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I think degeneracy only applies to hydrogen atoms, according to page 36 of the textbook... If you were asking why the gaseous state occupies more space than the liquid and solid states, that answer would be because as you heat any group of molecules up, it will transition from solid to liquid to gas. At each state the molecules are able to overcome the attraction that they have among themselves because of added energy, and eventually they overcome said attraction and are farther apart from one another. This shows that gaseous phases take up more space than the other two. Tell me if I misunderstood your question.
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