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My teacher and textbook distinguish between the $sp$,$sp^2$ and $sp^3$ hybrid orbitals' shapes by saying that the first has linear shape, the second has trigonal shape, and the third has tetrahedral shape. Are they saying this because in the case of $sp$ hybridization, since 2 different orbitals hybridized to form this orbital, the total number of hybridized orbitals will also be 2(stated by MO theory)? So since 2 bonds are created, the shape of molecule will be linear. Similarly in $sp^2$, there will be 3 hybridized orbitals therefore 3 bonds, thus trigonal shape. Is this what it means to say that the $sp$ has "linear shape"? (Meaning that the "shape of the hybridized orbital" is just the same as the molecule formed when that hybridization takes place.)

Also, won't this not consistently be true when lone electron pairs are involved as based on VSEPR theory, their repulsions affect the geometry of the molecule? Or is it that the shape of hybrid orbitals is the same despite lone pairs because sometimes lone pairs themselves are inside hybrid orbitals?

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    $\begingroup$ Well, the shapes of the orbitals are alike as they come from linear combinations of the same orbitals. However, they coordinate in different ways. More precisely, the coordination determines how the organisations will combine. $\endgroup$ Commented Aug 29, 2022 at 0:02
  • $\begingroup$ Related: chemistry.stackexchange.com/q/82133/72973 $\endgroup$
    – Karsten
    Commented Aug 29, 2022 at 18:01

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