Year 11 Chemistry Module 2 ⏱ ~35 min Lesson 6 of 20 IQ3 Begins

Concentration

A cup of coffee and an espresso both contain caffeine — but one hits harder. That difference is concentration. Every time a nurse measures an IV drip rate, a pool technician tests chlorine levels, or a chemist prepares a reagent, they're working with this concept. It is the single most used calculation in Year 11 and 12 Chemistry.

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Think First

If you dissolve one teaspoon of sugar in a small cup of water versus the same teaspoon in a swimming pool, the amount of sugar is the same — but something is very different. What is different, and how would you describe that difference using a mathematical expression? What two quantities would you need to measure?

Type your initial thoughts below:

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📐

Formula Reference — This Lesson

$c = \dfrac{n}{V}$
c = concentration (mol L⁻¹) n = moles of solute (mol) V = volume of solution (L)
Find c: $c = n \div V$  |  Find n: $n = c \times V$  |  Find V: $V = n \div c$
n moles (mol) c concentration (mol L⁻¹) V volume (L) c = n ÷ V | n = c × V | V = n ÷ c Cover the quantity you want to find
⚠️ Critical habit: V must be in litres (L) before substituting. If given mL, divide by 1000 first. This is the #1 source of errors in concentration calculations.

Know

  • Definition: concentration = moles of solute ÷ volume of solution
  • Units: mol L⁻¹ (also written M or mol/L)
  • Solute, solvent, solution — key terms

Understand

  • Why concentration depends on both amount AND volume
  • Why mL must be converted to L before calculating
  • Difference between mol L⁻¹ and g L⁻¹

Can Do

  • Calculate c, n, or V using c = n ÷ V
  • Convert g L⁻¹ to mol L⁻¹ and back
  • Solve multi-step problems involving concentration + molar mass
Key Terms
MoleThe SI unit for amount of substance; contains exactly 6.022 × 10²³ particles.
Avogadro's Number6.022 × 10²³ — the number of particles in one mole of a substance.
Molar MassThe mass of one mole of a substance, measured in g/mol.
Limiting ReagentThe reactant that is completely consumed first, limiting the amount of product formed.
Empirical FormulaThe simplest whole-number ratio of atoms in a compound.
Molecular FormulaThe actual number of atoms of each element in a molecule of a compound.

Misconceptions to Fix

Wrong: The limiting reagent is the one present in the smallest mass.

Right: The limiting reagent is the reactant that runs out first based on mole ratios, not mass.

🔬

What Is Concentration?

A solution is a homogeneous mixture of a solute (the substance being dissolved) in a solvent (the dissolving medium, usually water). Concentration tells you how much solute is packed into a given volume of solution.

In chemistry, concentration is almost always expressed in moles per litre (mol L⁻¹) — also called molarity. This unit connects the macroscopic world (litres of solution you can measure in a lab) to the microscopic world (moles of particles) via a single formula.

DILUTE 0.1 mol L⁻¹ few solute particles MODERATE 0.5 mol L⁻¹ moderate particles CONCENTRATED 2.0 mol L⁻¹ many solute particles

The Critical Unit Conversion

The volume in c = n ÷ V must be in litres. Laboratory volumes are almost always given in millilitres. This conversion must become automatic.

250 mL millilitres — do NOT use directly ÷ 1000 0.250 L litres ✓ substitute this
Why this matters: If you substitute 250 mL directly instead of 0.250 L, your concentration will be 1000 times too small. A student who gets the formula right but forgets the conversion will lose marks every time. Build the habit: see mL → divide by 1000 → then substitute.

Concentration in g L⁻¹ vs mol L⁻¹

Sometimes concentration is given or required in grams per litre (g L⁻¹). To convert between the two, use molar mass as the bridge.

g L⁻¹ → mol L⁻¹: divide by MM
   c (mol L⁻¹) = c (g L⁻¹) ÷ MM

mol L⁻¹ → g L⁻¹: multiply by MM
   c (g L⁻¹) = c (mol L⁻¹) × MM
Interactive: Concentration Explorer
↗ Drag to rotate · Scroll to zoom · Double-click to reset Interactive 3D

Worked Example 1 — Finding concentration

Stepwise
0.500 mol of sodium hydroxide (NaOH) is dissolved to make 250 mL of solution. Calculate the concentration in mol L⁻¹.
  1. 1
    Identify and convert units
    n = 0.500 mol  |  V = 250 mL
    V = 250 ÷ 1000 = 0.250 L
    ⚠️ Convert mL → L before substituting
  2. 2
    Apply formula
    c = n ÷ V = 0.500 ÷ 0.250
    c = 2.00 mol L⁻¹
✓ Answerc = 2.00 mol L⁻¹

