For N2O4(g) 2NO2(g), Delta H deg = +57.2 kJ and the standard molar entropies are S deg(N2O4) = 304.2 and S deg(NO2) = 240.0 J K^-1mol^-1. Assuming Delta H deg and Delta S deg do not vary with temperature, the reaction becomes spontaneous (standard conditions) above about

JEE Advanced levelSingle correct optionDifficulty 3 of 3td054

For $N X_{2} O X_{4} (g) 2 NO X_{2} (g)$ , $Δ H^{\circ} = + 57.2 kJ$ and the standard molar entropies are $S^{\circ} (N X_{2} O X_{4}) = 304.2$ and $S^{\circ} (NO X_{2}) = 240.0 J K^{- 1} mo l^{- 1}$ . Assuming $Δ H^{\circ}$ and $Δ S^{\circ}$ do not vary with temperature, the reaction becomes spontaneous (standard conditions) above about

Δ S^{\circ} = 2 (240.0) - 304.2 = 175.8 J K^{- 1}

. Spontaneity needs

Δ G^{\circ} = Δ H^{\circ} - T Δ S^{\circ} < 0

, i.e.

T > 57200/175.8 = 325.4 K

. Adding the entropies instead of subtracting reactants from products gives the wrong threshold.