Vapour Density Application in Stoichiometry & Mole Concept | JEE & NEET Chemistry Notes

Vapour Density & Mole Concept

A Comprehensive Guide for JEE (Main & Advanced) and NEET Aspirants

Introduction to Vapour Density

In the realm of physical chemistry, specifically within Stoichiometry and the Mole Concept, Vapour Density (VD) is a crucial parameter for determining the molecular mass of gaseous substances. For students preparing for JEE and NEET, understanding the relationship between density, volume, and mass is fundamental to solving complex gas laws and stoichiometry problems.

Definition and Formula

Vapour Density is defined as the ratio of the mass of a certain volume of a gas or vapour to the mass of the same volume of hydrogen gas at the same temperature and pressure.

Since it is a ratio of two similar quantities (masses), Vapour Density is a unitless quantity. It falls under the category of Relative Density.

$$ \text{Vapour Density (VD)} = \frac{\text{Mass of 'V' volume of gas at T, P}}{\text{Mass of 'V' volume of } H_2 \text{ gas at T, P}} $$

Relation between Molecular Mass and Vapour Density

According to Avogadro's Hypothesis, equal volumes of all gases contain an equal number of molecules at the same temperature and pressure. Let $V$ volume contain $n$ molecules.

$$ VD = \frac{\text{Mass of } n \text{ molecules of gas}}{\text{Mass of } n \text{ molecules of } H_2} $$

If we consider $n = 1$ (1 molecule):

$$ VD = \frac{\text{Mass of 1 molecule of gas}}{\text{Mass of 1 molecule of } H_2} $$

Since the mass of 1 molecule of $H_2$ is 2 amu (approx):

$$ VD = \frac{\text{Molecular Mass of Gas}}{2} $$

$$ \text{Molecular Mass (M)} = 2 \times \text{Vapour Density (VD)} $$

Note: This relationship is valid only for gases and vapours, not for solids or liquids.

Applications in Stoichiometry & NEET/JEE

1. Determination of Molecular Formula

In empirical formula problems, often the Vapour Density is given instead of molar mass.

• Step 1: Calculate Molecular Mass using $M = 2 \times VD$.
• Step 2: Calculate Empirical Formula Mass.
• Step 3: Find $n = \frac{\text{Molecular Mass}}{\text{Empirical Formula Mass}}$.
• Step 4: Molecular Formula = $(\text{Empirical Formula})_n$.

2. Vapour Density of a Mixture

For a mixture of non-reacting gases, we use the concept of Average Relative Molecular Mass ($M_{avg}$).

$$ M_{avg} = \frac{n_1M_1 + n_2M_2 + ...}{n_1 + n_2 + ...} $$

Consequently, the Vapour Density of the mixture ($VD_{mix}$) is:

$$ VD_{mix} = \frac{M_{avg}}{2} $$

3. Key Points for Exam

• Absolute Density ($d = PM/RT$) is different from Vapour Density. Absolute density has units (g/L), while VD is unitless.
• VD is independent of temperature and pressure changes, whereas Absolute Density changes with T and P.
• For an ideal gas at STP, Density (g/L) = $M / 22.4$. Therefore, $VD = (d_{STP} \times 22.4) / 2 = 11.2 \times d_{STP}$.

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