Question

Cyclopropane \(\left(\mathrm{C}_{3} \mathrm{H}_{6}\right)\) has the shape of a triangle in which a \(\mathrm{C}\) atom is bonded to two \(\mathrm{H}\) atoms and two other \(\mathrm{C}\) atoms at each corner. Cubane \(\left(\mathrm{C}_{8} \mathrm{H}_{8}\right)\) has the shape of a cube in which a \(\mathrm{C}\) atom is bonded to one \(\mathrm{H}\) atom and three other \(\mathrm{C}\) atoms at each corner. (a) Draw Lewis structures of these molecules. (b) Compare the CCC angles in these molecules with those predicted for an \(s p^{3}\) -hybridized \(\mathrm{C}\) atom. (c) Would you expect these molecules to be easy to make?

Short answer

Both molecules have significant angle strain, making them unstable and difficult to synthesize.

Step-by-step solution

Draw Cyclopropane Lewis Structure

Cyclopropane, \(\text{C}_3\text{H}_6\), is a triangle with each carbon atom bonded to 2 hydrogens. Start by placing the 3 carbon atoms in a triangle shape. Then, connect each carbon atom to 2 hydrogen atoms. Finally, ensure all atoms have the correct number of bonds (Hydrogens should have 1 bond, and Carbons should have 4 bonds).

Draw Cubane Lewis Structure

Cubane, \(\text{C}_8\text{H}_8\), is shaped like a cube with a carbon atom at each corner. First, form a cube framework using 8 carbon atoms. Each carbon atom is bonded to one hydrogen, which sits outside the cube structure, and to three other carbon atoms. Make sure that each carbon has four bonds and each hydrogen atom has one bond.

Analyze CCC Bond Angles in Cyclopropane

In cyclopropane, each CCC angle is approximately 60 degrees due to the equilateral triangular shape. This is considerably smaller than the ideal \(109.5^\circ\) angle for \(sp^3\)-hybridized carbon atoms, which creates angle strain in the cyclopropane molecule.

Analyze CCC Bond Angles in Cubane

In cubane, each CCC bond angle should be approximately 90 degrees, as they are part of a cube. This angle is also smaller than the ideal \(109.5^\circ\) for \(sp^3\)-hybridized carbon atoms, producing angle strain, similar to cyclopropane but less severe than 60 degrees.

Assess Molecule Stability and Ease of Formation

Due to the significant deviation from the ideal \(sp^3\) bond angle, both cyclopropane and cubane experience significant angle strain. This angle strain makes these molecules highly unstable and, thus, challenging to synthesize and maintain without decomposition or reaction.

Key concepts

Lewis Structures

Lewis structures are schematic representations of molecules showing how atoms are bonded together. In a Lewis structure, each line signifies a chemical bond, and each atom aims to satisfy the octet rule, seeking eight electrons in its outer shell. Cyclopropane, represented by \( ext{C}_3 ext{H}_6\), forms a triangle. In its Lewis structure, three carbon atoms are arranged in a triangular pattern. Each carbon connects to two hydrogen atoms and the two neighboring carbon atoms. This ensures that each carbon has four bonds (following the octet rule), and each hydrogen has one bond.
Cubane, \(\text{C}_8\text{H}_8\), forms a cube structure. Here, eight carbon atoms occupy the corners of a cube, and each carbon connects to three other carbons and one hydrogen atom. It's essential to illustrate correctly how these atoms connect in space to understand their 3D arrangement. Drawing Lewis structures offers a primary glimpse into the molecular shape and bonding of these compounds.

sp3 Hybridization

In organic chemistry, hybridization plays a crucial role in understanding how carbon atoms form bonds. Carbon exhibits different hybridizations, with \(sp^3\) being one of them. In \(sp^3\) hybridization, one s orbital and three p orbitals mix to form four equivalent hybrid orbitals. These hybrid orbitals arrange themselves tetrahedrally around the carbon atom, producing bond angles of approximately \(109.5^\circ\).
For cyclopropane and cubane, even though these molecules theoretically have \(sp^3\)-hybridized carbons, their observed bond angles deviate significantly from this ideal. Cyclopropane features bond angles near \(60^\circ\), while cubane displays angles around \(90^\circ\). This deviation arises from the geometrical shapes—triangle and cube—forcing the carbon atoms to adapt differently from the natural tetrahedral arrangement. Understanding \(sp^3\) hybridization helps in grasping how these angles arise in various molecular structures.

Angle Strain

Angle strain occurs when bond angles deviate from their ideal values, which causes increased molecular tension. This phenomenon is evident in ring structures like cyclopropane and cubic structures like cubane. Typically, \(sp^3\)-hybridized carbon atoms prefer a bond angle of \(109.5^\circ\). However, in cyclopropane, each \(CCC\) bond angle measures approximately \(60^\circ\).
Similarly, cubane forces a \(90^\circ\) bond angle between carbon atoms. This deviation results in significant angle strain because it compresses or stretches chemical bonds, destabilizing the molecule. Cyclopropane experiences a drastic bond angle reduction, leading to a high level of strain and, consequently, potential instability and reactivity. Cubane, while not as strained as cyclopropane, still experiences enough strain to significantly impact stability.

Molecule Stability

Molecule stability is significantly influenced by factors such as angle strain, bonding, and overall electron distribution. When the ideal bond angles deviate due to structural constraints, it can lead to instability. Both cyclopropane and cubane show substantial angle strain, deviating vastly from the ideal \(109.5^\circ\) angle expected in \(sp^3\) hybridized systems.
Due to these deviations, these molecules are considered to have high internal stress. This stress can make them prone to decomposition or unusual reactivity, as the bonds are stretched or compressed from their preferred positions. Consequently, synthesizing such molecules requires precise control over conditions. Once formed, their inherent instability makes them difficult to maintain, limiting their practical applications without special storage or handling requirements.