Chemistry • Year 11 • Module 2 • Lesson 8

Concentration in Context

Lock in the key vocabulary, the purity formulas, and the correct calculation sequence before tackling harder contextual problems.

Build · Vocab & Recall

1. Term–definition match

The definitions below are shuffled. In the right-hand column write the matching term from this list: percentage purity, pure substance, impure sample, m(pure), m(sample), ppm, ppb, mg L−1, back-calculation, % w/v. 10 marks (1 each)

#DefinitionMatching term
1.1The ratio of the mass of the desired substance to the total mass of the sample, expressed as a percentage.
1.2A substance that contains only one chemical species with no contaminants.
1.3A sample that contains the desired substance together with one or more contaminants.
1.4The mass of only the desired chemical species within a sample, after accounting for impurities.
1.5The total mass of a weighed sample, including impurities.
1.6Parts per million; for dilute aqueous solutions, numerically equal to 1 milligram per litre.
1.7Parts per billion; a unit of concentration equal to 1 microgram per litre (µg L−1) in dilute aqueous solutions.
1.8A concentration unit expressing milligrams of solute dissolved per litre of solution.
1.9The process of working from a target concentration backwards to find the mass of sample that must be weighed out.
1.10A concentration expression where the number of grams of solute per 100 mL of solution is stated; 1% w/v = 10 g L−1.
Stuck? Revisit the Key Terms panel in the lesson.

2. True or false — with correction

Circle T or F for each statement. If the statement is false, write the corrected version on the line below it. 12 marks (1 T/F + 1 correction each)

2.1 When a sample is labelled “95% pure”, the mass of the pure substance equals the total sample mass.    T  /  F

2.2 Purity must be applied before converting mass to moles in any calculation involving an impure sample.    T  /  F

2.3 To convert a concentration from mg L−1 to mol L−1, you multiply by the molar mass.    T  /  F

2.4 When back-calculating the mass of an impure sample needed, the mass of impure sample is always greater than the mass of pure substance required.    T  /  F

2.5 A concentration of 0.9% NaCl (w/v) means there are 9 g of NaCl per 1000 mL of solution, which equals 9 g L−1.    T  /  F

2.6 The formula for percentage purity is: % purity = (msample ÷ mpure) × 100.    T  /  F

Stuck? Revisit the Percentage Purity card and the Unit Conversions summary in the lesson.

3. Fill-in-the-blank paragraph

Use the word bank to complete the passage. Each word is used once. 8 marks (1 per blank)

Word bank:

purity  ·  molar mass  ·  back-calculate  ·  impurities  ·  larger  ·  moles  ·  litres  ·  divide

Real chemicals from suppliers always contain small amounts of ___________, so you must account for ___________ before calculating moles. The correct order is: first find m(pure) by multiplying the sample mass by the purity fraction, then convert m(pure) to ___________ by dividing by the ___________, then finally divide by the volume in ___________ to get the concentration. To convert a concentration in g L−1 to mol L−1, you ___________ by the molar mass. When a chemist needs to prepare a solution of a specific concentration from an impure reagent, they must ___________ from the target concentration to find the required sample mass. The mass of impure sample required is always ___________ than the mass of pure substance needed.

Stuck? Revisit the Calculation Order box and the Common Mistakes section in the lesson.

4. Function recall

Answer each question in 1–2 sentences using precise terms from the lesson. 8 marks (2 each)

4.1 What is the purpose of applying the purity fraction to a sample mass, and why must this happen before you use n = m ÷ MM?

4.2 Explain what “ppm” means in a water-quality report and how you convert a reading in mg L−1 to mol L−1.

4.3 A bottle of NaOH is labelled 97% pure. What does this mean for the actual moles of NaOH in a 10.0 g sample weighed on a balance?

4.4 Why is the impure sample mass always greater than the mass of pure substance needed in a back-calculation?

Stuck? Revisit Worked Examples 1 and 2 and the Copy Into Your Books section.

5. Build a concept map

Draw labelled arrows between the seven terms below to show how they connect in a purity calculation. Each arrow must carry a linking phrase (e.g. “is multiplied by”, “divided by”, “is converted to”). Aim for at least 6 labelled arrows. 6 marks (1 per valid labelled arrow)

Supplied terms: m(sample) · purity fraction · m(pure) · molar mass · n (moles) · volume (L) · concentration (mol L−1).

m(sample)
purity fraction
m(pure)
molar mass
n (moles)
volume (L)
concentration (mol L−1)
Hint arrows: m(sample) × purity fraction → m(pure); m(pure) ÷ molar mass → n; n ÷ volume → concentration; concentration × volume → n (reverse); n × molar mass → m(pure) (reverse).

