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All single bonds are sigma bonds. All double bonds have one pi bond and one sigma bond. All triple bonds have one sigma bond and two pi bonds and so on. Pi bonds do not allow the molecule to rotate as much as sigma bonds do.
Yes, the first bond would be a sigma bond, followed by a pi bond for each additional bond. For example, for a sp hybridization (triple bond), there would be one sigma bond and two pi bonds (using the two empty 2p orbitals).
Yes, all single bonds are sigma as single bonds are the weakest and thus have the most room for rotation and movement. Double and triple bonds are stronger and thus resist movement hence making them pi bonds.
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