Final answer:
The mass of sodium acetate added to 500.0 ml of 0.200 M acetic acid to create a pH 5.00 buffer is determined using the Henderson-Hasselbalch equation, followed by conversion of molarity to mass using the molar mass of sodium acetate.
Step-by-step explanation:
To calculate the mass of sodium acetate (NaCH3CO2) that must be added to 500.0 ml of 0.200 M acetic acid to form a pH 5.00 buffer solution, we need to use the Henderson-Hasselbalch equation:
pH = pKa + log([A-]/[HA])
where pKa is the acid dissociation constant of acetic acid (about 4.76), [A-] is the acetate ion concentration, and [HA] is the acetic acid concentration.
First, we need to rearrange the equation to solve for the acetate ion concentration [A-]:
[A-] = [HA] * 10(pH - pKa)
Since the [HA] (acetic acid concentration) is given as 0.200 M, and the desired pH is 5.00:
[A-] = 0.200 M * 10(5.00 - 4.76)
Calculating the [A-] gives us the molarity of sodium acetate required. Then, we need to convert this molarity to mass using the molar mass of sodium acetate (82.03 g/mol for anhydrous NaCH3CO2, different if hydrated).
Mass of sodium acetate = [A-] * Volume * Molar Mass
With the volume of the solution in liters and the calculated molarity [A-], we can find the mass of sodium acetate required to create the buffer.