Q.The correct thermodynamic conditions for the spontaneous reaction at all temperature is (NEET Phase - I)

Exothermicity favours spontaneity but doesn't guarantee it (ammonium nitrate dissolves spontaneously despite being endothermic), and entropy increase alone doesn't guarantee it either -- predicting spontaneity needs a function combining both. Gibbs free energy, $G=H-TS$ (Josiah Willard Gibbs, 1870s -- originally the "available energy" to do work), is extensive and a single-valued state function; at constant $T$, $\Delta G=\Delta H-T\Delta S$. Combining the first and second laws shows that for a SPONTANEOUS process $\Delta G<0$ (equivalently $\Delta H-T\Delta S<0$); at equilibrium $\Delta G=0$; for a non-spontaneous process $\Delta G>0$. $T\Delta S$ is energy NOT available for useful work, so $\Delta G$ is the net energy that IS available -- hence "free" energy; more precisely, $-\Delta G=w-P\Delta V$ at constant $T,P$, meaning the decrease in free energy equals the MAXIMUM work obtainable other than ordinary expansion work. …