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Question 31

Amongst the following, the linear species is:

To identify the linear species, we apply VSEPR theory by counting the steric number (number of bonding pairs + lone pairs) around the central atom of each molecule.

For $$\text{NO}_2$$: nitrogen is the central atom with 17 total valence electrons (5 from N + 6+6 from two O). After forming two N-O bonds, nitrogen has one unpaired electron remaining. The electron geometry is trigonal planar (steric number 3), and the molecular geometry is bent with a bond angle of about 134°. This is not linear.

For $$\text{Cl}_2\text{O}$$: oxygen is the central atom with 20 valence electrons (7+7 from two Cl + 6 from O). Oxygen forms two single bonds with chlorine and has two lone pairs, giving a steric number of 4. The molecular geometry is bent (similar to water), so this is not linear.

For $$\text{O}_3$$: the central oxygen has 18 valence electrons (6+6+6). After forming bonds with the two terminal oxygens, the central oxygen has one lone pair, giving a steric number of 3. The molecular geometry is bent with a bond angle of about 117°. This is not linear.

For $$\text{N}_3^-$$: this ion has 16 valence electrons (5+5+5 from three N + 1 for the negative charge). The central nitrogen forms two double bonds with the terminal nitrogen atoms and has no lone pairs, giving a steric number of 2. With two bonding regions and zero lone pairs, the geometry is linear with a bond angle of 180°.

Therefore, the linear species is $$\text{N}_3^-$$, which is Option D.

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