The compound \(\mathrm{NF}_{3}\) is quite stable, but \(\mathrm{NCl}_{3}\) is very unstable (NCl \(_{3}\) was first synthesized in 1811 by P. L. Dulong, who lost three fingers and an eye studying its properties). The compounds \(\mathrm{NBr}_{3}\) and \(\mathrm{NI}_{3}\) are unknown, although the explosive compound \(\mathrm{NI}_{3} \cdot \mathrm{NH}_{3}\) is known. Account for the instability of these halides of nitrogen.

Nitrogen halides are compounds formed by nitrogen and different types of halogens (F, Cl, Br, and I). Examine the given stability: \(\mathrm{NF}_{3}\) is relatively stable, while \(\mathrm{NCl}_{3}\) is very unstable. \(\mathrm{NBr}_{3}\) and \(\mathrm{NI}_{3}\) are unknown, but we do know about the existence of \(\mathrm{NI}_{3} \cdot \mathrm{NH}_{3}\).

Bond strength between two atoms is influenced by the electronegativity difference between them, which affects the bond polarity and its stability. Nitrogen has an electronegativity of 3.04, and the electronegativity for F, Cl, Br, and I are 3.98, 3.16, 2.96, and 2.66, respectively. Notice that the electronegativity difference between nitrogen and fluorine is the least, making the \(\mathrm{NF}_{3}\) bond the least polar and, therefore, the most stable of all nitrogen halides.

Orbitals surrounding the nitrogen atoms in nitrogen halides may contain lone pairs of electrons. These lone pairs can repel the bonding pairs, contributing to the instability of the molecules. In the case of \(\mathrm{NCl}_{3}\), the electron repulsion may lead to the dissociation of the molecule into \(\mathrm{NCl}\) and \(\mathrm{Cl}_{2}\), which explains its high reactivity and instability.

As we move down the halogen group, the atomic size increases, leading to longer and weaker N-X bonds for larger halogens like Br and I. This results in weaker and more unstable compounds. Therefore, \(\mathrm{NBr}_{3}\) and \(\mathrm{NI}_{3}\) are unknown and highly unstable, in collaboration with electron repulsion.

While the unstable nature of the large iodine atom makes \(\mathrm{NI}_{3}\) unknown on its own, the addition of \(\mathrm{NH}_{3}\) acts as a stabilizing force in the formation of \(\mathrm{NI}_{3} \cdot \mathrm{NH}_{3}\). This is because the lone pair electrons on the nitrogen in \(\mathrm{NH}_{3}\) can form strong coordinate bonds with the iodine atoms, which can result in stronger \(\mathrm{NI}_{3} \cdot \mathrm{NH}_{3}\) bonds and stabilization. In conclusion, the instability of the nitrogen halides can be attributed to factors such as electronegativity difference, electron repulsion, and atomic size. \(\mathrm{NF}_{3}\) is relatively stable due to the lesser electronegativity difference and bond polarity, whereas \(\mathrm{NCl}_{3}\) is very unstable primarily because of electron repulsion and bond polarity. The unstable nature of \(\mathrm{NBr}_{3}\) and \(\mathrm{NI}_{3}\) can be ascribed to increased atomic size and electron repulsion, while \(\mathrm{NI}_{3} \cdot \mathrm{NH}_{3}\) is more stable because of the coordinating bond formation.