Question

Draw condensed structural formulas for four different structural isomers with the molecular formula \(\mathrm{C}_{4} \mathrm{H}_{8}\).

Short answer

The four condensed structural formulas for the different structural isomers of the molecular formula C4H8 are: 1. 1-butene: \(CH_{2}=CHCH_{2}CH_{3}\) 2. 2-butene: \(CH_{3}CH=CHCH_{3}\) 3. 3-methyl-1-propene: \(CH_{2}=CHCH(CH_{3})\) 4. 2-methyl-1-propene: \(CH_{2}=C(CH_{3})CH_{3}\)

Step-by-step solution

Identify the type of isomers

The molecular formula C4H8 indicates that we are dealing with hydrocarbons. Since the number of hydrogens is less than twice the number of carbons plus two (CnH2n+2), these compounds are not saturated hydrocarbons (alkanes). They must have a double bond, making them alkenes.

Draw carbon chains with different lengths

Since we have four carbon atoms in the formula, we can either have a straight chain of 4 carbons or a chain of 3 carbons with one carbon branching out.

Position the double bond and branches

We need to place the double bond at different positions in these carbon chains to generate unique isomers. Isomer 1: A straight chain with the double bond between carbons 1 and 2 - 1-butene \(CH_{2}=CHCH_{2}CH_{3}\) Isomer 2: A straight chain with the double bond between carbons 2 and 3 - 2-butene \(CH_{3}CH=CHCH_{3}\) Isomer 3: A carbon chain with three carbons in a straight line and the double bond between carbons 1 and 2, with the fourth carbon branching off of carbon 2 - 3-methyl-1-propene \(CH_{2}=CHCH(CH_{3})\) Isomer 4: A carbon chain with three carbons in a straight line and the double bond between carbons 1 and 2, with the fourth carbon branching off of carbon 2 - 2-methyl-1-propene \(CH_{2}=C(CH_{3})CH_{3}\) These four condensed structural formulas represent four different structural isomers of the molecular formula C4H8.

Key concepts

Molecular Formula

A molecular formula is a simple representation of the different types and numbers of atoms in a chemical compound. It uses element symbols and numerical subscripts to show the quantities of each atom. For instance, for hydrocarbon compounds like \(\mathrm{C}_4 \mathrm{H}_8\), it indicates there are four carbon atoms and eight hydrogen atoms in each molecule.
This formula doesn't specify how the atoms are connected, which means it doesn't provide any structural information. For compounds with the same molecular formula, there can be different arrangements of atoms, known as isomers. In the case of \(\mathrm{C}_4 \mathrm{H}_8\), the molecular formula reveals that it is an alkene due to the presence of fewer hydrogen atoms than an alkane with the same number of carbons. This leads us to explore structural variations or isomers that share this formula.

Condensed Structural Formula

A condensed structural formula offers more detail than a molecular formula by showing the arrangement of atoms in a molecule. It provides a shorthand method to depict the sequence of atoms and their connections in organic compounds.
Unlike a full structural formula that illustrates all bonds explicitly, the condensed version simplifies this information by grouping together atoms connected to central atoms. For example, the isomers of \(\mathrm{C}_4 \mathrm{H}_8\) can be written in condensed forms that represent how the atoms are linked with each other:

• Isomer 1: \(CH_{2}=CHCH_{2}CH_{3}\) represents 1-butene, where the double bond is between the first two carbons.
• Isomer 2: \(CH_{3}CH=CHCH_{3}\) stands for 2-butene, showing the double bond between the second and third carbon atoms.
• Isomer 3: \(CH_{2}=CHCH(CH_{3})\) indicates 3-methyl-1-propene, with a methyl branch coming off one of the carbons.
• Isomer 4: \(CH_{2}=C(CH_{3})CH_{3}\) is 2-methyl-1-propene, another variation owing to a branching methyl group.

Condensed structural formulas efficiently convey the connectivity of atoms and allow chemists to visualize different isomers.

Alkenes

Alkenes are a category of hydrocarbons distinguished by containing at least one carbon-carbon double bond. This double bond introduces a level of unsaturation, reducing the number of hydrogen atoms paired with carbon, hence fitting the general formula \(\mathrm{C}_n\mathrm{H}_{2n}\).
For the molecular formula \(\mathrm{C}_4\mathrm{H}_8\), being an alkene means these compounds won't be fully saturated like their alkane counterparts. Instead, these molecules can exist as different structural variants, called structural isomers, depending on where the double bond is located and the configuration of the carbon backbone.
This double bond not only distinguishes alkenes but also introduces interesting chemical properties. The presence of the double bond makes alkenes more reactive than alkanes. This allows for reactions such as polymerization and addition reactions to occur, expanding their utility in various chemical processes.
Understanding alkenes and their potential for forming structural isomers is foundational in organic chemistry, as they demonstrate the diversity and complexity even simple hydrocarbons exhibit.