Problem 78 - Chemistry and Chemical Reactivity

Question

Draw structures and name the four alkenes that have the formula \(\mathrm{C}_{4} \mathrm{H}_{8}\)

Step-by-Step Solution

Answer

The alkenes are But-1-ene, Cis-But-2-ene, Trans-But-2-ene, and 2-Methylpropene.

Step 1: Understand the Molecular Formula

The molecular formula \( \mathrm{C}_4 \mathrm{H}_8 \) indicates that these are alkenes, which are hydrocarbons containing at least one carbon-carbon double bond. The general formula for alkenes is \( \mathrm{C}_n \mathrm{H}_{2n} \), which matches our given formula.

Step 2: Drawing But-1-ene

Start by creating the simplest linear structure. Draw a chain of four carbon atoms. Place a double bond between the first and second carbon atoms. The structure is:- \( \text{CH}_2=CH-CH_2-CH_3 \)This is named But-1-ene.

Step 3: Drawing But-2-ene

Place a double bond between the second and third carbon atoms in a linear chain of four carbon atoms.- \( \text{CH}_3-CH=CH-CH_3 \)This can exist as two geometrical isomers due to the double bond:- **Cis-But-2-ene**: Both methyl groups on the same side.- **Trans-But-2-ene**: Methyl groups on opposite sides.

Step 4: Drawing 2-Methylpropene

Create a branched structure by placing a double bond at the first carbon and a methyl group on the second carbon.- \( \text{CH}_2=C(CH_3)-CH_3 \)This structure is named 2-Methylpropene.

Key Concepts

Molecular Formula

The molecular formula is like a chemical equation that tells us the number of each type of atom present in a molecule. For alkenes, the molecular formula takes the shape of \( \mathrm{C}_n \mathrm{H}_{2n} \). This indicates that alkenes have twice as many hydrogen atoms as carbon atoms. This specific ratio hints at the presence of a carbon-carbon double bond, which is the defining feature of alkenes.
Given the formula \( \mathrm{C}_4 \mathrm{H}_8 \), we know we're dealing with an alkene. There's a total of four carbons and eight hydrogens. Starting with such a molecular formula guides us to arrange carbon and hydrogen atoms while forming possible double bonds. Each arrangement could give rise to different structures, or isomers, of the same molecular formula.

Carbon-Carbon Double Bond

A carbon-carbon double bond is what distinguishes alkenes from other hydrocarbons. This type of bond is symbolized by \( = \) and makes alkenes more reactive than alkanes, which only contain single bonds. This double bond consists of one sigma (σ) bond and one pi (π) bond. Such a configuration restricts the rotation around the double bond, leading to the possibility of different spatial orientations of the attached groups.

• Single bonds: allow free rotation.
• Double bonds: restrict rotation.

This restriction is key to understanding why alkenes can form geometrical isomers. It's crucial to remember that each carbon in the double bond must be bonded to two different groups or atoms to allow for these isomers.

Geometrical Isomers

Geometrical isomers, also known as cis-trans isomers, are forms of a molecule that have the same molecular formula but differ in spatial arrangement. In alkenes, these isomers arise due to the restricted rotation around the double bond.
For example, in But-2-ene, you have:

• Cis-But-2-ene: Methyl groups are on the same side of the double bond, leading to a bent or angled shape.
• Trans-But-2-ene: Methyl groups are on opposite sides, resulting in a more linear shape.

This slight change in shape has significant effects. Geometrical isomers often have different physical properties such as boiling point and solubility. Recognizing these isomers helps in understanding the diverse behavior of molecular structures in chemical reactions.