Step 1: Concept
The shape of a molecule is determined by the arrangement of atoms around the central atom. This can be predicted using the Valence Shell Electron Pair Repulsion (VSEPR) theory, which states that electron pairs around a central atom will arrange themselves to minimize repulsion.
Step 2: Meaning
In VSEPR theory, the number and type of bonding pairs and lone pairs on the central atom determine the molecular shape. A linear molecule has two regions of electron density, resulting in a straight line between the atoms involved.
Step 3: Analysis
Let's analyze each option:
A) $\text{CO}_2$
Carbon (C) is the central atom.
It has 4 valence electrons and forms double bonds with both oxygen (O) atoms.
There are no lone pairs on carbon in this molecule.
The two regions of electron density around carbon are bonding pairs, leading to a linear shape.
B) $\text{H}_2\text{O}$
Oxygen (O) is the central atom.
It has 6 valence electrons and forms single bonds with both hydrogen (H) atoms.
There are two lone pairs on oxygen in this molecule.
The four regions of electron density around oxygen result in a bent shape, not linear.
C) $\text{SO}_2$
Sulfur (S) is the central atom.
It has 6 valence electrons and forms double bonds with both oxygen (O) atoms.
There is one lone pair on sulfur in this molecule.
The four regions of electron density around sulfur result in a bent shape, not linear.
D) $\text{NH}_3$
Nitrogen (N) is the central atom.
It has 5 valence electrons and forms single bonds with three hydrogen (H) atoms.
There is one lone pair on nitrogen in this molecule.
The four regions of electron density around nitrogen result in a trigonal pyramidal shape, not linear.
Step 4: Conclusion
The only molecule that has a linear shape is $\text{CO}_2$.
Final Answer: (A)