How to Determine the Number of Pi Bonds in a Molecule Using the MO Model?

[yecko]

Homework Statement

http://i.imgur.com/HunOeH0.png

Homework Equations

MO model

The Attempt at a Solution

as far as i know, number of pi bond is equal to 3 - the "power" of p (the hybridized bond formed)
the answer "4" is only calculated from the 4 elements' bond in part b, so why the central O and C atom is not considered with calculation of pi bond? Thanks!

 

[Ygggdrasil]

Each single bond consists of one sigma bond. Each double bond consists of one sigma bond and one pi bond.

 

[yecko]

Does that means the number of pi bond is independent to degree of hybridization?
Thanks!

 

[Ygggdrasil]

Does that means the number of pi bond is independent to degree of hybridization?
Thanks!

They are not independent as you generally need an unhybridized p-orbital to form a pi bond, but the number of unhybridized p-orbitals will not always be indicative of the number of pi bonds. It's much easier to simply count the number of double and triple bonds shown in the molecule.