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'Extreme Dissociation' printed from https://nrich.maths.org/
Why do this problem?
This problem provides a good exercise in linking two areas of
mathematics: concentration and logarithms. Students will need to
flip between the two descriptions of acidity which will require
careful, clear thinking. The context is fascinating and this will
encourage a 'concrete' and practical engagement with logarithms. It
will also help to give some numerical intuition as to the
concentrations involved in pH calculations.
Possible approach
This question uses the advanced concept of logarithms but will
also use basic ideas about concentrations and moles. Students will
need to remember basic ideas about the meaning of a 'concentration'
in order to work out the extreme concentrations given in the
problem.
Key questions
What equations do you need to flip between the pH and the
concentration of $H^+$ ions?
What knowledge of physical chemistry is required to do this
problem?
Possible extension
Possible support
You might try and get started using the pH formula with the
problem
Temperature
pH