### Why do this problem?

This

problem
gives practice in mathematical reasoning in a genuine scientific
context. It involves reasonably basic mathematics of combinatorics
but requires more advanced inductive reasoning. It might prove an
interesting context for the prospective mathematician and will
definitely be useful for those interested in studying chemistry at
university.

### Possible approach

As this problem does not fit directly into the typical
chemistry or mathematics classroom it could be used as an end of
term activity in which the focus is to encourage some clear
mathematical thinking in a cross-curricular context.

Suggest that students interested in both chemistry and
mathematics try the problem, either individually or in small
groups. The basic chemical knowledge required is simply that of
isotopes and atomic mass. The mass spectrometer might be
unfamiliar, but should be simple to grasp in essence.

The focus throughout the problem should be on clarity in the
mathematical explanations, and there will be an element of
convincing others of the soundness of any resulting analysis.

When this problem was created it caused a great deal of
discussions amongst students. Hopefully some of this discussion
might be replicated amongst your students.

Finally, note that this problem is of an industrial, real
world sort. It gives a flavour of the types of real questions which
might be asked to professional scientists and mathematicians, where
errors in mathematical reasoning can be highly costly . It gives
great practice in such thinking.

### Key questions

Have you understood the chemical terms?

Which numbers seem to stand out, when compared with the
periodic table?

Are you clear as to which aspects of you calculations are
mathematically certain?

### Possible extension

Extension is built into this problem directly.

### Possible support

To make this problem more straightforward, provide copies of
the periodic table. Suggest that students write down all the
diatomic gasses that they know and start from these.

For a more straightforward foray into combinatoric chemistry,
try the problem

Heavy
Hydrocarbons.