Acid-Base Titrations (First 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 ΔpH/ΔV vs Volume which represents the first derivative (slope) of the pH data (ΔpH/ΔV).

Vb (mL) pH  ΔV (mL) ΔpH Vave (mL) ΔpH/ΔV Vb (mL) pH  ΔV (mL) ΔpH Vave (mL) ΔpH/ΔV
  1.00 3.15 1.00      
15.00
  4.90
1.00
0.150
14.50
0.15
  2.00 3.24
1.00
0.090
  1.50
0.09
16.00
  5.20
1.00
0.300
15.50
0.30
  3.00 3.39
1.00
0.150
  2.50
0.15
16.50
  5.40
0.50
0.200
16.25
0.40
  4.00 3.54
1.00
0.150
  3.50
0.15
17.00
  5.60
0.50
0.200
16.75
0.40
  5.00 3.63
1.00
0.090
  4.50
0.09
17.50
  5.95
0.50
0.350
17.25
0.70
  6.00 3.78
1.00
0.150
  5.50
0.15
18.00
  6.60
0.50
0.650
17.75
1.30
  7.00 3.85
1.00
0.070
  6.50
0.07
18.50
  7.30
0.50
0.700
18.25
1.40
  8.00 3.98
1.00
0.130
  7.50
0.13
18.70
  7.60
0.20
0.300
18.60
1.50
  9.00 4.11
1.00
0.130
  8.50
0.13
18.90
  8.15
0.20
0.550
18.80
2.75
10.00 4.20
1.00
0.090
  9.50
0.09
19.10
  9.95
0.20
1.800
19.00
9.00
10.50 4.26
0.50
0.060
10.25
0.12
19.30
10.50
0.20
0.550
19.20
2.75
11.00 4.31
0.50
0.050
10.75
0.10
20.50
10.90
1.20
0.400
19.90
0.33
11.50 4.39
0.50
0.080
11.25
0.16
21.00
11.80
0.50
0.900
20.75
1.80
12.00 4.47
0.50
0.080
11.75
0.16
21.50
12.20
0.50
0.400
21.25
0.80
13.00 4.60
1.00
0.130
12.50
0.13
22.50
12.30
1.00
0.100
22.00
0.10
14.00 4.75
1.00
0.150
13.50
0.15
23.50
12.35
1.00
0.050
23.00
0.05

When ΔpH/ΔV is at its maximum value (the highest point on the graph), it represents the inflection point of the titration. Note the equivalence point found on the Acid-Base Titrations (Titration Curve) page is in very close agreement with the 19.10 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 (Second Derivative), and Acid-Base Titrations (Gran Plot).

 

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