Chemical Thermodynamics Part 3

The standard enthalpy of formation of an element in its standard state is zero at every temperature, by definition.Oxygen's standard state is $\mathrm{O}_2(\mathrm{g})$, hence $\Delta_{\mathrm{f}} H_{500}^{\circ}$ for $\mathrm{O}_2(\mathrm{g})$ is zero.$\mathrm{O}(\mathrm{g})$ is not the standard state of oxygen, so $\Delta_{\mathrm{f}} H_{298}^{\circ}$ for $\mathrm{O}(\mathrm{g})$ is not zero (it is about $+249\ \mathrm{kJ\,mol^{-1}}$).The term 'standard state' does not imply that the temperature is $0^{\circ}\mathrm{C}$; for a pure gas the standard state only fixes the pressure at $1\ \mathrm{bar}$, while the temperature is conventionally taken as $298\ \mathrm{K}$ for thermochemical data.Since the choice of $273\ \mathrm{K}$ in the last statement is arbitrary and not part of the definition, that statement is also incorrect.Therefore, the correct statement is: $\Delta_{\mathrm{f}} H_{500}^{\circ}$ is zero for $\mathrm{O}_2(\mathrm{g})$.