How To Calculate A Steric Number

As well as their unique properties, different molecules have different geometries. You can use valence shell electron pair repulsion alongside the steric number of a molecule to determine its geometric structure. This is one of the reasons that understanding what the steric number of a molecule is and how you calculate it is crucial for chemistry students and anybody looking to investigate molecular geometry.

The process of finding the steric number is pretty straightforward though, as long as you can count molecular bonds and use a molecule's Lewis structure to find lone electron pairs.

The steric number of a molecule is the number of other atoms bonded to the central atom of the molecule plus the number of lone pairs of electrons attached to it.

This is used to determine molecular geometry because electrons in pairs repel each other, whether those pairs are bonding electrons or lone pairs not bonded to a particular atom. Because they position themselves so as to achieve maximum separation, the relatively simple measure of the steric number tells you the overall shape of the molecule.

For a molecule with a steric number of 2, there will be a linear structure, and for a steric number of 3 there will be a trigonal planar structure. Continuing in the same way, a steric number of 4 leads to tetrahedral structure, 5 gives a trigonal bipyramidal structure and a steric number of 6 leads to an octahedral structure.

The steric number formula can be written down directly based on the definition given above, as:

Steric number = (number of atoms bonded to the central atom) + (number of lone pairs of electrons on the central atom)

The challenge in calculating the steric number is therefore less one of actual calculation and more of looking at the structure of the molecule in terms of bonding electrons and finding the two numbers you need. This is fairly easy to do if you look at the Lewis structure of the molecule and understand how to find a lone electron pair.

The Lewis structure of a molecule is a representation of the electrons in the valence shell for the atoms in the molecule, generally represented by dots surrounding the atoms, which are shown by their standard symbols (e.g. O for oxygen, C for carbon, H for hydrogen and Cl for chlorine).

First, draw the atoms and their bonds according to the molecular formula and/or what you already know about the molecule. For example, water (H₂O) is represented by a central O atom, with two H atoms connected by a single bond (individual straight line) on either side of it.

Fill in the remaining electrons in the valence shell (i.e. the ones available for bonding not currently part of a bond). For oxygen, there are six valence electrons, and two of these are involved in the bonds with the hydrogen atoms, leaving four valence electrons to fill in. Draw two pairs of dots around the O symbol to complete the diagram.

The lone pairs for oxygen are these two pairs of electrons not involved in molecular bonding. Of course, other situations lead to different types of Lewis structures, and you'll have to think a little more in certain cases.

For example, electrons don't form pairs unless there are no "spaces" available outside of a pair, e.g. in carbon, there are four valence electrons, but with eight total spots available, the electrons don't need to form pairs to fit in the shell and so they don't.

Using the steric number formula is easy once you've drawn the Lewis structure for the molecule in question. Look at the central atom and count each of the bonds (even if it's a double or triple bond) attached to it as one each. Then look at the dots surrounding the atom: are there any pairs not involved in bonding? If so, add one to the total for each example.

For H₂O, the central oxygen atom is bonded to two hydrogen atoms, and there are two pairs of electrons remaining around it. This can be inserted into the steric number formula to find the result:

\(\begin{aligned}
\text{Steric number} &= \text{(number of atoms bonded to the central atom)} + \text{(number of lone pairs of electrons on the central atom)} \
&= 2 + 2 \
&= 4
\end{aligned}\)

And so water has a tetrahedral structure, although part of this structure is composed of the lone pairs of electrons.