Prepare for University - Mathematical Chemistry

Age 16 to 18
Challenge Level
Here we collect 10 essential problems to get you thinking before you embark on your degree course in chemistry. They will give you a good mathematical grounding in the topics likely to arise in your degree course - we have included a short explanation of why each problem might be useful to you.

Remember, these problems are designed to make you think and there is not necessarily a 'right' answer. Approach them in a thoughtful way; it is to be hoped that they are both interesting and stimulating. What questions do they raise in you mind? Where do these questions lead you? Take them to a level that feels comfortable for you.

Finally, once you have done the problems, study the solutions. These will give you additional insights into the problems and the underlying mathematics and science.

Additional problems of interest will be found on the main chemNRICH pages.

Reductant ratios Refresh you skills with percentages, ratio and moles by investigating what the empirical formula of this mixture of iron oxides tell you about its consituents.
Exact dilutions Dilution calculations are crucial in the lab. This problem will develop your understanding of the ideas. There are other related problems on the chemNRICH pages.
Mixing pH This will get you thinking about pH and the use of the logarithm formula. There are other related problems on the chemNRICH pages.
Molecular sequencer This problem will hone your skills with the combinatoric aspects of chemistry.
Spectrometry detective You will need to make good use of your problem solving skills, understanding of combinatorics and knowledge of atomic masses and compounds to make sense of these spectrometry data.
Diamonds aren't forever Familiarise yourself with the use of the ideal gas equation and the properties of diamonds in this sequence of problems.
Striking gold By investigating some of the issues raised by Geiger and Marsden's famous scattering experiment in which they fired alpha particles at a sheet of gold you will refine your problem solving skills in measurement and estimation.
Catalyse that! Think about rates of reaction and graphs in this thought provoking problem which works at a range of levels.
CSI: Chemical scene investigation This entertaining extended crime challenge will give your analytical chemistry skills a thorough workout.
The real hydrogen atom This problem is just for those with further mathematics experience! Whilst challenging, it will give a real insight into the mathematics which can be involved in the applications of quantum mechanics to chemistry. It will also be great for honing your mathematical and problem solving skills.

You are also advised to read our interactive article which take you through a fascinating area of chemistry. You will need a pencil and paper to hand as calculations are required throughout.