Final answer:
The pH of a 0.1 M solution of sodium acetate can be estimated using the Henderson-Hasselbalch equation. Since sodium acetate produces acetate ions in solution and acts as a weak base, the pH of the solution will be higher than 7. Exact pH calculation would need additional data on the acetate ion's hydrolysis.
Step-by-step explanation:
To calculate the pH of a 0.1 M solution of sodium acetate when the pKa of acetic acid is 4.76, we can use the Henderson-Hasselbalch equation. This equation relates the pH of a buffer solution to the pKa and the concentrations of the acid and its conjugate base. Since sodium acetate is a salt that dissociates to produce acetate ions (the conjugate base of acetic acid) and sodium ions, we can assume that the concentration of acetate ions is the same as the initial concentration of sodium acetate, which is 0.1 M.
The Henderson-Hasselbalch equation is given by:
pH = pKa + log([A-]/[HA])
Since we don't have the concentration of acetic acid (HA) explicitly, we can make the assumption (valid when dealing with a salt of a weak acid) that the solution is essentially a buffer system where the concentration of [A-] (acetate) is equal to sodium acetate concentration. However, because sodium acetate is a weak base, the solution will be basic and the pH will be higher than 7. The exact pH would require additional data for a precise calculation, including the degree of hydrolysis for the acetate ion.