Question

Ethylene, \(\mathrm{C}_{2} \mathrm{H}_{4},\) and tetrafluoroethylene, \(\mathrm{C}_{2} \mathrm{~F}_{4},\) are used to make the polymers polyethylene and polytetrafluoroethylene (Teflon), respectively. (a) Draw the Lewis structures for \(\mathrm{C}_{2} \mathrm{H}_{4}\) and \(\mathrm{C}_{2} \mathrm{~F}_{4},\) and give the ideal \(\mathrm{H}-\mathrm{C}-\mathrm{H}\) and \(\mathrm{F}-\mathrm{C}-\mathrm{F}\) bond angles. (b) The actual \(\mathrm{H}-\mathrm{C}-\mathrm{H}\) and \(\mathrm{F}-\mathrm{C}-\mathrm{F}\) bond angles are \(117.4^{\circ}\) and \(112.4^{\circ},\) respectively. Explain these deviations.

Short answer

Ideal bond angles are 120 degrees. Actual H-C-H and F-C-F bond angles are 117.4 degrees and 112.4 degrees due to differences in repulsion between hydrogen and fluorine atoms.

Step-by-step solution

- Draw the Lewis structures

Draw the Lewis structures for both ethylene(C_{2}H_{4}) and tetrafluoroethylene (C_{2}F_{4}). For ethylene, each carbon atom is connected by a double bond, and each carbon is also connected to two hydrogen atoms. For tetrafluoroethylene, each carbon atom is connected by a double bond, and each carbon is connected to two fluorine atoms.

- Determine the Ideal Bond Angles

The ideal bond angle around the central carbon atoms in both C_{2}H_{4} and C_{2}F_{4} can be determined by recognizing that they both form a planar trigonal geometry around each carbon due to sp2 hybridization. This gives ideal bond angles of 120 degrees for H-C-H and F-C-F.

- Compare Ideal and Actual Bond Angles

The actual H-C-H bond angle in C_{2}H_{4} is 117.4 degrees, which is slightly less than the ideal 120 degrees. The actual F-C-F bond angle in C_{2}F_{4} is 112.4 degrees, which is also less than the ideal 120 degrees. The deviation in H-C-H from the ideal is explained by the repulsion between hydrogen atoms being less than the repulsion between fluorine atoms, which are larger and exert greater electron cloud repulsion, thus compressing the bond angles more significantly in C_{2}F_{4}.

Key concepts

Lewis Structures

Lewis structures help us understand the arrangement of atoms and electrons in a molecule. They depict each atom's valence electrons and show how these electrons are shared or transferred to form bonds.

For \(\text{C}_{2}\text{H}_{4}\), each carbon atom forms a double bond with the other carbon. Additionally, each carbon binds to two hydrogen atoms. The Lewis structure would look like this:


In tetrafluoroethylene (\(\text{C}_{2}\text{F}_{4}\)), each carbon also forms a double bond with the other carbon, but each carbon binds to two fluorine atoms instead. Fluorine atoms have more electrons and are more electronegative than hydrogen atoms. Their Lewis structure looks like this:


Drawing these structures helps identify possible bond angles and understand molecular geometry.

sp2 Hybridization

To understand bond angles, it's essential to grasp the concept of sp2 hybridization. Hybridization is the process where atomic orbitals mix to form new hybrid orbitals, suitable for making chemical bonds.

In both \(\text{C}_{2}\text{H}_{4}\) and \(\text{C}_{2}\text{F}_{4}\), each carbon atom undergoes sp2 hybridization. This means that one s orbital and two p orbitals mix to form three sp2 hybrid orbitals. These hybrid orbitals arrange themselves in a planar trigonal geometry to minimize repulsion, resulting in bond angles of 120 degrees.

The remaining p orbital (one on each carbon) overlaps to form a \(\text{pi}\) bond, complementing the \(\text{sigma}\) bond formed by the sp2 hybrid orbitals. Together, these form the double bond between the carbons.

Molecular Geometry

Molecular geometry refers to the three-dimensional arrangement of atoms within a molecule. It's determined by the number of bonding and non-bonding electron pairs around the central atoms.

In ethylene (\(\text{C}_{2}\text{H}_{4}\)), each carbon atom forms two \(\text{sigma}\) bonds with hydrogen atoms and one \(\text{sigma}\) bond along with one \(\text{pi}\) bond with the other carbon atom. This results in a planar trigonal geometry, which ideally has bond angles of 120 degrees.

However, the actual \(\text{H-C-H}\) bond angle in ethylene is around 117.4 degrees. This slight deviation can be attributed to the small size of hydrogen, which results in lesser electron repulsion. Tetrafluoroethylene also has a planar trigonal geometry, with ideal bond angles of 120 degrees. The larger size of fluorine atoms and their greater electron repulsion reduce the \(\text{F-C-F}\) bond angle to 112.4 degrees.

Understanding these subtle deviations helps explain real-world molecular structures more accurately.