A solution of an unknown weak acid, HA, is titrated with 0.100 M NaOH solution. The

equivalence point is achieved when 36.12 mL of NaOH have been added. After the
equivalence point is reached, 18.06 mL of 0.100 M HCl are added to the solution and the pH
at that point is found to be 5.20. What is the pKa of this unknown acid?

If I didn't mess up somewhere the pKa = 5.20. Interesting problem.

mmols NaOH added = 36.12 x 0.1 = 3.612
...........HA + NaOH ==> NaA + H2O
So at the equivalence point you have 3.612 mmols NaA in solution.

Now you add 18.06 mL x 0.1M = 1.806 mmols
..........A^- + H^+ ==> HA
I........3.612...0......0
add............1.806.......
C......-1.806.-1.806....+1.806
E........1.806....0.....+1.806

Use the Henderson-Hasselbalch equation and solve for pKa
5.20 = pKa + log (1.806)/(1.806)
pKa = ?

Thank you very much!!! Now it makes sense

Excellent job! Thanks a lot

To determine the pKa of the unknown acid HA, we need to follow a step-by-step process. Here's how we can approach this:

Step 1: Determine the number of moles of NaOH added at the equivalence point.
To do this, we use the concentration of the NaOH solution and the volume of NaOH added at the equivalence point. Given that the NaOH solution has a concentration of 0.100 M and 36.12 mL of NaOH is added, we can calculate the number of moles of NaOH using the formula:

moles of NaOH = concentration x volume
= 0.100 M x 0.03612 L

Step 2: Calculate the number of moles of HCl that react with the remaining unreacted NaOH.
Since NaOH and HCl react in a 1:1 ratio, the moles of HCl that react will be the same as the moles of unreacted NaOH from the previous step.

moles of HCl = moles of NaOH
= 0.100 M x 0.03612 L

Step 3: Determine the initial number of moles of the unknown acid HA.
At the equivalence point, all of the moles of NaOH react with the moles of HA. Therefore, the initial number of moles of HA can be calculated as:

moles of HA = moles of NaOH
= 0.100 M x 0.03612 L

Step 4: Calculate the concentration of the unknown acid HA in the solution.
To calculate the concentration of HA, we need to consider the total volume of the solution at the equivalence point. The volume of NaOH added at the equivalence point was 36.12 mL. We also need to account for the volume of HCl added after the equivalence point, which is 18.06 mL. Thus, the total volume is:

total volume = volume of NaOH added + volume of HCl added
= 0.03612 L + 0.01806 L

Step 5: Determine the concentration of HA.
Using the total volume and the number of moles of HA calculated previously, we can calculate the concentration of HA using the following formula:

concentration of HA = moles of HA / total volume

Step 6: Calculate the pKa value of the unknown acid HA.
Finally, we can determine the pKa of HA by using the Henderson-Hasselbalch equation, which relates the pH, pKa, and the concentrations of the acid and its conjugate base:

pH = pKa + log([A-] / [HA])

Given that the pH at the point of adding HCl is 5.20 and we have the concentration of HA, we can rearrange the Henderson-Hasselbalch equation to solve for pKa:

pKa = pH - log([A-] / [HA])

In this case, [A-] refers to the concentration of the conjugate base, which is the remaining concentration of unreacted NaOH. It can be calculated as:

[A-] = moles of NaOH / total volume

By substituting the known values into the equation, we can calculate the pKa of the unknown acid HA.