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 6.

Step 1: Understand the Compound Formula

The compound given is \(\mathrm{C}_{4} \mathrm{H}_{8}\). This is an alkene formula, which follows the general pattern of \(\mathrm{C}_{n}\mathrm{H}_{2n}\), indicating one degree of unsaturation. We need to consider structures with a double bond or a ring structure as potential isomers.

Step 2: Identify Possible Structures

For \(\mathrm{C}_{4} \mathrm{H}_{8}\), we need to find all possible structural isomers. Start by considering all the linear and branched carbon chains that can exist with four carbon atoms and satisfy \(\mathrm{C}_{4} \mathrm{H}_{8}\).

Step 3: Draw Linear Alkenes

Consider the linear alkenes and where a double bond could be placed. We can have:1. \(\mathrm{CH}_3\mathrm{-CH} = \mathrm{CH}-\mathrm{CH}_3\) (1-butene)2. \(\mathrm{CH}_2= \mathrm{CH}-\mathrm{CH}_2-\mathrm{CH}_3\) (2-butene, which includes \(cis\) and \(trans\) forms)Note: \(cis\) and \(trans\) are considered different isomers.

Step 4: Consider Branched Alkenes

For branched structures, consider:1. \(\mathrm{CH}_3-\overset{\mathrm{CH}_3}{\overset{|}{\mathrm{CH}_{2}}}-\mathrm{CH}_2\) (isobutene or 2-methylpropene)

Step 5: Consider Cyclic Structures

Though this is less common for this type of question, investigate ring formations:1. Cyclobutane \((\mathrm{C}_4\mathrm{H}_8)\)2. Methylcyclopropane

Step 6: Count the Isomers

Add up all the unique structures: 1. 1-butene 2. cis-2-butene 3. trans-2-butene 4. 2-methylpropene 5. cyclobutane 6. methylcyclopropane That totals six isomers.

Key Concepts

Alkene Isomers

Alkene isomers are compounds with the same molecular formula but different arrangements of carbon and hydrogen atoms, specifically featuring a double bond between carbon atoms. Alkenes are unsaturated hydrocarbons that follow the general formula \(\mathrm{C}_{n}\mathrm{H}_{2n}\), making them distinct from alkanes that are fully saturated.

In the case of \(\mathrm{C}_{4}\mathrm{H}_{8}\), we are looking for different ways to arrange its carbon and hydrogen atoms to form alkenes. Consider where the double bond can be located in a linear setup:

• 1-butene: the double bond is between the first and second carbon atoms.
• 2-butene: the placement of the double bond between the second and third carbon atoms allows for geometric isomers, which include cis and trans configurations.

Each position of the double bond results in a distinct molecular structure, giving each isomer unique properties. These properties affect physical characteristics such as boiling points and chemical reactivity.

Structural Isomers

Structural isomers, also known as constitutional isomers, possess the same molecular formula but differ in how their atoms are connected. This variance gives rise to a set of unique compounds even though they share the same number of each type of atom.

For \(\mathrm{C}_{4}\mathrm{H}_{8}\), we not only arrange the carbon atoms linearly but also consider branching. A common example of a branched alkene is 2-methylpropene, also known as isobutene. Here, instead of a continuous chain, a carbon atom branches off as a substituent.

• This kind of branching impacts physical properties like melting and boiling points.
• It can also influence chemical reactions, as the location of the double bond and branching can affect reactivity.

The concept of structural isomers emphasizes the diversity possible even within constraints of a set formula, allowing for innovation and exploration in organic chemistry.

Cyclic Compounds

Cyclic compounds are another intriguing form of isomerism. In these structures, the carbon chain forms a closed ring instead of an open chain. This adds a unique dimension to isomerism, as these structures still adhere to the formula \(\mathrm{C}_{n}\mathrm{H}_{2n}\), like alkenes.

Examples in this context include cyclobutane and methylcyclopropane. Such ring formations modify the molecular geometry and bring about differences in chemical properties when compared to their linear and branched counterparts.

• Cyclobutane: This forms a square-like structure with four carbon atoms, maintaining the \(\mathrm{C}_{4}\mathrm{H}_{8}\) formula through its cyclic form.
• Methylcyclopropane: Smaller rings, like this three-membered ring, are formed with one carbon branch off the ring.

Understanding cyclic compounds broadens the scope of organic structures and showcases the versatility of carbon bonding. This understanding is crucial for recognizing how minor changes in atomic arrangement impact a compound's characteristics significantly.