Chemistry Reference
In-Depth Information
Illustration of mathematical logical facts
. Descriptions of many chemical
facts are based on abstract mathematical terms. Substantial mathematical reasoning
is necessary for the deduction and use of equilibrium constants, for example,
to recognize that the equilibrium of a weak acid is almost completely on the side
of the molecules. The “glass-tube-cylinder model” (see E4.2) should be introduced,
before equilibrium constants come into play. It is to demonstrate that equilibria
do not only occur with a ratio of 50:50 (glass tubes of equal size in the model
experiment), but also with ratios of 20:80 or 10:90 (glass tubes with different
diameters). If the single steps of this experiment are plotted in a graph (
x
-axis)
with the measured volumes in both cylinders (
y
-axis), two pairs of curves can
be observed (see Fig.
6.16
): equilibria and corresponding equilibrium constants
can be understood with this model experiment. Another statistical game can show
the same mathematical relationship.
The following rules regulate the game with A- and B-spheres:
- At the beginning 140 A-spheres are located in a glass bowl, no B-spheres are
present
- Per time unit one sphere is taken out of the bowl: in case it is an A-sphere (that
is certain at the start), it is changed to a B-sphere
- If it is a B-sphere, it is changed with the probability of 1:2 (throw a coin!) into
an A-sphere. In case the coin decision is negative, the B-sphere is put back into
the bowl
The result after 400 time units is shown in Fig.
6.16
(top): the model equilibrium
is reached after about 300 time units, the number of B-spheres in the bowl is double
that of the A-spheres.
If one starts with 140 B-spheres instead of A-spheres and plays with the same
rules, the same model equilibrium as before is reached (see bottom of Fig.
6.16
):
n
(B):
n
(A)
2:1. If equilibrium is reached you can continue and play another
200 time units: the ratio of 1:2 will not change.
The transfer to reality shows the properties of a
dynamic
equilibrium: the
forward reaction and the backward reaction are going on and on, but the concen-
trations of particles stay constant. The mathematical terms for these observations
are the equilibrium constants: they are easier to understand with those models than
without. Another nice model experiment shows the “Apple fight” of Dickerson and
Geis [
24
] in Fig.
6.17
.
Illustration of processes in chemical engineering
. If a production process
for plastics is to be discussed in class, an experiment takes the part of a model.
The experimental production of a nylon thread from the simple starting chemicals
adipine acid and hexamethylene diamine, for example, can be demonstrated
by pouring some mL acid on top of some mL hexamethylene diamine. A thin
film forms at the interface, a thread can be drawn out of the beaker with the help
of a glass rod. This model experiment serves as a basis for demonstrating the
production of nylon or other polymers in chemical engineering.
Construction of hypotheses
. Mental models of molecules allow the prediction
of characteristics and specific reactions. If students are already familiar with the
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