Problem 82 - Chemistry: The Central Science in SI Units, Global Edition

Question

How many structural isomers are there for a five-member straight carbon chain with one double bond? For a six-member straight carbon chain with two double bonds?

Step-by-Step Solution

Answer

There are 4 possible unique isomers for a five-member straight carbon chain with one double bond, and 6 unique isomers for a six-member straight carbon chain with two double bonds.

Step 1: Scenario 1: Five-member carbon chain with one double bond

To analyze the possibilities of placing a double bond in a 5-carbon chain (n=5), we can go in the following way: 1. Place the double bond between carbon 1 and carbon 2: C=C-C-C-C 2. Place the double bond between carbon 2 and carbon 3: C-C=C-C-C 3. Place the double bond between carbon 3 and carbon 4: C-C-C=C-C 4. Place the double bond between carbon 4 and carbon 5: C-C-C-C=C So, there are 4 possible unique isomers for a five-member straight carbon chain with one double bond.

Step 2: Scenario 2: Six-member carbon chain with two double bonds

For the six-member carbon chain (n=6) with two double bonds, we'll analyze different ways to place the double bonds: 1. Double bonds between carbon 1-2 and 3-4: C=C-C=C-C-C 2. Double bonds between carbon 1-2 and 4-5: C=C-C-C=C-C 3. Double bonds between carbon 1-2 and 5-6: C=C-C-C-C=C 4. Double bonds between carbon 2-3 and 4-5: C-C=C-C=C-C 5. Double bonds between carbon 2-3 and 5-6: C-C=C-C-C=C 6. Double bonds between carbon 3-4 and 5-6: C-C-C=C-C=C Thus, there are 6 unique isomers for a six-member straight carbon chain with two double bonds.

Key Concepts

Carbon Chain

In organic chemistry, a carbon chain refers to a sequence of carbon atoms bonded together. These carbon atoms form the backbone for various organic molecules. The length and arrangement of the carbon chain are crucial in determining the properties and classification of the molecule. For example, in a straight chain, carbon atoms are linked one after another without any branching.

• A five-member carbon chain consists of five connected carbon atoms.
• Similarly, a six-member chain has six connected carbon atoms.

Changes in the carbon chain can result in different structural isomers, which are molecules with the same molecular formula but distinct structures. Understanding how carbon chains are formed and manipulated is fundamental in studying organic chemistry.

Double Bond

A double bond in organic chemistry is a strong chemical bond formed when two pairs of electrons are shared between two atoms. In hydrocarbon chains, this usually occurs between carbon atoms. Double bonds are represented by the symbol '=' in structural formulas. These bonds significantly influence the shape and reactivity of the molecule.

• They restrict rotation around the bond, leading to different possible spatial arrangements.
• This rotation limitation gives rise to different configurations or geometric isomers, like cis and trans isomers.

The presence of a double bond in a carbon chain influences how the molecule reacts with other chemicals, playing a crucial role in reactions such as hydrogenation and polymerization.

Organic Chemistry

Organic chemistry centers around the study of carbon-containing compounds and their properties, structures, and transformations. At its heart is the study of carbon chains and how they're modified by different bonds, such as single, double, and triple bonds.

• Organic chemistry includes the study of various structural isomers, like those discussed in the exercise.
• The arrangement of atoms and the types of bonds determine a compound's properties and reactivity.

Structural isomers, like those of the five-member and six-member carbon chains, illustrate how a single molecular formula can yield distinct compounds with varying chemical behaviors. This field is essential for many aspects of science, including pharmacology, materials science, and biochemistry.

Chemical Structure

Chemical structure refers to the arrangement of atoms within a molecule, including how they are bonded together. In organic molecules, this structure determines the physical and chemical properties of the molecule.

• The arrangement includes the backbone carbon chain and any double or triple bonds.
• Isomerism results from different possible structures sharing the same molecular formula.

Understanding chemical structures helps chemists to predict how molecules will interact in reactions and what potential uses they might have. For example, recognizing the presence of a double bond in a carbon chain informs chemists about possible reactivity sites and molecular stability. This knowledge is crucial for designing synthesis pathways in chemical manufacturing.