Is there a piece of lab equipment that could record or measure the change of pH over a period of time?

Question

In a way that could be used for a rate of reaction experiment.

Answer 1

Yep. You can buy digital pH meters that will hook up to a computer and plot pH data points every so often.

Alternatively you could use a series of indicators and do a titration.

Answer 2

Recorders (pen/paper) can be attached to a pH meter to trace the pH versus time.