.

Short answer

The buffering action of a liter of \(0.10 \mathrm{M}\) acetic acid containing \(0.1\) mole of sodium acetate is due to the equilibrium between the weak acid and its conjugate base, which in this case are acetic acid (\(CH_3COOH\)) and the acetate ion (\(CH_3COO^-\)). This buffering system resists changes in pH by consuming added protons or hydroxide ions and preventing substantial changes in pH levels. When a strong acid is added, the equilibrium shifts to consume the added protons according to the reaction : \(CH_3COO^- (aq) + H_3O^+(aq) \rightleftharpoons CH_3COOH (aq) + H_2O (l)\). On the other hand, when a strong base is added, the equilibrium shifts to consume added hydroxide ions through the reaction: \(CH_3COOH (aq) + OH^-(aq) \rightleftharpoons CH_3COO^- (aq) + H_2O(l)\). The buffering process can be encapsulated by the equilibrium constant expression for acetic acid: \(K_\mathrm{a} = \frac{[CH_3COO^-][H_3O^+]}{[CH_3COOH]}\). Ionic equations help to visualize these shifts in equilibrium on a molecular level.

Step-by-step solution

Identify the components of the buffer system

A buffer solution contains a weak acid and its conjugate base. In this case, the weak acid is acetic acid (CH₃COOH) and the conjugate base is the acetate ion (CH₃COO⁻), which comes from sodium acetate (NaCH₃COO).

Write the equilibrium expression for acetic acid

The equilibrium reaction for acetic acid is as follows: \(CH_3COOH (aq) + H_2O (l) \rightleftharpoons CH_3COO^- (aq) + H_3O^+(aq)\) The equilibrium constant expression for this reaction is: \[K_\mathrm{a} = \frac{[CH_3COO^-][H_3O^+]}{[CH_3COOH]}\]

Define the components in the buffer before the addition of a strong acid or base

The buffer is initially composed of 0.10 M acetic acid and 0.10 mol of sodium acetate in 1 L of solution, which is also 0.10 M. Assuming the dissociation of sodium acetate is complete, the initial concentrations are: [CH₃COOH] = 0.10 M [CH₃COO⁻] = 0.10 M For simplicity, we will consider the concentration of hydronium ions ([H₃O⁺]) and hydroxide ions ([OH⁻]) to be negligible at this point.

Explain the buffering action upon the addition of a strong acid

When a strong acid such as HCl is added to the buffer solution, it donates protons (H⁺) to the solution. The added protons react with the acetate ions (CH₃COO⁻) present in the solution, which act as a proton acceptor: \(CH_3COO^- (aq) + H_3O^+(aq) \rightleftharpoons CH_3COOH (aq) + H_2O (l)\) This reaction consumes the added protons and prevents a significant increase in the concentration of H₃O⁺ ions, thus resisting a large change in pH.

Explain the buffering action upon the addition of a strong base

When a strong base such as NaOH is added to the buffer solution, it donates hydroxide ions (OH⁻) to the solution. The added hydroxide ions react with the acetic acid (CH₃COOH) present in the solution, which acts as a proton donor: \(CH_3COOH (aq) + OH^-(aq) \rightleftharpoons CH_3COO^- (aq) + H_2O(l)\) This reaction consumes the added hydroxide ions and prevents a significant increase in the concentration of OH⁻ ions, thus resisting a large change in pH.

Conclusion

The buffering action of a solution containing 0.10 M acetic acid and 0.1 mole of sodium acetate can be explained by the equilibrium between the weak acid and its conjugate base. When a small amount of strong acid or base is added to the buffer, the equilibrium is shifted, consuming the added protons or hydroxide ions and resisting significant changes in pH. ionic equations help to visualize these processes on a molecular level.

