The data for this homework assignment can be found her: Titration Curve Data.xlsx Download Titration Curve Data.xlsx. Please note that there are 3 tabs for the 3 sets of data.

Plot the pH of the solution vs. volume of NaOH added in an Excel spreadsheet and graph. Make a scatter plot with smoothed lines connecting the points. This should give a titration curve.

Using the pH and V_NaOH data from your titrations, calculate ΔpH/ΔV_NaOH and V_NaOH first derivative values. Create a scatter plot with smoothed lines connecting the points. This is your first derivative plot.

For each set of data, identify the equivalence points from the plot maxima. Label the equivalence points (volume and pH) on your graphs.

Determine the pKa values for your weak acid and weak base equivalence points using the pH obtained at the half equivalence point for each graph. Label the pKa’s (and volume) on your graphs.

Using derivatives to find the endpoint of a titration

A first derivative of any function measures the slope of that function at any given point. On a titration curve, the slope is at its maximum at the equivalence point. It is very difficult to pinpoint the exact equivalence point on a titration curve, but by plotting the change in pH/change in NaOH volume (the first derivative of pH as a function of NaOH added) vs. V_NaOH, the equivalence point is identified by a sharp maximum in the plot. Because first derivative data involve the changes in pH and volume between data points, you will always have one less first derivative points than you have titration data points. See the example data below:

TITRATION DATA

FIRST DERIVATIVE DATA

SECOND DERIVATIVE DATA

pH

V_NaOH (mL)

ΔpH/ΔV_NaOH

V_NaOH (mL)

Δ (ΔpH/ΔV_NaOH)

V_NaOH (mL)

4.56

26.22

4.66

26.38

0.625

26.30

4.83

26.45

2.43

26.42

1.805

26.42

5.33

27.11

0.758

26.78

−1.672

26.78

Note that because there are four titration data points in the above example, there will be three first derivative points. The first two titration data points are used to compute the 1^st first derivative point. The 2^nd and 3^rd titration data points are used to compute the 2^nd first derivative point, and the 3^rd and 4^th titration data points are used to compute the 3^rd first derivative points.

Here is how the 1^st first derivative points were calculated. ΔpH/ΔV_NaOH is equal to the change in pH (4.66 - 4.56 = 0.10) divided by the change in NaOH volume (26.38 - 26.22 = 0.16). The V_NaOH value calculated in the first derivative is simply the average of the two titration V_NaOH values used. The endpoint can be seen by the volume of titrant corresponding to the maximum value on the graph.

Second derivatives can also be used to determine the equivalence points of a titration. These are constructed in a similar manner as the first derivative analysis. However, the endpoint in this instance is found by determining the volume at which the second derivative curve crosses the x-axis.

