Can a reaction be both exothermic and nonspontaneous?
The spontaneity of a reaction is given by $\Delta G$
$\Delta G < 0$ = spontaneous reaction
$\Delta G > 0$ = nonspontaneous reaction
$\Delta G$ is quantitatively described by the formula
$$\Delta G = \Delta H - T \Delta S$$
$\Delta H$ is negative (exotermic reaction)
When $T \Delta S$ product is more negative (smaller) than $\Delta H$, we have $\Delta G > 0$ and the reaction is nonspontaneous