Answer
38.17 kJ
Work Step by Step
$\Delta_{r}S^{\circ}=113\,J/K$
Boiling point: $T_{b}=(64.6+273.15)\,K=337.8\,K$
$\Delta_{r}S^{\circ}_{vap}=\frac{\Delta H_{vap}}{T_{b}}\implies\Delta H_{vap}=\Delta_{r}S^{\circ}_{vap}\times T_{b}$
$=113.0\,J/K\times337.8\,K=38.17\,kJ$