Year 11 Chemistry Module 2 ⏱ ~35 min Lesson 2 of 20

Molar Mass

Every tablet your pharmacist counts, every dose in an IV bag, every gram of fertiliser spread across a paddock — all calculated using molar mass. It's the single most-used formula in practical chemistry, and it lives on the periodic table you already have.

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📐

Formula Reference — This Lesson

n = m ÷ MM

n = amount of substance (mol) m = mass (g) MM = molar mass (g mol⁻¹)

Find n: n = m ÷ MM | Find m: m = n × MM | Find MM: MM = m ÷ n

📖 Know

Key Facts

What molar mass is and its units (g mol⁻¹)
Where to read molar mass from the periodic table
The formula n = m ÷ MM

💡 Understand

Concepts

Why molar mass equals relative atomic/molecular mass in g mol⁻¹
How to calculate MM for compounds from their formula
When to add atomic masses vs when to multiply

✅ Can Do

Skills

Calculate MM for elements and compounds
Find n, m or MM using n = m ÷ MM
Set up and check units in every calculation

📚 Core Content

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What Is Molar Mass?

In Lesson 1, you learned that one mole contains 6.022 × 10²³ particles. But how much does a mole actually weigh? That's where molar mass comes in.

The molar mass (MM) of a substance is the mass of one mole of that substance, measured in grams per mole (g mol⁻¹). The elegant fact is that molar mass numerically equals the relative atomic mass (or relative molecular mass) you read straight off the periodic table — just with units of g mol⁻¹ attached.

1 H Hydrogen 1.008

6 C Carbon 12.011

8 O Oxygen 15.999

11 Na Sodium 22.990

17 Cl Chlorine 35.450

Reading the periodic table: The larger number in each element's box is the relative atomic mass (RAM). This is the molar mass value you use. For example, oxygen has a RAM of 15.999, so the molar mass of O is 15.999 g mol⁻¹, and of O₂ it is 2 × 15.999 = 31.998 g mol⁻¹.

Calculating Molar Mass for Compounds

For a compound, add up the molar masses of every atom in the formula — multiplied by how many of each appear.

Example — Water (H₂O): 2 × H + 1 × O = 2(1.008) + 1(15.999) = 2.016 + 15.999 = 18.015 g mol⁻¹

Example — Sodium chloride (NaCl): 1 × Na + 1 × Cl = 22.990 + 35.450 = 58.440 g mol⁻¹

Example — Glucose (C₆H₁₂O₆): 6(12.011) + 12(1.008) + 6(15.999) = 72.066 + 12.096 + 95.994 = 180.156 g mol⁻¹

Brackets in formulas: For Ca(OH)₂, expand the brackets first. The subscript outside applies to everything inside: Ca(OH)₂ = Ca + 2O + 2H = 40.078 + 2(15.999) + 2(1.008) = 74.092 g mol⁻¹

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The Formula: n = m ÷ MM

Once you know the molar mass, you can convert between mass (grams, something you can weigh) and moles (amount of substance, something you can use in calculations). This formula is the workhorse of quantitative chemistry.

Cover what you want → the remaining two show the operation

The units do the work for you: if you divide grams by g mol⁻¹, you get mol. If you multiply mol by g mol⁻¹, you get grams. Always write your units and watch them cancel.

Units check: n = m ÷ MM gives: g ÷ g mol⁻¹ = g × mol g⁻¹ = mol ✓
m = n × MM gives: mol × g mol⁻¹ = g ✓

🧮 Worked Examples

Worked Example 1 — Finding moles from mass

Stepwise

Calculate the number of moles in 54 g of water (H₂O).

1

Calculate molar mass

H₂O: 2 × H + 1 × O

MM = 2(1.008) + 15.999 = 18.015 g mol⁻¹
2

Identify known values

m = 54 g | MM = 18.015 g mol⁻¹ | n = ?
3

Write the formula

n = m ÷ MM
4

Substitute values

n = 54 ÷ 18.015
5

Calculate and check units

n = 2.998 mol ≈ 3.0 mol

Units: g ÷ g mol⁻¹ = mol ✓

✓ Answer n = 3.0 mol of H₂O

Worked Example 2 — Finding mass from moles

Stepwise

What mass of sodium chloride (NaCl) contains 0.50 mol?

1

Calculate molar mass

NaCl: 1 × Na + 1 × Cl

MM = 22.990 + 35.450 = 58.440 g mol⁻¹
2

Identify known values

n = 0.50 mol | MM = 58.440 g mol⁻¹ | m = ?
3

Rearrange the formula

m = n × MM
4

Substitute values

m = 0.50 × 58.440
5

Calculate and check units

m = 29.22 g

Units: mol × g mol⁻¹ = g ✓

✓ Answer m = 29.22 g of NaCl

⚠️

Common Mistakes — Don't Lose Easy Marks

Using atomic mass instead of molar mass for a compound

For O₂, the molar mass is 2 × 16.00 = 32.00 g mol⁻¹, not 16.00 g mol⁻¹. The subscript in the formula tells you how many atoms are in one molecule — you must multiply by that number when calculating MM.

