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I need help with the first derivative plot and the second derivative plot? Can you plot the data tables with x and y values for both derivative plots, then I can graph it my

I need help with the first derivative plot and the second derivative plot? Can you plot the data tables with x and y values for both derivative plots, then I can graph it my

Chemistry
Chemistry
10th Edition
ISBN:9781305957404
Author:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste
Publisher:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste
Chapter1: Chemical Foundations
Section: Chapter Questions
Problem 1RQ: Define and explain the differences between the following terms. a. law and theory b. theory and...
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I need help with the first derivative plot and the second derivative plot? Can you plot the data tables with x and y values for both derivative plots, then I can graph it my

Volume HCI (mL) 1.43 2.76 4.21 5.67 6.81 8.01 9.88 11.66 13.21 14.76 16.33 16.82 17.45 17.62 17.71 17.84 17.97 18.09 18.25 19.67 21.65 22.76 24.33 PH 10.31 10.25 10.16 10.01 9.91 9.76 9.56 9.33 9.11 8.79 8.28 8.02 7.75 6.56 5.93 5.01 3.97 2.78 1.84 1.41 1.13 1.01
Transcribed Image Text:Volume HCI (mL) 1.43 2.76 4.21 5.67 6.81 8.01 9.88 11.66 13.21 14.76 16.33 16.82 17.45 17.62 17.71 17.84 17.97 18.09 18.25 19.67 21.65 22.76 24.33 PH 10.31 10.25 10.16 10.01 9.91 9.76 9.56 9.33 9.11 8.79 8.28 8.02 7.75 6.56 5.93 5.01 3.97 2.78 1.84 1.41 1.13 1.01
The first function is based on your raw data. Plot pH versus volume added. Imagining a smooth curve passing through your point-wise data points, see how clearly you can identify the point where there is the steepest negative slope. The volume at this point is the equivalence point. The second function is the rate of change of pH per volume versus volume. This corresponds to a "first derivative" in the vocabulary of calculus. For each successive pair of points in your raw data, you will generate one point of this function. For each two points (V₁, pH₁) and (V₂, pH₂), calculate the slope (pH₂-pH₁)/(√₂-V₁). This is a y-value. Assign this y-value to the x-value of the average of the two volumes, (V₁+V₂)/2. Plot this x-y data. There should be a "negative peak" or dip in the region of the equivalence point. The minimum point of this dip is the equivalence point. The third function corresponds to a second derivative. Once again, take pairs of data from the previous function and assign the slopes to the average (midpoint) volumes. This data might not lead to a clear conclusion unless you have many data points in the critical area. However, if you do, you should find an increasingly negative value rapidly changing to a positive value that then declines. The point at which the sign would change between the most negative and most positive values is the equivalence point.
Transcribed Image Text:The first function is based on your raw data. Plot pH versus volume added. Imagining a smooth curve passing through your point-wise data points, see how clearly you can identify the point where there is the steepest negative slope. The volume at this point is the equivalence point. The second function is the rate of change of pH per volume versus volume. This corresponds to a "first derivative" in the vocabulary of calculus. For each successive pair of points in your raw data, you will generate one point of this function. For each two points (V₁, pH₁) and (V₂, pH₂), calculate the slope (pH₂-pH₁)/(√₂-V₁). This is a y-value. Assign this y-value to the x-value of the average of the two volumes, (V₁+V₂)/2. Plot this x-y data. There should be a "negative peak" or dip in the region of the equivalence point. The minimum point of this dip is the equivalence point. The third function corresponds to a second derivative. Once again, take pairs of data from the previous function and assign the slopes to the average (midpoint) volumes. This data might not lead to a clear conclusion unless you have many data points in the critical area. However, if you do, you should find an increasingly negative value rapidly changing to a positive value that then declines. The point at which the sign would change between the most negative and most positive values is the equivalence point.
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