Sorry for the late reply to this thread.
it might be tough to create a fully working model without buying it.
It will be expensive to do either. The catalytic reaction requires some expensive materials, and most membranes (either PEM or others) require fairly cost prohibitive methods to manufacture.
I've seen some demonstration kits as low as $500 though.
I might suggest somthing with solar energy, since small solar cells are fairly cheap. You can demonstrate the Photoelectric Effect that got Einstein the Nobel Prize.
Chemists are physicists who don't do math.
