Acid-Base Titrations (Second Derivative)

The following data values are based on the sample data displayed on the Acid-Base Titrations (Titration Curve) page. The data is used to graph Δ(ΔpH/ΔV)/ΔV vs Volume which represents the second derivative of the pH data (Δ(ΔpH/ΔV)/ΔV).

Vave (mL) ΔpH/ΔV  ΔV (mL) Δ(ΔpH) Vave (mL) Δ(ΔpH/ΔV)/ΔV Vave (mL) ΔpH/ΔV  ΔV (mL) Δ(ΔpH) Vave (mL) Δ(ΔpH/ΔV)/ΔV
   1.50 0 01.00 0 0 0
15.50
  4.90
1.00
     0.15
15.00
   0.15
   2.50
3.24
1.00
0
 
0
16.25
  6.93
0.75
     2.03
15.88
   2.71
   3.50
3.39
1.00
   0.15
  3.00
  0.15
16.75
10.80
0.50
     3.87
16.50
   7.73
   4.50
3.54
1.00
   0.15
  4.00
  0.15
17.25
11.20
0.50
     0.40
17.00
   0.80
   5.50
3.63
1.00
   0.09
  5.00
  0.09
17.75
11.90
0.50
     0.70
17.50
   1.40
   6.50
3.78
1.00
   0.15
  6.00
  0.15
18.25
13.20
0.50
     1.30
18.00
   2.60
   7.50
3.85
1.00
   0.07
  7.00
  0.07
18.60
20.86
0.35
     7.66
18.43
 21.88
   8.50
3.98
1.00
   0.13
  8.00
  0.13
18.80
38.00
0.20
   17.14
18.70
 85.71
   9.50
4.11
1.00
   0.13
  9.00
  0.13
19.00
40.75
0.20
     2.75
18.90
 13.75
 10.25
5.60
0.75
   1.49
  9.88
  1.99
19.20
49.75
0.20
     9.00
19.10
 45.00
 10.75
8.52
0.50
   2.92
10.50
  5.84
19.90
15.00
0.70
 -34.75
19.55
-49.64
 11.25
8.62
0.50
   0.10
11.00
  0.20
20.75
12.82
0.85
 - 2.18
20.33
- 2.56
 11.75
8.78
0.50
   0.16
11.50
  0.32
21.25
23.60
0.50
 10.78
21.00
 21.55
 12.50
5.96
0.75
- 2.82
12.13
- 3.76
22.00
16.27
0.75
- 7.33
21.63
- 9.78
 13.50
4.60
1.00
- 1.36
13.00
- 1.36
23.00
12.30
1.00
- 3.97
22.50
- 3.97
 14.50
4.75
1.00
   0.15
14.00
  0.15
0 0 0 0 0
0

The equivalence point corresponds to the volume at which the second derivative is zero. Note the equivalence point found on the  Acid-Base Titrations (Titration Curve) page is in close agreement with the 19.60 mL.

This is not the only method to determine the equivalence point, so be sure to check out Acid-Base Titrations (Titration Curve), Acid-Base Titrations (First Derivative), and Acid-Base Titrations (Gran Plot).

 

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