Chemistry • Year 11 • Module 2 • Lesson 2
Molar Mass
Build HSC Band 5–6 extended-response technique: multi-step molar-mass problems, evaluation of student working, and experimental design for molar-mass determination.
1. Multi-step scenario — aspirin manufacturing quality control (Band 5–6)
8 marks Band 5–6
Scenario. Aspirin (acetylsalicylic acid, C9H8O4, MM = 180.16 g mol−1) is manufactured at a plant in Victoria. A quality-control analyst tests two batches:
- Batch 1: 10.00 g of product contains 9.76 g of pure aspirin.
- Batch 2: 10.00 g of product contains 9.64 g of pure aspirin.
The regulatory standard requires ≥ 97.0% purity by mass before a batch can be released to pharmacies. Each final tablet must contain exactly 300 mg of pure aspirin.
Q1. Respond to all five dot points below. Show full working for all calculations.
- Calculate the percentage purity (by mass) of each batch. State whether each batch passes or fails the regulatory standard.
- For the batch(es) that pass(es), calculate the number of moles of pure aspirin in a single 300 mg tablet. Show the molar mass calculation step explicitly.
- A tablet press produces 1500 tablets per minute. Calculate the mass of pure aspirin (in kg) required to operate the press for exactly 2 minutes, assuming all tablets pass quality control. Show all steps.
- The plant manager suggests that a batch with 96.5% purity could still be used by increasing the tablet mass to compensate. Calculate the new tablet mass (mg) that would deliver 300 mg of pure aspirin if the batch is only 96.5% pure.
- Evaluate whether the manager’s suggestion is scientifically valid. In your answer, consider the effect on the amount (mol) of aspirin per tablet, and identify one additional concern about this approach from a pharmaceutical safety perspective.
2. Evaluate student working — identify, explain and correct all errors (Band 5–6)
7 marks Band 4–6
Problem given to student: Calculate the number of moles in 24.3 g of magnesium hydroxide Mg(OH)2. (Mg = 24.305, O = 15.999, H = 1.008 g mol−1)
Student’s working (contains errors):
Step 1: MM = Mg + O + H = 24.305 + 15.999 + 1.008 = 41.312 g mol−1
Step 2: n = m × MM = 24.3 × 41.312 = 1003.9 mol
Step 3: Answer: n = 1004 mol
Q2. There are two errors in the student’s working. For each error:
- Identify exactly what is wrong (one sentence per error).
- Explain why it is incorrect, with reference to the rule or concept that was violated.
- Show the corrected working for that step.
Then write the fully corrected solution from start to finish.
Q1 — Sample Band 6 response (8 marks), annotated
Percentage purity and regulatory assessment:
Batch 1: % purity = (9.76 ÷ 10.00) × 100 = 97.6%. Since 97.6% ≥ 97.0%, Batch 1 passes. [1 mark: correct % with comparison]
Batch 2: % purity = (9.64 ÷ 10.00) × 100 = 96.4%. Since 96.4% < 97.0%, Batch 2 fails. [1 mark: correct % with comparison]
Moles per tablet (Batch 1 only, since only Batch 1 passes):
MM(C9H8O4) = 9(12.011) + 8(1.008) + 4(15.999) = 108.099 + 8.064 + 63.996 = 180.159 g mol−1 (given as 180.16 g mol−1). [1 mark: explicit MM step shown]
m(pure aspirin per tablet) = 300 mg = 0.300 g. n = 0.300 ÷ 180.16 = 1.665 × 10−3 mol. [1 mark: correct conversion + calculation]
Mass of aspirin for 2-minute production run:
Tablets in 2 min = 1500 × 2 = 3000 tablets. Mass = 3000 × 0.300 g = 900 g = 0.900 kg. [1 mark]
New tablet mass at 96.5% purity:
New tablet mass = 300 mg ÷ 0.965 = 310.9 mg ≈ 311 mg. [1 mark: correct calculation and unit]
Evaluation of the manager’s suggestion:
The moles of aspirin per tablet remain the same (0.300 g ÷ 180.16 = 1.665 × 10−3 mol), so the pharmacological dose is preserved [1]. However, the heavier tablet also delivers a larger mass of the impurity substance; if the impurity is pharmacologically active or toxic, patients would receive a higher dose of an uncharacterised substance with each tablet — this is a significant pharmaceutical safety concern [1].
Marking criteria (8 marks): 1 = Batch 1 % purity + correct pass/fail; 1 = Batch 2 % purity + correct fail; 1 = explicit MM calculation step; 1 = n per tablet (correct with unit conversion); 1 = press production mass (0.900 kg); 1 = new tablet mass (311 mg); 1 = evaluation noting moles preserved; 1 = safety concern identified and explained.
Q2 — Sample Band 6 error analysis (7 marks), annotated
Error 1 — Brackets not expanded: The student treated Mg(OH)2 as containing only 1 oxygen atom and 1 hydrogen atom, ignoring the subscript “2” outside the bracket. [1 — identification]
This violates the subscript rule: the subscript outside a bracket multiplies every atom inside. Mg(OH)2 = 1 Mg + 2 O + 2 H, not 1 Mg + 1 O + 1 H. [1 — explanation with rule]
Corrected Step 1: MM = 24.305 + 2(15.999) + 2(1.008) = 24.305 + 31.998 + 2.016 = 58.319 g mol−1. [1 — corrected step]
Error 2 — Multiplied instead of divided: In Step 2, the student wrote n = m × MM instead of n = m ÷ MM. [1 — identification]
This is incorrect because n = m ÷ MM (from the rearrangement of m = n × MM). Multiplying mass by molar mass gives units of g × g mol−1 = g2 mol−1, which is not a chemically meaningful unit. Dividing gives g ÷ (g mol−1) = mol ✓. [1 — explanation with unit analysis]
Corrected Step 2: n = m ÷ MM = 24.3 ÷ 58.319 = 0.4166 mol. [1 — corrected step]
Fully corrected solution:
MM(Mg(OH)2) = 24.305 + 2(15.999) + 2(1.008) = 58.319 g mol−1.
n = m ÷ MM = 24.3 ÷ 58.319 = 0.417 mol (3 s.f.). Units: g ÷ g mol−1 = mol ✓. [1 — correct final answer with units and s.f.]
Marking criteria (7 marks): 1 = Error 1 identification (brackets); 1 = Error 1 explanation (subscript rule); 1 = Corrected MM; 1 = Error 2 identification (wrong operation); 1 = Error 2 explanation (unit analysis); 1 = Corrected n calculation; 1 = correct final answer with unit and appropriate significant figures.