4.1.2 Molar Mass and Density of Gases

This topic explains the relationship between molar mass and density of gases. It shows how to calculate the molar mass of a gas from its density at STP.

Definition

Density: The mass per unit volume of a substance.

Molar Mass: The mass of one mole of a substance.

Main Idea

As the molar mass of all gases occupies the same volume at STP, the density of a gas depends on its molar mass. A gas having higher molar mass will have higher density and vice versa. The density of a gas can be calculated from its molar mass and molar volume. If the density of a gas at STP is determined, its molar mass can be calculated.

Core Concept

Density = MassVolume

For gases at STP: Density = Molar MassMolar Volume

Molar Mass = Density × 22.414

Detailed Explanation

Density of Gases

• Density is defined as the mass per unit volume of a substance.
• As the molar mass of all gases occupies the same volume at STP, the density of a gas depends on its molar mass.
• A gas having higher molar mass will have higher density and vice versa.
• So, density of a gas can be calculated from its molar mass and molar volume.
• If the density of gas at STP is determined, its molar mass can be calculated.

Relationship Between Molar Mass and Density

At STP, 1 mole of any gas occupies 22.414 dm³.

Therefore: Density = Molar Mass22.414 dm³

Rearranging: Molar Mass = Density × 22.414 dm³

Example 4.2: Gram Molecular Mass from Density

Problem: Calculate the gram molecular mass of a gas which has a density of 1.43 g/dm³ at STP.

Solution:

Given: - Density of gas at STP = 1.43 g/dm³

We know that: 1 dm³ of gas at STP = 1.43 g

Therefore: 22.4 dm³ of gas at STP = 1.43 × 22.4

= 32.032 g

As 22.4 dm³ of a gas at STP = molar mass

Therefore, gram molecular mass of gas is 32.032 amu.

Steps for Solving Problems

Given: - Density of gas at STP

Required: - Molar mass of gas

Formula: Molar Mass = Density × 22.414

Substitution: Molar Mass = 1.43 × 22.4

Calculation: Molar Mass = 32.032 g/mol

Final Answer: - Gram molecular mass of gas = 32.032 amu

Comparison of Densities

Observation: Higher molar mass → higher density.

Intermediate Level

Density and Molar Mass Relationship

At STP, 1 mole of any gas occupies 22.414 dm³.

Density = Molar MassMolar Volume

Molar Mass = Density × 22.414

Example 4.2: Molar Mass from Density

Given: - Density = 1.43 g/dm³ at STP

Required: - Molar mass

Formula: Molar Mass = Density × 22.414

Substitution: Molar Mass = 1.43 × 22.4

Calculation: Molar Mass = 32.032 g/mol

Final Answer: - Gram molecular mass = 32.032 amu

Density Comparison Table

Important Points

• 1. Density = mass/volume.
• 2. At STP, molar volume = 22.414 dm³.
• 3. Density = molar mass / 22.414.
• 4. Molar mass = density × 22.414.
• 5. Higher molar mass → higher density.
• 6. Example: Density 1.43 g/dm³ → Molar mass 32.032 g/mol.

Remember

• - Density: Mass/volume
• - Molar volume at STP: 22.414 dm³
• - Density = Molar mass / 22.414
• - Molar mass = Density × 22.414
• - Higher molar mass → higher density

Common Mistakes

• 1. Forgetting to multiply by 22.414: Molar mass = density × 22.414.
• 2. Confusing density with molar mass: Density is g/dm³; molar mass is g/mol.
• 3. Using the wrong molar volume: Molar volume is 22.414 dm³ at STP.
• 4. Thinking all gases have the same density: Density depends on molar mass.

Quick Revision

• Density = mass/volume.
• At STP, molar volume = 22.414 dm³.
• Density = molar mass / 22.414.
• Molar mass = density × 22.414.
• Higher molar mass → higher density.
• Example: Density 1.43 g/dm³ → Molar mass 32.032 g/mol.

60-Second Revision

• Density: Mass/volume
• Molar volume at STP: 22.414 dm³
• Density = Molar mass / 22.414
• Molar mass = Density × 22.414
• Higher molar mass → higher density

QUALITY VALIDATION

• Topic: 4.1.2 Molar Mass and Density of Gases
• Chapter: 4 (Stoichiometry)

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