This has the catalyst in the same phase as the reactants. Typically everything will be present as a gas or contained in a single liquid phase. The examples contain one of each of these . . .
Examples of homogeneous catalysis
The reaction between persulphate ions and iodide ions
This is a solution reaction that you may well only meet in the context of catalysis, but it is a lovely example!
Persulphate ions (peroxodisulphate ions), S2O82-, are very powerful oxidising agents. Iodide ions are very easily oxidised to iodine. And yet the reaction between them in solution in water is very slow.
If you look at the equation, it is easy to see why that is:


The reaction needs a collision between two negative ions. Repulsion is going to get seriously in the way of that!
The catalysed reaction avoids that problem completely. The catalyst can be either iron(II) or iron(III) ions which are added to the same solution. This is another good example of the use of transition metal compounds as catalysts because of their ability to change oxidation state.
For the sake of argument, we'll take the catalyst to be iron(II) ions. As you will see shortly, it doesn't actually matter whether you use iron(II) or iron(III) ions.
The persulphate ions oxidise the iron(II) ions to iron(III) ions. In the process the persulphate ions are reduced to sulphate ions.


The iron(III) ions are strong enough oxidising agents to oxidise iodide ions to iodine. In the process, they are reduced back to iron(II) ions again.


Both of these individual stages in the overall reaction involve collision between positive and negative ions. This will be much more likely to be successful than collision between two negative ions in the uncatalysed reaction.
What happens if you use iron(III) ions as the catalyst instead of iron(II) ions? The reactions simply happen in a different order.
The destruction of atmospheric ozone
This is a good example of homogeneous catalysis where everything is present as a gas.
Ozone, O3, is constantly being formed and broken up again in the high atmosphere by the action of ultraviolet light. Ordinary oxygen molecules absorb ultraviolet light and break into individual oxygen atoms. These have unpaired electrons, and are known as free radicals. They are very reactive.


The oxygen radicals can then combine with ordinary oxygen molecules to make ozone.


Ozone can also be split up again into ordinary oxygen and an oxygen radical by absorbing ultraviolet light.


This formation and breaking up of ozone is going on all the time. Taken together, these reactions stop a lot of harmful ultraviolet radiation penetrating the atmosphere to reach the surface of the Earth.
The catalytic reaction we are interested in destroys the ozone and so stops it absorbing UV in this way.
Chlorofluorocarbons (CFCs) like CF2Cl2, for example, were used extensively in aerosols and as refrigerants. Their slow breakdown in the atmosphere produces chlorine atoms - chlorine free radicals. These catalyse the destruction of the ozone.
This happens in two stages. In the first, the ozone is broken up and a new free radical is produced.


The chlorine radical catalyst is regenerated by a second reaction. This can happen in two ways depending on whether the ClO radical hits an ozone molecule or an oxygen radical.
If it hits an oxygen radical (produced from one of the reactions we've looked at previously):


Or if it hits an ozone molecule:


Because the chlorine radical keeps on being regenerated, each one can destroy thousands of ozone molecules.