When a 30 mM aq solution of sodium acetate was prepared in the lab it had a pH of 8.8. Calculate the amount of acetic acid (in g) to be added to 0.5 L of this sodium acetate solution in order to bring its pH to the target value of 5.00.
To calculate the amount of acetic acid needed to adjust the pH of the sodium acetate solution, we need to understand the acid-base equilibrium involved. Sodium acetate is the conjugate base of acetic acid, so adding acetic acid to the solution will increase the concentration of acetic acid and shift the equilibrium towards the acid form.
To find the amount of acetic acid needed, we can use the Henderson-Hasselbalch equation:
pH = pKa + log([A-]/[HA])
Where pH is the target value of 5.00, pKa is the dissociation constant of acetic acid (which is approximately 4.74), [A-] is the concentration of the acetate ion (which is equal to 30 mM in this case), and [HA] is the concentration of acetic acid we want to find.
1. First, let's convert the concentration of acetate ion from mM to moles per liter (M):
[A-] = 30 mM = 0.030 M
2. Now, we can rearrange the Henderson-Hasselbalch equation to solve for [HA]:
[HA] = 10^(pH - pKa) * [A-]
[HA] = 10^(5.00 - 4.74) * 0.030
[HA] = 0.303 * 0.030
[HA] = 0.00909 M
3. Finally, we multiply the concentration of acetic acid by the volume of the sodium acetate solution (0.5 L) to find the amount of acetic acid needed in grams:
Amount of acetic acid (g) = [HA] * Volume
Amount of acetic acid (g) = 0.00909 M * 0.5 L * 60.05 g/mol
Amount of acetic acid (g) = 0.2726 g
Therefore, approximately 0.2726 grams of acetic acid should be added to 0.5 L of the sodium acetate solution to bring its pH to the target value of 5.00.