4.1 Mole

This topic explains the mole concept — what it is, how it is used, and its relationship with Avogadro's number, molar mass, and molar volume.

Definition

Mole: The amount of substance that contains 6.023 × 10²³ representative particles.

Avogadro's Number: The experimentally determined number 6.023 × 10²³, which represents the number of particles in one mole of a substance.

Main Idea

Chemists use the mole as the SI unit to weigh and count atoms, molecules, and ions. Just as a dozen represents 12 identical things, a mole represents 6.023 × 10²³ particles of a substance. The atomic mass, formula mass, and molecular weight of a substance in grams are equal to one mole of the substance.

Core Concept

• 1 mole = 6.023 × 10²³ representative particles (atoms, molecules, or ions).
• 1 mole of any substance = its atomic mass, formula mass, or molecular mass in grams.
• 1 mole of any gas at STP occupies 22.414 dm³ (molar volume).

Detailed Explanation

What is a Mole?

• A mole is the amount of substance that contains 6.023 × 10²³ representative particles.
• This experimentally determined number is called Avogadro's number.
• Just as a dozen represents 12 identical things, a mole represents 6.023 × 10²³ particles of a substance.

• A mole of carbon is 6.023 × 10²³ carbon atoms.
• A mole of sodium is 6.023 × 10²³ Na atoms.
• One mole of water is 6.023 × 10²³ H₂O molecules.

Representative Particles

• Atoms
• Molecules
• Ions

This relationship allows us to convert moles into representative particles and vice versa.

Mole and Mass

The atomic mass, formula mass, and molecular weight of a substance in grams are equal to one mole of the substance.

• One mole of O atoms = **16 g**
• One mole of O₂ molecules = **32 g**
• One mole of H₂O molecules = **18 g**
• One mole of Na ions = **23 g**
• One mole of NaCl formula units = 58.5 g

Molar Volume (Vm)

• One mole of any gas at STP (standard temperature and pressure) 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.

• 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

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

Molar Mass and 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.
• 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.

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.

Intermediate Level

Key Relationships

Examples

• 1 mole O = 16 g
• 1 mole O₂ = 32 g
• 1 mole H₂O = 18 g
• 1 mole Na⁺ = 23 g
• 1 mole NaCl = 58.5 g

Molar Volume

• 22.414 dm³ of any gas at STP = 1 mole = 6.02 × 10²³ molecules.
• This is called molar volume.

Density and Molar Mass

Density = MassVolume

For gases at STP: Molar mass = Density × 22.414

Important Points

• 1. 1 mole = 6.023 × 10²³ particles.
• 2. Avogadro's number = 6.023 × 10²³.
• 3. 1 mole of atoms = atomic mass in grams.
• 4. 1 mole of molecules = molecular mass in grams.
• 5. 1 mole of any gas at STP = 22.414 dm³.
• 6. Molar volume = 22.414 dm³.
• 7. Density = mass/volume.
• 8. Molar mass = density × 22.414.

Remember

• - 1 mole: 6.023 × 10²³ particles
• - 1 mole of atoms: Atomic mass in grams
• - 1 mole of molecules: Molecular mass in grams
• - 1 mole of gas at STP: 22.414 dm³
• - Molar volume: 22.414 dm³
• - Molar mass: Density × 22.414

Common Mistakes

• 1. Confusing mole with mass: 1 mole of different substances has different masses.
• 2. Forgetting Avogadro's number: 6.023 × 10²³.
• 3. Thinking molar volume applies to all conditions: It applies at STP only.
• 4. Mixing up atomic mass and molecular mass: Atomic mass = 1 atom; molecular mass = 1 molecule.

Quick Revision

• 1 mole = 6.023 × 10²³ particles.
• Avogadro's number = 6.023 × 10²³.
• 1 mole of atoms = atomic mass in grams.
• 1 mole of molecules = molecular mass in grams.
• 1 mole of any gas at STP = 22.414 dm³.
• Molar volume = 22.414 dm³.
• Density = mass/volume.
• Molar mass = density × 22.414.

60-Second Revision

• 1 mole: 6.023 × 10²³ particles
• 1 mole of atoms: Atomic mass in grams
• 1 mole of molecules: Molecular mass in grams
• 1 mole of gas at STP: 22.414 dm³
• Molar volume: 22.414 dm³
• Molar mass: Density × 22.414

QUALITY VALIDATION

• Topic: 4.1 Mole
• Chapter: 4 (Stoichiometry)

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