4.1.1 Molar Volume (Vₘ)

This topic explains molar volume — the volume occupied by one mole of any gas at standard temperature and pressure (STP).

Definition

Molar volume is the volume occupied by one mole of any gas at STP.

Value

V_m = 22.414 dm³ at STP

Key Relationships

Examples

Example 1: Volume of 2.5 moles of Cl₂ V = 2.5 × 22.414 = 56.035 dm³

Example 2: Molar mass from density M = 1.43 × 22.4 = 32.032 g/mol

Key Point

• Molar volume applies to all gases at STP.
• It is independent of the identity of the gas.

Main Idea

One mole of any gas at STP occupies a volume of 22.414 dm³. This volume is called the molar volume. With the help of this relationship, we can convert the mass of a gas at STP into its volume and vice versa.

Core Concept

• **1 mole of any gas at STP = 22.414 dm³**
• This relationship applies to all gases at STP, regardless of their identity.
• STP (Standard Temperature and Pressure) = 0°C (273 K) and 1 atm (760 mm Hg).

Detailed Explanation

What is Molar Volume?

• One mole of any gas at STP occupies a volume of 22.414 dm³.
• This volume is called molar volume.
• With the help of this relationship, we can convert the mass of a gas at STP into its volume and vice versa.

Key Relationships

22.414 dm³ of any gas at STP = 1 mole = 6.02 × 10²³ molecules

• 22.414 dm³ of H₂ gas at STP = 2 g = 6.02 × 10²³ molecules
• 22.414 dm³ of NH₃ gas at STP = 17 g = 6.02 × 10²³ molecules

Example 4.1: Volume of 2.5 Moles of Chlorine at STP

Problem: Determine the volume of 2.5 moles of chlorine molecules at STP.

Solution:

We know that: 22.414 dm³ of Cl₂ at STP = 1 mole

Or 1 mole of Cl₂ occupies a volume of 22.414 dm³ at STP.

2.5 mole of Cl₂ occupy a volume of 22.414 dm³ × 2.5 = 56.035 dm³

Final Answer: 2.5 moles of Cl₂ occupy 56.035 dm³ at STP.

Using Molar Volume in Calculations

To find volume from moles: Volume = Moles × 22.414 dm³

To find moles from volume: Moles = Volume22.414 dm³

Molar Volume and Density

• 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.
• 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.

Formula: Density = Molar massMolar volume

Molar mass = Density × 22.414

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:

1 dm³ of gas at STP = 1.43 g

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.

Important Points

• 1. Molar volume = 22.414 dm³ at STP.
• 2. STP = 0°C and 1 atm.
• 3. 1 mole of any gas at STP = 22.414 dm³.
• 4. Volume = moles × 22.414.
• 5. Moles = volume / 22.414.
• 6. Density = molar mass / 22.414.
• 7. Molar mass = density × 22.414.

Remember

• - Molar volume: 22.414 dm³ at STP
• - STP: 0°C and 1 atm
• - 1 mole of any gas at STP: 22.414 dm³
• - Volume: moles × 22.414
• - Moles: volume / 22.414
• - Molar mass: density × 22.414

Common Mistakes

• 1. Thinking molar volume applies to all conditions: It applies at STP only.
• 2. Confusing molar volume with molar mass: Molar volume is 22.414 dm³; molar mass is in g/mol.
• 3. Forgetting that all gases have the same molar volume at STP: It is independent of the gas.
• 4. Mixing up the formulas: Volume = moles × 22.414; Moles = volume / 22.414.

Quick Revision

• Molar volume = 22.414 dm³ at STP.
• STP = 0°C and 1 atm.
• 1 mole of any gas at STP = 22.414 dm³.
• Volume = moles × 22.414.
• Moles = volume / 22.414.
• Density = molar mass / 22.414.
• Molar mass = density × 22.414.

60-Second Revision

• Molar volume: 22.414 dm³ at STP
• STP: 0°C and 1 atm
• 1 mole of any gas at STP: 22.414 dm³
• Volume: moles × 22.414
• Moles: volume / 22.414
• Molar mass: density × 22.414

QUALITY VALIDATION

• Topic: 4.1.1 Molar Volume (Vₘ)
• Chapter: 4 (Stoichiometry)

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