Question

What would the graph of the product versus time graph of an enzymatic reaction look like if you run the reaction for hours? Would it keep increasing?

Answer 1

http://ibchem4u.wikispaces.com/file/view/product_conc_Vs_time.png/331293442/269x278/product_conc_Vs_time.png

As you can see, the graph flats out after a while, so when you run it for hours eventually the graph becomes horizontal because there is no substrate left to convert into product.

Answer 2

Yes you could run out of substrate, but this all depends on the rate of the reaction. If your reaction is very slow then you could possibly run it for a very very long time before running out. However if it is very fast it may flat-line after only a few minutes. The best answers to these questions are part of an area of chemistry known as enzyme kinetics. Basically in any enzymatic reaction you need to know the rate of your enzyme, the concentration of your substrates, the concentration of your enzyme, and any other properties that may inhibit or speed up the reaction.

Wikipedia has a pretty good article on enzyme kinetics if you are looking for more info: https://en.wikipedia.org/wiki/Enzyme_kinetics