Animated Solution for Chemistry - Chemical Bonding and Molecular Structure: The number of species having non-pyramidal shape among the following is (i) ${\text{SO}}_3$ (ii) ${\text{NO}}_3^{-}$ (iii) ${\text{PCl}}_3$ (iv) ${\text{CO}}_3^{2-}$

A Journey Through VSEPR Theory

Have you ever wondered why water is bent, but carbon dioxide is perfectly straight? The invisible architecture of the universe is governed by a beautifully simple concept: electrons hate each other. Because electrons are negatively charged, they repel one another and try to get as far apart as physically possible. This is the heart of Valence Shell Electron Pair Repulsion (VSEPR) Theory.

In this problem, we are tasked with acting as molecular architects. We need to look at four different species—${\text{SO}}_3$, ${\text{NO}}_3^{-}$, ${\text{PCl}}_3$, and ${\text{CO}}_3^{2-}$—and determine which of them are not shaped like a pyramid. To do this, we need our master key: the Steric Number.

Steric Number

The steric number ($H$) tells us how many electron domains (bonds and lone pairs) are surrounding the central atom. The formula is incredibly powerful:

Here, $V$ is the number of valence electrons on the central atom. $M$ is the number of monovalent atoms (like hydrogen or halogens) attached to it. $C$ is the cationic (positive) charge, and $A$ is the anionic (negative) charge.

Let's apply this master key to our suspects.

1. Sulfur Trioxide (${\text{SO}}_3$) Sulfur sits in Group 16, so it has $6$ valence electrons ($V=6$). It is bonded to three oxygen atoms. But wait! Oxygen is divalent (it forms double bonds), so it does not count towards $M$. Therefore, $M=0$. There is no charge on the molecule.

A steric number of $3$ means the central sulfur atom is $s{p}^2$ hybridized. Since it is bonded to exactly $3$ oxygen atoms, there are no lone pairs left over ($3-3=0$). Three bonds pushing away from each other will naturally form a flat triangle. Thus, ${\text{SO}}_3$ is Trigonal Planar.

2. Nitrate Ion (${\text{NO}}_3^{-}$) Nitrogen is in Group 15, giving it $5$ valence electrons ($V=5$). Again, oxygen is divalent, so $M=0$. However, we have a negative charge, meaning the molecule has gained an extra electron ($A=1$).

Just like sulfur trioxide, the nitrate ion has a steric number of $3$, $s{p}^2$ hybridization, and zero lone pairs. It is also perfectly flat. Shape: Trigonal Planar.

3. Phosphorus Trichloride (${\text{PCl}}_3$) Now for the plot twist. Phosphorus is in Group 15 ($V=5$). It is bonded to three chlorine atoms. Chlorine is a halogen and only needs one electron to complete its octet, making it monovalent ($M=3$). There is no charge.

A steric number of $4$ means the phosphorus atom is $s{p}^3$ hybridized, which normally forms a tetrahedron. But look closely: there are only $3$ chlorine atoms attached. This means one of the four electron domains is an invisible lone pair ($4-3=1$). This lone pair sits on top of the phosphorus atom, pushing the three chlorine atoms down. The result? A three-sided pyramid. Shape: Trigonal Pyramidal.

4. Carbonate Ion (${\text{CO}}_3^{2-}$) Finally, let's look at the carbonate ion. Carbon has $4$ valence electrons ($V=4$). Oxygen is divalent ($M=0$). The ion has a $-2$ charge, meaning it has gained two extra electrons ($A=2$).

We are back to a steric number of $3$. With $s{p}^2$ hybridization and zero lone pairs, the carbonate ion is flat. Shape: Trigonal Planar.

The question asks for the number of species having a non-pyramidal shape.

- ${\text{SO}}_3$: Trigonal Planar (Non-pyramidal) - ${\text{NO}}_3^{-}$: Trigonal Planar (Non-pyramidal) - ${\text{PCl}}_3$: Trigonal Pyramidal - ${\text{CO}}_3^{2-}$: Trigonal Planar (Non-pyramidal)

Exactly three of these species are flat and non-pyramidal. Therefore, the final answer is 3.