Key concepts

Acetic Acid Equilibrium

In chemistry, an equilibrium describes a state where the reactants and products of a reaction are present at concentrations that don't change over time. For acetic acid, this is represented by the reaction:\[ \text{CH}_3\text{COOH} \rightleftharpoons \text{CH}_3\text{COO}^- + \text{H}_3\text{O}^+ \]This means acetic acid partially dissociates into acetate ions and hydronium ions in water. Acetic acid is a weak acid because it does not dissociate completely. This equilibrium can be quantified using its acid dissociation constant, \(K_a\):\[ K_a = \frac{[\text{CH}_3\text{COO}^-][\text{H}_3\text{O}^+]}{[\text{CH}_3\text{COOH}]} \]Understanding this equilibrium helps explain the role acetic acid plays in buffer solutions.

• Acetic acid weakly dissociates, maintaining a supply of both acetic acid and acetate ions.
• Dynamic balance: The reaction can shift to accommodate changes in the system, maintaining equilibrium.
• Key to buffering action: This equilibrium is central to a buffer's ability to resist pH changes.

Buffering Action

Buffering action is the ability of a buffer solution to resist changes in pH when strong acids or bases are added. It relies on the equilibrium between a weak acid and its conjugate base. In our buffer, acetic acid (\(\text{CH}_3\text{COOH}\)) acts as the weak acid, while the acetate ion (\(\text{CH}_3\text{COO}^-\)) from sodium acetate is its conjugate base.When a strong acid like HCl is added, it adds protons (\(\text{H}^+\)). These protons are neutralized by the acetate ions converting into acetic acid, thereby minimizing pH change:\[\text{CH}_3\text{COO}^- + \text{H}^+ \rightarrow \text{CH}_3\text{COOH} \]Similarly, if a strong base like NaOH is added, resulting hydroxide ions (\(\text{OH}^-\)) react with the acetic acid forming acetate ions and water, again minimizing pH impact:\[\text{CH}_3\text{COOH} + \text{OH}^- \rightarrow \text{CH}_3\text{COO}^- + \text{H}_2\text{O} \]Thus, buffers work due to

• Their ability to consume added acids or bases.
• Their partial dissociation allowing for equilibrium shifts.
• Their maintenance of consistent pH levels in solutions.

Conjugate Base

A conjugate base forms when an acid donates a proton (\(\text{H}^+\)). In our buffer, the acetate ion (\(\text{CH}_3\text{COO}^-\)) is the conjugate base of acetic acid (\(\text{CH}_3\text{COOH}\)).Conjugate bases are important because:

• They react with acids. When too much acid is added, the conjugate base can absorb excess \(\text{H}^+\) ions, maintaining equilibrium.
• They provide a balance. Conjugate bases help stabilize the pH by replenishing necessary ions.
• They support buffering. Conjugate bases in buffer solutions ensure minimal pH fluctuation.

In essence, the conjugate base is crucial for the buffering action.

• Acetate ions, as the conjugate base, react with added \(\text{H}^+\) to form acetic acid, lowering \(\text{H}_3\text{O}^+\) increase.
• With strong bases, the formation of more acetate ions helps negate \(\text{OH}^-\) impact.

Ionic Equations

Ionic equations help us visualize chemical reactions by focusing on the ions that actually participate. They simplify understanding of chemical processes, particularly important in solutions like buffers.For example, consider this ionic equation representing a reaction with a strong acid:\[\text{CH}_3\text{COO}^- + \text{H}^+ \rightarrow \text{CH}_3\text{COOH} \]This equation shows how acetate ions neutralize the added \(\text{H}^+\), forming acetic acid.When a strong base is involved:\[\text{CH}_3\text{COOH} + \text{OH}^- \rightarrow \text{CH}_3\text{COO}^- + \text{H}_2\text{O} \]Here, we see acetic acid reacting with hydroxide ions to produce acetate ions and water, thus maintaining equilibrium.Key aspects of ionic equations:

• They highlight the ions responsible for the reactions, making it easier to understand buffering.
• They simplify complex reactions by focusing on the significant ionic interactions.
• By examining these equations, one can see how buffers resist pH changes effectively.