# Calculating Titration Curves

Department of Chemistry
California State University, Fresno
March 16, 1997

Computing a titration curve is an extension of the Initial/Final Spreadsheet method for computing the pH of a mixture. We write down the balanced chemical reaction, then list all the possible reacting species by millimoles, and sum up all volumes used. Then we decide what will react, and list all the millimoles of products. For pH titrations, we must then decide what kind of acid-base system we have produced (Strong Acid, Strong Base, Weak Acid, Weak Base, Buffer, Amphiprotic) and solve for the pH.

As an example we will titrate 3.00 millimoles of the weak acid HA, Ka = 1.5x10-6 with 0.100 M NaOH.

The balanced reaction is:

 HA + NaOH --> NaA + H2O Compound Form HA + Na+ + OH- --> Na+ + A- + H2O Ionic Form HA + OH- --> A- + H2O Net Ionic Form

The reactions are listed here in three forms to emphasize the materials actually in solution. Students often confuse this titration reaction with the dissociation reactions used in deriving the equations for determining pH.

A symptom of this confusion occurs when students find they have 100 mL of a solution containing 2 millimoles of NaA (CNaA = 0.02 M) and 1 millimole of HA (CHA=0.01 M), where the pH of the buffer will be around 5 ([H+] = 10-5 M) and yet they write [H+] = [A-] when trying to solve for the pH, because they remember this relationship from the pure Weak Acid calculation. Note the actual concentrations of the important species in the following Initial/Final Spreadsheet.

First we summarize what we know about the system we are titrating:

 Vo 100 mm HA 3 Ka of HA 1.5e-06 pKa 5.824 Kw 1e-14 M of NaOH 0.1

Then we set up a series of Initial/Final Spreadsheets, one for each total amount of titrant added. Note that in each case we identify the system we end up with, then compute its pH using the simple pH calculations we learned in the Survival Guide.

 mL NaOH mm NaOH mm HA mm NaA Vol, mL pH type, pH Initial 0 0 3.000 0 100 Final 0 3.000 0 WA Molarities 3.00E-02 100 3.67 Initial 10 1.000 3.000 0 110 Final 0 2.000 1.000 Buffer Molarities 1.82E-02 9.09E-03 110 5.52 Initial 15 1.500 3.000 0 115 Final 0 1.500 1.500 Buffer Molarities 1.30E-02 1.30E-02 115 5.82 Initial 20 2.000 3.000 0 120 Final 0 1.000 2.000 Buffer Molarities 8.33E-03 1.67E-02 120 6.12 Initial 30 3.000 3.000 0 130 Final 0 0.000 3.000 WB Molarities 0.00E+00 2.31E-02 130 9.09 Initial 40 4.000 3.000 0 140 Final 1.000 0.000 3.000 SB Molarities 0.00714 0.00E+00 2.14E-02 140 11.85

Finally, we plot our points and draw in the titration curve. Because we didn't calculate very many points in the end point region, we need a rule about whether to make the break sharp or not. Generally, if there are 4 pH units of break in the end point region, the break will be sharp.

The main reason for calculating a titration curve this way is to provide practice in calculating a variety of pH problems using the Initial/Final Spreadsheet method. If you want exact titration curves, there is a better way using Advanced Methods. If you want quick information on the approximate shape of a titration curve, the Quick and Dirty Sketch method works well. See the other pages on titration curves for these two methods.