Problem 11 - A Complete Resource Book in Chemistry for JEE Main

Question

The correct relationship between molecular mass and vapour density is (a) V.D. \(=2 \mathrm{M}\) (b) V.D. \(=\frac{M}{2}\) (c) \(\mathrm{M}=(\mathrm{V} \cdot \mathrm{D} .)^{\frac{1}{2}}\) (d) V.D. \(=\mathrm{M}^{2}\)

Step-by-Step Solution

Answer

The correct answer is (b) V.D. \(=\frac{M}{2}\).

Step 1: Understanding the Terms

First, we need to understand the terms involved. Molecular mass \(M\) is the mass of a molecule. Vapor density (V.D.) is the density of a vapor relative to that of hydrogen, and it is defined as the ratio of the mass of a given volume of gas to that of the same volume of hydrogen under the same conditions.

Step 2: Relating Molecular Mass and Vapor Density

The relationship between molecular mass \(M\) and vapor density (V.D.) can be established using the definition of vapor density. It has been empirically shown that\[\text{V.D.} = \frac{\text{M}}{2}\]Therefore, vapor density can be directly calculated as half of the molecular mass.

Step 3: Evaluating the Options

Now evaluate each given option:- Option (a) implies \(\text{V.D.} = 2M\), which does not match the definition.- Option (b) implies \(\text{V.D.} = \frac{M}{2}\), which matches the established relationship.- Option (c)\(M = \text{(V.D.)}^{\frac{1}{2}}\) is incorrect based on the relationship.- Option (d)\(\text{V.D.} = M^{2}\) is also incorrect.

Key Concepts

Vapor Density and Its Importance

Vapor density is a key concept in understanding gases, especially when comparing them to hydrogen. It measures how much heavier or lighter a gas is compared to hydrogen, the lightest element available. This comparison is done under the same conditions of temperature and pressure, which makes the comparison fair and accurate.
To calculate vapor density, we use the formula: \[ \text{V.D.} = \frac{\text{mass of a given volume of gas}}{\text{mass of the same volume of hydrogen}} \]This makes vapor density a dimensionless quantity, providing a straightforward relation to molecular mass. By convention, vapor densities are computed in regards to hydrogen, setting its vapor density as 1. Understanding vapor density is crucial because it helps in determining molecular formulas and understanding the properties of gases.
Key points to remember:

• Vapor density simplifies the comparison between different gases.
• Helps infer molecular masses and relationships between molecules.
• Essential for studying gases' behavior under varying conditions.

Role of Chemistry Education

In chemistry education, connecting concepts like vapor density to real-world applications enriches the learning experience. Understanding vapor density helps students grasp larger concepts such as gas laws, chemical reactions, and the behavior of substances at different environmental conditions.
Through education, students learn how vapor density is relevant in practical scenarios. For instance, it is fundamental in industries where knowing the properties of gases is critical, such as in pharmaceuticals and environmental science. Chemistry courses in schools and colleges often include experiments that make these concepts tangible.
Educators emphasize the importance of comprehension over rote learning. By using examples, illustrations, and practical experiments, educators engage students, creating a strong foundation for chemistry principles.

• Connects theoretical knowledge with practical applications.
• Encourages critical thinking and problem-solving skills.
• Provides a foundation for advanced studies in chemistry and related fields.

JEE Main Syllabus and Its Focus

For students preparing for India's JEE Main examination, a solid understanding of vapor density is indispensable. The JEE Main syllabus includes essential topics of physical chemistry, where concepts like vapor density demonstrate critical thinking and problem-solving.
This aspect of the syllabus highlights the understanding of relationships between different chemical quantities and their application in solving complex problems. The exam tests how well students can apply these concepts to deduce and derive solutions to questions that are often linked to everyday chemistry.
Mastering this topic can be very beneficial, as it serves as a fundamental stepping stone to more difficult topics.

• Essential for problem-solving in physical chemistry questions.
• Serves as a building block for understanding more complex topics.
• Helps in achieving a competitive edge in the examination.