In a sn2 reaction why do we need sp3 hybrid orbital and not sp2 for the substrate

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In a sn2 reaction why do we need sp3 hybrid orbital and not sp2 for the substrate

Chemistry
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I'm guessing it is because their are some lone pairs of electrons on the molecule.
Because the geometry at the reaction center is inverted during the reaction, and that can't happen if the reaction center is sp2 hybridized -- the pi bonding will prevent it. Or, to put it another way, the transition state has to consist of three bonds in the plane and two bonds (one forming, one breaking) along the internuclear axis between substrate and nucleophile. This can't happen if the substrate has pi bonding occupying the necessary space. Or more precisely, it can happen, but it takes a lot more energy.

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