Why do compounds often have different properties from the elements that make it up?

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By properties do you mean "physical characteristics" such as solid, liquid, or gas at room temperature?  acidity? etc.?  The "properties" of compounds depend on their volatility or stability on the molecular level, and what features their electronic rings possess.  Actually, there are few if any cases where an element has the same properties as the compounds it can form-- for example,hydrogen and oxgen are gases but water is not. The basic answer is that "properties" do not really exist on the atomic level; you could say, I suppose, that iron or copper have "properties," but even there, we deal with them in their ore form as mixtures, or as oxides.  There therefore is no reason why compounds should maintain the "properties" of their constituent elements.   

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