Final answer:
The pH of a solution containing 4 parts acetic acid to 1 part sodium acetate is calculated using the Henderson-Hasselbalch equation. Given the pKa of acetic acid is 4.76, the pH calculates to approximately 4.16, with the closest provided answer being 4.38.
Step-by-step explanation:
The pH of a solution that contains 4 parts acetic acid and 1 part sodium acetate is closely related to the buffer capacity of this mixture. The acetic acid (CH3COOH) and its conjugate base, the acetate anion (CH3COO-), combine to form a buffer solution. Using the Henderson-Hasselbalch equation, pH = pKa + log([A-]/[HA]), where pKa is the acid dissociation constant for acetic acid, [A-] is the concentration of the acetate ion, and [HA] is the concentration of acetic acid, we can calculate the pH.
Given a pKa of 4.76 for acetic acid and a ratio of 4 parts acetic acid to 1 part sodium acetate, the solution's pH is pKa + log(1/4), which equals 4.76 + log(0.25) = 4.76 - 0.60 = 4.16. Therefore, the closest option provided is (b) 4.38.