Write the equation that shows how a buffer made by dissolving CH₃COOH and CH₃COO⁻Na⁺ in water prevents the pH of a solution from changing appreciably when
a. a small amount of H⁺ is added to the solution.
b. a small amount of HO⁻ is added to the solution.

Verified step by step guidance

1. Step 1: Understand the concept of a buffer solution. A buffer solution resists changes in pH when small amounts of acid (H⁺) or base (OH⁻) are added. In this case, the buffer is composed of acetic acid (CH₃COOH, a weak acid) and its conjugate base, acetate ion (CH₃COO⁻), provided by CH₃COONa.
2. Step 2: Write the equilibrium reaction for acetic acid in water: CH₃COOH ⇌ CH₃COO⁻ + H⁺. This equilibrium shows how acetic acid can donate protons (H⁺) and how acetate ion can accept protons.
3. Step 3: Address part (a): When a small amount of H⁺ is added to the solution, the acetate ion (CH₃COO⁻) reacts with the added H⁺ to form acetic acid (CH₃COOH). The reaction is: CH₃COO⁻ + H⁺ → CH₃COOH. This prevents the pH from decreasing significantly.
4. Step 4: Address part (b): When a small amount of OH⁻ is added to the solution, the acetic acid (CH₃COOH) reacts with the OH⁻ to form water and acetate ion (CH₃COO⁻). The reaction is: CH₃COOH + OH⁻ → CH₃COO⁻ + H₂O. This prevents the pH from increasing significantly.
5. Step 5: Summarize the buffer action: The buffer works by utilizing the equilibrium between CH₃COOH and CH₃COO⁻. When H⁺ is added, CH₃COO⁻ neutralizes it, and when OH⁻ is added, CH₃COOH neutralizes it. This dynamic equilibrium maintains the pH of the solution within a narrow range.

Key Concepts

Buffer Solutions

Buffer solutions are mixtures that resist changes in pH when small amounts of acid or base are added. They typically consist of a weak acid and its conjugate base, or a weak base and its conjugate acid. In this case, acetic acid (CH3COOH) and its conjugate base acetate (CH3COO−) form a buffer that stabilizes the pH of the solution.

Weak Acid and Conjugate Base Reaction

When a weak acid like acetic acid is present in a solution, it can donate protons (H+) to neutralize added bases. Conversely, the conjugate base (acetate ion) can accept protons to neutralize added acids. This dynamic equilibrium allows the buffer to maintain a relatively constant pH despite the addition of small amounts of H+ or OH−.

Henderson-Hasselbalch Equation

The Henderson-Hasselbalch equation relates the pH of a buffer solution to the concentration of the weak acid and its conjugate base. It is expressed as pH = pKa + log([A−]/[HA]), where [A−] is the concentration of the conjugate base and [HA] is the concentration of the weak acid. This equation helps predict how the pH will change with the addition of acids or bases.