Question

Why is the change in free energy zero when substances are in their elemental state?

Answer 1

Because you don't need to do anything to them to form them from their standard state.

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The formation reaction is simply the reaction that starts with the elements in their standard state and forms `"1 mol"` of the product at that standard state.

If you wanted to form `"NH"_3(g)` at standard state, `25^@ "C"` and `"1 bar"`, you would write

`1/2"N"_2(g) + 3/2"H"_2(g) -> "NH"_3(g)`

since nitrogen element and hydrogen element are `"N"_2(g)` and `"H"_2(g)` respectively, at `25^@ "C"` and `"1 bar"`. If you simply want to form nitrogen gas at `25^@ "C"` and `"1 bar"`, then

`"N"_2(g) -> "N"_2(g)`

Clearly, nothing happened to go from `"N"_2(g)` to `"N"_2(g)`:

`DeltaG_(f,"N"_2(g))^@ -= DeltaG_(rxn)^@` for forming `"N"_2(g)` from `"N"_2(g)`

And the final and initial states are the same, so by definition of a state function, `DeltaG_(f,N_2(g))^@ = "0 kJ/mol"`.