How are chemical reactions organized in prokaryotic and eukaryotic cells?
Okay, this is my first post on this site so please bear with me when it comes to the format of my response!

To begin with I'm going to try and answer your question by clarifying some things.


  In prokaryotic cells I thought there were no
  organelles so does that mean that every reaction depends on the
  diffusion of the reactants throughout the cell and that any reaction
  could happen anywhere in the cell?


Yes and no, the fact that there are no membrane bound organelles in prokaryotic cells means a majority of the reactions occur in the cell's cytoplasm via diffusion but something to keep in mind is the selectiveness of the cell's membrane will regulate the substances entering the cell in turn controlling that reactions that occur within it.  


  What I'm getting at is that if everything is just floating around
  freely within a cell, wouldn't a lot of reactions interfere with each
  other?


When it comes to  eukaryotic cells structures do not float around freely like soup, there is cytoskeleton composed tubules and filaments that is used for  intracellular transport, this skeleton acts like a road system to move substances between static organelles. Prokaryotic cells do not require this since they do not have membrane bound organelles and the diffusion of substances into the cell is controlled by the cellular membrane.


  in eukaryotic cells, are organelles always used to compartmentalize
  stages in chemical synthesis?


Not always, you can look at things like cellular respiration to see glycolysis occurring in the cytoplasm.

I hope this helped out some!