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There is no difference between the terms spontaneous and favorable in terms of chemical reactions. The formal term is actually spontaneous, but modern connotations of that word may make it seem that spontaneous reactions happen very quickly. Rather, the term means that the reaction is favorable and will happen, regardless of the rate of the reaction.
They both mean that the reaction will occur without energy coming from external sources being necessary. I think, as the people said above, there's been a shift toward using the word favorable, because spontaneous comes with the connotation that it will happen quickly, when in reality it just means the reaction will happen by itself over a differing amount of time.
When a reaction is spontaneous, it does not require a net input of energy to occur. For example, the melting of ice occurs spontaneously, or the diffusion of air does not require an effort whereas performing these reactions in the reverse direction would require an effort. When a reaction is spontaneous, it means that it occurs because it is favorable and since it is more favorable and thus more stable than the current state, it does not require energy input. For a reaction to be favorable, it does not have to achieve lower energy, however, as seen in the example of the expansion of air transferred from a smaller container to a larger container. In that case, the energy of the air particles does not alter but the entropy of the system increases which makes this reaction more favorable and thus likely to occur.
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