Ar & Mr
Section: 3. Stoichiometry | Syllabus: Cambridge AS Level Physics 9702
What is Relative Atomic Mass (Aᵣ)? Relative Atomic Mass (Aᵣ) The average mass of an atom of an element compared to 1/12th the mass of a carbon-12 atom. Relative atomic mass tells us how heavy an atom is compared to the standard (carbon-12).
Symbol: Aᵣ (A with subscript r) It's a ratio , so it has no units Found in the periodic table for each element Takes into account different isotopes and their abundances Important Aᵣ has no units because it's a comparison (ratio).
Carbon-12 is defined as exactly 12. Common Relative Atomic Masses You should know these common Aᵣ values (usually given in exams): Element Symbol Aᵣ Hydrogen H 1 Carbon C 12 Nitrogen N 14 Oxygen O 16 Sodium Na 23 Magnesium Mg 24 Aluminium Al 27 Sulfur S 32 Chlorine Cl 35.5 Calcium Ca 40 Iron Fe 56 Copper Cu 64 Note Most Aᵣ values are whole numbers or close to them.
Chlorine (35.5) is an exception because it has two abundant isotopes (Cl-35 and Cl-37) in roughly 3:1 ratio. What is Relative Formula Mass (Mᵣ)? Relative Formula Mass (Mᵣ) The sum of the relative atomic masses of all atoms in a formula.
For compounds with simple molecules, it's also called relative molecular mass. Mᵣ tells us the total mass of one formula unit or molecule. Symbol: Mᵣ (M with subscript r) Also has no units (it's a ratio) Calculate by adding up all the Aᵣ values Must account for subscripts in formulae Formula: Mᵣ = Sum of (Aᵣ × number of atoms) Calculating Mᵣ - Simple Examples Example 1: Water (H₂O) Formula: H₂O Contains: 2 hydrogen, 1 oxygen Mᵣ = (2 × Aᵣ of H) + (1 × Aᵣ of O) Mᵣ = (2 × 1) + (1 × 16) Mᵣ = 2 + 16 Mᵣ = 18 Example 2: Carbon Dioxide (CO₂) Formula: CO₂ Contains: 1 carbon, 2 oxygen Mᵣ = (1 × Aᵣ of C) + (2 × Aᵣ of O) Mᵣ = (1 × 12) + (2 × 16) Mᵣ = 12 + 32 Mᵣ = 44 Example 3: Sodium Chloride (NaCl) Formula: NaCl Contains: 1 sodium, 1 chlorine Mᵣ = (1 × Aᵣ of Na) + (1 × Aᵣ of Cl) Mᵣ = (1 × 23) + (1 × 35.5) Mᵣ = 23 + 35.5 Mᵣ = 58.5 Calculating Mᵣ - Complex Examples Example 4: Sulfuric Acid (H₂SO₄) Formula: H₂SO₄ Contains: 2 hydrogen, 1 sulfur, 4 oxygen Mᵣ = (2 × 1) + (1 × 32) + (4 × 16) Mᵣ = 2 + 32 + 64 Mᵣ = 98 Example 5: Calcium Hydroxide [Ca(OH)₂] Formula: Ca(OH)₂ Contains: 1 calcium, 2 oxygen (in brackets), 2 hydrogen (in brackets) Remember: The subscript 2 multiplies everything in the bracket!
Mᵣ = (1 × 40) + (2 × 16) + (2 × 1) Mᵣ = 40 + 32 + 2 Mᵣ = 74 Example 6: Aluminium Sulfate [Al₂(SO₄)₃] Formula: Al₂(SO₄)₃ Contains: 2 aluminium, 3 sulfur (in bracket ×3), 12 oxygen (4 in bracket ×3) Mᵣ = (2 × 27) + (3 × 32) + (12 × 16) Mᵣ = 54 + 96 + 192 Mᵣ = 342 Tip for Brackets For Ca(OH)₂: The 2 outside multiplies BOTH O and H.
For Al₂(SO₄)₃: The 3 outside multiplies both S and O₄, giving 3 S and 12 O total. Step-by-Step Method for Calculating Mᵣ Write down the formula clearly Count how many of each atom (watch for brackets!) Look up Aᵣ values (usually given in exam) Multiply Aᵣ by number of atoms for each element Add them all up Write answer (no units needed) Common Mistakes to Avoid ❌ Forgetting to multiply by subscripts ❌ Ignoring brackets - the outside number multiplies everything inside ❌ Adding units (Mᵣ has no units!) ❌ Using incorrect Aᵣ values - always check the data given Practice Calculations Compound Formula Calculation Mᵣ Ammonia NH₃ 14 + (3 × 1) 17 Methane CH₄ 12 + (4 × 1) 16 Calcium carbonate CaCO₃ 40 + 12 + (3 × 16) 100 Magnesium chloride MgCl₂ 24 + (2 × 35.5) 95 Copper sulfate CuSO₄ 64 + 32 + (4 × 16) 160 Sodium hydroxide NaOH 23 + 16 + 1 40 Nitric acid HNO₃ 1 + 14 + (3 × 16) 63 Glucose C₆H₁₂O₆ (6 × 12) + (12 × 1) + (6 × 16) 180 Why Are Aᵣ and Mᵣ Important?
Uses of Relative Masses Calculating moles: Number of moles = mass ÷ Mᵣ Reacting masses: Working out how much of each reactant needed Percentage composition: Finding % of each element in a compound Empirical formulae: Converting mass data to formulae Concentration calculations: Working out molarity of solutions Link to Moles Mᵣ is essential for mole calculations.
One mole of any substance has a mass equal to its Mᵣ in grams. For example, 1 mole of H₂O has mass 18 g. Isotopes and Relative Atomic Mass Isotopes Atoms of the same element with different numbers of neutrons (same proton number, different mass number).
Aᵣ is an average that takes into account different isotopes and how abundant they are. Example: Chlorine Isotopes Chlorine has two isotopes: • Cl-35: 75% abundant • Cl-37: 25% abundant Aᵣ of Cl = (35 × 0.75) + (37 × 0.25) Aᵣ of Cl = 26.25 + 9.25 Aᵣ of Cl = 35.5 This is why chlorine's Aᵣ is 35.5, not a whole number!
Calculating Aᵣ from Isotope Data Formula: Aᵣ = Σ(mass number × % abundance ÷ 100) Example: Copper Isotopes Copper has two isotopes: • Cu-63: 70% abundant • Cu-65: 30% abundant Aᵣ = (63 × 70/100) + (65 × 30/100) Aᵣ = 44.1 + 19.5 Aᵣ = 63.6 Percentage Composition Percentage Composition The percentage by mass of each element in a compound.
Formula for Percentage Composition % of element = (Aᵣ × number of atoms / Mᵣ) × 100 Example: Percentage of Carbon in CO₂ Step 1: Calculate Mᵣ of C…
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