Question

Propylene oxide is used to make many products, including plastics such as polyurethane. One method for synthesizing it involves oxidizing propene with hydrogen peroxide: (a) What are the molecular shape and ideal bond angle around each carbon atom in propylene oxide? (b) Predict any deviation from the ideal for the actual \(\mathrm{C}-\mathrm{C}-\mathrm{C}\) bond angles (assume the three atoms in the ring form an equilateral triangle).

Short answer

Each carbon in propylene oxide is \(\text{sp}^3\) hybridized with ideal bond angles of 109.5 degrees. Actual \(\text{C}-\text{C}-\text{C}\) bond angles are closer to 60 degrees due to ring strain.

Step-by-step solution

- Determine molecular shape and bond angles for each carbon in propylene oxide

Propylene oxide has the structure: \( \text{CH}_2\text{CHCH}_2\text{O} \). Each carbon atom in the ring is bonded to three other atoms (either hydrogen or oxygen), so it is \(\text{sp}^3\) hybridized. The ideal bond angle for \(\text{sp}^3\) hybridization is 109.5 degrees.

- Analyze the ring structure

Since the three carbon atoms and one oxygen atom form a three-membered ring (an epoxide), we must consider the ring strain. Ideally, for a three-membered ring, the bond angles should add up to 180 degrees (since an equilateral triangle has internal angles of 60 degrees).

- Predict deviation from ideal bond angles

Although each \(\text{sp}^3\) hybridized carbon has an ideal bond angle of 109.5 degrees, the actual \(\text{C}-\text{C}-\text{C}\) bond angles in the ring will be less than this due to ring strain. The bond angles will be closer to 60 degrees because the atom positions approximate an equilateral triangle rather than the tetrahedral angle.

Key concepts

Molecular Shape around Carbon Atoms

The molecular shape describes how atoms in a molecule are arranged in space. In propylene oxide, each carbon atom is bonded to three other atoms - either hydrogen or oxygen. This configuration makes these carbons \(\text{sp}^3\) hybridized.

When a carbon atom is \(\text{sp}^3\) hybridized, it takes on a tetrahedral shape. This means each carbon in propylene oxide is in a tetrahedral geometry. Imagine each carbon with its four bonds positioned as far apart from each other as possible.
This arrangement minimizes electron repulsion.

However, because propylene oxide has a ring structure, consider the ring as an equilateral triangle. Deviations occur from the ideal tetrahedral shape due to the constraints of the ring.

Bond Angles in Propylene Oxide

Bond angles are the angles between two bonds originating from the same atom. For \(\text{sp}^3\) hybridized atoms, the ideal bond angle is 109.5 degrees. This is seen in molecules like methane where bond angles are perfect due to no ring strain.

But in propylene oxide, the situation changes.
The three-membered ring structure forces the bond angles to differ from this ideal. Based on the ring being a triangle,
each internal angle theoretically approaches 60 degrees.

Thus, the internal \(\text{C}-\text{C}-\text{C}\) bond angles are much smaller than 109.5 degrees. This significant deviation is due to the tight ring structure which compresses the angles.

sp3 Hybridization

In chemistry, hybridization explains the mixing of orbitals to form new hybrid orbitals.
For the carbons in propylene oxide, the \(\text{sp}^3\) hybridization is crucial. Each carbon has one \(s\) orbital and three \(p\) orbitals that hybridize to form four equivalent \(\text{sp}^3\)-hybrid orbitals.

These four hybrid orbitals arrange themselves in a tetrahedral geometry around each carbon atom,
with the aim to minimize repulsions between electrons.

Due to this, the expected bond angle is 109.5 degrees. But, due to the ring structure in propylene oxide, you observe the angles are smaller
as the ring strain forces the angles to compress.

Ring Strain in Propylene Oxide

Ring strain occurs when bond angles deviate from their ideal values
to accommodate a ring structure.
In propylene oxide, this is especially significant.
The three-membered ring structure causes notable strain.

As mentioned earlier, ideal \(\text{sp}^3\) bond angles are about 109.5 degrees.
However, a three-membered ring forces the bond angles to approximate 60 degrees instead.
This discrepancy results in increased energy within the molecule,
known as ring strain.
Ring strain can affect the molecule’s reactivity and stability.
This makes three-membered rings like propylene oxide more reactive than larger rings or chains,
due to the higher internal strain trying to relieve itself.