Final answer:
To create a buffer with a pH of 4.00, 1.74 mL of 0.10 M sodium acetate should be added to 100 mL of 0.10 M acetic acid, as calculated using the Henderson-Hasselbalch equation.
Step-by-step explanation:
To calculate the volume of 0.10 M sodium acetate needed to be added to 100 mL of 0.10 M acetic acid to achieve a buffer with a pH of 4.00, we use the Henderson-Hasselbalch equation. This equation is as follows:
\[pH = pKa + \log \frac{[A^-]}{[HA]}\]
Where pH is the desired pH, pKa is the acid dissociation constant for acetic acid, [A^-] is the concentration of the acetate ion, and [HA] is the concentration of acetic acid.
For acetic acid, pKa is approximately 4.76. We rearrange the equation to solve for \([A^-]\):
\[[A^-] = [HA] \times 10^{(pH-pKa)}\]
Using the desired pH of 4.00, we find:
\[[A^-] = 0.10 \times 10^{(4.00 - 4.76)} = 0.100 \times 10^{-0.76} \approx 0.0174 M\]
Since the sodium acetate concentration is also 0.10 M, we can determine the volume needed:
\[V_{acetate} = \frac{moles\,of\,acetate}{concentration\,of\,sodium\,acetate}\]
\[V_{acetate} = \frac{0.0174 \times 0.100\,L}{0.10 M} = 0.00174\,L\]
To achieve a pH of 4.00, we thus need to add 0.00174 L or 1.74 mL of 0.10 M sodium acetate to the solution.