Worked Example 2 — Finding volume

Stepwise
What volume of 2.00 mol L⁻¹ hydrochloric acid (HCl) contains 0.300 mol of HCl?
  1. 1
    Identify known quantities
    c = 2.00 mol L⁻¹  |  n = 0.300 mol  |  V = ?
  2. 2
    Rearrange and solve
    V = n ÷ c = 0.300 ÷ 2.00 = 0.150 L
    = 150 mL
✓ AnswerV = 0.150 L (150 mL)

Worked Example 3 — Multi-step: mass → moles → concentration

Stepwise
5.85 g of sodium chloride (NaCl) is dissolved in water to make 500 mL of solution. Calculate the concentration in mol L⁻¹. (Na = 22.990, Cl = 35.453)
  1. 1
    Calculate molar mass
    MM(NaCl) = 22.990 + 35.453 = 58.443 g mol⁻¹
  2. 2
    Convert mass → moles
    n = m ÷ MM = 5.85 ÷ 58.443 = 0.1001 mol
  3. 3
    Convert volume and find concentration
    V = 500 ÷ 1000 = 0.500 L
    c = n ÷ V = 0.1001 ÷ 0.500 = 0.200 mol L⁻¹
✓ Answerc = 0.200 mol L⁻¹
⚠️

Common Mistakes

Substituting mL instead of L
c = 0.5 ÷ 250 = 0.002 mol L⁻¹ ✗ — answer is 1000 times too small. The unit mol L⁻¹ demands litres in the denominator.
✓ Fix: Always write the unit conversion step explicitly: 250 mL ÷ 1000 = 0.250 L, then substitute 0.250.
Confusing the volume of solute with the volume of solution
If you dissolve 50 mL of ethanol in 200 mL of water, the solution volume is NOT 200 mL — it's approximately 250 mL (though not exactly, due to volume contraction). The formula uses the volume of the total solution, not the solvent alone.
✓ Fix: The V in c = n/V is the volume of the final solution — the number you read on the volumetric flask or measuring cylinder after everything is mixed and made up to volume.
Using g L⁻¹ concentration directly in c = n/V
If a question gives concentration in g L⁻¹, you cannot substitute it directly — c = n/V only works with mol L⁻¹. You must first convert g L⁻¹ to mol L⁻¹ by dividing by MM.
✓ Fix: c (mol L⁻¹) = c (g L⁻¹) ÷ MM. Always check units before substituting.

📓 Copy Into Your Books

📖 Definitions

  • Solute — substance being dissolved
  • Solvent — dissolving medium (usually water)
  • Solution — homogeneous mixture of solute in solvent
  • Concentration (c) — moles of solute per litre of solution

📐 Formula & Rearrangements

  • c = n ÷ V (find concentration)
  • n = c × V (find moles)
  • V = n ÷ c (find volume)
  • Units: mol L⁻¹ | mol | L

⚠️ Critical Habit

  • V must be in litres — always convert mL ÷ 1000
  • c (mol L⁻¹) = c (g L⁻¹) ÷ MM
  • V in formula = volume of solution, not solvent

🔗 Multi-Step Pathway

  • Mass → moles: n = m ÷ MM
  • Moles + volume → concentration: c = n ÷ V
  • Concentration + volume → moles: n = c × V

📝 How are you completing this lesson?

📊 Activity 1 — Practice Drill

Applying c = n ÷ V

Four problems — all three rearrangements plus a unit conversion problem. Show working before revealing answers.

  1. 1 Calculate the concentration of a solution made by dissolving 0.400 mol of glucose in 2.00 L of solution.

    n = 0.400 mol, V = 2.00 L (already in litres) c = n ÷ V = 0.400 ÷ 2.00 = 0.200 mol L⁻¹
  2. 2 How many moles of KNO₃ are in 400 mL of a 0.250 mol L⁻¹ solution?

