A-Level Enthalpy, entropy and the feasibility of reactions: worked solution

Question

For the equilibrium N2(g) + 3H2(g) ⇌ 2NH3(g), work out the temperature (in K) above or below which the reaction becomes spontaneous, using your answers to (a) and (c). (If you were unable to obtain answers for (a) and (c), take ΔH° = −120 kJ and ΔS° = −250 J K⁻¹ for this part only; note these are not the actual answers.)

Using the given values DH = -120 kJ = -120000 J and DS = -250 J/K. A reaction is spontaneous (feasible) when DG = DH - T*DS < 0. At the changeover temperature DG = 0, so T = DH/DS = (-120000)/(-250) = 480 K. Since both DH and DS are negative, DG = DH - T*DS becomes negative only when T is small enough: -120000 + 250T < 0 gives T < 480 K. So the reaction is spontaneous below 480 K.