The standard entropy change for the reaction
$$4Fe(s) + 3O_2(g) \to 2Fe_2O_3(s)$$ is $$-550$$ J K$$^{-1}$$ at $$298$$ K
[Given : The standard enthalpy change for the reaction is $$-165$$ kJ mol$$^{-1}$$]. The temperature in K at which the reaction attains equilibrium is (Nearest Integer) ______

To determine the temperature at which the reaction attains equilibrium, we note that $$\Delta S^\circ = -550$$ J K$$^{-1}$$ and $$\Delta H^\circ = -165$$ kJ mol$$^{-1}$$ = $$-165000$$ J mol$$^{-1}$$.

At equilibrium, $$\Delta G^\circ = 0$$ and thus we apply the relationship $$\Delta G^\circ = \Delta H^\circ - T\Delta S^\circ$$. Setting $$\Delta G^\circ$$ to zero leads to $$0 = \Delta H^\circ - T\Delta S^\circ$$, which upon rearranging yields $$T = \frac{\Delta H^\circ}{\Delta S^\circ}$$.

Substituting the numerical values gives $$T = \frac{-165000}{-550} = \frac{165000}{550} = 300 \text{ K}$$.

The reaction attains equilibrium at 300 K.