Predict the number and nature of bonds using Molecular Orbital Theory

I found the following question in a high school chemistry problem book:



> 
> According to Molecular Orbital Theory which of the following is true:
> 
> 
> (A) In $C\_2$ molecule both the bonds are $\pi$ bonds.
> 
> 
> (B) In $C\_2^{2-}$ ion there is one $\sigma$ and one $\pi$ bond.
> 
> 
> 


Both of these are true. But how can one know this using Molecular Orbital Theory?


P.S.: I don't know anything about Quantum Mechanics as I am a high school student. My textbooks only provide a result-oriented explanation. I would appreciate if the answers keep this in mind.




I presume you can draw the homonuclear diatomic MO diagram for these two species. 


As you probably already know, the s orbitals of the carbons form bonding and antibonding orbitals, both of which are filled. (The net effect of this is the “lone pairs” on each carbon.) 


The p orbitals for 2 pi bonds and a sigma bond. Due to s-p mixing, the pi bonds are lower in energy and are filled first, and these 2 bonds (with their 4 electrons) are the 2 bonds we see in C2. 


Add another 2 electrons to the system and you realise they fill the sigma bonding orbital, which means that the C2 2- anion has 2 pi bonds and a sigma bond (for a total bond order of 3). 


Hope this helped.


 1

According to the same book (Resonance Chemistry for JEE Main and Advanced), bond order of $1$, $2$ and $3$ correspond to single, double and triple bond.


This is a rule of thumb and most common molecules, such as $O\_2$, $N\_2$, etc., seem to follow it.


 0