= Solution
The <standard entropy of reaction> is
$$
\Delta_rS^\circ=282.15-217.94-202.79=-138.58\,\mathrm{J\,K^{-1}\,mol^{-1}}.
$$
Using $\Delta_rG^\circ=\Delta_rH^\circ-T\Delta_rS^\circ$,
$$
\Delta_rH^\circ=-73.01+298(-0.13858)=-114.30684\,\mathrm{kJ\,mol^{-1}}.
$$
The formation enthalpy of elemental fluorine gas is zero in its standard state. Thus
$$
\boxed{\Delta_fH^\circ(\mathrm{ClF_3})=\Delta_rH^\circ+\Delta_fH^\circ(\mathrm{ClF})=-164.60\,\mathrm{kJ\,mol^{-1}}.}
$$
The large negative entropy change is consistent with converting two gas molecules to one; it is already included in the Gibbs-energy relation.
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