The Mole (Copy)

What is “Amount of Substance”?

• In physics and chemistry, the amount of substance is a fundamental quantity used to count particles (atoms, molecules, ions).
• It is one of the seven SI base quantities, just like time (s), length (m), and mass (kg).
• The SI unit for amount of substance is the mole (mol).
• It allows scientists to relate microscopic particle counts to measurable quantities in experiments.

Definition of One Mole

• One mole of a substance is defined as:

  The amount of that substance which contains the same number of particles as there are in exactly 12 grams of carbon-12.

• This number of particles is called the Avogadro constant (Nₐ).
• Nₐ = 6.022 × 10²³ particles/mol
  • These “particles” can be atoms, molecules, ions, electrons, or any other specified entities.

Written and Compiled By Sir Hunain Zia, World Record Holder With 154 Total A Grades, 7 Distinctions and 11 World Records For Educate A Change A2 Level Physics Full Scale Course

Avogadro Constant (Nₐ)

• Nₐ = 6.022 × 10²³ mol⁻¹
• This is a fixed constant, just like c (speed of light) or h (Planck’s constant).
• It bridges the gap between the microscopic world (atoms) and the macroscopic world (grams, litres).

Relationship Between Moles and Number of Particles

• The number of particles (N) in a sample is given by:

  N = n × Nₐ

  where:
  N = total number of particles
  n = amount of substance in moles (mol)
  Nₐ = 6.022 × 10²³ mol⁻¹

Using Moles in Practice

1. Mass and Molar Mass Relationship:

• The molar mass (M) is the mass of 1 mole of a substance (in g/mol or kg/mol).
• Relationship:

  n = m / M

  where:
  n = number of moles (mol)
  m = mass of the sample (g or kg)
  M = molar mass (g/mol or kg/mol)

2. Volume (for gases at room conditions):

• At room temperature and pressure (RTP), 1 mole of an ideal gas occupies approximately 24 dm³ (or 0.024 m³).

Written and Compiled By Sir Hunain Zia, World Record Holder With 154 Total A Grades, 7 Distinctions and 11 World Records For Educate A Change A2 Level Physics Full Scale Course

Example Calculations

Example 1:
How many molecules are there in 2 mol of oxygen gas (O₂)?

N = n × Nₐ = 2 × 6.022 × 10²³ = 1.2044 × 10²⁴ molecules

Example 2:
Find the number of moles in 36 g of water (H₂O). (M = 18 g/mol)

n = m / M = 36 / 18 = 2 mol

Example 3:
If a gas sample contains 1.5 × 10²⁴ particles, how many moles of gas is this?

n = N / Nₐ = (1.5 × 10²⁴) / (6.022 × 10²³) ≈ 2.49 mol

Key Concepts Recap

Why the Mole is Important in Physics

• Allows direct calculation of:
  • Gas properties using the ideal gas equation (PV = nRT)
  • Internal energy and kinetic energy per mole
  • Thermal energy transfer on a molecular level
• Essential for:
  • Thermodynamics
  • Kinetic theory
  • Atomic physics
  • Molecular energy models

Written and Compiled By Sir Hunain Zia, World Record Holder With 154 Total A Grades, 7 Distinctions and 11 World Records For Educate A Change A2 Level Physics Full Scale Course