This lesson is all about how chemists count atoms and molecules, which are too small to count individually. Mastering these calculations is crucial for chemistry.

1. Short Notes: Core Concepts

A. Why do we need special units?

• Atoms are incredibly small. Expressing their mass in grams results in tiny, inconvenient numbers (e.g., one carbon atom is about 1.99 x 10⁻²³ g).

• To simplify this, scientists created a relative scale.

B. Relative Atomic Mass (Ar)

• Definition: The average mass of an atom of an element compared to 1/12th the mass of a carbon-12 atom.

• Key Idea: It's a ratio, so it has NO UNITS.

• You will be given these values in the exam (e.g., C=12, H=1, O=16, Na=23).

C. Relative Molecular Mass (Mr)

• Definition: The sum of the relative atomic masses of all the atoms in a molecule.

• How to Calculate: Simply add up the Ar values for every atom in the chemical formula.

• Key Idea: Like Ar, it is a ratio and has NO UNITS.

• Example: Water (H₂O)

  • There are 2 Hydrogen atoms and 1 Oxygen atom.

  • Mr(H₂O) = (2 × Ar(H)) + (1 × Ar(O)) = (2 × 1) + 16 = 18.

D. The Mole (mol)

• What is it? The mole is the SI unit for the "amount of substance". It's a specific number used for counting particles (atoms, molecules, ions).

• The Number: One mole of any substance contains 6.022 x 10²³ particles.

• Avogadro's Constant (L): This special number, 6.022 x 10²³, is called Avogadro's Constant.

E. Molar Mass (M)

• Definition: The mass of one mole of a substance.

• How to find it: It is numerically equal to the Ar or Mr, but it HAS UNITS: grams per mole (g/mol).

  • If Ar of Carbon (C) is 12, its Molar Mass (M) is 12 g/mol.

  • If Mr of Water (H₂O) is 18, its Molar Mass (M) is 18 g/mol.

F. The Main Formula This connects mass, moles, and molar mass. It is the most important formula in this topic.

• Number of moles (n) = Mass (m) / Molar Mass (M)

2. Tips & Tricks for the Exam

• Units are a big clue!

  • If the number has no units, it's Ar or Mr.

  • If the unit is grams (g), it's a mass (m).

  • If the unit is g/mol, it's the Molar Mass (M).

  • If the unit is mol, it's the number of moles (n).

• The Mole Triangle: Cover the quantity you want to find to see the formula.

  • mass (m) = moles (n) × Molar Mass (M)

  • moles (n) = mass (m) / Molar Mass (M)

  • Molar Mass (M) = mass (m) / moles (n)

3. Important Points & Common Exam Questions

• Calculating Mr: You will definitely be asked to calculate the relative molecular mass of a compound.

  • Example Question: Calculate the Mr of sulfuric acid (H₂SO₄). (Ar: H=1, S=32, O=16)

  • Answer: Mr(H₂SO₄) = (2 × 1) + 32 + (4 × 16) = 2 + 32 + 64 = 98.

• Calculating Moles from Mass: This is the most common calculation.

  • Example Question: How many moles are in 22 g of carbon dioxide (CO₂)? (Mr of CO₂ = 44)

  • Answer: Molar Mass (M) of CO₂ = 44 g/mol. n = m / M -> n = 22 g / 44 g/mol = 0.5 mol.

• Calculating Mass from Moles:

  • Example Question: What is the mass of 2 moles of water (H₂O)? (Mr of H₂O = 18)

  • Answer: Molar Mass (M) of H₂O = 18 g/mol. m = n × M -> m = 2 mol × 18 g/mol = 36 g.

• Calculations with Avogadro's Constant:

  • Example Question: How many molecules are there in 0.5 moles of CO₂?

  • Answer: Number of molecules = moles × Avogadro's Constant = 0.5 × (6.022 × 10²³) = 3.011 × 10²³ molecules.