Linking Moles, Mass & Mr
Section: 3. Stoichiometry | Syllabus: Cambridge AS Level Physics 9702
The Mole-Mass Relationship The mass of one mole of a substance (in grams) is numerically equal to its relative formula mass (Mr). Examples: Mr of carbon (C) = 12, so 1 mole of C has a mass of 12 g Mr of water (H₂O) = 18, so 1 mole of H₂O has a mass of 18 g Mr of sodium chloride (NaCl) = 58.5, so 1 mole of NaCl has a mass of 58.5 g This simple relationship is the key to all mole calculations involving mass!
The Mole Formula Triangle The three key equations: Mass (g) = Moles (mol) × Mr Moles (mol) = Mass (g) ÷ Mr Mr = Mass (g) ÷ Moles (mol) You can remember this with the triangle: Mass ------- Moles × Mr Cover the quantity you want to find, and the triangle shows the formula: Cover Mass → Mass = Moles × Mr Cover Moles → Moles = Mass ÷ Mr Cover Mr → Mr = Mass ÷ Moles Calculating Mass from Moles Mass = Moles × Mr Example 1: Calculate the mass of 2 moles of carbon dioxide (CO₂).
Step 1: Find Mr of CO₂ C = 12, O = 16 Mr of CO₂ = 12 + (2 × 16) = 12 + 32 = 44 Step 2: Use the formula Mass = moles × Mr Mass = 2 × 44 = 88 g Example 2: Calculate the mass of 0.5 moles of water (H₂O).
Step 1: Find Mr of H₂O H = 1, O = 16 Mr of H₂O = (2 × 1) + 16 = 2 + 16 = 18 Step 2: Use the formula Mass = moles × Mr Mass = 0.5 × 18 = 9 g Calculating Moles from Mass Moles = Mass ÷ Mr This is the most commonly used formula in mole calculations!
Example 3: Calculate the number of moles in 88 g of carbon dioxide (CO₂). Step 1: Find Mr of CO₂ Mr of CO₂ = 12 + (2 × 16) = 44 Step 2: Use the formula Moles = mass ÷ Mr Moles = 88 ÷ 44 = 2 mol Example 4: Calculate the number of moles in 54 g of water (H₂O).
Step 1: Find Mr of H₂O Mr of H₂O = (2 × 1) + 16 = 18 Step 2: Use the formula Moles = mass ÷ Mr Moles = 54 ÷ 18 = 3 mol Step-by-Step Method Follow these steps for any mole-mass calculation: Step 1: Write down what you know (mass, moles, or Mr) Step 2: Calculate Mr if not given (add up all Ar values) Step 3: Identify which formula to use: Finding mass?
→ Mass = Moles × Mr Finding moles? → Moles = Mass ÷ Mr Finding Mr? → Mr = Mass ÷ Moles Step 4: Substitute values into the formula Step 5: Calculate and include units More Complex Examples Example 5: Calculate the mass of 0.25 moles of calcium carbonate (CaCO₃).
Step 1: Find Mr of CaCO₃ Ca = 40, C = 12, O = 16 Mr of CaCO₃ = 40 + 12 + (3 × 16) = 40 + 12 + 48 = 100 Step 2: Use the formula Mass = moles × Mr Mass = 0.25 × 100 = 25 g Example 6: Calculate the number of moles in 49 g of sulfuric acid (H₂SO₄).
Step 1: Find Mr of H₂SO₄ H = 1, S = 32, O = 16 Mr of H₂SO₄ = (2 × 1) + 32 + (4 × 16) = 2 + 32 + 64 = 98 Step 2: Use the formula Moles = mass ÷ Mr Moles = 49 ÷ 98 = 0.5 mol Working with Large Numbers Example 7: Calculate the number of moles in 2400 g of carbon (C).
Step 1: Ar of C = 12 (so Mr = 12) Step 2: Use the formula Moles = mass ÷ Mr Moles = 2400 ÷ 12 = 200 mol Step 3: This seems like a lot! But carbon atoms are very small, so 200 moles is reasonable for a large sample.
Working with Small Numbers Example 8: Calculate the mass of 0.01 moles of sodium chloride (NaCl). Step 1: Find Mr of NaCl Na = 23, Cl = 35.5 Mr of NaCl = 23 + 35.5 = 58.5 Step 2: Use the formula Mass = moles × Mr Mass = 0.01 × 58.5 = 0.585 g Units Summary Quantity Symbol Unit Mass m grams (g) Moles n moles (mol) Relative formula mass Mr no units Important: Mr has no units!
It's a relative value comparing to carbon-12. Practice Strategy For mass calculations: Always calculate Mr first Check if you're finding mass or moles Use the correct formula Show your working clearly Common patterns: If mass is larger than Mr → more than 1 mole If mass equals Mr → exactly 1 mole If mass is smaller than Mr → less than 1 mole Linking to Avogadro's Constant You can combine the mole-mass relationship with Avogadro's constant: Number of particles = (Mass ÷ Mr) × Avogadro's constant N = (m ÷ Mr) × Nₐ Example 9: How many molecules are in 88 g of CO₂?
Step 1: Find moles Mr of CO₂ = 44 Moles = 88 ÷ 44 = 2 mol Step 2: Find molecules Molecules = 2 × 6.02 × 10²³ = 1.204 × 10²⁴ molecules Common Mistakes to Avoid Using the wrong formula: Remember moles = mass ÷ Mr (NOT mass × Mr) Forgetting to calculate Mr: Always calculate Mr before using it in the formula Wrong Mr calculation: Don't forget to multiply by subscripts (e.g., in CO₂, there are 2 oxygen atoms) Mixing up units: Make sure mass is in grams, not kg or mg Calculator errors: Check your division and multiplication carefully Not showing working: Always show Mr calculation and formula used Key Points Summary The mass of 1 mole (in grams) equals the Mr value Moles = Mass ÷ Mr (most important formula!) Mass = Moles × Mr Mr = Mass ÷ Moles Always calculate Mr before using formulas Mass must be in grams (g) Mr has no units Show all working in exam questions Use the triangle to remember which formula to use
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