Which one of the following does not have sp² hybridised carbon?

The correct option is Acetonitrile.

To determine which compound does not contain an
${\mathrm{sp}}^2$
hybridized carbon atom, we can analyze the bonding structure and count the number of $\sigma$-bonds (sigma bonds) formed by each carbon atom in the given molecules:

1. Acetone (CH₃-CO-CH₃):
The central carbonyl carbon is double-bonded to an oxygen atom and single-bonded to two methyl groups. It forms 3 $\sigma$-bonds and 1 $\pi$-bond, which gives it an
${\mathrm{sp}}^2$
hybridization state.

2. Acetic acid (CH₃-COOH):
The carbonyl carbon is double-bonded to an oxygen atom, single-bonded to a hydroxyl group (-OH), and single-bonded to a methyl group. It forms 3 $\sigma$-bonds, making it
${\mathrm{sp}}^2$
hybridized.

3. Acetamide (CH₃-CONH₂):
The carbonyl carbon is double-bonded to an oxygen atom, single-bonded to an amino group (-NH₂), and single-bonded to a methyl group. It forms 3 $\sigma$-bonds, which corresponds to
${\mathrm{sp}}^2$
hybridization.

4. Acetonitrile (CH₃-C≡N):
The methyl carbon (CH₃) is single-bonded to three hydrogen atoms and one carbon atom, making it
${\mathrm{sp}}^3$
hybridized. The nitrile carbon (C≡N) is triple-bonded to a nitrogen atom and single-bonded to the methyl carbon. It forms 2 $\sigma$-bonds and 2 $\pi$-bonds, resulting in an
$\mathrm{sp}$
hybridization state.

Since acetonitrile contains only
${\mathrm{sp}}^3$
and
$\mathrm{sp}$
hybridized carbon atoms, it does not have any
${\mathrm{sp}}^2$
hybridized carbon.