The signs of $\Delta_r H^{\circ}$ and $\Delta_r S^{\circ}$ for a reaction to be spontaneous at all temperatures respectively are

$A$ chemical reaction cannot occur at all if

Gibbs free energy $(G)$ is defined as

Identify from the following the correct set of thermodynamic conditions for the reaction to be spontaneous at all temperatures.

The standard enthalpy of the decomposition of $N_2O_4$ to $NO_2$ is $58.04 \, kJ$ and standard entropy of this reaction is $176.7 \, J/K$. The standard free energy change for this reaction at $25 \, ^oC$ is $..... \, kJ$

For the reaction occurring in the gaseous phase: $PCl_{5(g)} \rightleftharpoons PCl_{3(g)} + Cl_{2(g)}$,which of the following conditions is correct for the reaction to be spontaneous at high temperatures?