Chemistry (9701) | Shapes of organic molecules; σ and π bonds

Shapes of Organic Molecules; σ and π Bonds

Welcome to one of the most fundamental topics in organic chemistry! You might be used to drawing organic molecules flat on paper, but in reality, they exist in 3D space. Their shape and structure dictate everything—how they react, their physical properties, and even their biological activity.

In this chapter, we are going to dive deep into how carbon uses special tricks (called hybridisation) to form bonds, resulting in specific, predictable shapes and bond angles. Don't worry if words like $sp^2$ or $\pi$ seem intimidating right now; we will break them down step-by-step!

1. Classifying Organic Molecular Structures

Organic molecules can be described based on how their carbon atoms are connected (Syllabus 13.3.1).

• Straight-chained (or continuous chain): Carbon atoms are linked one after the other in a single line. Example: Hexane.
• Branched: The main carbon chain has smaller carbon groups (alkyl groups) attached to it as side chains. Example: 2-Methylpentane.
• Cyclic: The chain of carbon atoms forms a ring structure. Example: Cyclohexane.

2. The Role of Hybridisation in Determining Shape

The shape of a molecule is determined by the arrangement of electron pairs (both bonding pairs and lone pairs) around the central atoms. For carbon, we use the concept of hybridisation, where atomic orbitals ($s$ and $p$) mix to form new, equivalent hybrid orbitals that allow for strong, symmetrical bonding.

2.1 $sp^3$ Hybridisation: Single Bonds Only (Saturated)

This type of hybridisation happens when a carbon atom is surrounded only by single bonds (no double or triple bonds).

Formation:

One $s$ atomic orbital mixes with three $p$ atomic orbitals to form four equivalent $sp^3$ hybrid orbitals.

Shape and Angle:

• Shape: Tetrahedral
• Bond Angle: 109.5°
• Bonds Formed: All four $sp^3$ orbitals form sigma ($\sigma$) bonds (single bonds) by overlapping head-on with other atoms’ orbitals.

Analogy: Think of a four-legged stool. To be stable, the legs (bonds) must spread out as far apart as possible in three dimensions, creating the tetrahedral shape.

Example: Methane (\(CH_4\)) and Ethane (\(C_2H_6\)).

2.2 $sp^2$ Hybridisation: The Double Bond (Alkenes)

This occurs when a carbon atom is involved in a double bond.

Formation:

One $s$ orbital mixes with two $p$ orbitals to form three equivalent $sp^2$ hybrid orbitals. One $p$ orbital is left unhybridised.

Shape and Angle:

• Shape (around the carbon): Trigonal Planar
• Bond Angle: 120°
• Planarity: The three atoms attached to the $sp^2$ carbon lie in a single flat plane (planar arrangement).

Bonds Formed (Syllabus 13.3.3):

The double bond consists of two parts:

1. One sigma ($\sigma$) bond: Formed by the direct, head-on overlap of two $sp^2$ orbitals between the carbon atoms.
2. One pi ($\pi$) bond: Formed by the sideways overlap of the two adjacent, unhybridised $p$ orbitals (one from each carbon atom). This creates electron density clouds above and below the plane of the $\sigma$ bond.

Example: Ethene (\(C_2H_4\)).

2.3 $sp$ Hybridisation: The Triple Bond (Alkynes)

This occurs when a carbon atom is involved in a triple bond.

Formation:

One $s$ orbital mixes with one $p$ orbital to form two equivalent $sp$ hybrid orbitals. Two $p$ orbitals are left unhybridised.

Shape and Angle:

• Shape (around the carbon): Linear (straight line)
• Bond Angle: 180°

Bonds Formed (Syllabus 13.3.3):

The triple bond consists of three parts:

1. One sigma ($\sigma$) bond: Formed by the direct, head-on overlap of two $sp$ orbitals.
2. Two pi ($\pi$) bonds: Formed by the sideways overlap of the two sets of perpendicular unhybridised $p$ orbitals.

Example: Ethyne (\(C_2H_2\)) and Hydrogen Cyanide (\(HCN\)).

3. Detailing Sigma ($\sigma$) and Pi ($\pi$) Bonds

Understanding the difference between $\sigma$ and $\pi$ bonds is crucial, especially for explaining the reactivity of double and triple bonds.

3.1 Sigma ($\sigma$) Bonds

The $\sigma$ bond is the most common type of covalent bond, formed by the simplest type of orbital overlap.

• Mechanism: Formed by the direct overlap (head-on) of orbitals along the internuclear axis (the imaginary line connecting the two atomic nuclei).
• In all Bonds: Every single covalent bond (C-C, C-H, O-H, etc.) is a $\sigma$ bond. A double or triple bond always contains exactly one $\sigma$ bond.
• Strength: They are very strong bonds.
• Rotation: Atoms joined by a single $\sigma$ bond are free to rotate around the bond axis. (Imagine two balls joined by a single rod—they can spin freely relative to each other).

3.2 Pi ($\pi$) Bonds

$\pi$ bonds are the 'extra' bonds found in multiple bond systems.

• Mechanism: Formed by the sideways overlap of adjacent unhybridised $p$ orbitals. The electron density is concentrated in two regions, one above and one below the plane of the $\sigma$ bond.
• Location: Found in double bonds (1 $\pi$) and triple bonds (2 $\pi$).
• Strength: They are generally weaker and more exposed than $\sigma$ bonds. This vulnerability is why alkenes are more reactive than alkanes!
• Rotation: The sideways overlap prevents free rotation around the C=C axis. If the atoms tried to rotate, the $\pi$ overlap would break. This restricted rotation is the origin of geometrical (cis/trans) isomerism (which you will cover later in this chapter, 13.4).

Key Takeaway: A double bond is always $1 \sigma$ and $1 \pi$. A triple bond is always $1 \sigma$ and $2 \pi$.

4. The Shape of Aromatic Molecules: Benzene

A specific and very important application of $sp^2$ hybridisation and $\pi$ bonding is found in aromatic molecules, such as benzene (Syllabus 29.3.1).

4.1 Benzene Structure and Hybridisation

Benzene (\(C_6H_6\)) is a ring of six carbon atoms.

Hybridisation:

• Every carbon atom in the ring is bonded to three other atoms (two carbons and one hydrogen). Therefore, every carbon atom is $sp^2$ hybridised.

Shape and Bond Angles:

• Since all carbons are $sp^2$, the entire ring structure is planar (flat).
• All bond angles in the hexagonal ring are 120°.

4.2 The Delocalised $\pi$ System

The bonding in benzene is special and explains its unusual stability (often called aromatic stabilisation).

$\sigma$ Bonds: Formed by the head-on overlap of $sp^2$ orbitals.

Delocalised $\pi$ System:

• Each of the six carbon atoms has one unhybridised $p$ orbital remaining.
• Instead of forming isolated $\pi$ bonds (like in ethene), all six $p$ orbitals overlap sideways with both neighbouring $p$ orbitals simultaneously around the entire ring.
• This creates a continuous, circular cloud of electron density (the delocalised $\pi$ system) above and below the planar ring.

Did you know? The delocalised $\pi$ electrons are not fixed to any two specific atoms. They are spread over all six carbon atoms, making the molecule highly stable compared to a hypothetical structure with alternating single and double bonds.