Option A:

It claims that the standard state for a pure gas is defined at 1 bar and 273 K.

In modern thermochemistry, the standard state generally means the pure substance at 1 bar, but the standard temperature most commonly used is 298 K (25°C), not 273 K (0°C).

Thus, Option A is incorrect.

Option B:

It states that the standard enthalpy of formation $$\Delta_f H^\circ_{500}$$ is zero for $$O_2(g)$$.

By convention, the standard enthalpy of formation for an element in its most stable form is defined as zero. Even though typical tables list $$\Delta_f H^\circ_{298}$$ values, if one were to evaluate the formation enthalpy at any temperature where the element remains in its standard state, the reaction

$$O_2(g) \rightarrow O_2(g)$$

has no change in enthalpy.

Therefore, by definition, $$\Delta_f H^\circ_{500}(O_2(g)) = 0$$.

This makes Option B correct.

Option C:

It claims that $$\Delta_f H^\circ_{298}$$ is zero for $$O(g)$$ (atomic oxygen).

However, the standard state of oxygen is diatomic $$O_2(g)$$, not atomic oxygen. Since $$O(g)$$ is not the most stable form of oxygen under standard conditions, its formation enthalpy is not zero.

Hence, Option C is incorrect.

Option D:

It asserts that the term "standard state" implies that the temperature is 0°C (273 K).

In fact, "standard state" typically specifies a standard pressure (1 bar) and a chosen temperature—commonly 298 K for tabulated thermodynamic data—not necessarily 0°C.

Thus, Option D is also incorrect.

To summarize:

The only correct statement is Option B.

Therefore, the correct answer is: Option B.