What is the difference between a heterogeneous catalyst and a homogeneous catalyst?

Homogeneous catalyst - catalyst is in the same phase as the reactants. Heterogeneous catalyst - catalyst is in a different phase as the reactants. What this means is that the reactants will be either a gas, liquid/aqueous or solid and if the catalyst is in the same state/phase (for example: all are gases) the catalyst will be homogeneous. If the catalyst is in a different state (for example: Haber process where the reactants are gases and the catalyst is a solid) it would be a heterogeneous catalyst. Heterogeneous and homogeneous catalysts go through a different process of catalysing reactions. Homogeneous catalysts usually lower the activation energy of a reaction by acting as a "electron carrier" between molecules that struggle to do this by themselves. An example of this is I^- reacting with S₂O₈^2- . They struggle to react as they are both negatively charged and therefore repel each other. Fe²⁺/Fe³⁺ works as a catalyst as Fe³⁺ takes an electron from I^- causing it to form I₂ and turning itself into Fe²⁺ which then goes on to react with S₂O₈^2- where it gives the electron it gained so it can turn into SO₄^2- . Heterogeneous catalysts are usually solids that one of the reactants can bond to so that the probability of a successful collision is increased. This can either be by holding the molecule in a certain position so that it is easier for the other reactant to successfully collide or as the molecule is bonded to the catalyst it weakens another bond within the molecule meaning the bond is more likely to break and therefore react.