1. Titration curve
Typical ph titration of a weak monoprotic acid vs strong base

2. Step 1
Draw the best smooth line through as many points as possible extending the line in the general trend of the titration.

3. Step 2
Draw the line through the vertical region of the graph. Bisect this line by measuring the distance between the two original lines. The equivalence point is the center point on this line.

4. Step 3
At the volume of one-half the equivalence point volume, the pH = pKa

5. ΔpH/Δvolume vs. average volume
First derivative plot for determining the equivalence point of a titration.

6. Calculating the First Derivative
Volume of NaOH pH
Average Volume
34.68 mL
6.49
34.78 mL
6.53
35.08 mL
8.40

7. Δ2pH/Δ2volume vs. average volume
Change in slope from first derivative platted against change in the average volume

8. Calculating the Second Derivative
Average Volume
Average of the Average Volume of NaOH reacted
34.73
0.4
34.93
6.23

9. Calculating the pKa Mathematically
calculate the pH from a variation in the Henderson-Hasselbach equation
data in the table is taken from the pH titration studied earlier which has an equivalence point at 10.0 mL. Using the first data point in the table above, the pKa calculates to be 4.75 with an average value of 4.76.
Volume pH
pKa
2.15
4.00
4.75
3.30
4.20
4.74
4.61
4.50
5.00
6.93
4.82