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    Are properties of a compound different or the same to the properties of its elements?

    They're usually different, although you can infer the properties of a compound from those of the atoms. For example, fluorine atoms are very reactive, and so often form very strong bonds and therefore very stable compounds.
    Usually in chemistry one focuses on what the electrons do. Elements on the left of the periodic table easily lose electrons, and elements on the right easily gain electrons. Though comparing the electronegativity (how easily they steal electrons) of two elements, we can predict how strong a bond between them would be, which then tells us how that bond could be broken, and therefore it's chemical properties.
    If you study Chemistry at A level, you should end up with reasonable confidence in predicting the properties of a compound, given its structure.

    As above, they are often different

    The classic school experiment is to react iron (metal, magnetic) and sulfur (yellow, smelly) and you end up with iron sulfide, which is very different from both.
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