Compare the following criteria for spontaneity of a reaction based on the values of $\Delta_{\text{r}}H^0$,$\Delta_{\text{r}}S^0$,and $\Delta_{\text{r}}G^0$:

$\Delta_{\text{r}}H^0$	$\Delta_{\text{r}}S^0$	$\Delta_{\text{r}}G^0$	Description
$(a) (+)$	$(-)$	$(+)$	$(i) \text{ Non-spontaneous at all temperatures}$
$(b) (-)$	$(-)$	$(-)$	$(ii) \text{ Spontaneous at low temperatures}$
$(c) (-)$	$(+)$	$(-)$	$(iii) \text{ Spontaneous at all temperatures}$

(A) The spontaneity of a reaction is determined by the Gibbs free energy equation: $\Delta G = \Delta H - T\Delta S$.
$1$. If $\Delta H > 0$ (endothermic) and $\Delta S < 0$ (entropy decreases),then $\Delta G$ will always be positive at all temperatures. Thus,the reaction is non-spontaneous at all temperatures. $(a-i)$.
$2$. If $\Delta H < 0$ (exothermic) and $\Delta S < 0$ (entropy decreases),then $\Delta G$ will be negative only at low temperatures (where $|\Delta H| > |T\Delta S|$). Thus,the reaction is spontaneous at low temperatures. $(b-ii)$.
$3$. If $\Delta H < 0$ (exothermic) and $\Delta S > 0$ (entropy increases),then $\Delta G$ will always be negative at all temperatures. Thus,the reaction is spontaneous at all temperatures. $(c-iii)$.
Therefore,the correct matching is $(a-i, b-ii, c-iii)$.