Question

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

Short answer

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

Step-by-step solution

Understanding Isomers

Isomers are compounds with the same molecular formula but differing structures. For alkanes like \( ext{C}_4 ext{H}_8\), the types of isomers can include structural isomers (chain, position, functional group isomers) and stereoisomers. However, given that \( ext{C}_4 ext{H}_8\) isn't fully saturated, it can be an alkene or a cycloalkane.

Identifying Possible Structures

For \( ext{C}_4 ext{H}_8\), consider both alkenes (with double bonds) and cycloalkanes. For alkenes, try placing the double bond in different positions to create structural isomers. For cycloalkanes, build cyclic structures that fit the formula.

Drawing and Counting Isomers

1. **Alkenes**: But-1-ene, But-2-ene (cis and trans) are possible. Thus, there are 3 alkene isomers including stereoisomers for but-2-ene. 2. **Cycloalkanes**: Cyclobutane and methylcyclopropane can both fit the formula. Two more isomers are identified here.

Verifying and Summing Up

Verify the structures we drew by ensuring they correspond to the molecular formula. Counting the unique structures gives us: But-1-ene, But-2-ene (trans and cis), Cyclobutane, and Methylcyclopropane. In total, there are 5 distinct isomers.

Key concepts

Alkenes

Alkenes are hydrocarbons that contain at least one carbon-carbon double bond. This double bond is the defining feature of alkenes and is represented in chemical structures as two lines connecting the carbon atoms. Because of this double bond, alkenes are unsaturated hydrocarbons, meaning they have fewer hydrogen atoms compared to alkanes with the same number of carbon atoms. For instance, in the molecular formula of an alkene, such as \( \mathrm{C}_4 \mathrm{H}_8 \), the ratio of hydrogen to carbon is lower than that of alkanes.

When naming alkenes, the position of the double bond is crucial. For example, in but-1-ene and but-2-ene, the numbers indicate the first carbon atom of the double bond's position in the longest carbon chain. This position can affect the physical and chemical properties of the alkene. Additionally, but-2-ene can exist as two stereoisomers (cis and trans), due to the restricted rotation around the double bond.

Cycloalkanes

Cycloalkanes are a type of saturated hydrocarbon where carbon atoms are connected in a ring or cyclic structure. Even though they are saturated, meaning all their carbon-carbon bonds are single bonds, they have the general formula \( \mathrm{C}_n \mathrm{H}_{2n} \), similar to alkenes due to the cycle formation. This formula arises because one carbon-carbon bond is used to close the ring, reducing the number of hydrogen atoms.

In the case of \( \mathrm{C}_4 \mathrm{H}_8 \), cyclobutane is a common cycloalkane isomer, consisting of a four-carbon ring. Another isomer is methylcyclopropane, where a propane ring has a methyl group substituted for one hydrogen. The cyclic nature of cycloalkanes allows them to adopt various conformations, which can influence their stability and reactivity.

Structural Isomers

Structural isomers have the same molecular formula but differ in how their atoms are arranged or connected. This difference can include variations in the carbon skeleton, the position of functional groups, or branching patterns. For example, \( \mathrm{C}_4 \mathrm{H}_8 \) has several structural isomers, including both alkenes and cycloalkanes.

• In the alkenes, but-1-ene and but-2-ene are structural isomers due to the varied position of the double bond.
• Cyclobutane and methylcyclopropane are cycloalkane structural isomers as they both feature four carbon atoms in cyclic arrangements with distinct connectivity.

These different arrangements impact the properties such as boiling point, density, and reactivity of each isomer.

Stereoisomers

Stereoisomers are isomers that have the same bonding sequence but differ in the three-dimensional arrangement of atoms. A common type of stereoisomerism arises from the presence of a double bond, like in alkenes, where the spatial arrangement around the double bond can differ, leading to different isomers.

In \( \mathrm{C}_4 \mathrm{H}_8 \), but-2-ene can exist as two stereoisomers: cis-but-2-ene and trans-but-2-ene. These isomers differ in the relative positions of the substituent groups attached to the double-bonded carbons.

• Cis isomer: Both substituents are on the same side of the double bond.
• Trans isomer: The substituents are on opposite sides.

These differences are significant because they can dramatically affect the physical properties (such as boiling and melting points) and even the chemical reactivity of the molecules.