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So from what I understand, pure elements in their most common state (like carbon graphite or O2 gas) are in their most stable form. So, since the standard enthalpy of formation is defined as the enthalpy to form a mole of a substance from pure elements in their standard states, these pure forms have enthalpies of zero.
From my understanding, purity is referring to there being only one element in the sample. So, for a sample to be in its stable state, it would need to be in its purest form. For instance, there could only be Oxygen in a gas sample (no other gases) for one to claim the sample is in its most stable state.
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