Problem 54 - A Complete Resource Book in Chemistry for JEE Main

Question

Molecular weight of an unknown compound \([\mathrm{A}]\) is 82\. Compound [A] will be (a) \(\mathrm{CH}_{3}-\mathrm{CH}_{2}-\mathrm{C} \equiv \mathrm{C}-\mathrm{CH}_{2}-\mathrm{CH}_{3}\) (b) \(\mathrm{CH}_{2}=\mathrm{CH}_{2}-\mathrm{CH}_{2}-\mathrm{CH}_{2}-\mathrm{CH}=\mathrm{CH}_{2}\) (c) CC1=CCCC1 (d) all of these

Step-by-Step Solution

Answer

The answer is (d) all of these.

Step 1: Confirm Molecular Weight

First, verify that the molecular weight of each given compound can match the weight of 82. Use periodic table atomic weights: C = 12, H = 1.

Step 2: Calculate Molecular Weight of Compound (a)

Compound (a) is \( \text{CH}_3-\text{CH}_2-\text{C} \equiv \text{C}-\text{CH}_2-\text{CH}_3 \). It contains 6 carbons and 10 hydrogens. Calculate weight: \((6 \times 12) + (10 \times 1) = 82\.\) This matches the unknown compound.

Step 3: Calculate Molecular Weight of Compound (b)

Compound (b) is \( \text{CH}_2=\text{CH}-\text{CH}_2-\text{CH}_2-\text{CH}=\text{CH}_2 \). It contains 6 carbons and 10 hydrogens. Calculate weight: \((6 \times 12) + (10 \times 1) = 82\.\) This matches the unknown compound.

Step 4: Calculate Molecular Weight of Compound (c)

Compound (c) is cyclohexene, \( \text{C}_6\text{H}_{10} \). It contains 6 carbons and 10 hydrogens. Calculate weight: \((6 \times 12) + (10 \times 1) = 82\.\) This matches the unknown compound.

Step 5: Determine the Correct Option

All three compounds (a), (b), and (c) match the molecular weight of 82. Thus, the correct answer must be option (d) 'all of these'.

Key Concepts

Periodic Table Atomic Weights

The periodic table is a crucial tool in chemistry that helps us determine the atomic weights of various elements, which is fundamental in calculating molecular weights. Each element on the periodic table is represented with a specific atomic weight, for example:

• Carbon (C) has an atomic weight of 12.
• Hydrogen (H) has an atomic weight of 1.

These weights are actually average values because they take into account the abundance of each isotope of the element.

When solving problems, having a good understanding of these atomic weights is essential. They allow us to calculate the molecular weights of compounds by simply adding up the atomic weights of all the atoms present in a molecule. This calculation is typically the first step in understanding the composition of a chemical formula, and is especially useful in determining whether a specific molecule matches a given molecular weight.

Chemical Formula Analysis

Chemical formula analysis involves understanding and dissecting the composition of a chemical compound by looking at its molecular formula. This skill allows you to see how many atoms of each element are present in the compound. For instance, in compound (a) with the formula \( ext{CH}_3- ext{CH}_2- ext{C} \equiv ext{C}- ext{CH}_2- ext{CH}_3 \), there are:

• 6 carbon atoms (C)
• 10 hydrogen atoms (H)

By analyzing the formula, we can calculate the molecular weight:
\( (6 \times 12) + (10 \times 1) = 82 \).

This approach is systematic and allows us to verify whether the calculated molecular weight matches the expected value. Repeating this process for different compounds, such as (b) and (c) in our problem, reveals whether any of these compounds could potentially be the unknown compound given its weight.

Organic Chemistry Problem Solving

Organic chemistry often requires a methodical approach to solve problems, such as determining the molecular weight of unknown compounds. This process typically involves analyzing organic molecules, which are compounds primarily made of carbon and hydrogen.

Taking the given unknown compound with a molecular weight of 82, we start by using the periodic table to obtain atomic weights. Then, each potential compound is carefully analyzed through its chemical formula.

In this example, three different compounds were shown to have the same molecular weight when calculated:

• Compound (a) with the structure \( ext{CH}_3- ext{CH}_2- ext{C} \equiv ext{C}- ext{CH}_2- ext{CH}_3 \)
• Compound (b) \( ext{CH}_2=\text{CH}-\text{CH}_2-\text{CH}_2-\text{CH}=\text{CH}_2 \)
• Compound (c) cyclohexene, a ring structure \( ext{C}_6 ext{H}_{10} \)

All of these compounds fit the molecular weight of 82, thus leading to the conclusion that the correct option is (d) 'all of these'. This exemplifies the logical deduction required in organic chemistry and illustrates that different molecular structures can share the same molecular weight, demonstrating isomerism.