Animated Solution for Chemistry - Chemical Bonding and Molecular Structure: The molecule having smallest bond angle is

When we look at the trichlorides of Group 15 elements—specifically ${\text{NCl}}_3$, ${\text{PCl}}_3$, ${\text{AsCl}}_3$, and ${\text{SbCl}}_3$—we are dealing with a classic case of $s{p}^3$ hybridization. The central atom in each of these molecules possesses five valence electrons. Three of these electrons are shared with chlorine atoms to form sigma bonds, leaving one non-bonding pair, or a lone pair, sitting atop the central atom.

This arrangement gives the molecules a trigonal pyramidal geometry. If all four electron domains were identical bond pairs, the bond angle would be a perfect $109.5^{\circ }$. However, the presence of the lone pair changes the game entirely.

According to the Valence Shell Electron Pair Repulsion (VSEPR) theory, not all electron pairs repel each other equally. A lone pair is held exclusively by the central atom, making it spread out more in space compared to a bond pair, which is constrained between two nuclei.

Because of this, the repulsion between a lone pair and a bond pair (lp-bp repulsion) is significantly stronger than the repulsion between two bond pairs (bp-bp repulsion). This dominant lone pair acts like a heavy weight, pushing the three $\text{M-Cl}$ bonds closer together and compressing the bond angle $\theta$ to something less than $109.5^{\circ }$.

To determine which molecule has the smallest bond angle, we must look at the central atoms: Nitrogen (N), Phosphorus (P), Arsenic (As), and Antimony (Sb). As we descend Group 15 in the periodic table, the atomic radius increases, and the electronegativity of the central atom decreases. Nitrogen is highly electronegative, while Antimony is the least electronegative of the group.

In ${\text{NCl}}_3$, the highly electronegative Nitrogen atom pulls the shared electron pairs of the $\text{N-Cl}$ bonds very close to itself. Because these bond pairs are crowded tightly around the Nitrogen nucleus, the repulsion between them (bp-bp repulsion) is very strong. This strong internal resistance fights back against the downward push of the lone pair, keeping the bond angle relatively large.

Now, contrast this with ${\text{SbCl}}_3$. Antimony is a large atom with low electronegativity. It cannot hold onto the shared electrons as tightly as Nitrogen does. Consequently, the bond pairs shift away from the Antimony atom and move closer to the more electronegative Chlorine atoms.

With the bond pairs further away from the central atom, the electron density near Antimony drops, and the bp-bp repulsion weakens significantly. Because the bond pairs are no longer fighting back as strongly, the lone pair at the top can easily push the bonds even closer together.

Therefore, as we go down the group, the bond angle steadily decreases: ${\text{NCl}}_3>{\text{PCl}}_3>{\text{AsCl}}_3>{\text{SbCl}}_3$. The molecule with the smallest bond angle is undoubtedly ${\text{SbCl}}_3$.