Chemical Bonding: Question 5

Worked solution

Step 1: Recall how sigma and pi bonds form

A $\sigma$ bond forms from the direct, “end-on” overlap of two orbitals along the axis joining the two nuclei. Every single covalent bond is a $\sigma$ bond, and every multiple bond (double or triple) contains exactly one $\sigma$ bond as its first component.

A $\pi$ bond forms from the sideways overlap of two unhybridised $p$ orbitals, one above and one below the internuclear axis. A double bond adds one extra $\pi$ bond on top of the $\sigma$ bond; a triple bond adds two extra $\pi$ bonds on top of the $\sigma$ bond.

Step 2: Identify every bond in ethyne

Ethyne, $\text{H–C}{\equiv}\text{C–H}$, contains three bonds in total:

• Two C–H bonds (one at each end of the molecule).
• One C≡C triple bond (between the two carbon atoms).

Step 3: Classify each bond as sigma or pi

• Each C–H bond is a single bond, so it is one $\sigma$ bond. Two C–H bonds contribute $2\sigma$.
• The C≡C triple bond consists of one $\sigma$ bond (from direct overlap of $sp$ hybrid orbitals on the two carbons) plus two $\pi$ bonds (from sideways overlap of two perpendicular pairs of unhybridised $p$ orbitals). This contributes $1\sigma$ and $2\pi$.

Step 4: Add up the totals

$\sigma \text{ bonds} = \underbrace{2}_{\text{C–H bonds}} + \underbrace{1}_{\text{C–C triple bond}} = 3$

$\pi \text{ bonds} = \underbrace{0}_{\text{C–H bonds}} + \underbrace{2}_{\text{C–C triple bond}} = 2$

So ethyne contains $3\sigma$ bonds and $2\pi$ bonds in total.

Why the other options are wrong

• B ($2\sigma$ and $3\pi$): this swaps the sigma and pi counts. A triple bond is $1\sigma + 2\pi$, not $2\sigma + 1\pi$, and there are two C–H $\sigma$ bonds to add as well.
• C ($4\sigma$ and $1\pi$): this undercounts the $\pi$ bonds in the triple bond (only one instead of two) while overcounting the $\sigma$ bonds.
• D ($5\sigma$ and $0\pi$): this treats every bond, including the triple bond, as if it were made only of $\sigma$ bonds, ignoring the sideways $p$-orbital overlap that forms $\pi$ bonds altogether.

Final answer

• Ethyne contains $\boxed{3\sigma}$ bonds and $\boxed{2\pi}$ bonds, option A.