Problem 39 - Chemistry Matter and Change

Question

Draw the Lewis structure for ethylene, \(\mathrm{C}_{2} \mathrm{H}_{4}\)

Step-by-Step Solution

Answer

The Lewis structure of ethylene has a double bond between two carbon atoms and each carbon bonded to two hydrogens.

Step 1: Count the Valence Electrons

Start by determining the number of valence electrons for each atom in ethylene, \\( \mathrm{C}_{2}\ \mathrm{H}_{4} \). Carbon has 4 valence electrons each and there are two carbons, so \( 4 \times 2 = 8 \). Hydrogen has 1 valence electron each and there are four hydrogens, so \( 1 \times 4 = 4 \). In total, ethylene has \( 8 + 4 = 12 \) valence electrons.

Step 2: Determine the Skeletal Structure

In ethylene, the carbons form the backbone. Draw two carbon atoms connected with a single bond. Each carbon needs to satisfy the octet rule, so distribute the hydrogens around the carbons to form the simplest structure: \( \text{H} - \text{C} - \text{C} - \text{H} \).

Step 3: Complete the Octet for Carbon

With the skeletal structure in place, carbon atoms need 8 electrons to satisfy the octet rule. Given the hydrogen atoms bonded to each carbon, place a second bond between the two carbon atoms to share more electrons. This results in a double bond between the carbon atoms: \( \text{H} \ \text{H} \) \( \vert \qquad \vert \) \( \text{C} = \text{C} \) \( \vert \qquad \vert \) \( \text{H} \ \text{H} \)

Step 4: Distribute Remaining Electrons if Necessary

After placing the double bond, count the electrons used. Each hydrogen forms a single bond with a carbon atom, using 8 electrons (4 bonds from hydrogens) and the \( C=C \) bond uses 4 more electrons. Thus, all 12 electrons are accounted for, and the structure is complete with no lone pairs needed.

Key Concepts

Valence Electrons

Valence electrons are the outermost electrons of an atom and they play a crucial role in forming chemical bonds. These are the electrons available for bonding, determining how an atom interacts with others. Valence electrons are particularly important when drawing Lewis structures because they help us figure out how atoms will be arranged and bonded.
For ethylene, \( \mathrm{C}_{2}\mathrm{H}_{4} \), counting valence electrons is the first step. Each carbon atom brings 4 valence electrons, and since there are two carbon atoms, you have a total of 8 from carbon. Each hydrogen atom provides 1 valence electron, totaling 4 more. Thus, ethylene has a grand total of 12 valence electrons.

• Carbon: 4 valence electrons per atom × 2 atoms = 8 electrons
• Hydrogen: 1 valence electron per atom × 4 atoms = 4 electrons
• Total valence electrons = 12

These 12 electrons are what you will distribute to achieve a stable arrangement that follows key principles like the octet rule.

Octet Rule

The octet rule is a guiding principle for understanding how atoms bond. According to this rule, atoms tend to adjust their electron sharing or transfer in such a way that each atom achieves an electron configuration similar to the nearest noble gas. This often means that atoms aim to have eight electrons in their valence shell.
Carbon, with four valence electrons, needs four more to complete an octet. In ethylene, \( \mathrm{C}_{2}\mathrm{H}_{4} \), each carbon aims to fulfill the octet rule. This is accomplished by forming bonds with hydrogen and by sharing electrons with another carbon—specifically, by forming a double bond.

• The \( \mathrm{C=C} \) double bond—sharing two pairs of electrons, helps each carbon atom to obtain eight electrons in its valence shell, thus satisfying their octets.
• Hydrogen atoms only need 2 electrons to mimic helium, so their single bonds with carbon fulfill their electron requirements.

The successful application of the octet rule ensures that the molecule is stable.

Skeletal Structure

The skeletal structure forms the backbone of a molecule and provides a roadmap for placing atoms and bonds. When constructing a skeletal structure, the arrangement of atoms in a linear or branched fashion is often based on common bonding patterns typical to the involved elements.
For ethylene, \( \mathrm{C}_{2}\mathrm{H}_{4} \), the skeletal structure can initially be visualized as a simple lineup of carbon atoms—a conventional approach for hydrocarbons. These carbons are connected first by a single bond, and then the remaining valence electrons help form additional bonds to achieve stable octets.

• The core structure has carbon at the center: \( \text{C} - \text{C} \).
• Hydrogen atoms are placed around the carbons to fulfill their bonding needs: \(\text{H} - \text{C} - \text{C} - \text{H}\).
• The completion of the skeletal structure involves converting the single bond between carbon atoms into a double bond to use up the remaining valence electrons efficiently.

Crafting this basic skeletal arrangement paves the way for the correct placement of electrons, ensuring that the octet rule is followed and all electrons are accounted for in the formation of a stable molecule.