Problem 137 - A Complete Resource Book in Chemistry for JEE Main

Question

The total number of isomers which are primary amines with a molecular formula \(\mathrm{C}_{4} \mathrm{H}_{7} \mathrm{~N}\), having no \(\mathrm{C} \equiv \mathrm{C}\) bond is

Step-by-Step Solution

Answer

There are 3 isomers for primary amines with this molecular formula.

Step 1: Understand what is to be found

We need to find the total number of primary amines with the molecular formula \( ext{C}_4 ext{H}_7 ext{N}\) that do not have any triple bonds (\( ext{C} \equiv \text{C}\)). A primary amine is characterized by the \(- ext{NH}_2\) group attached to a secondary carbon (a carbon atom bonded with only one other carbon atom).

Step 2: Understand structural limits

The formula \( ext{C}_4 ext{H}_7 ext{N}\) without a triple bond allows either alkenes or cycloalkanes, but since we require primary amines, focus on open-chain structures since cycloalkanes will not give primary amines due to impossible hydrogen assignments for the formula.

Step 3: Design possible structures

We begin with 4 carbon atoms and assign bonds to ensure the molecule meets the saturation requirements (no \( ext{C} \equiv \text{C}\) bonds). Possible structures needing exploration are: linear chains ending with \(- ext{NH}_2\) group or with a double bond maintaining primary amine placement.

Step 4: Draw isomer structures

1. **Straight Chain:** \( ext{NH}_2- ext{CH}_2- ext{CH}_2- ext{CH}= ext{CH}_2\), called 1-butenamine. 2. **Positioned Doubling:** \( ext{CH}_3- ext{CH}_2- ext{CH}( ext{NH}_2)- ext{CH}_3\), rearranging within breaking and reposition of the \( ext{NH}_2\) group.3. **Branching:** \( ext{NH}_2- ext{CH}( ext{CH}_3)- ext{CH}= ext{CH}_2\), having isobutyl structure.4. **Isomers of previous:** A similar arrangement with double bond placement.Complete exploration within the formula's condition leads to 3 potential structures discussed.

Step 5: Validate and count structural results

Each structure meets the conditions without a triple bond and positioning \(- ext{NH}_2\) for primary amines correctly. Review each ensuring C4 framework integrity while retaining maximal saturation. The verification confirms 3 legitimate and possible structures for primary amines.

Key Concepts

Structural isomerism

Structural isomerism is a fascinating concept in organic chemistry where two or more compounds have the same molecular formula but differ in the connectivity of their atoms. This essentially means that, while they may look similar at first glance due to having the same numbers and types of atoms, the way these atoms are arranged is different.
This can result in diverse chemical properties and reactivities. A simple analogy could be like having the same lego blocks but assembling them into different structures.
For primary amines, structural isomerism is evident when we explore different arrangements of carbon and nitrogen atoms under the \(\text{C}_4\text{H}_7\text{N}\) formula with no \(\text{C} \equiv \text{C}\) bonds. To identify valid structures, we must consider open-chain formations because cyclic arrangements can lead to incorrect hydrogen counts for this formula.
Structural isomers in primary amines arise mainly from the placement of the \(-\text{NH}_2\) group along a linear or branched carbon chain.

Organic chemistry formulas

Organic chemistry relies heavily on understanding and utilizing formulas to predict and construct molecular structures. In this context, the formula \(\text{C}_4\text{H}_7\text{N}\) guides the creation of potential isomers as primary amines. Recognizing the absence of triple bonds indicates a focus on alkanes and alkenes and excluding alkynes, which have \(\text{C} \equiv \text{C}\) bonds.

• Each carbon atom is tetravalent, meaning it forms four bonds, and nitrogen is trivalent, forming three, which affects how molecules are structured.
• Additionally, hydrogen completes the saturation requirements for these molecules.

To construct primary amines, the \(-\text{NH}_2\) functional group is added to these carbon chains, adhering to the rules of valency and saturation. Accurate construction assures that the number of carbons, hydrogens, and nitrogen matches the given formula consistently.

Molecular structure validation

Molecular structure validation involves checking if a proposed molecular structure fits the molecular formula both in terms of atom count and connectivity. When faced with a formula like \(\text{C}_4\text{H}_7\text{N}\), this process ensures that the structure meets the required saturation state, specifically without any \(\text{C} \equiv \text{C}\) bonds in this exercise.

• Each carbon must form four bonds, nitrogen three, and hydrogen one, satisfying the valency rules.
• For primary amines, the \(-\text{NH}_2\) group needs to bind to a terminal carbon in a linear sequence, avoiding any cyclic structures.

By going through the structures discovered in the exercise, we verify that each satisfies the molecular constraints set by the formula. This includes confirming accurate placement of double bonds and maintaining the presence of the \(-\text{NH}_2\) group appropriately. Through validation, we confirm the three valid structural arrangements respects these rules, each manifesting as a proper primary amine isomer.