Transcribed Image Text:Volume (mL) 01 0.02 0.04 0.06 0.09 0.11 Volume (mL) 0.02 0.09 0.16 0.23 0.32 0.42 pH 10.4 10.3 pH 3.3 3.4 3.5 3.6 3.7 3.8 25.00 9.0 12.50 12.50 4.7 25.00 25.00 25.01 9.1 10.2 10.1 10.0 9.9 4.6 9.2 12.51 4.5 9.3 0.15 0.19 1.52 3.03 1.1 1.2 9.8 9.7 9.6 9.5 9.4 9.3 9.2 12.51 4.4 4.3 4.2 0.55 0.70 0.89 1.12 1.40 1.74 2.16 2.66 3.26 3.97 4.81 3.9 4.0 4.1 4.2 4.3 4.4 4.5 4.6 4.7 25.01 9.4 024 0.30 0.38 0.48 0.60 12.52 12.52 25.01 9.5 25.02 9.6 1.3 1.4 4.47 12.53 4.1 25.02 9.7 12.54 4.0 25.03 25.04 25.05 5.79 0.75 0.92 9.8 9.1 9.0 8.9 8.8 12.55 12.56 3.9 3.8 9.9 1.14 6.98 1.5 4.8 4.9 1.41 10.0 1.72 2.09 2.52 3.02 3.58 4.19 8.7 8.6 5.77 6.85 8.05 9.36 10.74 12.17 13.61 15.01 16.36 8.04 1.6 12.57 3.7 5.0 5.1 25.06 10.1 12.59 3.6 8.5 8.4 8.3 8.2 5.2 5.3 5.4 5.5 5.6 5.7 5.8 25.08 25.10 10.2 10.3 8.95 9.73 1.7 12.62 3.5 1.8 12.65 3.4 25.13 25.16 10.4 4.86 5.56 6.27 6.99 7.69 8.35 8.96 8.1 8.0 7.9 7.8 7.7 7.6 7.5 12.69 12.74 3.3 10.5 10.40 10.95 1.9 2.0 3.2 25.20 25.25 10.6 17.61 18.75 19.77 5.9 6.0 12.80 3.1 10.7 6.1 6.2 6.3 6.4 6.5 6.6 6.7 6.8 12.88 3.0 25.32 10.8 11.40 11.78 20.66 21.42 22.07 22.62 23.07 2.1 9.51 10.00 10.43 10.80 7.4 7.3 7.2 7.1 12.98 2.9 25.40 10.9 2.2 13.11 2.8 25.50 11.0 13.28 2.7 25.64 25.81 11.1 11.11 11.37 11.59 11.76 11.91 12.02 12.12 7.0 6.9 6.8 6.7 6.6 6.5 6.4 23.44 23.75 13.49 2.6 11.2 23.99 24.19 24.36 6.9 7.0 7.1 13.77 2.5 26.02 26.29 11.3 14.12 2.4 11.4 24.49 24.59 24.67 24.74 24.79 7.2 7.3 7.4 7.5 7.6 7.7 14.59 2.3 26.63 11.5 11.6 12.20 12.26 12.31 12.35 6.3 6.2 6.1 6.0 15.21 2.2 27.07 16.04 17.19 2.1 27.64 11.7 24.84 2.0 28.37 11.8 12.38 12.40 12.42 12.44 5.9 5.8 5.7 5.6 5.5 5.4 5.3 24.87 24.90 7.8 7.9 18.81 1.9 29.31 30.56 11.9 24.92 24.93 24.95 24.96 24.97 24.98 24.98 8.0 8.1 8.2 8.3 8.4 8.5 8.6 8.7 8.8 21.20 1.8 12.0 12.45 12.46 12.47 12.48 12.48 12.49 12.49 32.20 12.1 34.42 12.2 5.2 5.1 5.0 4.9 37.46 12.3 24.99 24.99 41.77 12.4 12.50 4.8 24.99 8.9

Question

The data for this homework assignment can be found her: Titration Curve Data.xlsx Download Titration Curve Data.xlsx. Please note that there are 3 tabs for the 3 sets of data.

Plot the pH of the solution vs. volume of NaOH added in an Excel spreadsheet and graph. Make a scatter plot with smoothed lines connecting the points. This should give a titration curve.
Using the pH and V_NaOH data from your titrations, calculate ΔpH/ΔV_NaOH and V_NaOH first derivative values. Create a scatter plot with smoothed lines connecting the points. This is your first derivative plot.
For each set of data, identify the equivalence points from the plot maxima. Label the equivalence points (volume and pH) on your graphs.
Determine the pKa values for your weak acid and weak base equivalence points using the pH obtained at the half equivalence point for each graph. Label the pKa’s (and volume) on your graphs.

Using derivatives to find the endpoint of a titration

A first derivative of any function measures the slope of that function at any given point. On a titration curve, the slope is at its maximum at the equivalence point. It is very difficult to pinpoint the exact equivalence point on a titration curve, but by plotting the change in pH/change in NaOH volume (the first derivative of pH as a function of NaOH added) vs. V_NaOH, the equivalence point is identified by a sharp maximum in the plot. Because first derivative data involve the changes in pH and volume between data points, you will always have one less first derivative points than you have titration data points. See the example data below:

TITRATION DATA	FIRST DERIVATIVE DATA	SECOND DERIVATIVE DATA
pH	V_NaOH (mL)	ΔpH/ΔV_NaOH	V_NaOH (mL)	Δ (ΔpH/ΔV_NaOH)	V_NaOH (mL)
4.56	26.22
4.66	26.38	0.625	26.30
4.83	26.45	2.43	26.42	1.805	26.42
5.33	27.11	0.758	26.78	−1.672	26.78

Note that because there are four titration data points in the above example, there will be three first derivative points. The first two titration data points are used to compute the 1^st first derivative point. The 2^nd and 3^rd titration data points are used to compute the 2^nd first derivative point, and the 3^rd and 4^th titration data points are used to compute the 3^rd first derivative points.

