A buffer contains 0.10 mol of acetic acid and 0.13 mol of sodium acetate in 1.00 L. (a) What is the pH of this buffer?

Verified step by step guidance

1. Identify the components of the buffer: acetic acid (CH₃COOH) and sodium acetate (CH₃COONa).
2. Use the Henderson-Hasselbalch equation for buffer solutions: \( \text{pH} = \text{pK}_a + \log \left( \frac{[\text{A}^-]}{[\text{HA}]} \right) \), where \([\text{A}^-]\) is the concentration of the acetate ion and \([\text{HA}]\) is the concentration of acetic acid.
3. Find the \(\text{pK}_a\) of acetic acid, which is approximately 4.76.
4. Calculate the concentrations of acetic acid and acetate ion: \([\text{HA}] = 0.10 \text{ M}\) and \([\text{A}^-] = 0.13 \text{ M}\).
5. Substitute the values into the Henderson-Hasselbalch equation to find the pH: \( \text{pH} = 4.76 + \log \left( \frac{0.13}{0.10} \right) \).

Key Concepts

Buffer Solutions

A buffer solution is a system that resists changes in pH upon the addition of small amounts of acid or base. It typically consists of a weak acid and its conjugate base, or a weak base and its conjugate acid. In this case, acetic acid (a weak acid) and sodium acetate (its conjugate base) form a buffer that helps maintain a stable pH.

Henderson-Hasselbalch Equation

The Henderson-Hasselbalch equation is a mathematical formula used to calculate the pH of a buffer solution. It is expressed as pH = pKa + log([A-]/[HA]), where pKa is the negative logarithm of the acid dissociation constant, [A-] is the concentration of the conjugate base, and [HA] is the concentration of the weak acid. This equation is essential for determining the pH of the given buffer.

Acetic Acid and Sodium Acetate

Acetic acid (CH3COOH) is a weak acid that partially dissociates in solution, while sodium acetate (CH3COONa) is its salt that fully dissociates to provide acetate ions (CH3COO-). The presence of both in the buffer allows for the equilibrium between the acid and its conjugate base, which is crucial for maintaining the pH when acids or bases are added.