Problem 15 - A Complete Resource Book in Chemistry for JEE Main

Question

The total number of isomers for \(\mathrm{C}_{4} \mathrm{H}_{8}\) are (a) 8 (b) 7 (c) 6 (d) 5

Step-by-Step Solution

Answer

The total number of isomers for \(\mathrm{C}_4 \mathrm{H}_8\) is 5.

Step 1: Identify the Molecular Formula and Isomers

The molecular formula given is \( \mathrm{C}_4 \mathrm{H}_8 \). This formula indicates an alkene, which has a double bond, or a cycloalkane, which is a ring structure.

Step 2: Determine the possible alkene structures

For alkenes, we look at different positions for the double bond in a four-carbon chain. These positions are 1-butene and 2-butene. Furthermore, 2-butene can exist in two geometric isomers (cis and trans). Thus, there are three possible alkene structures: 1-butene, cis-2-butene, and trans-2-butene.

Step 3: Determine the possible cycloalkane structures

A cycloalkane will form a closed ring. The possible structures are cyclobutane, methylcyclopropane, and ethylidene-cyclopropane (also called vinylcyclopropane).

Step 4: Count all unique structures

Adding the alkenes and cycloalkane structures, there are: 1. 1-butene, 2. cis-2-butene, 3. trans-2-butene, 4. cyclobutane, 5. methylcyclopropane.

Key Concepts

Isomerism

In organic chemistry, isomerism refers to the phenomenon where molecules with the same molecular formula have different arrangements of atoms. These variations often result in distinct physical and chemical properties. The two primary types of isomerism are structural isomerism and stereoisomerism.

• Structural isomerism arises when atoms are connected in different orders, leading to variations such as chain isomerism, where carbon chains differ in branching.
• Stereoisomerism, on the other hand, occurs when atoms are connected in the same order, but differ in spatial orientation. This can be further divided into geometric (cis-trans) isomerism, typically seen in alkenes, and optical isomerism, which is related to chiral molecules.

For the molecular formula \( \text{C}_4 \text{H}_8 \), the presence of a double bond or a ring offers various possibilities for isomerism. Understanding these variations is crucial for predicting the properties and reactivity of different isomers.

Alkene Structures

Alkenes are hydrocarbons that contain carbon-carbon double bonds, represented by the general formula \( \text{C}_n \text{H}_{2n} \). The double bond introduces a degree of unsaturation, distinct from alkanes with only single bonds. One key feature of alkenes is the possibility of geometric isomers (cis and trans) due to restricted rotation around the double bond.

For \( \text{C}_4 \text{H}_8 \), various alkene structures are possible:

• 1-butene: A linear structure with the double bond between the first and second carbon atoms.
• 2-butene: The double bond is between the second and third carbon atoms, allowing for cis-trans isomerism.
  • cis-2-butene: Hydrogen atoms are on the same side of the double bond, creating a polar molecule.
  • trans-2-butene: Hydrogen atoms are on opposite sides, offering stability and non-polarity.

Recognizing these structures and their isomerism helps understand how alkenes behave in chemical reactions and their uses in industry and nature.

Cycloalkane Structures

Cycloalkanes are saturated hydrocarbons that form ring structures and follow the formula \( \text{C}_n \text{H}_{2n} \), similar to alkenes due to the presence of rings. Although they lack double bonds, the ring structure introduces a distinct geometry that affects physical and chemical properties.

Possible cycloalkane structures for \( \text{C}_4 \text{H}_8 \) include:

• Cyclobutane: A four-membered ring that introduces angle strain due to its square structure.
• Methylcyclopropane: A three-membered ring with an additional methyl group, slightly relieving some strain of the cyclopropane.
• Vinylcyclopropane (ethylidene-cyclopropane): This structure includes a vinyl group attached, modifying its reactivity.

Understanding cycloalkane structures is vital, as their strained rings often lead to unique reactions, making them interesting subjects in synthetic chemistry and industrial applications.