The number of molecules/ions that show linear geometry among the following is ______. SO2, BeCl2, CO2, N3 – , NO2, F2O, XeF2, NO2 + , I3 – , O3

1. VSEPR Theory Refresher

VSEPR stands for Valence Shell Electron Pair Repulsion. It says that electron pairs—bonding or lone—repel each other and arrange themselves to minimise this repulsion. The steric number (SN) tells you the total directions of repulsion: $\text{SN} = \text{number of sigma bonds} + \text{number of lone pairs on central atom}$

• SN = 2 → electronic geometry is linear.
• SN = 3 → trigonal planar (could give bent shape if 1 lone pair).
• SN = 4 → tetrahedral (bent if 2 lone pairs).
• SN = 5 → trigonal bipyramidal (linear if formula is AX_2E_3).
• SN = 6 → octahedral (linear if formula is AX_2E_4).

2. Step-wise Logic a Student Follows

1. Write Lewis structure to count sigma bonds and lone pairs on the central atom.
2. Compute steric number.
3. Match SN to parent electronic geometry.
4. Deduce the molecular shape (AX_mE_n notation)—linear, bent, trigonal planar, etc.
5. Mark as linear or not.
6. Count all linear cases.

3. Why each step?

Lewis structure lets you see lone pairs (balloons). Steric number is a shortcut so you never mis-classify geometry. AX_mE_n notation directly tells the shape:
• $AX\_2$ with no lone pairs → linear
• $AX\_2E\_3$ (trigonal bipyramidal arrangement) → also linear because the two X’s occupy axial positions 180° apart.
• Similar idea applies for $AX\_2E\_4$ in octahedral arrangement (e.g. I_3^–).
Identifying these special cases quickly delivers the answer.

What is the question?

You are given 10 different chemical species and you have to count how many of them are straight-line shaped (we call that linear geometry).

How to think about it like a 10-year-old?

Imagine each molecule as a set of balls (atoms) joined by sticks (bonds). A linear molecule is like a straight pencil—all balls sit in one straight row. To know if the balls can sit in a row, we need to know how many invisible balloons (lone-pair electrons) are pushing the sticks around. If the balloons are arranged so that the balls must stand in a straight line, the molecule is linear. If balloons push the sticks down into a V-shape, it is bent and not linear.

The question wants us to use a rulebook called VSEPR theory (Valence Shell Electron Pair Repulsion) to decide the shape for each molecule and simply count the straight ones.

Step 1 – Write steric numbers & shapes

1. $SO_2$: S with 2 sigma bonds + 1 lone pair → SN = 3 → bent (not linear).
2. $BeCl_2$: Be with 2 sigma bonds, no lone pair → SN = 2 → linear.
3. $CO_2$: C with 2 sigma bonds, no lone pair → SN = 2 → linear.
4. $N_3^-$ (azide ion): central N forms 2 sigma bonds, no lone pairs → SN = 2 → linear.
5. $NO_2$ (nitrogen dioxide): N with 2 sigma bonds + 1 unpaired electron → effective SN ≈ 3 → bent.
6. $F_2O$ (OF2): O with 2 sigma bonds + 2 lone pairs → SN = 4 → bent.
7. $XeF_2$: Xe with 2 sigma bonds + 3 lone pairs → SN = 5 ($AX_2E_3$) → linear.
8. $NO_2^+$ (nitronium ion): N with 2 sigma bonds, 0 lone pair → SN = 2 → linear.
9. $I_3^-$: I with 2 sigma bonds + 3 lone pairs → SN = 5 ($AX_2E_3$) → linear.
10. $O_3$ (ozone): central O with 2 sigma bonds + 1 lone pair → SN = 3 → bent.

Step 2 – List the linear ones

$BeCl_2$, $CO_2$, $N_3^-$, $XeF_2$, $NO_2^+$, $I_3^-$ ➝ 6 molecules/ions.

Final Answer

$\boxed{6}$