Although nitrogen trifluoride \(\left(\mathrm{NF}_{3}\right)\) is a thermally
stable compound, nitrogen triiodide \(\left(\mathrm{NI}_{3}\right)\) is known to
be a highly explosive material. \(\mathrm{NI}_{3}\) can be synthesized according
to the equation
$$
\mathrm{BN}(s)+3 \mathrm{IF}(g) \longrightarrow
\mathrm{BF}_{3}(g)+\mathrm{NI}_{3}(g)
$$
a. What is the enthalpy of formation for \(\mathrm{NI}_{3}(s)\) given the
enthalpy of reaction \((-307 \mathrm{~kJ})\) and the enthalpies of formation for
\(\mathrm{BN}(s)(-254 \mathrm{~kJ} / \mathrm{mol}), \mathrm{IF}(g)(-96
\mathrm{~kJ} / \mathrm{mol})\),
and \(\mathrm{BF}_{3}(g)(-1136 \mathrm{~kJ} / \mathrm{mol})\) ?
b. It is reported that when the synthesis of \(\mathrm{NI}_{3}\) is conducted
using 4 moles of IF for every 1 mole of \(\mathrm{BN}\), one of the by-products
isolated is
\(\left[\mathrm{IF}_{2}\right]^{+}\left[\mathrm{BF}_{4}\right]_{-}^{-} .\) What
are the molecular geometries of the species in this by-product? What are the
hybridizations of the central atoms in each species in the by-product?