✓ Fix: Always write out the MM calculation step explicitly — e.g. "MM(O₂) = 2 × 15.999 = 31.998 g mol⁻¹" — before substituting into n = m ÷ MM.

Forgetting to expand brackets in compound formulas

For Ca(OH)₂, a student might count only 1 oxygen and 1 hydrogen — missing the ×2 from the subscript. The correct expansion is: Ca + 2(O + H) = Ca + 2O + 2H, giving MM = 40.078 + 2(15.999) + 2(1.008) = 74.092 g mol⁻¹, not the incorrect 57.085 g mol⁻¹.

✓ Fix: When you see brackets with a subscript, always distribute the subscript across every atom inside before summing.

Dividing when you should multiply (and vice versa)

Getting n and m confused in the formula causes the calculation to go backwards. If you have grams and want moles, divide by MM. If you have moles and want grams, multiply by MM.

✓ Fix: Use the triangle. Cover up what you want, and the remaining two values show whether to multiply or divide.

📓 Copy Into Your Books

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📖 Key Definitions

Molar mass (MM) — mass of one mole of a substance, in g mol⁻¹
Relative atomic mass (RAM) — from the periodic table, used to calculate MM
m — mass in grams
n — amount in moles

📐 Formula & Rearrangements

n = m ÷ MM (find moles)
m = n × MM (find mass)
MM = m ÷ n (find molar mass)

🔢 Calculating MM

Read RAM from the periodic table for each element
Multiply RAM by the subscript for that element
Add results for all elements in the formula
Expand brackets before summing

✅ Units Check

n = m ÷ MM → g ÷ g mol⁻¹ = mol ✓
m = n × MM → mol × g mol⁻¹ = g ✓
MM always in g mol⁻¹
m always in grams (convert if given in kg)

🧪 Activities

📊 Activity 1 — Practice Drill

Applying n = m ÷ MM

Three problems, increasing difficulty. Attempt each before revealing the answer. Show all working — including the MM calculation.

1 Calculate the number of moles in 88 g of carbon dioxide (CO₂).

MM(CO₂) = 12.011 + 2(15.999) = 12.011 + 31.998 = 44.009 g mol⁻¹ n = m ÷ MM = 88 ÷ 44.009 = 2.0 mol
2 What mass of calcium carbonate (CaCO₃) is in 0.25 mol?

MM(CaCO₃) = 40.078 + 12.011 + 3(15.999) = 40.078 + 12.011 + 47.997 = 100.086 g mol⁻¹ m = n × MM = 0.25 × 100.086 = 25.02 g
3 A student dissolves 14.7 g of sulfuric acid (H₂SO₄) in water. Calculate the amount in moles. (S = 32.06 g mol⁻¹)

MM(H₂SO₄) = 2(1.008) + 32.06 + 4(15.999) = 2.016 + 32.06 + 63.996 = 98.072 g mol⁻¹ n = m ÷ MM = 14.7 ÷ 98.072 = 0.1499 mol ≈ 0.150 mol

Type your working below before revealing answers above:

Complete these problems in your workbook.

✏️ Complete in your workbook

🔍 Activity 2 — Error Spotting

Find the Mistake

The worked solution below contains two deliberate errors. Your job is to find them, explain why each is wrong, and write the correct working. This is a high-value exam skill.

⚠️ Student's Working — contains errors

Problem: Calculate the number of moles in 49.0 g of calcium hydroxide, Ca(OH)₂.

Step 1: MM(Ca(OH)₂) = 40.078 + 15.999 + 1.008 = 57.085 g mol⁻¹

Step 2: n = m ÷ MM

Step 3: n = 49.0 ÷ 57.085

Step 4: n = 0.858 mol

Your task:
A) Identify both errors. For each, explain: (i) what the student did wrong, and (ii) what they should have done instead.
B) Write the complete correct working and give the correct answer.

Type your response below:

Answer in your workbook.

