The Mole
Section: 3. Stoichiometry | Syllabus: Cambridge AS Level Physics 9702
What is a Mole? The mole (mol) is the unit for amount of substance in chemistry. One mole contains exactly 6.02 × 10²³ particles (atoms, molecules, ions, or electrons). Think of a mole like "a dozen" - just as a dozen always means 12 items, a mole always means 6.02 × 10²³ particles, regardless of what those particles are.
Examples: 1 mole of carbon atoms = 6.02 × 10²³ carbon atoms 1 mole of water molecules = 6.02 × 10²³ H₂O molecules 1 mole of sodium ions = 6.02 × 10²³ Na⁺ ions Avogadro's Constant Avogadro's constant (Nₐ) = 6.02 × 10²³ mol⁻¹ This is the number of particles in one mole of any substance.
This constant is named after the Italian scientist Amedeo Avogadro. It's one of the fundamental constants in chemistry. Note: You may also see Avogadro's constant written as 6.022 × 10²³ mol⁻¹ (more precise) or even just 6 × 10²³ mol⁻¹ (in simpler calculations).
Why Do We Need Moles? Atoms and molecules are incredibly small. Working with individual atoms would be impractical: A single carbon atom has a mass of about 2 × 10⁻²³ g (0.00000000000000000000002 g) Even a small sample contains billions of billions of atoms We need a convenient unit to count particles in realistic amounts The mole allows us to: Count atoms by weighing them Relate microscopic particles to macroscopic masses we can measure Calculate how much of each substance is needed in reactions Calculating Number of Particles Number of particles = Moles × Avogadro's constant N = n × Nₐ Where: N = number of particles n = number of moles (mol) Nₐ = 6.02 × 10²³ mol⁻¹ Example 1: How many atoms are in 2 moles of carbon?
N = n × Nₐ = 2 × 6.02 × 10²³ = 1.204 × 10²⁴ atoms Example 2: How many molecules are in 0.5 moles of water? N = n × Nₐ = 0.5 × 6.02 × 10²³ = 3.01 × 10²³ molecules Calculating Moles from Particles Rearranging the formula: Moles = Number of particles ÷ Avogadro's constant n = N ÷ Nₐ Example 3: How many moles is 1.204 × 10²⁴ atoms of oxygen?
n = N ÷ Nₐ = (1.204 × 10²⁴) ÷ (6.02 × 10²³) = 2 mol Example 4: How many moles is 3.01 × 10²² molecules of CO₂? n = N ÷ Nₐ = (3.01 × 10²²) ÷ (6.02 × 10²³) = 0.05 mol Counting Atoms in Molecules When dealing with molecules, remember to account for all atoms in the formula: Example 5: How many atoms of hydrogen are in 1 mole of H₂O?
1 mole of H₂O contains 6.02 × 10²³ molecules Each molecule has 2 hydrogen atoms Total H atoms = 2 × 6.02 × 10²³ = 1.204 × 10²⁴ atoms Example 6: How many atoms of oxygen are in 0.1 mole of CO₂? 0.1 mole of CO₂ contains 0.1 × 6.02 × 10²³ = 6.02 × 10²² molecules Each molecule has 2 oxygen atoms Total O atoms = 2 × 6.02 × 10²² = 1.204 × 10²³ atoms Working with Standard Form When working with Avogadro's constant, you'll often need to use standard form (scientific notation): Key skills: Multiplying in standard form: multiply the numbers, add the powers Example: (2 × 10³) × (3 × 10⁴) = 6 × 10⁷ Dividing in standard form: divide the numbers, subtract the powers Example: (6 × 10⁸) ÷ (2 × 10³) = 3 × 10⁵ Moles of Different Particles The mole applies to any type of particle: Substance 1 mole contains Particles Carbon (C) 6.02 × 10²³ atoms Oxygen gas (O₂) 6.02 × 10²³ molecules Sodium chloride (NaCl) 6.02 × 10²³ formula units Sodium ions (Na⁺) 6.02 × 10²³ ions Electrons (e⁻) 6.02 × 10²³ electrons Common Exam Questions Type 1: Calculate number of particles from moles Strategy: Multiply moles by 6.02 × 10²³ Type 2: Calculate moles from number of particles Strategy: Divide particles by 6.02 × 10²³ Type 3: Count specific atoms in molecules Strategy: Find total molecules, then multiply by number of that atom per molecule Common Mistakes to Avoid Forgetting the units: Always include mol⁻¹ for Avogadro's constant Mixing up the formula: Remember n × Nₐ gives particles, not particles ÷ Nₐ Calculator errors with standard form: Make sure your calculator is in scientific mode Not accounting for multiple atoms: Remember H₂O has 2 H atoms and 1 O atom per molecule Rounding too early: Keep full precision until the final answer Key Points Summary 1 mole = 6.02 × 10²³ particles (Avogadro's constant) The mole is the unit for amount of substance Number of particles = moles × Avogadro's constant (N = n × Nₐ) Moles = number of particles ÷ Avogadro's constant (n = N ÷ Nₐ) Always specify what type of particle (atoms, molecules, ions, etc.) Account for all atoms when counting atoms in molecules Use standard form correctly in calculations
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