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What are the factors that decide which type of hybridization will take place in an atom...

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What are the factors that decide which type of hybridization will take place in an atom at the time of bonding?

In the methane molecule carbon undergoes sp3 hybridisation but in ethene it undergoes sp2 and in ethyne it undergoes sp.

What is the reason for this?

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If you are asking why ethane forms in nature as ethane and not ethylene or ethyne, I'm not sure that anyone can really answer that on the atomic level.  In terms of chemical synthesis, you can think of all carbon bonds as inherently single bonds.  Even in multiple bonds, there is still one underlying pair of electrons making a direct covalent bond like a single bond; you just have an additional set or two of p electrons making additional bonds in the double and triple bond case. In terms of chemical synthesis, this usually happens when the chemistry allows vacant p orbitals to exists on adjacent carbon atoms.  This can happen if there is a good electronegative leaving group (like a halogen) on a carbon atom.  The electrons that form the carbon halogen bond can go to the halogen to make an anion, thus leaving a vacant p orbital on the carbon.  A base can remove a proton from the adjacent carbon, and the resulting electrons form the carbon-carbon double bond.  This type of process is called dehydrohalogenation and is illustrated in the first link below.


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