The enthalpy of formation for elements is defined as zero when they are in their standard states. This is because no energy is required to form an element from itself in its most stable form.

The enthalpy of formation, often referred to as the heat of formation, quantifies the energy change associated with the formation of one mole of a substance from its constituent elements in their standard states. The standard state of an element is its most stable physical form at a pressure of $1 \, \text{bar}$ and a specified temperature, typically $298 \, \text{K}$. For instance, the standard state of oxygen is represented by $O_2$ gas, while the standard state of carbon is graphite.

By definition, the enthalpy of formation for an element in its standard state is zero. This is due to the fact that there is no energy change involved in the formation of a substance from itself. In simpler terms, it requires no energy to convert oxygen gas into oxygen gas or graphite into graphite. Therefore, the enthalpy of formation for elements in their standard states is always zero.

This convention is particularly useful in thermochemical calculations. When determining the enthalpy change for a chemical reaction, we can utilize the enthalpies of formation for both the reactants and the products. The enthalpy change for the reaction is calculated as the sum of the enthalpies of formation of the products, minus the sum of the enthalpies of formation of the reactants. Since the enthalpies of formation for elements in their standard states are zero, they do not affect the overall enthalpy change of the reaction.

It is important to highlight that the enthalpy of formation is not universally zero for all isotopes of an element. For example, the enthalpy of formation for deuterium, an isotope of hydrogen, is not zero because it is not in its most stable state. Similarly, enthalpy of formation for elements in different physical states (such as diamond compared to graphite for carbon) or different allotropes (such as ozone compared to oxygen for oxygen) may not be zero. These instances represent exceptions to the general rule that the enthalpy of formation for elements in their standard states is zero.