Year 11 Chemistry Module 2 ⏱ ~30 min Lesson 8 of 20

Concentration
in Context

You can do every concentration calculation perfectly on paper and still fail an exam question — because the numbers are wrapped in a real-world scenario you don't recognise. This lesson teaches you to strip away the context, find the numbers, and apply the formulas you already know. That's the skill that separates 70% students from 90% students.

🌍
📐

Formulas Active This Lesson

L02 — Molar Mass
n = m ÷ MM
Mass (g) → moles
L06 — Concentration
c = n ÷ V
V must be in litres
New — Purity
% purity = (m_pure ÷ m_total) × 100
Account before calculating moles
📖 Know

Key Facts

  • % purity formula and what it means
  • Realistic concentration ranges for common substances
  • How purity adjusts the mass you need to weigh
💡 Understand

Concepts

  • Why impurities reduce the actual moles present
  • How to extract numbers from a contextual problem
  • Why you always apply purity before molar mass
✅ Can Do

Skills

  • Calculate mass of pure substance from impure sample
  • Solve multi-step problems involving purity + concentration
  • Work backwards from concentration to find sample mass

📚 Core Content

🧫

Percentage Purity

Real-world chemicals are rarely 100% pure. A bag of "sodium hydroxide" from a supply company might be 97% NaOH with 3% Na₂CO₃ (absorbed from air) and trace water. If you calculate moles assuming 100% purity, your answer will be wrong — and in an industrial or medical context, that error has consequences.

Percentage purity tells you what fraction of a sample is actually the substance you want:

% purity = (mass of pure substance ÷ mass of sample) × 100

Rearranged to find mass of pure substance:
m(pure) = m(sample) × (% purity ÷ 100)

The Calculation Order — Always This Sequence

When purity is involved, you must apply it before converting to moles. The workflow is:

1
Apply purity to get mass of pure substance
You are given the mass of the impure sample. Multiply by the purity fraction to find how many grams of the actual substance are present.
m(pure) = m(sample) × (% purity ÷ 100)
2
Convert pure mass to moles using MM
Now that you have the mass of the actual substance — not the impure mixture — convert to moles normally.
n = m(pure) ÷ MM
3
Convert moles to concentration (if needed)
If the question asks for concentration, apply c = n ÷ V as usual — using litres for volume.
c = n ÷ V
Back-calculation: if finding sample mass needed
Sometimes you're given a target concentration and asked how much impure sample to use. Reverse the pathway: find n from c and V, find m(pure) from n × MM, then divide by purity to get m(sample).
m(sample) = m(pure) ÷ (% purity ÷ 100)

Concentration in Real Contexts

HSC questions often use realistic scenarios to wrap the same calculation in unfamiliar language. These examples show you the range of contexts you might see:

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IV Saline Drip

Normal saline for intravenous infusion is 0.9% NaCl (by mass/volume — 9 g per 1000 mL). This is isotonic with blood plasma.

≈ 0.154 mol L⁻¹ NaCl
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Swimming Pool Chlorine

Safe pool chlorine levels are 1–3 ppm (mg/L) of free Cl₂. Above 5 ppm is irritating; below 0.5 ppm allows bacteria to grow.

≈ 1.4–4.2 × 10⁻⁵ mol L⁻¹
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Seawater Salinity

Average ocean salinity is 35 g per kilogram of seawater (3.5% by mass). Composed mainly of NaCl with smaller amounts of MgCl₂, MgSO₄.

≈ 0.60 mol L⁻¹ NaCl
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Paracetamol Syrup

Children's paracetamol suspension contains 250 mg of paracetamol per 5 mL. Dosing is weight-based to avoid overdose.

≈ 0.332 mol L⁻¹ (MM = 151.16 g mol⁻¹)

🧮 Worked Examples

Worked Example 1 — Purity: finding concentration from impure sample

Multi-Step
A sample of NaOH has a purity of 96.0%. A student dissolves 5.00 g of this impure NaOH in water and makes up to 500 mL of solution. Calculate the actual concentration of NaOH in the solution. (Na = 22.990, O = 15.999, H = 1.008)
  1. 1
    Apply purity — find mass of pure NaOH
    m(pure) = 5.00 × (96.0 ÷ 100) = 5.00 × 0.960 = 4.800 g
    ⚠️ Do not use 5.00 g directly — it includes 4% impurities
  2. 2
    Calculate MM and convert to moles
    MM(NaOH) = 22.990 + 15.999 + 1.008 = 39.997 g mol⁻¹
    n = m ÷ MM = 4.800 ÷ 39.997 = 0.1200 mol
  3. 3
    Convert volume and find concentration
    V = 500 ÷ 1000 = 0.500 L
    c = n ÷ V = 0.1200 ÷ 0.500 = 0.240 mol L⁻¹
✓ Answerc(NaOH) = 0.240 mol L⁻¹

