Final answer:
To create a buffer with a pH of 4.94 from a 0.25 M acetic acid solution using the Henderson-Hasselbalch equation, 0.198 moles of sodium acetate needs to be added.
Step-by-step explanation:
The question asks how many moles of sodium acetate must be added to 500 mL of 0.25 M acetic acid solution to produce a buffer with a pH of 4.94. The pKa of acetic acid is 4.74. To solve this, we use the Henderson-Hasselbalch equation:
pH = pKa + log ([A-]/[HA])
Where [A-] is the concentration of the acetate ion and [HA] is the concentration of acetic acid. To create a buffer with a pH of 4.94, we rearrange the equation to solve for the [A-] to [HA] ratio.
4.94 = 4.74 + log ([A-]/[HA])
[A-]/[HA] = 10^(4.94 − 4.74)
[A-]/[HA] = 10^0.20 ≈ 1.58
The initial concentration of acetic acid ([HA]) is 0.25 M. To find the moles of acetate ([A-]), we use the volume of the solution (0.5 L) and the calculated ratio:
Moles of acetic acid = 0.25 M * 0.5 L = 0.125 moles
[A-] = 1.58 * [HA]
[A-] = 1.58 * 0.125 moles
[A-] = 0.198 moles
Therefore, to achieve the desired pH, 0.198 moles of sodium acetate must be added to the acetic acid solution.