Why is the enthalpy of formation of oxygen zero?

Enthalpy of formation means the enthalpy change which occurs (change in energy) when 1 mole of a compound forms from the individual elements present in the compound.

Example: the formation of #"1 mol"# of water from the elements (hydrogen and oxygen)

#"H"_2(g) + 1/2"O"_2(g) -> "H"_2"O"(l)#, #DeltaH_"rxn" = -"285.8 kJ/mol"#

The elements which will form #"H"_2"O"# in this reaction are present in their elemental states.

The enthalpy of formation for an element in its elemental state will always be #0# because it takes no energy to form a naturally-occurring compound.

So in this case, #DeltaH_("rxn", "H"_2"O") = DeltaH_(f,"H"_2"O")#.

I'll try and focus a little more on why the value for the standard state enthalpy of formation of elements in their natural state was set to zero.

Enthalpy, which is a state function, has a very interesting property - it depends on the initial and the final states of the system, but not on how the system got from one state to the other.

An important implication of this is that enthalpy, which essentially expresses the ability to produce heat, cannot be measured, or more specifically, absolute enthalpy cannot be measured. We can only measure changes in enthalpy.

Now, the enthalpy change for a formation reaction is called enthalpy of formation. When a substance is formed from the most stable form of its elements, a change in enthalpy takes place. You can view the reactants as the initial state and the product as the final state.

But in the case of natural elements in their most stable state, no change in enthalpy takes place because the reactants and the product are the same. The element is already formed, so a formation reaction is not necessary. An element can't "react" to form itself.

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So, if no change in enthalpy takes place, shouldn't zero be the best choice to describe the enthalpy of formation for an element in its standard state?

The truth is that zero was an arbitrary, but pragmatic choice (if that's even possible) both because it's more suitable to associate no change with zero, and because it's easier to compare to zero.

Since no absolute measures can be made on enthalpy values, a relative scale is the next best thing. And what better zero point on this scale if not the most stable elements in their standard state?