Problem 27 - Basic Principles of Organic Chemistry

Question

A radical of structure \(\mathrm{CH}_{3} \dot{\mathrm{C}}=\mathrm{CHBr}\) is involved in the light-induced addition of \(\mathrm{HBr}\) to propyne. What geometry would you expect it to have? Draw an atomic-orbital picture of the radical with particular attention to the hybridization of orbitals at the radical center.

Step-by-Step Solution

Answer

The radical has a trigonal planar geometry with \( sp^2 \) hybridization.

Step 1: Identify the Radical Center

The radical center in the molecule \( \mathrm{CH}_{3} \dot{\mathrm{C}}=\mathrm{CHBr} \) is the carbon that is bonded directly to the bromine atom (")). This carbon is denoted as \( \dot{\mathrm{C}} \), which also indicates the presence of an unpaired electron making it a radical.

Step 2: Determine the Hybridization

The carbon with the unpaired electron in \( \mathrm{CH}_{3} \dot{\mathrm{C}}=\mathrm{CHBr} \) forms a double bond with another carbon. It is involved in two sigma bonds and one pi bond: one sigma bond with bromine, one sigma bond with the \( \mathrm{CH}_3 \) group, and a pi bond with the adjacent carbon. The hybridization of this carbon is \( sp^2 \).

Step 3: Assess Geometry

Since the radical center (\( \dot{\mathrm{C}} \)) in \( sp^2 \) hybridization is involved with three electron regions, it adopts a trigonal planar geometry around the radical carbon. The three equivalent \( sp^2 \) hybrid orbitals lie in the same plane at 120° to each other.

Step 4: Draw Atomic-Orbital Picture

In a trigonal planar configuration, the carbon atom at the radical center has three \( sp^2 \) hybrid orbitals forming bonds and an unhybridized \( p \) orbital that is perpendicular to the plane. The unpaired electron resides in the \( p \) orbital, which makes \( \mathrm{CH}_{3} \dot{\mathrm{C}}=\mathrm{CHBr} \) a planar radical.

Key Concepts

Trigonal Planar Geometry

Trigonal planar geometry is often associated with molecules where the central atom is bonded to three other atoms and generally involves

• three regions of electron density
• one atom with hybridization at the center

In the case of the radical \( \mathrm{CH}_{3} \dot{\mathrm{C}}=\mathrm{CHBr} \), the central carbon with the unpaired electron is hybridized as \( sp^2 \). This means it has three hybrid orbitals, all in one plane. These orbitals are 120 degrees apart from one another, forming a flat triangular shape, hence the adjective "planar."
This geometric arrangement maximizes the distance between electron pairs, reducing repulsion and providing stability to the molecule.
When you visualize trigonal planar geometry, think of a triangle on a flat surface, where the carbon atom serves as the center, connected to three atoms, allowing perfect angles between each bond.
Understanding this geometry is crucial, especially in understanding reactions and chemical behaviors where molecules need specific orientations to react or bond accurately.

Unpaired Electron

An unpaired electron is one that does not have a buddy electron to pair with. In chemical terms, unpaired electrons make atoms or molecules radicals, which are highly reactive. For the radical \( \mathrm{CH}_{3} \dot{\mathrm{C}}=\mathrm{CHBr} \), the dot over \( \mathrm{C} \) highlights the presence of the unpaired electron, distinguishing it as the radical center of this molecule.
An unpaired electron can occupy the non-bonding orbital, contributing to the radical's reactivity as it seeks another electron to achieve a more stable configuration.
This quest for stability drives many organic reactions, including addition reactions typical in radicals, where they capture an electron by forming new bonds.
Radicals can participate in

• combining with other radicals
• extracting atoms from other molecules

This intrinsic property of unpaired electrons makes radicals significant in mechanisms of chemical reactions, especially in additions and polymerizations. Their reactivity is integral to many industrial processes like polymer production.

Atomic Orbital

Atomic orbitals are regions of space around a nucleus where an electron is likely to be found. They come in various shapes such as

• spherically shaped \( s \) orbitals
• dumbbell-shaped \( p \) orbitals

In the radical \( \mathrm{CH}_{3} \dot{\mathrm{C}}=\mathrm{CHBr} \), the central carbon atom undergoes \( sp^2 \) hybridization, meaning it forms three equivalent hybrid orbitals by mixing one \( s \) and two \( p \) orbitals together.
These \( sp^2 \) orbitals help form sigma bonds with neighboring atoms, lying all in one plane, while the remaining unhybridized \( p \) orbital sits perpendicular to this plane.
Such an unhybridized \( p \) orbital is where the unpaired electron resides, contributing to the overall planar shape and reactivity of the molecule.
Atomic orbitals are foundational to understanding molecular shapes, bonding types, and electronic structures. They're like the building blocks that allow chemists to predict molecular behavior, bond angles, and reaction patterns.