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First, let's break down the words so it will be easier to remember. Equilibrium means that things are in a state of balance. Homo is a Greek prefix that means same, and hetero is a Greek prefix that means different. A homogeneous equilibrium is where everything in the reaction reaching a balance is in the same phase. An example would be when everything in the reaction is in the gaseous phase. A heterogeneous equilibrium is where the reaction is balanced but the agents of that reaction are in different phases. An example would be a reaction between a gas and a solid. See the links below for more details. The chemguide link also contains equation examples in case you need them.
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