For the decomposition reaction of $N_2O_4$,$\Delta H = 58.04 \, kJ$ and $\Delta S = 176.7 \, J/K$. Calculate $\Delta G$ in $kJ$ at $T = 298 \, K$.

State the criteria for a spontaneous process in terms of $\Delta G$ at constant pressure and temperature.

For a reaction to be spontaneous at all temperatures, the values of enthalpy change $\Delta H$ and entropy change $\Delta S$ should be:

At a temperature of $298 \ K$,if $\Delta H < T \Delta S$,what is the value of the equilibrium constant $K$?

$\Delta G$ is net energy available to do useful work and is thus a measure of "free energy". Show mathematically that $\Delta G$ is a measure of free energy. Find the unit of $\Delta G$. If a reaction has positive enthalpy change and positive entropy change,under what condition will the reaction be spontaneous?

For a given chemical reaction $A \rightarrow B$ at $300 \ K$,the free energy change is $-49.4 \ kJ \ mol^{-1}$ and the enthalpy of reaction is $51.4 \ kJ \ mol^{-1}$. The entropy change of the reaction is $..... \ J \ K^{-1} \ mol^{-1}$.