Chem 2: # of pi bonds in a molecule

[CausativeAgent]

Homework Statement

How many pi bonds are in the molecule C12H18?

Homework Equations

I have in my notes the formula (6nPi+2-total # of electrons)/2.

The Attempt at a Solution

Unfortunately I can't find an explanation for this formula in the book and I don't remember what was shown in lecture. I do know that there are 66 valence electrons total in this molecule. I also understand the basic definitions of pi and sigma bonds.

 

[mrjeffy321]

As I remember it,
For every single bond, you have one “sigma” bond.
If you have a double bond, you have one “sigma” bond and one “pi” bond.
If you have a triple bond, you have 1 sigma bond and two pi bonds.

So to find the total number of pi bonds in the molecule, you need to identify the number of double and triple bonds in the molecule.
# of pi bonds = (# double bonds) + (2 * # of triple bonds)

It would help to draw out the structure with the appropriate bonds between the atoms.

 

[CausativeAgent]

Thanks for the reply. But I'm almost positive there is a quicker way to do it using that formula. This would be one of many questions on a one hour test and drawing the lewis structure for something that big would take me forever. One thing to add for clarification is I think technically that formula is for the maximum number of pi bonds. Also, it is not 100% accurate and may be off by one or two.

 

[chemisttree]

The empirical formula (C12H18) doesn't have enough information to tell you that without making at least one assumption. That assumption would be that the compound contains either a known number of cyclic structures or no cyclic structures. For acyclic compounds, the empirical formula should be CnH2n+2. You can prove this to yourself by inspection (try ethane, propane, etc...).

So, for a C12 molecule, the hydrogens should equal to 2(12)+2=26. We have 18 and at least 2 hydrogens must be removed to form each pi bond or cyclic structure. For example C6H12 could be cyclohexane (no pi bonds) or hexene (any of 3 isomers with 1 pi bond). If we assume that the molecule is acyclic, C12H18 has 8 fewer hydrogens that would be predicted for a saturated compound and therefore has 4 pi bonds.

For the answer to the question regarding the maximum number of pi bonds, assume that the molecule is acyclic.

 

[CausativeAgent]

I finally just decided to ask my teacher. Your method does yield the correct answer but it shows a greater depth of understanding than we're required to have at this point. It turns out that formula just means six multiplied by the number of atoms that can potentially form pi bonds plus two minus the total # of valence electrons, all divided by two. So for C12H18 it would be:

(6x12+2-66)/2 = 4