    Convert: V = 400 mL ÷ 1000 = 0.400 L n = c × V = 0.250 × 0.400 = 0.100 mol
  3. 3 What volume of 0.500 mol L⁻¹ sulfuric acid contains 0.0750 mol of H₂SO₄?

    c = 0.500 mol L⁻¹, n = 0.0750 mol V = n ÷ c = 0.0750 ÷ 0.500 = 0.150 L = 150 mL
  4. 4 A solution of copper sulfate (CuSO₄) has a concentration of 16.0 g L⁻¹. Express this in mol L⁻¹. (Cu = 63.546, S = 32.06, O = 15.999)

    MM(CuSO₄) = 63.546 + 32.06 + 4(15.999) = 159.602 g mol⁻¹ c (mol L⁻¹) = 16.0 ÷ 159.602 = 0.1002 mol L⁻¹

Type your working for all four problems:

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🔢 Activity 2 — Data Analysis

Complete the Concentration Table

The table below shows solution data. Calculate the missing values (shown as ?). Show all working in the space below.

SolutionMoles of solute (mol)Volume (mL)Volume (L)Concentration (mol L⁻¹)
NaOH0.500250??
HCl?100?2.00
CaCl₂0.0400??0.160
H₂SO₄1.50600??
KMnO₄?50.0?0.0200

Show all working below:

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Revisit — Think First

At the start of this lesson, you described the difference between dissolving sugar in a small cup versus a swimming pool, and thought about what quantities you'd need to measure.

The answer: concentration = amount of solute ÷ volume of solution, or c = n ÷ V (in mol L⁻¹). The amount of sugar (solute) stays the same, but the volume of the solution is much larger in the pool — so the concentration is far lower. You need to measure both the number of moles of solute and the volume in litres.

Reflect: how close was your initial idea to the formula c = n ÷ V?

Write a reflection in your workbook.

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MC

Multiple Choice

5 random questions from a replayable lesson bank — feedback shown immediately

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Extended Questions

ApplyBand 3

6. A nurse prepares an intravenous saline solution by dissolving 9.00 g of NaCl in water to produce 1.00 L of solution. Calculate the concentration of the solution in (a) mol L⁻¹ and (b) g L⁻¹. (Na = 22.990, Cl = 35.453) 4 MARKS

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ApplyBand 3

7. A chemist needs to deliver 0.0500 mol of H₂SO₄ to a reaction. They have a stock solution of 1.00 mol L⁻¹ sulfuric acid. What volume of stock solution should they measure out? Give your answer in mL. 3 MARKS

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AnalyseBand 4

8. A pool technician tests a swimming pool and finds that the chlorine concentration is 3.55 g L⁻¹ of Cl₂ (dissolved chlorine gas). The pool holds 50 000 L of water. Calculate the total mass of Cl₂ in the pool, and the number of Cl₂ molecules present. (Cl = 35.453) 5 MARKS

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EvaluateBand 5

9. A student prepares a solution by dissolving 5.85 g of NaCl in 100 mL of water. They claim the concentration is 1.00 mol L⁻¹. A second student says: "You made the solution incorrectly — you should have added water to the NaCl to produce exactly 100 mL of solution, not dissolved it in 100 mL of water." Evaluate both the concentration claim and the procedural claim. (Na = 22.990, Cl = 35.453) 5 MARKS

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CreateBand 6

10. A scientist needs to prepare 500 mL of a 0.500 mol L⁻¹ solution of potassium permanganate (KMnO₄) as a stock solution. They then plan to transfer two 50.0 mL aliquots — one for a titration experiment and one to compare the colour intensity at different concentrations. (a) Calculate the mass of KMnO₄ needed. (b) Outline a complete procedure to prepare the stock solution. (c) Calculate how many moles of KMnO₄ are in each 50.0 mL aliquot. (K = 39.098, Mn = 54.938, O = 15.999) 7 MARKS

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✅ Comprehensive Answers

📊 Activity 2 — Table Answers

NaOH: V = 250÷1000 = 0.250 L; c = 0.500÷0.250 = 2.00 mol L⁻¹

HCl: V = 100÷1000 = 0.100 L; n = c×V = 2.00×0.100 = 0.200 mol

CaCl₂: V = n÷c = 0.0400÷0.160 = 0.250 L = 250 mL

H₂SO₄: V = 600÷1000 = 0.600 L; c = 1.50÷0.600 = 2.50 mol L⁻¹

KMnO₄: V = 50.0÷1000 = 0.0500 L; n = c×V = 0.0200×0.0500 = 1.00×10⁻³ mol

❓ Multiple Choice

1. C — Must convert 150 mL → 0.150 L first. c = 0.30 ÷ 0.150 = 2.00 mol L⁻¹.

2. B — V = 0.500 L. c = 0.250 ÷ 0.500 = 0.500 mol L⁻¹.

3. A — V = 0.0250 L. n = 0.100 × 0.0250 = 2.50 × 10⁻³ mol.

4. D — MM(NaOH) = 39.997 g mol⁻¹. n = 4.00 ÷ 39.997 = 0.100 mol. V = 0.200 L. c = 0.100 ÷ 0.200 = 0.500 mol L⁻¹.

5. C — c = 18.0 ÷ 180.16 = 0.100 mol L⁻¹.

📝 Short Answer Model Answers

Q6 (4 marks):

