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.
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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 VNaOH data from your titrations, calculate ΔpH/ΔVNaOH and VNaOH 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. VNaOH, 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 |
VNaOH (mL) |
ΔpH/ΔVNaOH |
VNaOH (mL) |
Δ (ΔpH/ΔVNaOH) |
VNaOH (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 1st first derivative point. The 2nd and 3rd titration data points are used to compute the 2nd first derivative point, and the 3rd and 4th titration data points are used to compute the 3rd first derivative points.
Here is how the 1st first derivative points were calculated. ΔpH/ΔVNaOH 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 VNaOH value calculated in the first derivative is simply the average of the two titration VNaOH 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.
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