What is the total number of sigma and pi bonds in the following molecules? (a) C₂H₂ (b) C₂H₄

Exercises · 4.28

Q. What is the total number of sigma and pi bonds in the following molecules?

(a)

C_2H_2

(b)

C_2H_4

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Concept understanding — Bond Order Strength

Bond Order Strength: From Intuition to Precision

Imagine two people holding hands. If they just touch fingertips, a gentle breeze can separate them. If they clasp firmly, it takes more effort to pull them apart. If they lock arms, you need real force. That's the core idea behind bond order — it tells you how strongly two atoms are connected in a molecule.

The Intuition

In a chemical bond, atoms share electrons. The more electron pairs they share, the tighter the grip. A single bond (one shared pair) is like a handshake — it works, but it's easy to break. A double bond (two shared pairs) is like a firm clasp — stronger, shorter, harder to pull apart. A triple bond (three shared pairs) is like a wrestler's lock — very strong and very short.

This directly translates to real molecules:

C–C single bond: bond energy ≈ 350 kJ/mol, bond length ≈ 154 pm
C=C double bond: bond energy ≈ 610 kJ/mol, bond length ≈ 134 pm
C≡C triple bond: bond energy ≈ 835 kJ/mol, bond length ≈ 120 pm

More shared electrons → stronger bond → shorter bond. That's the pattern.

The Precise Definition

Bond order is the number of chemical bonds between a pair of atoms. For simple molecules, it's just the number of shared electron pairs:

\text{Bond Order} = \frac{\text{Number of bonding electrons} - \text{Number of antibonding electrons}}{2}

This formula matters most when you move beyond simple Lewis structures — for molecules with resonance or molecular orbital theory.

How Bond Order Determines Strength

Bond order and bond strength are directly proportional. Here's why:

More electron density between nuclei: Higher bond order means more electrons are concentrated in the region between the two nuclei. These electrons simultaneously attract both nuclei, pulling them together.
Greater electrostatic attraction: The shared electrons act like "glue." More glue means stronger adhesion.
Shorter bond length: Stronger attraction pulls the nuclei closer. Shorter bonds are harder to stretch or break.

Watch out

Don't confuse bond order with bond energy. Bond order tells you the number of bonds; bond energy tells you the energy required to break them. They're proportional, but not identical — a C=C bond isn't exactly twice as strong as a C–C bond (it's about 1.7 times stronger).

Real Examples

Molecule	Bond	Bond Order	Bond Energy (kJ/mol)	Bond Length (pm)
H₂	H–H	1	436	74
O₂	O=O	2	498	121
N₂	N≡N	3	945	110
F₂	F–F	1	159	142

Notice how N₂ with a triple bond is the strongest diatomic molecule — it takes 945 kJ/mol to break that bond. That's why nitrogen gas is so unreactive.

When Bond Order Gets Tricky

Some molecules don't have simple whole-number bond orders. Consider ozone (O₃): …

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The key is to draw the Lewis structure and count every single bond as one sigma bond, every double bond as one sigma + one pi, and every triple bond as one sigma + two pi. For (a) $C_2H_2$ (ethyne): 3 sigma, 2 pi bonds. For (b) $C_2H_4$ (ethene): 5 sigma, 1 pi bond.

Why bond order matters

A sigma bond is the first, strongest bond formed between two atoms — it lies directly along the internuclear axis. Any additional bond between the same pair of atoms must be a pi bond, formed by sideways overlap of p-orbitals. So:

Single bond = 1 sigma, 0 pi
Double bond = 1 sigma, 1 pi
Triple bond = 1 sigma, 2 pi

This rule is absolute. Once you know the connectivity and bond types in a molecule, counting becomes mechanical.

(a) $C_2H_2$ — Ethyne (acetylene)

Draw the structure. Each carbon needs four bonds. Hydrogen can only form one bond. The only way to satisfy both carbons is a triple bond between them, with each carbon also bonded to one hydrogen:

$H - C \equiv C - H$
Count sigma bonds. Every single bond is sigma. The triple bond contains one sigma bond. So:
- $C-H$ bonds: 2 sigma
- $C \equiv C$ bond: 1 sigma Total sigma = $2 + 1 = 3$
Count pi bonds. The triple bond contributes two pi bonds (the remaining two bonds in the triple bond). No other multiple bonds exist.

Total pi = $2$

Tip

In a triple bond, think: "one sigma, two pi" — the pi bonds are the extra two that make it a triple.

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Q.What is the total number of sigma and pi bonds in the following molecules?

Why bond order matters

(a) C2H2C_2H_2C2​H2​ — Ethyne (acetylene)

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(a) $C_2H_2$ — Ethyne (acetylene)

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