Problem 77 - Chemistry and Chemical Reactivity

Question

An alkene having the formula \(\mathrm{C}_{6} \mathrm{H}_{12}\) is known to have a six-carbon chain. How many isomeric species can be drawn based on this description? List the names of these species.

Step-by-Step Solution

Answer

There are 5 isomeric species: 1-hexene, cis-2-hexene, trans-2-hexene, 3-hexene.

Step 1: Determine the degree of unsaturation

The degree of unsaturation (or double bond equivalent, DBE) of a hydrocarbon is calculated using the formula: \( \text{DBE} = \frac{2+2C-H}{2} \). For \(C_6H_{12}\), substitute the values: \( \text{DBE} = \frac{2+2(6)-12}{2} = 1 \). This indicates one double bond or ring.

Step 2: Consider possible structures

Since the molecule has a six-carbon chain and a single degree of unsaturation, the structure must be a six-carbon alkene. We must consider the placement of the double bond along the carbon chain to find all possible isomers.

Step 3: Identify structural isomers

The isomers are determined by the position of the double bond in the hexene chain. These are: 1-hexene, 2-hexene, 3-hexene. The double bond cannot be in positions 4, 5, or 6 as these would repeat the previous structures due to symmetry.

Step 4: Identify stereoisomers

Examine the geometric (cis/trans) isomerism possible for each isomer with internal double bonds. **2-hexene** can have cis and trans forms. Thus, the isomers include: cis-2-hexene, trans-2-hexene, but 1-hexene and 3-hexene do not have such isomerism (due to terminal double bond and identical groups on one end for 3-hexene).

Key Concepts

Degree of Unsaturation

The degree of unsaturation is a crucial concept in organic chemistry that helps us determine the number of rings and/or pi bonds (double or triple bonds) in a molecule. This is often referred to as "double bond equivalent" (DBE). It provides insight into the structure of organic compounds without directly viewing them.
The degree of unsaturation formula is: \[ \text{DBE} = \frac{2+2C-H}{2} \] For hydrocarbons, like alkenes, where the formula is usually given in terms of carbon (C) and hydrogen (H) atoms, insert the values from the molecular formula. For instance, with a compound like \( \mathrm{C}_{6} \mathrm{H}_{12} \), you can calculate:

• The DBE is \( \frac{2+2(6)-12}{2} = 1 \)
• This tells us there is one double bond present in the molecule.

Understanding the degree of unsaturation lays the groundwork for predicting the types of structures, such as whether the molecule includes double bonds, triple bonds, or rings.

Structural Isomers

Structural isomers are a fascinating area of organic chemistry that breaks down into different arrangements of the same set of atoms. These isomers have the same molecular formula but differ in the connection of their atoms, resulting in distinct structural formulas. With alkenes like \( \mathrm{C}_{6} \mathrm{H}_{12} \), these differences arise through various placements of the double bonds.
For instance, with the formula \( \mathrm{C}_{6} \mathrm{H}_{12} \) and a six-carbon chain, possible structural isomers focus on where the double bond can sit along this chain:

• 1-Hexene
• 2-Hexene
• 3-Hexene

Consider that the double bond positions indicate a unique structural isomer only up to a point due to symmetry. That means any positioning beyond 3-hexene (such as 4-hexene) would mirror previous forms and not introduce a new structural isomer.

Stereoisomers

Stereoisomers offer a unique twist to isomerism by maintaining the same structural backbone but differing in spatial arrangements. This type of isomerism is especially prevalent in alkenes where double bonds restrict rotation, leading to geometric isomerism: cis (same side) and trans (opposite side) formations.
With compounds like \( \mathrm{C}_{6} \mathrm{H}_{12} \), the existence of stereoisomers depends on the internal double bonds.
Specifically, for 2-hexene, we have:

• Cis-2-hexene
• Trans-2-hexene

1-hexene does not show geometric isomerism because its double bond resides at the terminal position, making stereoisomerism impossible. Similarly, 3-hexene does not show this isomerism because identical groups surround the double bond on one end, precluding separate geometric forms.

Organic Chemistry

Organic chemistry is the branch of chemistry dedicated to the study of carbon-containing compounds, their structures, properties, and reactions. It covers not only a vast number of compounds but also an exciting array of structural arrangements.
In the realm of organic chemistry, alkenes like \( \mathrm{C}_{6} \mathrm{H}_{12} \) serve as quintessential examples due to their varied isomerism, demonstrating foundational concepts such as degrees of unsaturation, structural isomers, and stereoisomers.
Key focal points in organic chemistry include:

• Understanding molecular formulas and their significance in predicting structural possibilities.
• Exploring isomerism, which contributes to the diversity of organic molecules.
• Recognizing the impact of spatial configurations as seen in stereochemistry.

These aspects of organic chemistry are crucial for not only academic pursuits but also their application in fields like pharmaceuticals, materials science, and biochemistry.