Problem 71 - A Complete Resource Book in Chemistry for JEE Main

Question

The number of possible open chain (acyclic) isomeric compounds for molecular formula \(\mathrm{C}_{5} \mathrm{H}_{10}\) would be (a) 5 (b) 6 (c) 7 (d) 4

Step-by-Step Solution

Answer

There are 5 possible acyclic isomers.

Step 1: Identify Compound Type

Since we are given the formula \(\mathrm{C}_{5}\mathrm{H}_{10}\), we should recognize that this is a formula for an alkene (a hydrocarbon with at least one carbon-carbon double bond) or a cycloalkane.

Step 2: Determine Degree of Unsaturation

Calculate the degree of unsaturation using the known formula \(\text{degree of unsaturation} = \left(2 \times \text{number of carbon atoms} + 2 - \text{number of hydrogen atoms}\right)/2\). Substitute the values: \(\left(2 \times 5 + 2 - 10\right)/2 = 1\). This indicates one double bond or one ring.

Step 3: Explore Structural Possibilities

Since the problem specifies 'acyclic' compounds, we focus on alkenes. Consider all possible structures of alkenes with one double bond and five carbon atoms: linear (straight-chain) and branched-chain configurations.

Step 4: List Isomer Variants

List all linear and branched structures of alkenes with the given formula: 1. Pent-1-ene 2. Pent-2-ene 3. 2-Methylbut-1-ene 4. 3-Methylbut-1-ene 5. 2-Methylbut-2-ene Ensure that no option repeats and that all positional isomers are considered.

Step 5: Count Isomers

Count each unique isomer from the list provided: - Pent-1-ene - Pent-2-ene - 2-Methylbut-1-ene - 3-Methylbut-1-ene - 2-Methylbut-2-ene There are 5 distinct isomers.

Key Concepts

Alkene Isomerism

Isomerism in alkenes arises due to the presence of a carbon-carbon double bond. This feature permits the formation of different structural arrangements. Since alkenes have the general formula \( ext{C}_n ext{H}_{2n}\), isomers may vary either by changing the position of the double bond or by the arrangement of carbon atoms around the double bond.

**Types of Isomerism in Alkenes:**

• **Positional Isomerism:** Occurs when the double bond is moved to a different location within the carbon chain. For instance, shifting the double bond in pentene can result in pent-1-ene or pent-2-ene.


• **Chain Isomerism:** Happens when the carbon skeleton of the isomer changes. Branching within the chain, such as forming 2-methylbut-1-ene from pent-ene, is an example.

Positional and chain isomerism allow for multiple structural variants, each with unique chemical properties. Understanding these helps in predicting reactivity and physical characteristics of alkenes.

Degree of Unsaturation

The degree of unsaturation, also known as the index of hydrogen deficiency, is a useful concept in organic chemistry to determine the total number of rings and multiple bonds within a molecule. Calculating this index helps identify the types of hydrocarbons you’re dealing with.

**How to Calculate:**

• **Formula:** The degree of unsaturation is given by \((2 \times \text{no. of Carbons + 2 - no. of Hydrogens})/2\). In the case of \( ext{C}_5 ext{H}_{10}\), the calculation goes as \(2 \times 5 + 2 - 10) / 2 = 1\).


• This tells us that there is either one double bond or one ring present in the compound.

By using the degree of unsaturation, we can easily spot whether hydrocarbons are acyclic (alkenes) or cyclic (cycloalkenes). This helps set the stage for exploring various isomers, especially knowing that \( ext{C}_5 ext{H}_{10}\) must represent an alkene in this case.

Acyclic Compounds

Acyclic compounds, also known as open-chain compounds, consist entirely of carbon atoms arranged in a linear or branched format. They don't form rings, differentiating them from cyclic compounds which have rings.

**Characteristics of Acyclic Compounds:**

• **Straight or Branched Chain:** Acyclic compounds can be either straight-chained like hexane or branched like isopentane.


• **Common Examples:** Acyclic alkenes such as pent-1-ene and branched alkenes like 2-methylbut-1-ene fall under this category.

For acyclic compounds with a formula like \(\text{C}_5\text{H}_{10}\), each isomer arises due to different arrangements of the carbon chain or position of the double bond. Recognizing these variations is essential for distinguishing different alkenes from each other in organic chemistry.