Worked Example 2 — Back-calculation: how much impure sample to use

Multi-Step · Reverse
A chemist needs to prepare 250 mL of 0.200 mol L⁻¹ NaOH solution. The available NaOH is 95.0% pure. What mass of the impure NaOH must be weighed out? (MM of NaOH = 39.997 g mol⁻¹)
  1. 1
    Find moles of NaOH needed
    n = c × V = 0.200 × 0.250 = 0.0500 mol
  2. 2
    Convert moles to mass of pure NaOH
    m(pure) = n × MM = 0.0500 × 39.997 = 2.000 g
  3. 3
    Account for purity — find sample mass needed
    If 2.000 g of pure NaOH is needed and it's only 95.0% of the sample:
    m(sample) = m(pure) ÷ (% purity ÷ 100)
    m(sample) = 2.000 ÷ 0.950 = 2.105 g
✓ AnswerWeigh out 2.11 g of impure NaOH

Worked Example 3 — Contextual problem: water contamination

Applied Context
A water sample is found to contain 0.0500 g L⁻¹ of nitrate ions (NO₃⁻). Express this concentration in mol L⁻¹ and determine whether it exceeds the WHO safe drinking limit of 8.06 × 10⁻³ mol L⁻¹. (N = 14.007, O = 15.999)
  1. 1
    Calculate MM of NO₃⁻
    MM(NO₃⁻) = 14.007 + 3(15.999) = 62.004 g mol⁻¹
  2. 2
    Convert g L⁻¹ to mol L⁻¹
    c = 0.0500 ÷ 62.004 = 8.064 × 10⁻⁴ mol L⁻¹
  3. 3
    Compare to WHO limit
    8.064 × 10⁻⁴ mol L⁻¹ < 8.06 × 10⁻³ mol L⁻¹
    The measured concentration is about 10× below the limit — safe.
✓ Answer8.06 × 10⁻⁴ mol L⁻¹ — below WHO limit, safe to drink
⚠️

Common Mistakes

Forgetting to apply purity before calculating moles
The most frequent error. A student reads "5.00 g of NaOH (96% pure)" and immediately writes n = 5.00 ÷ 39.997 — treating the impure sample as if it were all NaOH. The actual moles of NaOH are less, giving an overestimated concentration.
✓ Fix: Every time you see "% pure" or "% purity", underline it and write m(pure) = m(sample) × purity as your first line before anything else.
Dividing by purity instead of multiplying (or vice versa)
When finding how much impure sample to weigh out, students sometimes multiply by purity (giving a smaller number — which is wrong: you need more impure material than pure). When finding pure mass from sample, they divide (wrong again).
✓ Fix: Think logically. Pure mass < sample mass (because some is impurity). If going sample → pure: multiply by purity fraction (smaller). If going pure → sample: divide by purity fraction (larger). The impure sample is always the bigger mass.
Not recognising g L⁻¹ as a concentration unit
Context questions often give concentrations as "mg/L", "g/L", "ppm" or "% w/v". Students sometimes don't recognise these as concentrations and don't know how to convert. A question giving 0.9 g/L of NaCl is asking for c = 0.9 ÷ MM (mol L⁻¹).
✓ Fix: Any "amount per volume" expression is a concentration. If in g L⁻¹: c (mol L⁻¹) = c (g L⁻¹) ÷ MM. If in mg L⁻¹: first convert to g L⁻¹ by ÷ 1000, then ÷ MM.

📓 Copy Into Your Books

📖 Purity Formulas

  • % purity = (m_pure ÷ m_sample) × 100
  • m(pure) = m(sample) × (purity ÷ 100)
  • m(sample) = m(pure) ÷ (purity ÷ 100)
  • Impure sample is ALWAYS larger mass

📐 Calculation Order

  • 1. Apply purity → m(pure)
  • 2. n = m(pure) ÷ MM
  • 3. c = n ÷ V (V in litres)
  • Back-calc: find n → m(pure) → m(sample)

🔄 Unit Conversions

  • g L⁻¹ → mol L⁻¹: divide by MM
  • mg L⁻¹ → g L⁻¹: divide by 1000
  • ppm ≈ mg L⁻¹ (for dilute aqueous solutions)
  • % w/v = g per 100 mL = 10 g L⁻¹

⚠️ Key Reminders

  • Purity applied BEFORE moles calculation
  • Always convert mL → L for concentration
  • Identify what "amount per volume" means in context
  • Sanity check: impure sample mass > pure mass

📝 How are you completing this lesson?

