Final answer:
The standard free energy of formation (ΔGf°) for an element in its standard state is zero. This is true for all elements in their most stable form at standard conditions of 25°C and 1 atm pressure.
Step-by-step explanation:
The standard free energy of formation (ΔGf°) for an element in its standard state is always zero. This is because the standard free energy change is based on the formation of 1 mole of a substance from its elements in their standard states. By definition, the formation of an element from itself does not involve any change in free energy; hence, the ΔGf° value is zero for all elements in their most stable form at standard conditions (25°C and 1 atm).
For example, the standard free energy of formation for oxygen gas (O2) and graphite, which are the most stable forms of oxygen and carbon, respectively, under standard conditions, is zero. This applies to all elements in their standard states, like Cl2 gas at 298.15 K, which also has ΔGf° = 0. The same principle is mirrored in the standard enthalpies of formation (ΔHf°), which are also zero for elements in their standard states.