Here is how the 1^st first derivative points were calculated. ΔpH/ΔV_NaOH is equal to the change in pH (4.66 - 4.56 = 0.10) divided by the change in NaOH volume (26.38 - 26.22 = 0.16). The V_NaOH value calculated in the first derivative is simply the average of the two titration V_NaOH values used. The endpoint can be seen by the volume of titrant corresponding to the maximum value on the graph.

Second derivatives can also be used to determine the equivalence points of a titration. These are constructed in a similar manner as the first derivative analysis. However, the endpoint in this instance is found by determining the volume at which the second derivative curve crosses the x-axis.

Volume
(mL)
01
0.02
0.04
0.06
0.09
0.11
Volume
(mL)
0.02
0.09
0.16
0.23
0.32
0.42
pH
10.4
10.3
pH
3.3
3.4
3.5
3.6
3.7
3.8
25.00
9.0
12.50
12.50
4.7
25.00
25.00
25.01
9.1
10.2
10.1
10.0
9.9
4.6
9.2
12.51
4.5
9.3
0.15
0.19
1.52
3.03
1.1
1.2
9.8
9.7
9.6
9.5
9.4
9.3
9.2
12.51
4.4
4.3
4.2
0.55
0.70
0.89
1.12
1.40
1.74
2.16
2.66
3.26
3.97
4.81
3.9
4.0
4.1
4.2
4.3
4.4
4.5
4.6
4.7
25.01
9.4
024
0.30
0.38
0.48
0.60
12.52
12.52
25.01
9.5
25.02
9.6
1.3
1.4
4.47
12.53
4.1
25.02
9.7
12.54
4.0
25.03
25.04
25.05
5.79
0.75
0.92
9.8
9.1
9.0
8.9
8.8
12.55
12.56
3.9
3.8
9.9
1.14
6.98
1.5
4.8
4.9
1.41
10.0
1.72
2.09
2.52
3.02
3.58
4.19
8.7
8.6
5.77
6.85
8.05
9.36
10.74
12.17
13.61
15.01
16.36
8.04
1.6
12.57
3.7
5.0
5.1
25.06
10.1
12.59
3.6
8.5
8.4
8.3
8.2
5.2
5.3
5.4
5.5
5.6
5.7
5.8
25.08
25.10
10.2
10.3
8.95
9.73
1.7
12.62
3.5
1.8
12.65
3.4
25.13
25.16
10.4
4.86
5.56
6.27
6.99
7.69
8.35
8.96
8.1
8.0
7.9
7.8
7.7
7.6
7.5
12.69
12.74
3.3
10.5
10.40
10.95
1.9
2.0
3.2
25.20
25.25
10.6
17.61
18.75
19.77
5.9
6.0
12.80
3.1
10.7
6.1
6.2
6.3
6.4
6.5
6.6
6.7
6.8
12.88
3.0
25.32
10.8
11.40
11.78
20.66
21.42
22.07
22.62
23.07
2.1
9.51
10.00
10.43
10.80
7.4
7.3
7.2
7.1
12.98
2.9
25.40
10.9
2.2
13.11
2.8
25.50
11.0
13.28
2.7
25.64
25.81
11.1
11.11
11.37
11.59
11.76
11.91
12.02
12.12
7.0
6.9
6.8
6.7
6.6
6.5
6.4
23.44
23.75
13.49
2.6
11.2
23.99
24.19
24.36
6.9
7.0
7.1
13.77
2.5
26.02
26.29
11.3
14.12
2.4
11.4
24.49
24.59
24.67
24.74
24.79
7.2
7.3
7.4
7.5
7.6
7.7
14.59
2.3
26.63
11.5
11.6
12.20
12.26
12.31
12.35
6.3
6.2
6.1
6.0
15.21
2.2
27.07
16.04
17.19
2.1
27.64
11.7
24.84
2.0
28.37
11.8
12.38
12.40
12.42
12.44
5.9
5.8
5.7
5.6
5.5
5.4
5.3
24.87
24.90
7.8
7.9
18.81
1.9
29.31
30.56
11.9
24.92
24.93
24.95
24.96
24.97
24.98
24.98
8.0
8.1
8.2
8.3
8.4
8.5
8.6
8.7
8.8
21.20
1.8
12.0
12.45
12.46
12.47
12.48
12.48
12.49
12.49
32.20
12.1
34.42
12.2
5.2
5.1
5.0
4.9
37.46
12.3
24.99
24.99
41.77
12.4
12.50
4.8
24.99
8.9

Accepted Answer

The objective of this question is to show the equivalence point can be determined by measuring the…