Question

Draw all possible isomers for the molecule \(\mathrm{C}_{4} \mathrm{H}_{8}\).

Short answer

Possible isomers include: 1-butene, cis/trans-2-butene, 2-methylpropene, cyclobutane, and methylcyclopropane.

Step-by-step solution

Understanding Isomers

Isomers are compounds that have the same molecular formula but differ in the arrangement of atoms in space. Since we are looking for isomers of \(\mathrm{C}_4\mathrm{H}_8\), we need to find structures that have exactly 4 carbon atoms and 8 hydrogen atoms but with different arrangements.

Identify Possible Structures

Given that the molecular formula is \(\mathrm{C}_4\mathrm{H}_8\), we recognize that this can represent either an alkene with one double bond or a cycloalkane with no double bonds. This helps us determine possible structural frameworks to explore.

Drawing Alkene Isomers

Start with linear alkenes. The simplest possibility is butene with a double bond in different positions:1. \(\mathrm{CH}_2=\mathrm{CHCH}_2\mathrm{CH}_3\) (1-butene)2. \(\mathrm{CH}_3\mathrm{CH}=\mathrm{CHCH}_3\) (2-butene) *Consider both trans-2-butene and cis-2-butene due to geometrical isomerism around the double bond.*

Drawing Branched Alkene Isomers

Consider branching in alkenes:1. \(\mathrm{CH}_2=C(\mathrm{CH}_3)\mathrm{CH}_2\mathrm{CH}_3\) (2-methylpropene), which involves a branched chain with the double bond.

Drawing Cycloalkane Isomers

Explore possible cyclic structures: 1. Cyclobutane (a four-carbon ring with no double bonds) 2. Methylcyclopropane (a three-carbon ring with a one-carbon branch).

Review and Confirm

Verify each drawn structure to ensure it fits the molecular formula \(\mathrm{C}_4\mathrm{H}_8\) and that no additional isomers have been overlooked. Check for distinct structural and geometrical isomers.

Key concepts

alkene

Alkenes are hydrocarbons that contain at least one carbon-carbon double bond. This makes them unsaturated, meaning they have fewer hydrogen atoms than their alkane counterparts. Alkenes follow the general formula \[\mathrm{C}_n\mathrm{H}_{2n}\] which is evident in the molecular formula for the compound of interest, \(\mathrm{C}_4\mathrm{H}_8\). In alkenes, the double bond can occur at different positions along the carbon chain, which gives rise to different structural isomers. For instance, with four carbon atoms as in butene, the double bond can be between the first and second carbon, forming 1-butene, or between the second and third carbon, forming 2-butene. Each positional change affects the compound's properties and reactions.

cycloalkane

Cycloalkanes are another type of hydrocarbon, characterized by having their carbon atoms linked in a ring. This type of structure results in the loss of two hydrogen atoms compared to their non-cyclic alkane counterparts. Cycloalkanes still follow the same general molecular formula as alkenes, \(\mathrm{C}_n\mathrm{H}_{2n}\). In the context of \(\mathrm{C}_4\mathrm{H}_8\), cycloalkanes can include structures like cyclobutane, which has a simple square ring of four carbons. There is also methylcyclopropane, where three carbons form a ring and the fourth is attached as a branch, offering a different isomer to consider.

geometrical isomerism

Geometrical isomerism, particularly in alkenes, arises from the presence of a double bond. This bond restricts rotation, creating distinct spatial configurations known as *cis* and *trans* isomers. For example, in 2-butene, the arrangement of substituents around the double bond creates two unique isomers:

• Cis-2-butene: where the larger groups are on the same side of the double bond.
• Trans-2-butene: where the larger groups are on opposite sides of the double bond.

Both isomers have the same molecular formula, \(\mathrm{C}_4\mathrm{H}_8\), but differ in physical properties such as boiling point and stability, illustrating an important aspect of isomerism in chemistry.

molecular formula

A molecular formula gives the exact number of different types of atoms in a molecule but does not show the bonds between them or the arrangement of the atoms. For example, \(\mathrm{C}_4\mathrm{H}_8\), indicates there are four carbon atoms and eight hydrogen atoms. This formula can represent several different structures, including both alkenes and cycloalkanes. The challenge often lies in identifying all possible isomers from a given molecular formula. It’s essential to explore different bonding patterns, positions for any potential double bonds, and rings to find all unique isomers.

chemical structures

Chemical structures provide a visual representation of where each atom in a molecule is located and how they are connected. These diagrams are crucial for understanding the specificity of isomers. Structures can show single, double, or even triple bonds, and indicate potential points of branching in a carbon chain. Different structures for \(\mathrm{C}_4\mathrm{H}_8\) can illustrate the presence of a double bond (as in alkenes) or a closed ring (as in cycloalkanes). Drawing all possible isomers helps in making sure every structural possibility is considered, including branched or linear arrangements, and understanding the chemical properties and reactivity of each potential molecule.