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.
Practise this lesson
Four printable worksheets that build from the foundations up to exam-style questions — start at whatever level suits you.
You know that atoms have different masses — a carbon atom is heavier than a hydrogen atom. How do you think chemists figure out how many grams of a substance they need to weigh out in order to have exactly one mole of it?
$$n = \dfrac{m}{MM}$$
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
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
Skills
- Calculate MM for elements and compounds
- Find n, m or MM using n = m ÷ MM
- Set up and check units in every calculation
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.
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. The diagram below shows the method for sulfuric acid, H₂SO₄.
Molar mass (MM) is the mass of one mole of a substance in g mol⁻¹, numerically equal to the relative atomic or molecular mass from the periodic table. For compounds, multiply each element's RAM by its subscript (expanding brackets first) and sum all contributions.
Pause — copy the highlighted definition into your book before moving on.
Did you get this? True or false: the molar mass of O₂ is 2 × 15.999 = 31.998 g mol⁻¹, not 15.999 g mol⁻¹.
Quick check: Which is the correct molar mass calculation for Ca(OH)₂?
We just saw how to calculate molar mass for any element or compound using the periodic table. That raises a question: once you know MM, how do you convert a weighed mass into moles (or back)? This card answers it → with 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.
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.
m = n × MM gives: mol × g mol⁻¹ = g ✓
n = m ÷ MM converts mass (g) to moles; rearranged, m = n × MM and MM = m ÷ n. Units confirm the formula: g ÷ (g mol⁻¹) = mol. Always convert kg to g before substituting.
Pause — write the highlighted equation into your book.
Fill the blanks: drag each token into the matching blank.
To find moles from grams, ___ by ___. To find grams from moles, ___ by MM. n is measured in ___ .
Did you get this? True or false: if a question gives mass in kilograms, you must convert to grams before substituting into n = m ÷ MM.
Two truths, one lie — about molar mass. Pick the lie.
Worked examples · reveal as you go
Calculate the number of moles in 54 g of water (H₂O).
What mass of sodium chloride (NaCl) contains 0.50 mol?
Put these steps for "What mass of NaCl contains 0.50 mol?" into the correct order.
- Calculate: m = 0.50 × 58.440 = 29.22 g of NaCl.
- List known and unknown values: n = 0.50 mol, MM = 58.440 g mol⁻¹, m = ?
- Calculate molar mass: MM(NaCl) = 22.990 + 35.450 = 58.440 g mol⁻¹.
- Rearrange the formula: m = n × MM.
Common errors · the 3 traps that cost 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.
Quick-fire practice · 5 reps +2 XP per reveal
Calculate the number of moles in 88 g of carbon dioxide (CO₂).
What mass of calcium carbonate (CaCO₃) is in 0.25 mol?
A student dissolves 14.7 g of sulfuric acid (H₂SO₄) in water. Calculate the amount in moles. (S = 32.06 g mol⁻¹)
Calculate the mass of 0.40 mol of glucose (C₆H₁₂O₆). (C = 12.011, H = 1.008, O = 15.999)
A sample of an unknown compound has a mass of 23.4 g and contains 0.30 mol. Calculate the molar mass of the compound.
Earlier you were asked: How do you think chemists figure out how many grams of a substance they need to weigh out in order to have exactly one mole of it?
The answer lies in molar mass — the mass in grams of one mole of a substance, which is numerically equal to the relative atomic (or formula) mass from the periodic table. Because one mole of carbon-12 was defined to be exactly 12 g, all other atomic masses scale consistently, so the periodic table directly gives you the grams per mole for any element or compound.
Pick your answer, then rate your confidence — that tells the system what to drill next.
Q1. 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.
Q2. 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)
Q3. 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)
Q4. A pharmaceutical company manufactures aspirin (C₉H₈O₄, MM = 180.16 g mol⁻¹). A quality-control test on a batch finds that 10.00 g of the product contains only 9.76 g of pure aspirin. (a) Calculate the number of moles of pure aspirin per tablet if the tablet mass is 500 mg. (b) Evaluate whether the batch passes the quality standard that requires ≥97.0% purity by mass. Show full working.
Q5. Design a procedure a student could use — with only a balance, distilled water, and a volumetric flask — to determine the molar mass of an unknown soluble salt. In your answer: (a) describe the measurements the student must take, (b) explain the calculation steps that lead from those measurements to the molar mass, and (c) identify one source of systematic error and explain how it would affect the result.
📖 Comprehensive answers (click to reveal)
Multiple choice — drill bank
MC answers and feedback are shown inline as you complete each question. Use the retry button to attempt a fresh set.
Key MC notes:
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
6. B — MM(Ca(H₂PO₄)₂) = 40.078 + 2(2×1.008 + 30.974 + 4×15.999) = 234.05 g mol⁻¹
7. C — MM(XCl₂) = 55.75 ÷ 0.500 = 111.50 g mol⁻¹. MM(X) = 111.50 − 2(35.453) = 40.59 ≈ calcium (Ca = 40.078)
Short answer model answers
Q1 (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].
Q2 (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, 1 for correct formula, 1 for substitution, 1 for final answer with units.
Q3 (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.
Q4 (5 marks): (a) % purity = 9.76 ÷ 10.00 = 97.6%. m(pure) per tablet = 0.500 g × 0.976 = 0.488 g. n = 0.488 ÷ 180.16 = 2.71 × 10⁻³ mol. (b) Since 97.6% ≥ 97.0%, the batch passes the quality standard.
Q5 (6 marks): (a) Measurements: (i) mass of empty volumetric flask (tare); (ii) mass with weighed sample of unknown salt; (iii) volume of flask (e.g. 250.0 mL). Dissolve the salt in distilled water, make up to the mark. Use a titration with a standard solution to find n(salt). (b) Calculation: n(salt) from titration; MM = m(salt weighed) ÷ n(salt). (c) Systematic error: the salt may absorb moisture from air (hygroscopic), so m(salt) appears larger than the true mass, making MM too large. Fix: dry the salt in an oven before weighing.
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