For reversible reaction :$${X_{\left( g \right)}} + 3{Y_{\left( g \right)}} \rightleftharpoons 2{Z_{\left( g \right)}};$$      $$\Delta H = - 40\,kJ\,mo{l^{ - 1}}$$
Standard entropies of $$X, Y$$  and $$Z$$  are $$60, 40$$   and $$50\,J\,{K^{ - 1}}\,mo{l^{ - 1}}$$   respectively. The temperature at which the above reaction is in equilibrium is

Solution :
$$\eqalign{ & X + 3Y \rightleftharpoons 2Z \cr & \Delta S = 2 \times 50 - \left( {60 + 3 \times 40} \right) \cr & \,\,\,\,\,\,\,\,\,\, = - 80\,J{K^{ - 1}}\,mo{l^{ - 1}} \cr & \Delta G = \Delta H - T\Delta S\,\,{\text{when}}\,\,\Delta G = 0 \cr & T = \frac{{\Delta H}}{{\Delta S}} \cr & \,\,\,\,\,\, = - 40 \times \frac{{1000}}{{ - 80}} \cr & \,\,\,\,\,\, = 500\,K \cr} $$