| Spreadsheet programs have been adopted in
many chemistry classes as a valuable tool for
not only conceptual understanding of chemistry
but also calculating complex chemical problems (1,2,3,4).
In addition, graphic representation helps students
appreciate the theories in depth and develop
their computer skills (5).
Fundamental aquatic chemistry concepts may
be introduced in general chemistry classes
by computing ionization fractions and buffer
intensity of aqueous phase carbonate systems.
This Excel spreadsheet may used to build graphic
presentations of a titration curve, distribution
diagram, and buffer intensity as a function
of pH. Accompanying activities are designed
to enhance the concepts of acid-base equilibrium
through exploring the relationship between
pKa /pKb,
pH of the solution, ionization fractions and
buffer intensity, and to exercise students’ graphing
skills.
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 as a fraction of overall
analytical concentration (CT).
For the carbonate system, there are three ionization
fractions: carbonic acid (a0),
bicarbonate (a1), and carbonate
(a2). If ionic strength
effects are neglected, the ionization fraction
of each carbonic species can be worked out
to the following, using the equilibria expressions
for Ka1 and Ka2.
(The derivation is worked out more completely
in the full documentation.)
These three equations show the relationship
between the ionization fraction of each carbonic
species and the pH of the solution. A plot
of these ionization fractions vs pH was also
made using Excel.
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 as following:
where CB and CA are
the added strong base and acid, respectively
in moles/liter.
Because the titration curve (figure below,
top graph) was plotted with pH on the abscissa,
and because C is directly proportional
to the volume of added 0.1M HCl, the buffer
intensity is proportional to the negative slope
of the titration curve.
Due to mathematical complexity, the well-known
approximate numerical expression (6) of
buffering intensity was derived in class and
used to calculate the buffer intensity of the
carbonate system.
β was then plotted vs pH.
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 = pKa1or
pKa2 , and minimal intensity
when any single carbonic species is dominant
in the solution.
Activity III: Analysis of the Graphs
To clearly understand the relationship between
the titration curve, ionization fraction, and
buffer intensity, the graphs of all these were
brought into a same worksheet for comparison
(Figure 2). (Note that all graphs have same
pH scale on the abscissa for convenient analysis.)
The combined graphs show clearly that when
the pH = pKa1 or
pKa2, buffer intensity
reaches its maximum, while the intensity is
at it minimum when any single carbonic species
is dominant.
This spreadsheet can be used for other acid-base
reactions as well, and a comparison among the
plots of different systems under similar conditions
would be useful for comparing their properties.
Literature Cited
- Lo, G. V. J.
Chem. Educ. 2000, 77, 532–533.
- de Levie, R. J.
Chem. Educ. 2000, 77, 534-535.
- Lannone, M. J.
Chem. Educ. 1998, 75, 1188-1189.
- Guiñon, J. L.;
García-Antón, J.; Pérez-Herranz
V. J.
Chem. Educ. 1999, 76, 1157-1160.
- Brown, P. J.
Chem. Educ. 2001, 78, 268-270.
- Snoeyink, V. L.; Jenkins
D. Water Chemistry; John Wiley & Sons:
New York, 1980; 149–153.
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