Question

Valence Bond Theory Write a hybridization and bonding scheme for each molecule that contains more than one interior atom. Indicate the hybridization about each interior atom. Sketch the structure, including overlapping orbitals, and label all bonds using the notation shown in Examples 7.1 and 7.2 . $$\begin{array}{l}{\text { a. } \mathrm{C}_{2} \mathrm{H}_{2} \text { (skeletal structure } \mathrm{HCCH} )} \\ {\text { b. } \mathrm{C}_{2} \mathrm{H}_{4}\left(\text { skeletal structure } \mathrm{H}_{2} \mathrm{CCH}_{2}\right)} \\ {\text { c. } \mathrm{C}_{2} \mathrm{H}_{6}\left(\text { skeletal structure } \mathrm{H}_{3} \mathrm{CCH}_{3}\right)}\end{array}$$

Short answer

C2H2 has two sp hybridized carbon atoms with a triple bond between them and single bonds to hydrogens. C2H4 has two sp2 hybridized carbon atoms with a double bond between them and single bonds to hydrogens. C2H6 has two sp3 hybridized carbon atoms each making a single bond with the other and three single bonds to hydrogens.

Step-by-step solution

Determine the Hybridization for C2H2

C2H2 has a triple bond between the two carbon atoms and a single bond to each hydrogen. Each carbon atom is surrounded by two regions of electron density (one for the triple bond and one for the single bond), which corresponds to sp hybridization.

Sketch the C2H2 Structure

For C2H2, place the two sp hybridized carbon atoms in the center with a triple bond between them using one sp orbital from each carbon. The other sp orbital on each carbon overlaps with an s orbital from hydrogen to form the CH bonds.

Determine the Hybridization for C2H4

In C2H4, each carbon is bonded to three atoms: one double bond with another carbon and two single bonds with hydrogen atoms. This gives three regions of electron density, which corresponds to sp2 hybridization.

Sketch the C2H4 Structure

For C2H4, arrange the two sp2 hybridized carbon atoms with a double bond between them. Each carbon atom will also form two sigma bonds with hydrogen atoms using the remaining sp2 orbitals. One unhybridized p orbital on each carbon will overlap sideways to form the pi bond of the double bond.

Determine the Hybridization for C2H6

In C2H6, each carbon atom is bonded to four atoms (another carbon and three hydrogen atoms). This gives four regions of electron density corresponding to sp3 hybridization.

Sketch the C2H6 Structure

For C2H6, connect the two sp3 hybridized carbon atoms with a single bond. Each carbon will form three additional single bonds with hydrogen atoms using the remaining sp3 orbitals. The structure is a tetrahedral geometry around each carbon atom.

Key concepts

sp Hybridization

When a carbon atom is involved in a triple bond, it undergoes what we call sp hybridization. This occurs as one s orbital and one p orbital from the atom mix to form two new equivalent orbitals. Each of these sp hybridized orbitals has an elongated shape, which allows for effective end-to-end overlap when forming bonds.

In the molecule C₂H₂ (acetylene), both carbon atoms are sp hybridized because they have two regions of electron density: a triple bond and a single bond. The structure shows the carbons linearly aligned with 180-degree angles between bonds, an arrangement that minimizes repulsion between the electrons involved in the bonds. For molecules like acetylene, recognizing the sp hybridization is crucial for understanding its properties and reactivity.

sp2 Hybridization

When talking about sp² hybridization, envision a carbon atom participating in a double bond with three total regions of electron density. This situation leads to the hybridization of one s orbital and two p orbitals, resulting in three sp² hybridized orbitals.

These orbitals are used to form sigma bonds, which are characterized by their head-on orbital overlap, creating a trigonal planar geometry with 120-degree bond angles. In the case of C₂H₄ (ethylene), each carbon atom is sp² hybridized and uses two of these orbitals for single bonds with hydrogen and one to bond with the other carbon. Moreover, the remaining unhybridized p orbital on each carbon forms the pi bond of the double bond, which requires a side-on overlap, adding to the overall strength of the double bond.

sp3 Hybridization

As we examine sp³ hybridization, we are referring to a carbon atom that is bonded to four other atoms, such as in C₂H₆ (ethane). This tetrahedral configuration emerges from one s orbital and three p orbitals hybridizing to create four sp³ orbitals.

Each sp³ orbital can form a stable sigma bond through end-to-end overlap, and the geometry of these bonds is tetrahedral, with roughly 109.5-degree bond angles. Thus, each carbon in ethane bonds to three hydrogens and one other carbon, all equally spaced around the central carbon atom. This three-dimensional structure impacts the molecule's physical properties and its reactions.

Molecular Bonding

Understanding molecular bonding is fundamental when analyzing compounds, as it dictates molecular geometry and reactivity. The type of hybridization gives us insights into the bond angles and shapes of molecules. For example, sp hybridization leads to linear structures, sp² hybridization results in trigonal planar geometries, and sp³ hybridization produces tetrahedral shapes.

Bonds formed during these processes are called sigma bonds, which result from direct overlaps of orbitals. Additionally, pi bonds may form when unhybridized p orbitals overlap sideways. The combination of sigma and pi bonds determines the double and triple bonds in compounds, influencing chemical characteristics and how the molecule interacts in reactions.

Orbital Overlap

The concept of orbital overlap is vital in valence bond theory. It provides an explanation for the formation of chemical bonds which is essentially the overlapping of atomic orbitals from two atoms. The quality of this overlap dictates the strength and length of the bond formed between atoms.

In the case of a sigma bond, like those formed in sp³ hybridized molecules, we can visualize direct end-to-end overlap. Pi bonds, however, such as those in sp² hybridized molecules, involve a side-to-side overlap. The various overlaps in hybridizations - sp, sp², and sp³ - show us how different molecular geometries arise and highlight the three-dimensional nature of molecules that is essential for predicting molecular behavior and reactivity.