Bonding, Nonbonding and Antibonding MOs

[Stratosphere]

Homework Statement

Ignoring any orbitals not in the valence shell how many orbitals are in each of the following molecules? How many are bonding, nonbonding, and antibonding? How many orbitals are occupied?
Co2

Homework Equations

The Attempt at a Solution

The answer it gives in the book is 4 of each. I tried it and I got confused. The solution it gives is this.

"Carbon dioxide has one carbon and two oxygens. Each of these three atoms contribute one 2s orbital and three 2p orbitals. Thus, there are a total of twelve atomic orbitals in the valence shells of these atoms and twelve molecular orbitals in the molecule. Each atom obeys the octet rule. There are a total of four each of bonding, nonbonding and antibonding molecular orbitals so eight orbitals are filled."

Can someone explain it a little bit clearer than that?

 

[x12179x]

Wikipedia has Carbon Dioxide as one of it's examples in the MO article:
http://en.wikipedia.org/wiki/Molecular_orbital_diagram#Carbon_Dioxide_MO_DiagramHere is my summary using the images from the wiki article:
The first image in the CO2 section is of the atomic orbitals (AO) of Carbon and Oxygen
The 2nd image are the Molecular Obritals (MO) when Carbon and Oxygen combine to become Carbon dioxide.

In the 2nd image, the 1st column shows which AOs the MO came from. The last column shows which MOs are Bonding, Anit-bonding and Non bonding.

For example:
Take AO1 (which is Carbon's 2s orbital) and AO8 (which are the two Oxygen's 2pz orbital)

When you combine an AO1 and two AO8 to make O=C=O (Carbon dioxide), you can either get what looks like MO1 or MO2.

In the image the AO1 orbital is blue (lets call it +)

Each of the AO8 orbital has 2 phases (red and blue, or - and +). When same phase overlap, it is called bonding, if opposite phase, it is anti-bonding.

With AO1 + 2 AO8, you can get:
O ===== C ===== O
(-)(+)... (+) ... (+)(-) Bonding
or
(+)(-) ...(+) ...(-)(+) Anti-bondingThe other MOs work the same way (from combining the AOs of C and O into O=C=O using the different possible phase orientations that exists)s orbital can only overlap with Pz orbital only because of it's orientation, so oxygen's two Py's and 2 Px's orbitals combine with carbon's 2s orbital to form a nonbonding orbital.

 

[Blueshift5]

Sure! Let's break it down step by step.

First, we need to understand what bonding, nonbonding, and antibonding molecular orbitals (MOs) are. These are different types of MOs that result from the combination of atomic orbitals (AOs) from different atoms in a molecule.

Bonding MOs are formed when two atomic orbitals combine in a way that increases electron density between the nuclei of the atoms, promoting bonding. Nonbonding MOs are formed when two atomic orbitals combine in a way that does not significantly affect electron density between the nuclei, resulting in no bonding or antibonding effects. Antibonding MOs are formed when two atomic orbitals combine in a way that decreases electron density between the nuclei, promoting antibonding.

Now, let's apply this to the molecule CO2. Each carbon atom has one 2s orbital and three 2p orbitals, and each oxygen atom also has one 2s orbital and three 2p orbitals. That's a total of twelve atomic orbitals in the valence shells of these atoms. When these atomic orbitals combine, they form twelve molecular orbitals.

The octet rule states that atoms tend to form bonds in order to achieve a stable octet (eight valence electrons). In CO2, each atom obeys the octet rule by sharing electrons with the other atom, forming a double bond between the carbon and each oxygen. This means that there are a total of four bonding MOs in CO2 - one for each double bond.

Since each oxygen atom has two lone pairs of electrons, there are also four nonbonding MOs in CO2 - two for each oxygen atom.

Finally, there are four antibonding MOs in CO2 - one for each double bond.

In terms of occupied orbitals, we can see that there are a total of eight filled orbitals - four bonding and four nonbonding MOs. The antibonding MOs are not filled because they promote antibonding and do not contribute to the stability of the molecule.

I hope this explanation helps to clarify the concept of bonding, nonbonding, and antibonding MOs in the molecule CO2. Let me know if you have any further questions.