Is My Assumption on Chemical Bonding in Hydrocarbons Correct?

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Harmony
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While studying chemical bonding for methane,ethyne etc., I have made the following assumption to help me to remember the sigma bond, pai bond, and hybrid orbitals.
1. Every single covalent bond around a carbon atom is a sigma bond.
2. Only one of the bond in double and triple covalent bond is a sigma bond. The others are pai bond.
3. If there are 4 sigma bond around a single carbon atom, sp^3 hybid orbitals are involved.

Is my assumption wrong? Or they are just suitable for certain hyddrocarbon?
 
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Actually it is not necessarily true that there is atleast one sigma bond in a double or triple bond. This is because since the bonds repell each other, you are going to have two pi bonds rather than a sigma and a pi. I am not completely sure though.
-scott
 
Thats right, if there are 4 bonds from a carbon, they are sp3.