To calculate the pH of the solution after the addition of KOH, we first need to determine the moles of acetic acid and the moles of KOH that reacted.
1. Calculate the moles of acetic acid:
The volume of acetic acid solution is given as 22 mL, which we can convert to liters:
22 mL รท 1000 mL/L = 0.022 L
Now, using the molarity of acetic acid (0.37 mol/L), we can calculate the moles of acetic acid:
Moles of acetic acid = Molarity ร Volume
Moles of acetic acid = 0.37 mol/L ร 0.022 L
2. Calculate the moles of KOH:
The volume of KOH solution added is given as roughly 18 mL, which we can also convert to liters:
18 mL รท 1000 mL/L = 0.018 L
Using the molarity of KOH (0.29 mol/L), we can calculate the moles of KOH:
Moles of KOH = Molarity ร Volume
Moles of KOH = 0.29 mol/L ร 0.018 L
3. Determine the limiting reactant:
To determine which reactant is limiting, compare the moles of KOH and acetic acid. The reactant with fewer moles is the limiting reactant.
In this case, it appears that KOH is the limiting reactant, as it will be completely consumed before the acetic acid.
4. Calculate the moles of acetic acid remaining:
Since KOH is the limiting reactant, all of the KOH will react with the acetic acid. Therefore, the remaining moles of acetic acid will be:
Moles of acetic acid remaining = Initial moles of acetic acid - Moles of KOH reacted
5. Calculate the concentration of acetic acid after the reaction:
The volume of the solution does not change, so the new concentration can be calculated using the moles of acetic acid remaining and the volume of the solution:
Concentration of acetic acid = Moles of acetic acid remaining / Volume of solution
6. Calculate the pKa and then the pH:
The Ka of acetic acid is given as 1.8 ร 10^(-5), so the pKa can be calculated as:
pKa = -log(Ka)
Finally, the pH can be calculated using the Henderson-Hasselbalch equation:
pH = pKa + log([concentration of acetic acid] / [concentration of acetate ion])
In this case, since acetic acid is a weak acid, most of it does not dissociate into acetate ions, and the [concentration of acetate ion] can be assumed to be negligible compared to the [concentration of acetic acid].
By plugging in the values, you should be able to calculate the pH of the solution after the addition of roughly 18 mL of KOH.