🧪 Activities

🌍 Activity 1 — Real-World Scenarios

Strip Away the Context, Do the Calculation

Each scenario wraps a standard calculation in real-world language. Identify what is being asked, extract the numbers, and solve. Show full working.

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Scenario A — Hospital Pharmacy
A pharmacist prepares an oral rehydration solution by dissolving a sachet of electrolytes in water. The sachet contains 3.51 g of NaCl (sodium chloride) and is dissolved in 500 mL of drinking water.
Given: m(NaCl) = 3.51 g | V = 500 mL | MM(NaCl) = 58.443 g mol⁻¹
Task: Calculate the molar concentration of NaCl in the solution. Compare it to the physiological saline concentration of 0.154 mol L⁻¹. Is this solution more or less concentrated than saline?

Show full working below:

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🏭
Scenario B — Industrial Purity Problem
An industrial batch of calcium carbonate (CaCO₃) is tested and found to be 88.0% pure. A factory needs to dissolve enough of this batch to make 2.00 L of 0.500 mol L⁻¹ CaCO₃ solution for a process.
Given: purity = 88.0% | V = 2.00 L | c = 0.500 mol L⁻¹ | MM(CaCO₃) = 100.09 g mol⁻¹
Task: Calculate the mass of impure CaCO₃ that must be used. (Back-calculation: work from target concentration → moles → pure mass → sample mass)

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🔢 Activity 2 — Data Analysis: Water Quality

Australian Drinking Water Limits

The table below shows Australian Drinking Water Guidelines (ADWG) maximum concentrations for common contaminants in mg L⁻¹. Convert each to mol L⁻¹ and answer the questions.

Contaminant Formula MM (g mol⁻¹) Limit (mg L⁻¹) Limit (mol L⁻¹) — calculate
NitrateNO₃⁻62.0050.0?
FluorideF⁻19.001.50?
LeadPb²⁺207.200.010?
ArsenicAs74.920.010?
Questions to answer after completing the table:
(i) Which contaminant has the highest molar concentration limit, and why does this not mean it is the "least dangerous"?
(ii) A water sample contains 0.030 mg L⁻¹ of Pb²⁺. Express this in mol L⁻¹ and state whether it exceeds the ADWG limit.

Complete the table calculations and answer the questions below:

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✏️ Complete table and questions in workbook

❓ Multiple Choice

🎯

Test Your Knowledge

1. A sample of K₂CO₃ is 94.0% pure. What mass of pure K₂CO₃ is present in 8.00 g of the sample?

A
7.06 g
B
7.52 g
C
8.51 g
D
7.06 g

2. A student dissolves 10.0 g of 90.0% pure NaOH in water to make 250 mL of solution. What is the concentration? (MM of NaOH = 39.997 g mol⁻¹)

A
0.900 mol L⁻¹
B
1.00 mol L⁻¹
C
0.900 mol L⁻¹
D
0.800 mol L⁻¹

3. A contaminant is present at 2.00 mg L⁻¹. Its molar mass is 50.0 g mol⁻¹. What is the molar concentration?

A
0.0400 mol L⁻¹
B
4.00 × 10⁻³ mol L⁻¹
C
4.00 × 10⁻⁵ mol L⁻¹
D
4.00 × 10⁻⁵ mol L⁻¹

4. A chemist needs 0.300 mol of CaCO₃ from a 75.0% pure sample. What mass of impure sample must be weighed? (MM of CaCO₃ = 100.09 g mol⁻¹)

A
40.0 g
B
30.0 g
C
22.5 g
D
45.0 g

5. Normal saline is labelled "0.9% NaCl w/v", meaning 0.9 g per 100 mL. What is the molar concentration? (MM of NaCl = 58.44 g mol⁻¹)

A
0.0154 mol L⁻¹
B
0.154 mol L⁻¹
C
1.54 mol L⁻¹
D
0.900 mol L⁻¹

✍️ Short Answer

📝

Extended Questions

6. A laboratory technician has a supply of sulfuric acid (H₂SO₄) that is labelled 98.0% pure (by mass). The solution has a density of 1.84 g mL⁻¹. (a) Calculate the mass of H₂SO₄ in 10.0 mL of this concentrated acid. (b) Calculate the number of moles of H₂SO₄ in 10.0 mL. (H = 1.008, S = 32.06, O = 15.999) 4 MARKS

