Final answer:
To prepare a buffer solution with a concentration of 0.05 M and a final volume of 1 L, the amounts of acetic acid and sodium acetate are calculated using the Henderson-Hasselbalch equation. The correct amounts are Acetic acid: 21 g and Sodium acetate: 61 g.
Step-by-step explanation:
To prepare a buffer solution of acetic acid and sodium acetate with a concentration of 0.05 M and a final volume of 1 L, you need to calculate the amount and mass of acetic acid and sodium acetate required. The pH of the buffer is expected to be 5.0, and the pKa of acetic acid is 4.74.
A buffer solution consists of a weak acid and its conjugate base. The Henderson-Hasselbalch equation can be used to calculate the ratio of the acid to base:
pH = pKa + log([conjugate base]/[acid])
In this case, we want the pH to be 5.0. Plugging in the values, we get:
5.0 = 4.74 + log([sodium acetate]/[acetic acid])
Solving for [sodium acetate]/[acetic acid], we find that the ratio should be approximately 1.778. Since the total volume of the buffer is 1 L, we can calculate the amount and mass of each component:
Amount of acetic acid = 0.05 M * x L = 0.05x mol
Amount of sodium acetate = 0.05 M * (1 - x) L = 0.05(1 - x) mol
Setting up the ratio equation:
1.778 = [0.05(1 - x)] / [0.05x]
Simplifying the equation, we get:
1.778 = (1 - x) / x
By solving this equation, we find that x is equal to approximately 0.359. Therefore, the amount of acetic acid required is 0.05 * 0.359 = 0.01795 mol or approximately 21 g (using the molar mass of acetic acid), and the amount of sodium acetate required is 0.05 * (1 - 0.359) = 0.02405 mol or approximately 61 g (using the molar mass of sodium acetate).
So, the correct answer is: Acetic acid: 21 g, Sodium acetate: 61 g (option a)