✏️ Answer in your workbook

❓ Multiple Choice

🎯

Test Your Knowledge

1. What is the molar mass of magnesium sulfate, MgSO₄? (Mg = 24.305, S = 32.06, O = 15.999)

72.364 g mol⁻¹

104.369 g mol⁻¹

120.361 g mol⁻¹

136.360 g mol⁻¹

2. Which of the following correctly gives the formula for calculating mass from moles and molar mass?

m = n ÷ MM

m = n × MM

m = MM ÷ n

m = MM + n

3. How many moles are in 71.0 g of chlorine gas (Cl₂)? (Cl = 35.45 g mol⁻¹)

1.00 mol

2.00 mol

0.50 mol

4.00 mol

4. What is the molar mass of aluminium hydroxide, Al(OH)₃? (Al = 26.982, O = 15.999, H = 1.008)

43.989 g mol⁻¹

60.997 g mol⁻¹

71.994 g mol⁻¹

78.003 g mol⁻¹

5. A sample of iron (Fe) has a mass of 167.2 g. How many moles does it contain? (Fe = 55.845 g mol⁻¹)

1.50 mol

2.50 mol

2.99 mol

3.50 mol

✍️ Short Answer

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Extended Questions

6. Define molar mass and explain why its numerical value equals the relative atomic mass found on the periodic table. In your answer, refer to the definition of the mole. 3 MARKS

Type your answer below:

Answer in your workbook.

✏️ Answer in your workbook

7. A chemistry technician needs to prepare 2.40 mol of glucose (C₆H₁₂O₆) for a fermentation experiment. Calculate the mass of glucose required. Show all working, including the molar mass calculation. (C = 12.011, H = 1.008, O = 15.999) 4 MARKS

Type your answer below:

Answer in your workbook.

✏️ Answer in your workbook

8. A student weighed out 13.3 g of anhydrous sodium carbonate (Na₂CO₃) and claimed it contained "about one-eighth of a mole." Is the student's claim correct? Show all working to justify your answer. (Na = 22.990, C = 12.011, O = 15.999) 4 MARKS

Type your answer below:

Answer in your workbook.

✏️ Answer in your workbook

✅ Comprehensive Answers

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🔍 Activity 2 — Error Spotting Model Answer

Error 1 (Step 1): The student failed to expand the brackets in Ca(OH)₂. The subscript 2 applies to both O and H inside the brackets, so the correct formula contains 1 Ca, 2 O, and 2 H atoms — not 1 Ca, 1 O, and 1 H. The correct MM calculation is:

MM = 40.078 + 2(15.999) + 2(1.008) = 40.078 + 31.998 + 2.016 = 74.092 g mol⁻¹

Error 2 (Steps 3–4): The student used the wrong molar mass (57.085 instead of 74.092), which propagated through to give the wrong answer. With the correct MM:

n = 49.0 ÷ 74.092 = 0.661 mol

The student's answer of 0.858 mol is incorrect on both counts.

❓ Multiple Choice

1. C — MgSO₄: 24.305 + 32.06 + 4(15.999) = 24.305 + 32.06 + 63.996 = 120.361 g mol⁻¹

2. B — m = n × MM. Rearranging n = m ÷ MM gives m = n × MM.

3. A — MM(Cl₂) = 2 × 35.45 = 70.90 g mol⁻¹. n = 71.0 ÷ 70.90 = 1.00 mol

4. D — Al(OH)₃: 26.982 + 3(15.999) + 3(1.008) = 26.982 + 47.997 + 3.024 = 78.003 g mol⁻¹

5. C — n = 167.2 ÷ 55.845 = 2.994 mol ≈ 2.99 mol

📝 Short Answer Model Answers

Q6 (3 marks): Molar mass is the mass in grams of one mole of a substance, expressed in g mol⁻¹ [1]. One mole is defined as 6.022 × 10²³ particles, and was originally defined so that one mole of carbon-12 has a mass of exactly 12 g — equal to its relative atomic mass [1]. Since all other atomic masses are defined relative to carbon-12, the molar mass of any element in g mol⁻¹ is numerically equal to its relative atomic mass from the periodic table [1].

Q7 (4 marks):

MM(C₆H₁₂O₆) = 6(12.011) + 12(1.008) + 6(15.999) = 72.066 + 12.096 + 95.994 = 180.156 g mol⁻¹ m = n × MM = 2.40 × 180.156 = 432.37 g ≈ 432 g

Award 1 mark for correct MM calculation, 1 mark for correct formula, 1 mark for correct substitution, 1 mark for correct final answer with units.

Q8 (4 marks):

MM(Na₂CO₃) = 2(22.990) + 12.011 + 3(15.999) = 45.980 + 12.011 + 47.997 = 105.988 g mol⁻¹ n = m ÷ MM = 13.3 ÷ 105.988 = 0.1255 mol

One-eighth of a mole = 0.125 mol. The student's calculated value (0.1255 mol) rounds to 0.125 mol, so the claim is essentially correct [1 mark for accepting with justification, or 1 mark for identifying that 0.1255 ≈ 0.125 mol]. Full marks require the working shown above.

Mark lesson as complete

Tick when you've finished all activities and checked your answers.

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