Analyzing Your Titration Curve
Analyzing Your Titration Curve
The equivalence point is the inflection point on your graph, where the curve changes from one direction to another. A good way to determine the inflection point is to apply calculus to the problem. Very broadly, calculus is a method to describe rates of change. The second derivative identifies where the rate of change switches from one direction to another. So, the equivalence point is where the 2nd derivative plot crosses 0 on the x-axis. You don’t need to be taking calculus to apply this calculation.
Here is how you find the equivalence point, using the 2nd derivative. Instructions include reminders about how to properly prepare your graph and table of the titration curve itself.
1. Open your file.
2. Label axes.
3. Round pH to 2 decimal points using the “Manual Column Options” dialog box which opens when you click on the top of the L2 column.
4. Perform 2nd derivative calculations this way:
a) Add a column to your table: go to the Data Menu, click on “New Calculated Column”. In the dialog box that opens up,
i) change the name to “2nd derivative”
ii) Under “Equation”:
click on “Functions”
click on “Calculus”
click on “secondDerivative”
(Second derivative should show up in box, followed by parentheses)
iii) Click on “Variables”,
click on “pH”
type a comma after “pH” in the box
click on “Variables” again,
click on “Volume”
(“pH”,”Volume” should show up in the parentheses)
(You have told the computer to calculate a second derivative of pH relative to volume.)
iv) Click on “done” (or okay, whatever it takes to say you are done defining terms).
You should see a third column appear next to the pH column in your table, which includes positive and negative numbers.
5. To see (and use) the graph of the 2nd derivative:
Go to “Insert”
Click on “graph”
A graph should appear on top of your titration curve, with “2nd derivative” as the y-axis label.
Use the “examine” function to find where the line crosses 0 on the x-axis. This is the inflection point of the titration curve, i.e. the equivalence point.
6. To print the graphs:
Resize and move the 2nd derivative graph to a place where it does not interfere with your titration curve. You can resize both graphs if you want to fit them as separate entities on the page, or “nest” the 2nd derivative graph within the titration graph itself.
Save your file, then print two copies – one for your own lab notebook, and one to turn in with your lab report.