1. Identify the type of molecules

All the given molecules are of the type $ECl_3$ where $E = N, P, As, Sb$.

Each central atom has:

• $5$ valence electrons
• forms $3$ bonds with $Cl$
• has $1$ lone pair

So, all have trigonal pyramidal shape with tetrahedral electron-pair geometry.

2. Factor affecting bond angle

For group 15 trichlorides, the bond angle generally decreases down the group:

$NCl_3 > PCl_3 > AsCl_3 > SbCl_3$

This happens because as we move down the group:

• size of central atom increases,
• hybridization becomes less effective,
• bonding tends toward nearly pure $p$-orbital character,
• bond angle approaches $90^\circ$.

Thus, the smallest bond angle should be for the heaviest central atom among the options, i.e. $SbCl_3$.

3. Check options

• A: $NCl_3$ — larger bond angle
• B: $AsCl_3$ — smaller than $PCl_3$, but not the smallest
• C: $SbCl_3$ — smallest bond angle
• D: $PCl_3$ — larger than $AsCl_3$ and $SbCl_3$

4. Final answer

The molecule having the smallest bond angle is:

$\boxed{SbCl_3}$

So, Option C is correct.