### Why do this problem?

This problem provides a meaningful logarithmic challenge
leading up to the derivation of the experimentally observable
titration curve. It will introduce along the way many fascinating
ideas from chemistry and human biology whilst keeping the focus
entirely mathematical.

### Possible approach

This question is best studied individually. There is a lot of
information to process and make sense of.

### Key questions

At each stage, how does the science have a clear, precise
mathematical meaning?

### Possible extension

Students who make it to the end of this question are doing
very well. They might like to pursue the ideas raised in
undergraduate science books.

### Possible support

You might try and get started using the pH formula with the
problem

Temperature
pH