The Aquatic Chemistry Spreadsheet was produced to help students work through the activities of producing a graph of a titration curve, a distribution diagram, and buffer intensity as a function of pH. These activities help students better understand acid–base equilibrium by exploring the relationship between pK_a/pK_b, pH, ionization fractions, and buffer intensity.

Preliminary Experiment

A preliminary experiment was conducted to create a titration curve of the carbonate system; 0.1 M Na₂CO₃ solution was titrated with 0.1 M HCl. Using Excel, students plotted volume of HCl added as a function of pH. While this is not the customary method of graphing a titration curve, it is necessary for comparison with graphs produced in the activities that follow.

Activity I: Ionization Fraction (a) and Distribution Diagram

Ionization fraction (a) is the relative amount of each species in a solution as a fraction of overall analytical concentration (C_T). For the carbonate system, there are three species and corresponding ionization fractions: carbonic acid (a₀), bicarbonate ion (a₁), and carbonate ion (a₂). If ionic strength effects are considered negligible, the ionization fraction of each carbonic species can be worked out to the following, using the equilibrium expressions for K_a1 and K_a2. (The derivation is worked out completely in the documentation.)

Students plotted the three ionization fractions versus pH using a separate worksheet.

Activity II: Graphic Representation of Buffer Intensity

Buffer intensity (β) is defined as the ability to keep the solution pH steady. In mathematical expression, the buffer intensity is expressed in the following way:

(1)

where C_B and C_A are the concentrations in moles per liter of added strong base or acid.

Because the titration curve (figure below, top graph) was plotted with pH on the abscissa, and because C_A is directly proportional to the volume of added 0.1 M HCl, the buffer intensity is proportional to the negative slope of the titration curve.

To avoid the mathematical complexity of equation (1), an approximate numerical expression (6) of buffer intensity was derived in class and used to calculate the buffer intensity of the carbonate system.

β was then plotted versus pH in a separate worksheet.

Screenshot of Excel spreadsheet with a graphic representation for 0.1 M Na₂CO₃ solution. The titration curve (concentration vs pH) is plotted on the top graph, ionization fraction and buffer intensity vs pH on the bottom. Vertical lines show the correlations of maximal buffering intensity at pH = pK_a1or pK_a2 , and minimal intensity when any single carbonic species is dominant in the solution.

Activity III: Analysis of the Graphs

To better understand the relationship between the titration curve, ionization fraction, and buffer intensity, the graphs of all these were combined into a fourth worksheet for comparison. (See screenshot. Note that all graphs have the same pH scale on the abscissa for convenient analysis.)

The combined graphs show that when the pH = pK_a1or pK_a2 , buffer intensity reaches its maximum, while the intensity is at a minimum when any single carbonic species is dominant.

Comments

This spreadsheet can be adapted for use with other acid–base systems as well. A comparison among the plots for different systems under similar conditions would be useful for comparing the properties of such systems.

Literature Cited

1. Lo, G. V. J. Chem. Educ. 2000, 77, 532–533.
2. de Levie, R. J. Chem. Educ. 2000, 77, 534-535.
3. Lannone, M. J. Chem. Educ. 1998, 75, 1188-1189.
4. Guiñon, J. L.; García-Antón, J.; Pérez-Herranz V. J. Chem. Educ. 1999, 76, 1157-1160.
5. Brown, P. J. Chem. Educ. 2001, 78, 268-270.
6. Snoeyink, V. L.; Jenkins D. Water Chemistry; John Wiley & Sons: New York, 1980; 149–153.