Use valence bond theory to write the hybridization and bonding scheme for NCCH3. Sketch the model with the right geometry?

Step 1. Draw the Lewis structure

(a) Start with a skeleton structure.

The two #"C"# atoms (least electronegative) will be the central atoms, with the #"N"# attached to one of the carbons.

(b) Attach the hydrogen atoms.

The question gives you a clue where they go.

The formula #"NCCH"_3# tells you that the three #"H"# atoms are attached to the terminal carbon atom.

(c) Add electrons so that every atom gets an octet.

There is only one good way to do it: put a triple bond between the #"C"# and the #"N"#, and a lone pair on the #"N"#.

Step 2. Use VSEPR theory to predict the geometry about each atom.

• The terminal #"C"# atom: four electron domains (3 #"C-H"# bonds and a #"C-C"# bond).
  ∴ Tetrahedral.
• The central #"C"# atom: two electron domains (a #"C-C"# bond and a #"C≡N"# bond).
  ∴ Linear.
• The #"N"# atom: two electron domains (a #"C≡N"# bond and a lone pair)

Step 3. Assign hybridizations to each atom

• The terminal #"C"# atom: tetrahedral. ∴ #"sp"^3# hybridized.
• The central #"C"# atom: linear. ∴ #"sp"# hybridized.
• The #"N"# atom: two electron domains. ∴ #"sp"# hybridized.

Step 4. Sketch the orbitals involved

Here is my drawing (apologies! I'm not a graphics artist).

My drawing may be confusing, so here is a description:

• #"H"# atoms: unhybridized #"1s"# orbitals
• Terminal #"C"# atom: #"sp"^3# hybridized; bond angles 109.5°
• #"C-H"# bonds: σ bonds formed by overlap of #"H 1s"# and #"C sp"^3# orbitals
• Central #"C"# atom: #"sp"# hybridized
• #"C-C"# bond: σ bond formed by overlap of #"C sp"^3# and #"C sp"# orbitals
• #"N"# atom: #"sp"# hybridized.
• #"C≡N"# bond: σ bond formed by overlap of #"C sp"# and #"N sp"# orbitals, plus two bonds formed by side-on overlap of unhybridized #"2p"# orbitals
• #"C-C-N"# bond angle = 180°

Here's a model of the molecule for comparison: