Final answer:
The pH of the buffer solution consisting of 0.20 M CH₃COOH and 0.20 M NaCH₃CO₂ with a pKa of 4.75 for acetic acid is 4.75, as predicted by the Henderson-Hasselbalch equation when the concentrations of the weak acid and its conjugate base are equal.
Step-by-step explanation:
The pH value of an aqueous buffer solution containing 0.20 M CH₃COOH (acetic acid) and 0.20 M NaCH₃CO₂ (sodium acetate) can be predicted using the Henderson-Hasselbalch equation:
pH = pKa + log ([A-]/[HA])
Where pKa is the acid dissociation constant of acetic acid, [A-] is the concentration of the acetate ion, and [HA] is the concentration of acetic acid.
Given that the pKa of CH₃COOH is 4.75 and the concentrations of both the acid and its conjugate base are equal (0.20 M), the pH of the buffer solution is 4.75.
In this buffer system, we have a weak acid (CH₃COOH) and its conjugate base (NaCH₃CO₂), both at the same concentration. According to the Henderson-Hasselbalch equation, when the concentrations of the weak acid and its conjugate base are equal, the pH of the solution is equal to the pKa of the weak acid. Since the given pKa value for acetic acid is 4.75, and the concentrations of CH₃COOH and NaCH₃CO₂ are both 0.20 M, we can directly infer that the pH of this buffer solution will also be 4.75, reflecting the pKa of acetic acid. This relationship is helpful for creating buffers with a desired pH and for understanding how buffers work in general. Buffers are important for maintaining a stable pH level in many biological and chemical systems.