MM(NaCl) = 22.990 + 35.453 = 58.443 g mol⁻¹ n = m ÷ MM = 9.00 ÷ 58.443 = 0.1540 mol (a) c = n ÷ V = 0.1540 ÷ 1.00 = 0.154 mol L⁻¹ (b) c (g L⁻¹) = 9.00 g ÷ 1.00 L = 9.00 g L⁻¹ (or: 0.154 × 58.443 = 9.00 g L⁻¹)

Q7 (3 marks):

V = n ÷ c = 0.0500 ÷ 1.00 = 0.0500 L = 50.0 mL

Q8 (5 marks):

Total mass = c × V = 3.55 × 50 000 = 177 500 g = 177.5 kg MM(Cl₂) = 2 × 35.453 = 70.906 g mol⁻¹ n = m ÷ MM = 177 500 ÷ 70.906 = 2503 mol N = n × Nₐ = 2503 × 6.022 × 10²³ = 1.507 × 10²⁷ molecules

❓ MC — Q6 & Q7

6. D — MM(NaCl) = 22.990 + 35.453 = 58.443 g mol⁻¹. m for 0.250 mol = 0.250 × 58.443 = 14.61 g ✓. In 500 mL: c = 0.250 ÷ 0.500 = 0.500 mol L⁻¹. The first student's preparation is valid. The second student's suggestion (250 mL) would give c = 1.00 mol L⁻¹, which is also valid but not what was asked. Neither approach is "wrong".

7. A — n = 0.200 × 0.250 = 0.0500 mol. MM(CuSO₄·5H₂O) = 63.546 + 32.06 + 4(15.999) + 5[2(1.008) + 15.999] = 249.68 g mol⁻¹. m = 0.0500 × 249.68 = 12.48 g. Dissolve, transfer to 250 mL volumetric flask, make up to the mark. Option D is wrong because it ignores the water of crystallisation when weighing out.

📝 Short Answer — Q9 & Q10

Q9 (5 marks):

Concentration check: MM(NaCl) = 58.443 g mol⁻¹ [1]. n = 5.85 ÷ 58.443 = 0.1001 mol [1]. If total volume ≈ 100 mL = 0.100 L: c = 0.1001 ÷ 0.100 = 1.00 mol L⁻¹ [1]. The concentration claim is approximately correct — but only if adding the solid to 100 mL of water does not significantly change the total volume.

Procedural evaluation: The second student is correct [1]. Adding water to a fixed volume of NaCl is wrong for accurate concentration preparation. To make exactly 100 mL of 1.00 mol L⁻¹, dissolve the NaCl in a small volume of water (~50 mL), then transfer to a 100 mL volumetric flask and add distilled water exactly to the 100 mL mark [1].

Q10 (7 marks):

(a) MM(KMnO₄) = 39.098 + 54.938 + 4(15.999) = 158.032 g mol⁻¹ [1] n = c × V = 0.500 × 0.500 = 0.250 mol [1] m = n × MM = 0.250 × 158.032 = 39.51 g [1]

(b) Procedure: Weigh 39.51 g of KMnO₄ on a balance [1]. Dissolve in ~300 mL of distilled water in a beaker with stirring. Once dissolved, quantitatively transfer to a 500 mL volumetric flask. Rinse the beaker 3× with small volumes of distilled water, adding the rinsings to the flask. Add distilled water to the 500 mL mark, stopper and invert several times to mix [1].

(c) n = c × V = 0.500 × 0.0500 = 0.0250 mol per aliquot [1]

Each 50.0 mL aliquot contains the same concentration and 0.0250 mol of KMnO₄ [1].

Science Jump

Science Jump — Concentration

Climb platforms, hit checkpoints, and answer questions on concentration in mol/L, n=cV calculations and solution preparation. Quick recall from lessons 1–6.

Mark lesson as complete

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