The correct statement amongst the following is :

The standard state of a substance means the pure substance at a standard pressure of $$1\;\text{bar}$$ and at a specified temperature. For most thermodynamic tables this specified temperature is $$298\;\text{K}$$, but any temperature can be chosen, provided it is clearly mentioned.

Checking each statement one by one:

Option A: The statement says the term ‘standard state’ implies the temperature is $$0^{\circ}\text{C}$$ ($$273\;\text{K}$$).
Definition shows that standard state does not fix the temperature; it only fixes the pressure (1 bar). Therefore this statement is false.

Option B: It claims “the standard state of a pure gas is the pure gas at a pressure of 1 bar and temperature 273 K”.
Again, standard pressure is indeed 1 bar, but the temperature need not be $$273\;\text{K}$$. Hence this statement is also false.

Option C: It states $$\Delta_f H^\theta_{298}$$ is zero for $$O(g)$$.
By definition, the standard enthalpy of formation $$\Delta_f H^\theta_T$$ of any element in its most stable form at temperature $$T$$ is taken as zero. At $$298\;\text{K}$$ the most stable form of oxygen is $$O_2(g)$$, not $$O(g)$$. Therefore $$\Delta_f H^\theta_{298} \neq 0$$ for atomic oxygen $$O(g)$$. Statement C is false.

Option D: It says $$\Delta_f H^\theta_{500}$$ is zero for $$O_2(g)$$.
Even at $$500\;\text{K}$$, $$O_2(g)$$ remains the thermodynamically most stable form of oxygen. Hence, by the same definition, $$\Delta_f H^\theta_{500} = 0$$ for $$O_2(g)$$. Statement D is true.

Since only Option D is correct, the given answer “4” (which corresponds to Option D) is verified.