Why is the standard enthalpy of formation of oxygen gas zero?

The standard enthalpy of formation of oxygen gas is zero because it is the reference state for elements in their standard states.

The standard enthalpy of formation, or ΔHf°, is a measure of the energy change when one mole of a substance in its standard state is formed from its pure elements in their standard states. The standard state of a substance is its most stable physical state at 1 bar and a specified temperature, usually 298.15 K. For oxygen, the standard state is O2 gas.

By definition, the standard enthalpy of formation of an element in its standard state is zero. This is because there is no formation process needed for an element in its standard state; it is already in that state. Therefore, there is no energy change associated with forming it. This is a convention that allows us to compare the enthalpies of formation of different substances.

For oxygen, this means that the standard enthalpy of formation of O2 gas is zero. This doesn't mean that oxygen gas has no energy. Rather, it means that the energy of oxygen gas is our reference point. When we say that the standard enthalpy of formation of a substance is a certain value, we mean that this is the energy change compared to the energy of the pure elements in their standard states.

In other words, the standard enthalpy of formation is a way of comparing the stabilities of different substances. A substance with a negative ΔHf° is more stable than the pure elements from which it is formed, because energy is released when it is formed. Conversely, a substance with a positive ΔHf° is less stable than the pure elements from which it is formed, because energy is absorbed when it is formed. The standard enthalpy of formation of oxygen gas is zero because oxygen gas is the reference state for elements in their standard states.

IB Chemistry Tutor Summary: The standard enthalpy of formation of oxygen gas is zero because oxygen in its gas form (O2) is used as the baseline or reference state. This means there is no energy change when it forms from itself. We compare the enthalpy changes of other substances to this baseline to determine their stability relative to pure oxygen gas.