6. Formula fill-in

Complete each formula below by filling in the missing symbol or expression. 6 marks (1 each)

#Formula (fill the blank)What it calculates
6.1m(pure) = m(sample) × ( _______ ÷ 100 )Mass of pure substance in the sample
6.2m(sample) = m(pure) ÷ ( _______ ÷ 100 )Sample mass needed for a given pure mass
6.3n = _______ ÷ MMMoles from mass of pure substance
6.4c = n ÷ _______Molar concentration (V must be in litres)
6.5c (mol L−1) = c (g L−1) ÷ _______Convert g L−1 to mol L−1
6.6c (g L−1) = c (mg L−1) ÷ _______Convert mg L−1 to g L−1
Stuck? Revisit the Formulas Active This Lesson panel at the top of the lesson.
Answers — Do not peek before attempting

Q1 — Term–definition match

1.1 percentage purity • 1.2 pure substance • 1.3 impure sample • 1.4 m(pure) • 1.5 m(sample) • 1.6 ppm • 1.7 ppb • 1.8 mg L−1 • 1.9 back-calculation • 1.10 % w/v.

Q2 — True / false with correction

2.1 False. If the sample is 95% pure, m(pure) = m(sample) × 0.95, which is less than the total sample mass — 5% is impurities.

2.2 True.

2.3 False. To convert mg L−1 to mol L−1, you first convert mg to g (divide by 1000), then divide by the molar mass. Multiplying gives the wrong answer.

2.4 True. Since only a fraction of the sample is the desired pure substance, you always need to weigh out more than the pure mass required. The impure sample is divided by the purity fraction, making it larger.

2.5 True. 0.9 g per 100 mL = 9 g per 1000 mL = 9 g L−1. Correct.

2.6 False. The correct formula is % purity = (mpure ÷ msample) × 100 — the pure mass is on top, the total sample mass is on the bottom.

Q3 — Cloze paragraph

In order: impurities / purity / moles / molar mass / litres / divide / back-calculate / larger.

Q4.1 — Purpose of applying purity first

Applying the purity fraction finds the mass of the actual chemical species (mpure) in the sample. The formula n = m ÷ MM assumes all the mass is the pure substance; using m(sample) directly would overestimate the moles because it includes the mass of the impurities, which do not contribute to the reaction.

Q4.2 — ppm and the mg L−1 to mol L−1 conversion

In a water-quality report, “ppm” means parts per million, numerically equivalent to mg L−1 for dilute aqueous solutions. To convert: first divide mg L−1 by 1000 to get g L−1, then divide by the molar mass (in g mol−1) to get mol L−1.

Q4.3 — 97% pure NaOH

The label means only 97% of the 10.0 g sample is actually NaOH; the remaining 3% is impurities (e.g. Na2CO3, water). So m(NaOH) = 10.0 × 0.97 = 9.70 g, giving n = 9.70 ÷ 39.997 = 0.243 mol — fewer moles than if the sample were 100% pure (0.250 mol).

Q4.4 — Why impure sample mass > pure mass needed

Only a fraction of the impure sample is the desired substance. To get the required amount of pure substance, you must weigh out enough of the mixture such that the fraction (purity ÷ 100) of it equals the pure mass needed. Dividing by a number less than 1 always gives a larger result: m(sample) = m(pure) ÷ (purity ÷ 100) > m(pure).

Q5 — Sample concept map

Correct maps should include arrows such as:

  • m(sample)multiplied by purity fraction givesm(pure)
  • m(pure)divided bymolar massgivesn (moles)
  • n (moles)divided byvolume (L)givesconcentration
  • concentrationmultiplied by volume givesn (moles) (reverse)
  • n (moles)multiplied by molar mass givesm(pure) (reverse)
  • m(pure)divided by purity fraction givesm(sample) (reverse)

Award 1 mark per valid labelled arrow (minimum 6).

Q6 — Formula fill-in

6.1 % purity • 6.2 % purity • 6.3 m(pure) • 6.4 V • 6.5 MM (molar mass) • 6.6 1000.