For the given decomposition reaction: $\text{PCl}_5\text{(g)} \rightleftharpoons \text{PCl}_3\text{(g)} + \text{Cl}_2\text{(g)}$

1. Enthalpy change ($\Delta H$): Decomposition reactions typically involve the breaking of bonds, which requires an input of energy. Therefore, the reaction is endothermic, meaning $\Delta H > 0$ (specifically, $\Delta_r H^\circ = 124.0 \text{ kJ mol}^{-1}$).
2. Entropy change ($\Delta S$): In this reaction, $1 \text{ mole}$ of a gaseous reactant decomposes to form $2 \text{ moles}$ of gaseous products ($\Delta n_g = 1 + 1 - 1 = +1$). Since the number of gaseous particles increases, the randomness or disorder of the system also increases. Therefore, $\Delta S > 0$.