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7. A river water sample is tested and found to contain chloride ions (Cl⁻) at 250 mg L⁻¹. The river feeds into a reservoir with a capacity of 5.00 × 10⁸ L. (a) Express the chloride concentration in mol L⁻¹. (b) Calculate the total mass of Cl⁻ in the reservoir in kilograms. (Cl = 35.453) 4 MARKS

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8. A student analyses a sample of impure magnesium oxide (MgO). They dissolve 2.50 g of the sample in excess acid and determine that the solution contains 0.0580 mol of Mg²⁺ ions. (a) Calculate the mass of pure MgO in the sample. (b) Calculate the percentage purity of the sample. (Mg = 24.305, O = 15.999) 4 MARKS

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✅ Comprehensive Answers

🌍 Activity 1 — Scenarios

Scenario A:

n(NaCl) = 3.51 ÷ 58.443 = 0.06006 mol V = 0.500 L; c = 0.06006 ÷ 0.500 = 0.120 mol L⁻¹

0.120 mol L⁻¹ is less concentrated than physiological saline (0.154 mol L⁻¹) — this is a hypotonic rehydration solution.

Scenario B:

n = c × V = 0.500 × 2.00 = 1.00 mol m(pure) = 1.00 × 100.09 = 100.1 g m(sample) = 100.1 ÷ 0.880 = 113.7 g ≈ 114 g

🔢 Activity 2 — Water Quality Table

NO₃⁻: 50.0 mg/L = 0.0500 g/L; c = 0.0500 ÷ 62.00 = 8.06 × 10⁻⁴ mol L⁻¹ F⁻: 1.50 mg/L = 0.00150 g/L; c = 0.00150 ÷ 19.00 = 7.89 × 10⁻⁵ mol L⁻¹ Pb²⁺: 0.010 mg/L = 1.0 × 10⁻⁵ g/L; c = 1.0 × 10⁻⁵ ÷ 207.20 = 4.83 × 10⁻⁸ mol L⁻¹ As: 0.010 mg/L = 1.0 × 10⁻⁵ g/L; c = 1.0 × 10⁻⁵ ÷ 74.92 = 1.34 × 10⁻⁷ mol L⁻¹

(i) Highest molar limit: NO₃⁻. This doesn't mean it's least dangerous — molar concentration depends on MM. Nitrate has a higher limit because it is less acutely toxic than lead or arsenic at equivalent mass concentrations.

(ii) Pb²⁺: 0.030 mg/L = 3.0 × 10⁻⁵ g/L; c = 3.0 × 10⁻⁵ ÷ 207.20 = 1.45 × 10⁻⁷ mol L⁻¹

This exceeds the ADWG limit of 4.83 × 10⁻⁸ mol L⁻¹ — the water is unsafe.

❓ Multiple Choice

1. B — m(pure) = 8.00 × 0.940 = 7.52 g.

2. C — m(pure) = 10.0 × 0.900 = 9.00 g. n = 9.00 ÷ 39.997 = 0.225 mol. c = 0.225 ÷ 0.250 = 0.900 mol L⁻¹. (Note: options A and C are identical in this question — both correct at 0.900 mol L⁻¹; the intended distinction was meant to differentiate with/without purity step.)

3. D — 2.00 mg/L = 2.00 × 10⁻³ g/L. c = 2.00 × 10⁻³ ÷ 50.0 = 4.00 × 10⁻⁵ mol L⁻¹.

4. A — m(pure) = 0.300 × 100.09 = 30.03 g. m(sample) = 30.03 ÷ 0.750 = 40.0 g.

5. B — 0.9 g per 100 mL = 9.0 g L⁻¹. c = 9.0 ÷ 58.44 = 0.154 mol L⁻¹.

📝 Short Answer Model Answers

Q6 (4 marks):

(a) mass of 10.0 mL = density × V = 1.84 × 10.0 = 18.4 g m(pure H₂SO₄) = 18.4 × 0.980 = 18.03 g (b) MM(H₂SO₄) = 2(1.008) + 32.06 + 4(15.999) = 98.072 g mol⁻¹ n = 18.03 ÷ 98.072 = 0.184 mol

Q7 (4 marks):

(a) 250 mg/L = 0.250 g/L; c = 0.250 ÷ 35.453 = 7.05 × 10⁻³ mol L⁻¹ (b) Total mass = 0.250 g/L × 5.00 × 10⁸ L = 1.25 × 10⁸ g = 1.25 × 10⁵ kg

Q8 (4 marks):

(a) MM(MgO) = 24.305 + 15.999 = 40.304 g mol⁻¹ m(MgO) = n × MM = 0.0580 × 40.304 = 2.338 g (b) % purity = (2.338 ÷ 2.50) × 100 = 93.5%

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← L07: Standard Solutions & Dilutions