Answer
$-108.7\text{ kJ}$
Work Step by Step
We combine the following reactions:
$ClF_{(g)}+\frac{1}{2}O_{2(g)}\Rightarrow \frac{1}{2}Cl_2O_{(g)}+\frac{1}{2}F_2O_{(g)}\text{ 83.7 kJ}$
$\frac{1}{2}Cl_2O_{(g)}+\frac{3}{2}F_2O_{(g)}\Rightarrow ClF_{3(g)}+O_{2(g)}\text{ -170.7 kJ}$
$F_{2(g)}+\frac{1}{2}O_{2(g)}\Rightarrow F_2O_{(g)}\text{ -21.7 kJ}$
$\Delta E = 83.7-170.7-21.7=-108.7\text{ kJ}$
